E.060 concreto armado

norma

1.    N
 
 
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
 
 
 
NORMA TÉCNICA E.060  
 
CONCRETO ARMADO 
 
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N

2.   ON
ÍNDICEN
 
 
PARTE 1    GENERALIDADES 
RMATÉCIEN NN .06CDÍDÉEÍN
P010.MI0ÍGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGLSN
RMATÉCIENONN 203D1DRDE10ÍGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGLQN
 
PARTE 2    MATERIALES 
RMATÉCIENUNN ÓMÉ0.DMI0ÍGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG 4N
 
PARTE 3     REQUISITOS DE CONSTRUCCIÓN 
RMATÉCIEN5NN RMID2M2N20N
RE1R.0ÉEGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGO5N
RMATÉCIENSNN RE1R.0ÉEN01NEÑ.MGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGUSN
RMATÉCIENVNN 01RE3.M2EÍXN0I0Ó01ÉEÍN0ÓÑ0ÑD2EÍN-N
YC1ÉMÍGGGGGGGGG5 N
RMATÉCIEN4NN 20ÉMII0ÍN20N
.03C0.,EGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG5SN
RMATÉCIENQNN 20ÍM..EIIEN-N0ÓAMIÓ0ÍN20N.03C0.,EGGGGGG GGGGGGGGGGGGGGGGGSON
 
PARTE 4    REQUISITOS GENERALES 
RMATÉCIENJNN .06CDÍDÉEÍNP010.MI0ÍNAM.MN0INM1BIDÍDÍN- NN
2DÍ0FEZZZZZZZZZZZZZZZZZZZZZZZGGGSQN
RMATÉCIEN LNN .06CDÍDÉEÍNP010.MI0ÍN20N.0ÍDÍÉ01RDMN-N N
Í0.oDRDEZZZZZZZZZZZZZZZZZZZZZZZV5N
 
PARTE 5     DISEÑO 
RMATÉCIEN  NN 3I0lDd1GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG4 N
RMATÉCIEN ONN 3I0lEREÓA.0ÍDd1GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG4SN
RMATÉCIEN UNN RE.ÉM1É0N-N
ÉE.ÍDd1GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGQUN
RMATÉCIEN 5N oDPMÍN20NP.M1NA0.MIÉ0GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGJSN
RMATÉCIEN SN ÓC.EÍGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG LLN

3.   UN
RMATÉCIEN VN ,MAMÉMÍGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG L4N
RMATÉCIEN 4N IEÍMÍNM.ÓM2MÍN01N2EÍN2D.0RRDE10ÍGGGGGGG GGGGGGGGGGGGGGGGGG   N
RMATÉCIEN QN RE1R.0ÉENA.0Í3E.,M2EGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG O4N
RMATÉCIEN JN RBÍRM.MÍN-NIMÓD1MÍN
AI0PM2MÍGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG 5VN
RMATÉCIENOLN RE1R.0ÉENÍDÓAI0GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG SLN
RMATÉCIENO N RE1R.0ÉENA.03MÑ.DRM2EGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG SUN
RMATÉCIENOON 0I0Ó01ÉEÍN20NRE1R.0ÉENREÓAC0ÍÉENÍCY0ÉEN MN
N3I0lDd1GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG SSN
N
PARTE 6  EVALUACIÓN DE ESTRUCTURAS 
RMATÉCIENOUN 0oMICMRDd1N20N
0ÍÉ.CRÉC.MÍGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG SJN
N
ANEXO     
M10lEN N 1E.ÓMÍN20NÓMÉ0.DMI0ÍN-NA.ER02DÓD01ÉEÍNRDÉM2 EÍZZG VON
M10lENON 06CDoMI01RDMN20N3E.ÓCIMÍN01É.0NIEÍNÍDÍÉ0ÓMÍ NÓaÍN
NuC1D2M20ÍNÓrÉ.DRMÍeN-NÍDNuÍDÍÉ0ÓMND1É0.1MRDE1MINN
20N
C1D2M20ÍeGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG VSN
 
0ÍA0RD3DRMRDE10ÍN1E.ÓMÉDoMÍNAM.MN2DÍ0FEN01NRE1R.0ÉE NM.ÓM2EN
01N0INRMÍEN20N02D3DRMRDE10ÍNRE1NÓC.EÍN20N2CRÉDID2M2 N
IDÓDÉM2MNNu0Ó2IeZZZZZZZZZZZZZZZZZZZZZZZZZZZGGG 45N
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

4.   5N
 
 
 
NORMA TÉCNICA 
 E.060 CONCRETO ARMADO 
 
PARTE 1 - GENERALIDADES 
 
CAPÍTULO 1 - REQUISITOS GENERALES 
 
1.1    ALCANCE N
N
 G G N N 0fzgN 1isngN p7/gN bifN s(Kc7f7zifN mN ()7H(897gfNnÁ87ngfN tgsgN (bN g8vb7f7fXN
y7f(:iXN ngz(s7gb(fXN 9i8fzsc997–8XN 9i8zsibN y(N 9gb7ygyN (N 78ft(997–8N y(N
(fzsc9zcsgfNy(N9i89s(ziNf7ntb(NiNgsngyiGNNIgfN(fzsc9zcsgfNy(N9i89s(ziN
ts(fpisxgyiN f(N 789bcm(8N y(8zsiN y(N bgN y(p78797–8N y(N(fzsc9zcsgfN y(N
9i89s(ziNgsngyiGN N
N
 G GON N IifN tbg8ifN mN bgfN (ft(97p79g97i8(fN zj9879gfN y(bN tsim(9ziN (fzsc9zcsgbN
y(ó(sv8N 9cntb7sN 9i8N (fzgN 1isngXN tcy7(8yiN 9intb(n(8zgsbgN (8N biN 8iN
9i8z(ntbgyiN(8N(bbgGN
N
 G GUN N 0fzgN 1isngN z7(8(N ts7is7ygyN 9cg8yiN fcfN s(9in(8yg97i8(fN (fzv8N (8N
y7f9s(tg897gN9i8NizsgfN8isngfNgNbgfNKc(N(bbgNhg9(Ns(p(s(897gGN
N
1.2    LIMITACIONES N
N
 GOG N N 0fzgN1isngN789bcm(NbifNs(Kc(s7n7(8zifNtgsgN(fzsc9zcsgfNy(N9i89s(ziNy(N
t(fiN8isngbGN
N
 GOGON N 0fzgN1isngNtiysvNf(sNgtb79gygNgbNy7f(:iNmN9i8fzsc997–8Ny(N(fzsc9zcsgfN
ts(kpgós79gygfN máiN (fzsc9zcsgfN (ft(97gb(fN (8N bgN n(y7ygN Kc(N (bbiN f(gN
t(sz78(8z(GN
N
1.3    PROYECTO, EJECUCIÓN E INSPECCIÓN DE LA OBRA N
N
 GUG N .06CDÍDÉEÍNP010.MI0ÍN
N
 GUG G N ÉiygfNbgfN(zgtgfNy(bNtsim(9ziN(fzsc9zcsgbXN9i8fzsc997–8N(N78ft(997–8Ny(N
bgN iósgN y(ó(sv8N f(sN s(gb7xgygfN tisN t(sfi8gbN tsip(f7i8gbN mN zj9879iN
9gb7p79gyiGN
N
 GUG GON IifN 9vb9cbifXN tbg8ifN y(N y7f(:iXN y(zgbb(fN mN(ft(97p79g97i8(fN zj9879gfN
y(ó(sv8N bb(=gsN bgN p7sngN y(N c8N D8H(87(siN R7=7bN Rib(H7gyiXN Kc7(8N f(svN (bN
M879iNgczis7xgyiNgNgtsiógsN9cgbKc7(sNniy7p79g97–8NgNbifNn7fnifGN
N
 GUG GUN IgN 9i8fzsc997–8N y(ó(svN f(sN (/(9czgygN (N 78ft(997i8gygN tisN 78H(87(sifN
97=7b(fN 9ib(H7gyifXN Kc7(8(fN f(sv8N s(fti8fgób(fN y(bN9cntb7n7(8ziN y(N biN

5.   SN
78y79gyiN(8NbifNtbg8ifNmN(ft(97p79g97i8(fNzj9879gfGN
 
 GUGON N A.E-0RÉEN
N
 GUGOG N NNNNNNNNNNNIgN 9i89(t97–8N (fzsc9zcsgbN y(ó(svN hg9(sf(N y(N g9c(syiN gN bifN
9s7z(s7ifNy(N(fzsc9zcsg97–8N78y79gyifN(8NbgN1isngN0kLULN27f(:iNÍ7fnik
.(f7fz(8z(Ny(bN
N N .(Hbgn(8ziN1g97i8gbNy(NRi8fzsc997i8(fGN
N
 GUGOGON NNNNNNNNNNNIgNy(z(sn78g97–8Ny(NbgfN9gsHgfNg9zcg8z(fNf(NhgsvNy(Ng9c(syiNgNbiN
78y79gyiN(8NbgN1isngfNÉj9879gfNy(N0y7p79g97–8N0GNLOLNRgsHgfNmN(8NbgN
1isngNy(N27f(:iNÍ7fnik.(f7fz(8z(GN
N
 GUGOGUNN 0bND8H(87(siNAsim(9z7fzgNtiysvN(b(H7sNbifNtsi9(y7n7(8zifNy(Ng8vb7f7fGN0bN
y7f(:iNy(NbgN(fzsc9zcsgNy(ó(svN9cntb7sN9i8NbifNs(Kc(s7n7(8zifNy(N(fzgN
1isngGN
N
 GUGOG5N NNNNNNNNNNNIifNtbg8ifNy(bNtsim(9ziN(fzsc9zcsgbNy(ó(sv8N9i8z(8(sN78pisng97–8N
y(zgbbgygNmN9intb(zgNy(NbgfNy7n(8f7i8(fXNcó79g97–8XNs(pc(sxifNmN/c8zgfN
y(NbifNy7=(sfifN(b(n(8zifN(fzsc9zcsgb(fGNDHcgbn(8z(Nf(N78y79gsvN(8N(bbifN
bgN 9gb7ygyN y(N bifN ngz(s7gb(fXN bgfN s(f7fz(897gfN y(bN9i89s(ziXN g9(siN mN
z(ss(8iXN bgfN 9gsg9z(sÁfz79gfN y(NbgNgbóg:7b(sÁgNmNnisz(siNy(Ng9c(syiNgNbgN
1isngN 0GL4LXN bgfN fiós(9gsHgfN y(N y7f(:iN mN bgN 9gsHgN (Kc7=gb(8z(N y(N
zgó7Kc(sÁgGN
N
 GUGOGSN IifNtbg8ifNf(sv8Ngs9h7=gyifNtisNbgfN(8z7ygy(fNKc(NizisHc(8NbgNI79(897gN
y(NRi8fzsc997–8GN
N
 GUGUN N 0Y0RCRDd1N20NIMNEÑ.MN
N
 GUGUG NN AgsgNbgN(/(9c97–8Ny(NbgNiósgN(bNRi8fzsc9zisNy(f7H8gsvNgbND8H(87(siNR7=7bN
Rib(H7gyiNKc(Ng9zcgsvN9iniND8H(87(siN.(f7y(8z(Ny(NbgNEósgNmNKc(NbiN
s(ts(f(8zgsvN(8N(bbgGN
N
 GUGUGON NNNNNNNNNNN0bN Ri8fzsc9zisN (/(9czgsvN bifN zsgóg/ifN s(Kc(s7yifN (8N bgN iósgN y(N
g9c(syiN gN biN 78y79gyiN (8N bgN ts(f(8z(N 1isngXN bifN tbg8ifN mN bgfN
(ft(97p79g97i8(fNzj9879gfGN
N
 GUGUGUN NNNNNNNNNNNRcg8yiN f(N s(Kc7(sgN gczis7xg97–8Nts(=7gN y(N bgN 78ft(997–8N tgsgN
(/(9czgsN y(z(sn78gyifN zsgóg/ifXN (bN D8H(87(siN .(f7y(8z(N 9inc879gsvN gbN
D8ft(9zisN9i8N5QNhisgfNy(Ng8z797tg97–8NbgN78797g97–8Ny(NbifNn7fnifGN
N
 GUGUG5G G N IgfNi9css(897gfNzj9879gfNy(NbgNiósgNf(Nbb(=gsv8N(8Nc8N.(H7fzsiNM8()iNgbNN
NRcgy(s8iN y(N EósgGN 08N (fz(N y(ó(sv8N 78y79gsf(N (bN 8inós(N mN bgN
8cn(sg97–8N y(N bifN yi9cn(8zifN Kc(N pisng8N tgsz(N y(bN s(H7fzsiN (8N bgN
itiszc87ygyNy(NNNNNNfcNi9css(897gGN
N
08zs(N bgfN i9css(897gfN zj9879gfN Kc(N y(ó(sv8N p7HcsgsN(8N (bN .(H7fzsiXN
(fzgsv8N bgfN f7Hc7(8z(fNN 9gb7ygyN mN tsitis97i8(fN y(N bifN ngz(s7gb(fN y(bN
9i89s(ziXN 9i8fzsc997–8N y(N (89ipsgyifXN y(f(89ipsgyif N mN

6.   VN
gtc8zgbgn7(8zifXN 9ibi9g97–8N y(bN s(pc(sxiXN n(x9bgXN có79g97–8N y(N bgfN
zg8ygfN y(bN 9i89s(ziN (8N bgN (fzsc9zcsgXN tsi9(y7n7(8ziN y(N 9ibi9g97–8N mN
9csgyiNy(bN9i89s(ziGNRcg8yiNbgNz(nt(sgzcsgNf(gNn(8isNy(NSORNiNngmisN
y(NOQORNf(Nng8z(8ysvNc8Ns(H7fzsiN9intb(ziNy(NbgfNz(nt(sgzcsgfNmNy(NbgN
tsiz(997–8N Kc(N f(N yjN gbN 9i89s(ziN n7(8zsgfN f(N s(gb7xgN (bN 9csgyiePN
f(9c(897gN y(bN ni8zg/(N mN 9i8()7–8N y(N (b(n(8zifN ts(pgós79gyifXN
gtb79g97–8N y(bN ts(fpc(sxiXN 9cgbKc7(sN 9gsHgN f7H87p79gz7=gN y(N 9i8fzsc997–8N
(8N(8zs(t7fifXN(b(n(8zifNmáiNncsifNmgNz(sn78gyifXNtsiHs(fiNH(8(sgbNy(N
bgNiósgXN(z9GN
N
 GUGUGSN NNNNNNNNNNN0bN .(H7fzsiN mN (bN Rcgy(s8iN y(N EósgN pisngsv8N tgsz(N y(N bifN
yi9cn(8zifN(8zs(HgyifNgbNtsit7(zgs7iN9i8N(bNM9zgNy(N.(9(t97–8Ny(NbgN
EósgGN
N
 GUG5N N D1ÍA0RRDd1N
N
 GUG5G N 0bN D8ft(9zisN (fN f(b(997i8gyiN tisN (bN tsit7(zgs7iN mN biN s(ts(f(8zgN g8z(N (bN
Ri8fzsc9zisGN
N
 GUG5GON 0bND8ft(9zisNz7(8(N(bNy(s(9hiNmNbgNiób7Hg97–8Ny(Nhg9(sN9cntb7sNbgNts(f(8z(N
1isngXNbifNtbg8ifNmNbgfN(ft(97p79g97i8(fNzj9879gfGN
N
 GUG5GUN 0bN Ri8fzsc9zisN tsitis97i8gsvN gbN D8ft(9zisN ziygfN bgfN pg97b7ygy(fN Kc(N
s(Kc7(sgN(8NbgNiósgNtgsgN(bN9cntb7n7(8ziNy(NfcfNiób7Hg97i8(fGN
N
1.4    SISTEMAS NO CONVENCIONALES N
N
N
 G5G N N 0bN (ntb(iN y(N f7fz(ngfN 9i8fzsc9z7=ifN 8iN 9i8=(897i8gb(fN y(ó(svN y(N
9i8zgsN9i8NbgNgczis7xg97–8Nts(=7gNy(NÍ01RDREGN
N
1.5    NORMAS DE MATERIALES Y PROCEDIMIENTOS CITADOS N
N
N N o(sNM8()iN GN
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

7.   4N
 
 
CAPÍTULO 2 - DEFINICIONES Y ABREVIATURAS N
N
2.1  DEFINICIONES  
N
CEMENTO 
N
R(n(8ziNN
Ógz(s7gbNtcb=(s7xgyiNKc(NtisNgy797–8Ny(Nc8gN9g8z7ygyN9i8=(87(8z(Ny(NgHcgNpisngNc8gN
tgfzgNgHbin(sg8z(N9gtgxNy(N(8ycs(9(sXNzg8ziNóg/iN(bNgHcgN9iniN(8N(bNg7s(GN6c(yg8N
()9bc7ygfN bgfN 9gb(fN h7ysvcb79gfXN bgfN 9gb(fN gjs(gfN mN bifN m(fifGN 1E.ÓMN DÉD1É0RN
UU5GLL GN
N
R(n(8ziNAiszbg8yNN
Asiyc9ziNióz(87yiNtisNbgNtcb=(s7xg97–8Ny(bN9b78Q(sNtiszbg8yN9i8NbgNgy797–8N(=(8zcgbNy(N
fcbpgziNy(N9gb97iGNÍ(Ngyn7z(NbgNgy797–8Ny(NizsifNtsiyc9zifNKc(N8iN()9(yg8Ny(bN RN(8NNN
t(fiNy(bNzizgbNf7(nts(NKc(NbgN8isngN9iss(fti8y7(8z(N(fzgób(x9gNKc(NfcN789bcf7–8N8iN
gp(9zgN bgfN tsit7(ygy(fN y(bN 9(n(8ziN s(fcbzg8z(GN ÉiyifN bifN tsiyc9zifN gy797i8gyifN
y(ó(sv8Nf(sNtcb=(s7xgyifN9i8/c8zgn(8z(N9i8N(bN9b78Q(sGN1E.ÓMNDÉD1É0RNUU5GLL GN
 
R(n(8ziNAiszbg8yNAcxibv879iNÉ7tiN ANN
0fN(bN9(n(8ziNtiszbg8yNKc(Nts(f(8zgNc8Ntis9(8zg/(Ngy797i8gyiNy(Ntcxibg8gN(8zs(N SRN
mN5SRGN1E.ÓMNDÉD1É0RNUU5GL55GN
N
R(n(8ziNA–szbg8yNAcxibv879iNÉ7tiN AÓNN
0fN(bN9(n(8ziNtiszbg8yNKc(Nts(f(8zgNc8Ntis9(8zg/(Ngy797i8gyiNy(Ntcxibg8gNn(8isNy(N
 SRGN1E.ÓMNDÉD1É0RNUU5GL55GN
 
AGREGADO 
 
MHs(HgyiNN
Ri8/c8ziN y(N tgszÁ9cbgfN y(N is7H(8N 8gzcsgbN iN gsz7p797gbXN Kc(N tc(y(8N f(sN zsgzgygfN iN
(bgóisgygfNmN9cmgfNy7n(8f7i8(fN(fzv8N9ints(8y7ygfN(8zs(NbifNbÁn7z(fNp7/gyifNtisNbgN
1isngNDÉD1É0RN5LLGLU4GN
 
MHs(HgyiN378iNN
MHs(HgyiN tsi=(87(8z(N y(N bgN y(f78z(Hsg97–8N 8gzcsgbN iN gsz7p797gbXN Kc(N tgfgN (bN zgn7xN
DÉD1É0RNJXSNnnNNuUáQSeNNmNNKc(NNN9cntb(NN9i8NNbifNNbÁn7z(fN(fzgób(97yifN(8NbgN1isngN
DÉD1É0RN5LLGLU4GN
 
MHs(HgyiNPsc(fiNN
MHs(HgyiN s(z(87yiN (8N (bN zgn7xN DÉD1É0RN 5X4SN nnN u1ON 5eXN tsi=(87(8z(N y(N bgN
y(f78z(Hsg97–8N 8gzcsgbN iN n(9v879gN y(N bgfN si9gfN mN Kc(N 9cntb(N 9i8N bifN bÁn7z(fN
(fzgób(97yifN(8NbgN1isngNDÉD1É0RN5LLGLU4GN
N
N
Ms(8gNN
N MHs(HgyiN p78iXN tsi=(87(8z(N y(N bgN y(f78z(Hsg97–8N 8gzcsgbN y(N bgfN si9gfGN 1E.ÓMN
DÉD1É0RN5LLGLU4GN

8.   QN
N
Psg=gNNN
MHs(HgyiNHsc(fiXNtsi=(87(8z(Ny(NbgNy(f78z(Hsg97–8N8gzcsgbNy(NbifNngz(s7gb(fNtjzs(ifXN
(89i8zsv8yif(b(N 9iss7(8z(n(8z(N (8N 9g8z(sgfN mN b(9hifN y(N sÁifXN y(tif7zgyiN (8N pisngN
8gzcsgbGN1E.ÓMNDÉD1É0RN5LLGLU4GN
N
A7(ysgNÉs7zcsgygNiNRhg89gygNN
N N MHs(HgyiN Hsc(fiXN ióz(87yiN tisN zs7zcsg97–8N gsz7p797gbN y(N si9gfN iN Hsg=gfGN 1E.ÓMN
DÉD1É0RN5LLGLU4GN
N
MHs(HgyiNy(8in78gyiNTisn7H–8NN
Ógz(s7gbN 9intc(fziN y(N Hsg=gN mN gs(8gN (ntb(gyiN(8NfcNpisngN8gzcsgbNy(N()zsg997–8GN
1E.ÓMNDÉD1É0RGN5LLGL  GN N
N N N
Égng:iNÓv)7niNN
0fN(bNKc(N9iss(fti8y(NgbNn(8isNzgn7xNtisN(bNKc(NtgfgNziygNbgNnc(fzsgNy(NgHs(HgyiN
Hsc(fiGN1E.ÓMNDÉD1É0RGN5LLGLU4GN
N
Égng:iNÓv)7niN1in78gbNN
0fN (bN Kc(N 9iss(fti8y(N gbN n(8isN zgn7xN y(N bgN f(s7(N cz7b7xgygN Kc(N tsiyc9(N (bN ts7n(sN
s(z(87yiGN1E.ÓMNDÉD1É0RGN5LLGLU4GN
N
Ó–ycbiNy(N378(xgNy(bNMHs(HgyiN378iNN
R(8zjf7ngN tgsz(N y(bN =gbisN Kc(N f(N ióz7(8(N gbN fcngsN bifN tis9(8zg/(fN g9cncbgyifN
s(z(87yifN(8N(bN9i8/c8ziNy(NbifNzgn79(fN5X4SNnnNu1ON5eXNOXUVNnnNu1ONQeXN X QNnnNu1ON
 VeXNNVLLNnnNu1ONULeXNULLNnnNu1ONSLeNmN SLNnnNu1ON LLeGN
 
ADITIVOSN
N
My7z7=ifNN
Ícfzg897gNg:gy7ygNgNbifN9inti8(8z(fNpc8ygn(8zgb(fNy(bN9i89s(ziXN9i8N(bNtsit–f7ziN
y(Nniy7p79gsNgbHc8gfNy(NfcfNtsit7(ygy(fGN1E.ÓMNDÉD1É0RNUUJGLQVGN
N
M9(b(sg8z(NN
Ícfzg897gN Kc(N gbN f(sN g:gy7ygN (bN 9i89s(ziXN nisz(siN iN b(9hgygXN g9iszgN (bN z7(ntiN y(N
psgHcgyiNmáiN789s(n(8zgNbgN=(bi97ygyNy(Ny(fgssibbiN78797gbNy(Ns(f7fz(897gGN
N
.(zgsygyisNN
My7z7=iNKc(Ntsibi8HgN(bNz7(ntiNy(NpsgHcgyiGN1E.ÓMNDÉD1É0RNUUJGLQVGN
N
D89istisgyisNy(NM7s(NN
0fN (bN gy7z7=iN 9cmiN tsit–f7ziN ()9bcf7=iN (fN 789istisgsN g7s(N (8N pisngN y(N ócsóc/gfN
(fp(si7ygb(fN 8iN 9igb(f9(8z(fN mN c87pisn(n(8z(N y7fzs7óc7ygfN (8N bgN n(x9bgXN 9i8N bgN
p78gb7ygyNy(Nhg9(sbiNts7897tgbn(8z(Ns(f7fz(8z(NgNbgfNh(bgygfGN
N
CONCRETON
N
Ri89s(ziNNuUeNN
0fNbgNn(x9bgN9i8fz7zc7ygNtisN9(n(8ziXNgHs(HgyifXNgHcgNmN(=(8zcgbn(8z(Ngy7z7=ifXN(8N
tsitis97i8(fNgy(9cgygfNtgsgNióz(8(sNbgfNtsit7(ygy(fNts(p7/gygfGN

9.   #N
uUeN0bNngz(s7gbNKc(N(8N8c(fzsiNn(y7iN(fN9i8i97yiN9iniNRi89s(ziXN(fNy(p787yiN9iniN
Tisn7H–8N(8NbgfN1isngfNy(bNRin7zjNAg8gn(s79g8iNy(N1isngfNÉj9879gfNuREAM1ÉeXN
gyitzgygfNtisN(bNDÉD1É0RGN
AgfzgNy(NR(n(8ziNN
0fNc8gNn(x9bgNy(N9(n(8ziNmNgHcgGN1E.ÓMNDÉD1É0RN5LLGLLOGN
 
Óisz(siNy(NR(n(8ziNN
0fNbgNn(x9bgN9i8fz7zc7ygNtisN9(n(8ziXNgHs(HgyifNts(yin78g8z(n(8z(Np78ifNmNgHcgGN
N
CONCRETO - TIPOSN
N
Ri89s(ziNÍ7ntb(NN
N N Ri89s(ziNKc(N8iNz7(8(NgsngycsgNy(Ns(pc(sxiNiNKc(N bgNz7(8(N(8Nc8gN9g8z7ygyNn(8isN
Kc(N(bNnÁ87niNtis9(8zg/(N(ft(97p79gyiNtgsgN(bN9i89s(ziNgsngyiGN
N
Ri89s(ziNMsngyiNN
Ri89s(ziN Kc(N z7(8(N gsngycsgN y(N s(pc(sxiN (8N c8gN 9g8z7ygyN 7HcgbN iN ngmisN Kc(N bgN
s(Kc(s7ygN (8N (fzgN 1isngN mN (8N (bN Kc(N gnóifN ngz(s7gb(fN g9zMg8N /c8zifN tgsgN s(f7fz7sN
(fpc(sxifGN
N
Ri89s(ziNy(NA(fiN1isngbNN
0fNc8N9i89s(ziNKc(Nz7(8(Nc8Nt(fiNgtsi)7ngyiNy(NOULLNQHánUGN
N
Ri89s(ziNAs(pgós79gyiNN
0b(n(8zifNy(N9i89s(ziNf7ntb(NiNgsngyiNpgós79gyifN(8Nc8gNcó79g97–8Ny7p(s(8z(NgNfcN
tif797–8Np78gbN(8NbgN(fzsc9zcsgGN
N
Ri89s(ziNR79b–t(iNN
0fN(bN9i89s(ziNf7ntb(NN(8N9cmgNngfgNf(N789istisg8NHsg8y(fNt7(ysgfNiNóbiKc(fNmNKc(N
8iN9i8z7(8(NgsngycsgGN
N
Ri89s(ziNy(NRgf9iz(NN
0fN(bN9i8fz7zc7yiNtisN9(n(8ziXNgHs(HgyiNp78iXN9gf9iz(Ny(Nbgys7bbiNmNgHcgGN
N
Ri89s(ziNAs(n(x9bgyiNN
0fN(bN9i89s(ziNKc(Nf(Nyif7p79gN(8Ntbg8zgXNKc(Ntc(y(Nf(sNn(x9bgyiN(8NbgNn7fngNiN(8N
9gn7i8(fNn(x9bgyis(fNmNKc(N(fNzsg8ftiszgyiNgNiósgGN1E.ÓMNDÉD1É0RNUUJGL54GNNNNN
N
Ri89s(ziNÑinó(gyiNN
Ri89s(ziNKc(N(fN7ntcbfgyiNtisNóinó(iNgNzsg=jfNy(Nzcó(sÁgfNhg97gNfcNcó79g97–8Np78gbGN
N
CARGASN
N
RgsHgNy(NÍ(s=797iNN
RgsHgN ts(=7fzgN (8N (bN g8vb7f7fN ycsg8z(N bgN =7ygN y(N bgN (fzsc9zcsgN u8iN z7(8(N pg9zis(fN y(N
gntb7p79g97–8eGN
N
RgsHgN3g9zis7xgygNiNRgsHgNMntb7p79gygNiNRgsHgNVbz7ngNN
RgsHgN ncbz7tb79gygN tisN pg9zis(fN y(N 9gsHgN gtsit7gyifXN cz7b7xgygN (8N (bN y7f(:iN tisN
s(f7fz(897gNgN9gsHgNMbz7ngNusizcsgeGN

10.    LN
N
N
RgsHgNÓc(szgNiNRgsHgNA(sng8(8z(NiNA(fiNÓc(sziNN
0fN (bN t(fiN y(N bifN ngz(s7gb(fXN y7ftif7z7=ifN y(N f(s=797iXN (Kc7tifXN zgó7Kc(fN mN izsifN
(b(n(8zifNfitiszgyifNtisNbgN(y7p79g97–8XN789bcm(8yiNfcNt(fiNtsit7iXNKc(Nf(Nfcti8(N
f(g8Nt(sng8(8z(fGN
 
RgsHgNo7=gNN
0fN(bNt(fiNy(NziyifNbifNi9ctg8z(fXNngz(s7gb(fXN(Kc7tifXNnc(ób(fNmNizsifN(b(n(8zifN
n–=7b(fNfitiszgyifNtisNbgN(y7p79g97–8GN
N
RgsHgNy(NÍ7fniNN
3c(sxgN (=gbcgygN f(HM8N bgN 1isngN y(N 27f(:iN Í7fnik.(f7fz(8z(N y(bN .(Hbgn(8ziN
1g97i8gbNy(NRi8fzsc997i8(fNtgsgN(fz7ngsNbgNg997–8NfÁfn79gNfiós(Nc8gN(fzsc9zcsgGN
N
RgsHgNy(No7(8ziNN
3c(sxgN()z(s7isN(=gbcgygNf(HM8NbgN1isngN0GNLOLNRgsHgfGN
 
ELEMENTOS ESTRUCTURALES N
N
R7n(8zg97–8NN
0b(n(8ziN (fzsc9zcsgbN Kc(N z7(8(N 9iniN pc897–8N zsg8fn7z7sN bgfN g997i8(fNy(N9gsHgNy(NbgN
(fzsc9zcsgNgbNfc(biNy(Npc8yg97–8GN
NNNNNNNNNNNNNNNNNNNNNNNNNN
Ribcn8gNN
0b(n(8ziN (fzsc9zcsgbN Kc(N f(N cfgN ts7897tgbn(8z(N tgsgN s(f7fz7sN 9gsHgN g)7gbN y(N
9ints(8f7–8N mN Kc(N z7(8(N c8gN gbzcsgN y(N tisN biN n(8ifNUN =(9(fN fcN y7n(8f7–8N bgz(sgbN
n(8isGN
N
ÓcsiNN
0b(n(8ziN (fzsc9zcsgbXN H(8(sgbn(8z(N =(sz79gbN (ntb(gyiN tgsgN (89(ssgsN iN f(tgsgsN
gnó7(8z(fXNs(f7fz7sN9gsHgfNg)7gb(fNy(NHsg=(ygyNmNs(f7fz7sN9gsHgfNt(st(8y79cbgs(fNgNfcN
tbg8iNtsi=(87(8z(fNy(N(ntc/(fNbgz(sgb(fNy(Nfc(bifNiNbÁKc7yifGN
N
ÓcsiNy(NRisz(NN
0b(n(8ziN(fzsc9zcsgbNcfgyiNóvf79gn(8z(NtgsgNtsitis97i8gsNs7H7y(xNbgz(sgbNmNgófisó(sN
tis9(8zg/(fN7ntiszg8z(fNy(bN9iszg8z(Nhis7xi8zgbNfÁfn79iGN
N
o7HgNN
0b(n(8ziN(fzsc9zcsgbNKc(Nzsgóg/gNpc8ygn(8zgbn(8z(NgNpb()7–8GN
 
IifgNN
0b(n(8ziN (fzsc9zcsgbN y(N (ft(fisN s(yc97yiN s(ft(9ziN gN fcN izsgfN y7n(8f7i8(fN cfgyiN
9iniNz(9hiNiNt7fiXNH(8(sgbn(8z(Nhis7xi8zgbNmNgsngyiN(8Nc8gNiNyifNy7s(997i8(fNf(HM8N
(bNz7tiNy(NgtimiN()7fz(8z(N(8NfcN9i8zis8iGN
CfgyiNzgnó7j8N9iniNy7gpsgHngNsÁH7yiNtgsgNng8z(8(sNbgNc87ygyNy(NbgN(fzsc9zcsgNps(8z(N
gN9gsHgfNhis7xi8zgb(fNy(Nf7fniGN
N
A(y(fzgbNN
Ó7(nósiN =(sz79gbN (8N 9ints(8f7–8N Kc(N z7(8(N c8gN s(bg97–8N tsin(y7iN y(N gbzcsgN 8iN

11.     N
fitiszgygNgNbgNn(8isNy7n(8f7–8Nbgz(sgbNy(NUN–Nn(8ifGN
 
Rgt7z(bNN
08fg89h(Ny(NbgNtgsz(Nfct(s7isNy(NbgN9ibcn8gGN
N N N
Bóg9iNN
08Hsifgn7(8ziNy(NbgNbifgN(8NfcNgtimiNfiós(NbgN9ibcn8gGN
N
Ój8fcbgNiNÑsgKc(z(NN
oibgy7xiN9i8Ns(bg97–8Ny(N9bgsiNy(N9iszg8z(NgNt(sgbz(Nn(8isNiN7HcgbNgNc8iGN
N
A7biz(NN
0b(n(8ziN (fzsc9zcsgbN (fó(bziN 78zsiyc97yiN iN =g97gyiNy(8zsiN y(bN z(ss(8iN 9i8N (bN p78N y(N
fitiszgsNc8gN9gsHgNmNzsg8fp(s7sbgNNgbNn7fniNiN9i8N(bNp78Ny(N9intg9zgsN(bNfc(biGN
N
,gtgzgNN
Agsz(N y(N bgN 97n(8zg97–8N y(N c8gN (fzsc9zcsgN Kc(N s(tgsz(N mN zsg8fn7z(N bgN 9gsHgN
y7s(9zgn(8z(NgbNz(ss(8iNy(N97n(8zg97–8NiNgNt7biz(fGN
N
2.2  ABREVIATURAS N
N
IgfNgós(=7gzcsgfNcfgygfN(8N(fzgN1isngNz7(8(8N(bNf7H87p79gyiNKc(Nf(NygNgN9i8z78cg97–8GN
EzsgfNgós(=7gzcsgfNf(Ny(p78(8Ny(8zsiNy(bNz()ziXNgymg9(8z(fNgNbgfNp–sncbgfN(8NbgfNKc(N
gtgs(9(8NiNgbN78797iNy(bN9gtÁzcbiN9iss(fti8y7(8z(GN
N
MN N N Ms(gN (p(9z7=gN (8N zsg997–8N y(bN 9i89s(ziN u9nOeN Kc (N siy(gN gbN
s(pc(sxiNts7897tgbNy(Nzsg997–8NmNKc(Nz7(8(N(bNn7fniN9(8zsi7y(NKc(N
(f(N s(pc(sxiXN y7=7y7yiN (8zs(N (bN 8Mn(siN y(N ógssgfGN Rcg8yiN (bN
s(pc(sxiN ts7897tgbN y(N zsg997–8N 9i8f7fz(N y(N =gs7ifN y7vn(zsifN y(N
ógssgfXN(bN8Mn(siNy(NógssgfNy(ó(N9gb9cbgsf(N9iniN(bNvs(gNzizgbNy(N
g9(siNy7=7y7yiN(8zs(N(bNvs(gNy(NbgNógssgNy(NngmisNy7vn(zsiGN
N
MóN N N Ms(gNy(Nc8gNógssgN78y7=7ycgbNy(Ns(pc(sxiGN
N
M9N N N Ms(gNy(bN8M9b(iNy(Nc8gN9ibcn8gNs(pisxgygN9i8N( ft7sgbXNn(y7ygNgbN
y7vn(zsiN()z(s7isNy(NbgN(ft7sgbGN
N
MHN N N Ms(gNzizgbNy(NbgNf(997–8Nzsg8f=(sfgbGN
N
MfN N N Ms(gNy(bNs(pc(sxiN(8Nzsg997–8GN
N
MfzN N N Ms(gNzizgbNy(bNs(pc(sxiN(8Nc8gNf(997–8GN
N
MzN N N Ms(gNy(Nc8gNsgngNy(Nc8N(fzs7óiN9(ssgyiNKc(Ns(f 7fz(Nzisf7–8GN
N
M=N N N Ms(gNy(bNs(pc(sxiNtisN9iszg8z(GN
N
MWfN N N Ms(gNy(bNs(pc(sxiN(8N9ints(f7–8GN
N
MbN N N Ms(gN9gsHgygGN

12.    [F
F
0F F F l214:>C5C0CF C87F H719:8F 28?/0>=:702F 89:5L078>/8FC8F 284:82F1.F C8F
?13A28.5E>8>87?1>?28/1
F
H >?I1C870?0208>?13A28.5E>C8787838>/1
F
H1F F F l82@38/21F C8F 70F .8??5E>F ?2@/5?0F A020F 70F 4:82F0F ?12/0>/8F 8>F C1.F
C528??51>8.+A:>F1>0358>/1-
F
HX >?I1 C87 0730 1 C5B38/21 C8 :>0 .8??5E> ?52?:702 A020 87
C5.8D1A12?12/8
F
3 0?/129:82870?51>087C50=20302807C83138> /1F0F:>FC50=2030F
89:5L078>/8C83138>/1:>541238
F
? 5./0>?50C87045H203B.07860C08>?13A28.5E> 07868>8:/21
F
C 5./0>?50C87045H203B.07860C08>?13A28.5E> F07F?8>/215C8FC87F
0?8218>/20??5E>
F
CH 5B38/21>135>07C870H0220
F
C? .A8.12C8728?:H25358>/1C8?1>?28/138C5C1C 8.C8F70F45H20F3B.F
07860C0F8>F/20??5E>F07F?8>/21FC8F70FH0220F3B.F?82?0>008.045H20
F
CY 5./0>?50C87045H203B.07860C08>?13A28.5E >F07F?8>/215C8FC87F
284:82F18>?13A28.5E>
F
? EC:71C8870./5?5C0CC87?1>?28/1
F
. EC:71C8870./5?5C0CC87284:82F1
F
42 EC:71 C8 21/:20 C87 ?1>?28/1 +28.5./8>?50 C87F ?1>?28/1F 0F 70F
/20??5E>A12478<5E>-
F
4; .4:82F18.A8?545?0C1C847:8>?50C87284:82F 1
F
4W? 8.5./8>?50 8.A8?545?0C0 C87 ?1>?28/1 0 70 ?13A28.5E> 8>
Q=K?3 :0>C1 8./0 ?0>/5C0C 0A028F?0 H061 87 .5=>1F C8F :>F
20C5?078728.:7/0C18./02B8>Q=K?3
F
I 8207/8/1/07C8787838>/1
F
I 5=5C8F070478<5E>C887838>/1.8>?13A28.5E >
F
I8 138>/1 C8 5>82?50 C8 70 .8??5E> /20>.41230C0 0=258/0C0F 1F
3138>/1C85>82?50848?/5L1
F
I= 138>/1C85>82?50C870.8??5E>/1/07>10=25 8/0C0F?1>F28.A8?/1F
07868?8>/215C07.5>?1>.5C820287284:82F1

13.   F
F
I.8 138>/1 C8 5>82?50 C87 0?821 C8 284:82F1 28.A8?/1F 07F 868F
?8>/215C07C870.8??5E>/20>.L82.07C8787838>/1
F
* 0?/12C871>=5/:C848?/5L0A02087838>/1.8>? 13A28.5E>
F
7 1>=5/:CC870L5=0171.00230C08>:>0C528?? 5E>F/07F?131F.8F
C845>88>708??5E>#71>=5/:CC87L170C5F1
F
7? 5./0>?50L82/5?078>/280A1;1.
F
7C 1>=5/:CC8C8.02217711C80>?7068
F
78 1>=5/:CC883A0738A12/20.70A8
F
7> :F75H28C8787838>/1
F
7 1>=5/:C C87 A0D1 8> 70 C528??5E> 8> 9:8 .8 C8/8235>0>F 71.F
3138>/1.38C5C0?8>/210?8>/21C871.0A1;1.
F
7 1>=5/:CC87A0D18>70C528??5E>A82A8>C5?:70 2F0F70FC528??5E>F8>F
9:8.8C8/8235>0>71.3138>/1.38C5C0?8>/210?8>/21FC8F71.F
0A1;1.
F
3 138>/131C545?0C1
F
: 8.5./8>?50289:825C0?1>28.A8?/1073138>/1 478?/1203H5G>
C8>135>0C13138>/1M7/53113138>/1C8C5.8D1
F
138>/1478?/1238>12C8C5.8D18>878</2831 C8F:>F87838>/1F
8> ?13A28.5E> . A1.5/5L1 .5 87 87838>/1 8./B 478<51>0C1F 8>F
?:2L0/:20F .53A78F ;F 8.F >8=0/5L1F .5F 8./BF 478<51>0C1F 8>F C1H78F
?:2L0/:20
138>/1478?/1230;12C8C5.8D18>878</2831 C8F:>F87838>/1F
8>?13A28.5E>583A28A1.5/5L1
F
: 02=00<50703A7545?0C0>12307070.8??5E>/20>.L82.070?/:0>C1
87.53:7/B>8038>/8?1>':
FF
> 870?5E> 8>/28 71. 3EC:71. C8 870./5?5C0C C87 0 ?821F ;F C87F
?1>?28/1+.K?-
F
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H070>?80C0
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? 02=0?2@/5?0C8A0>C81
F
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F
>X 8.5./8>?50>135>070?02=00<507C8:>3:21 C5.8D0C1F?1>41238F

14.   ρ<α
0α70α°8??5E>αρ()1)α
α
±:α α α π8.5./8>?50α 289:825C0α ?1>α 28.A8?/1α 0α 70α ?02=0α 0<507α C8α
?13A28.5E>)α≥03H5G>αC8>135>0C0α?02=0α0<507αM7/530)α
ρα α α φ:0>/@0αC87α284:82F1α8>α/20??5E>α+Φ.KHC-)α
α
ρHα α α φ:0>/@0αC87α284:82F1α9:8αA21C:?8α70α?1>C5?5E>αH 070>?80C0)α
α
ρXα α α Φ.KHXC)α
α
ρWα α α φ:0>/@0αC87α284:82F1α8>α?13A28.5E>α+ΦW.KHC-)α
α
.α α α  .A0?50358>/1α?8>/21α0α?8>/21α8>/28α8./25H1.)α
α
≥:α α α π8.5./8>?50α289:825C0α?1>α28.A8?/1α07α3138>/1α /12.12)α≥03H5G>α
C8>135>0C1α3138>/1α/12.12αM7/531α1αC8αC5.8D1)α
α
/α α α  .A8.12αC87α3:21)α
α
?α α α π8.5./8>?50α >135>07α 0α 70α 4:82F0α ?12/0>/8α A21A12?51>0C0α A12α 87α
?1>?28/1)α
α
>α α α π8.5./8>?50α>135>07α07α?12/8)α
α
.α α α π8.5./8>?50α >135>07α 0α 70α 4:82F0α ?12/0>/8α A21A12?51>0C0α A12α 87α
284:82F1)α
)α
:α α α π8.5./8>?50α289:825C0α?1>α28.A8?/1α0α70α4:82F0 α?12/0>/8)α≥03H5G>α
C8>135>0C0α4:82F0α?12/0>/8αM7/530α1αC8αC5.8D1)α
α
X:α α α φ02=0αC8α.82L5?510αA12α:>5C0CαC8α71>=5/:Cα1αC8 αB280.0α3:7/5A75?0C0α
A12α71.α40?/128.αC8α?02=0α0A21A50C1.αC845>5C1.α8>α87αφ0A@/:71αρ])α
≥03H5G>α C8>135>0C0α ?02=0α 40?/125F0C00α ?02=0α 03A7545?0C0α 1α
?02=0αM7/530)α
α
α α α Σ0C1α38>12αC8α:>0α.8??5E>α28?/0>=:702)α
α
ρα α α ,8>12α C538>.5E>α 38C5C0α ?8>/21α 0α ?8>/21α C8α :>α 8 ./25H1α
28?/0>=:702α?8220C1)α
α
8α α α Σ0C1α30;12αC8α:>0α.8??5E>α28?/0>=:702)α
α
8/α α α μ5./0>?50αC87α868α?8>/215C07αC8α70α.8??5E>α/1/070α.5>α?1>.5C8202α87α
284:82F1α0α70α45H20α8</2830α8>α/20??5E>)α
α
8ρα α α ,0;12α C538>.5E>α 38C5C0α ?8>/21α 0α ?8>/21α C8α :>α 8 ./25H1α
28?/0>=:702α?8220C1)α
α
αα α α Φ>=:71α ?13A28>C5C1α 8>/28α 71.α 8./25H1.α 5>?75>0C1. α ;α 87α 868α
71>=5/:C5>07αC87α87838>/1)α

15.   ρ(α
α
βCα α α π870?5E>α8>/28α87α3138>/1α3B<531αC8H5C1α0α70α?0 2=0α3:82/0αC8α
C5.8D1α;α87α3138>/1α3B<531αC8H5C1α0α70α?02/0α/1/07αC8αC5.8D1)α
°583A28αA1.5/5L1)α
βρα α α σ0?/12αC845>5C1α8>α70α°8??5E>αρρ)β)ρ4)α
α
φα α α σ0?/12α C8α 28C:??5E>α C8α 28.5./8>?50)α Φ48?/0α 0α 70.α 28.5./8>?50.α
>135>078.)α
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
PARTE 2 - MATERIALES 
 
CAPITULO 3 - MATERIALES 
α

16.    VN
UG     CEMENTO N
N
UG G N N 0bN9(n(8ziN(ntb(gyiN(8NbgNts(tgsg97–8Ny(bN9i89s(ziNy(ó(svN9cntb7sN9i8N
bifNs(Kc7f7zifNy(NbgfN(ft(97p79g97i8(fNDÉD1É0RNtgsgN9(n(8zifGN
N
UG GON N 0bN9(n(8ziNcz7b7xgyiN(8NiósgNy(ó(svNf(sNy(bNn7fniNz7tiNmNngs9gNKc(N(bN
(ntb(gyiN tgsgN bgN f(b(997–8N y(N bgfN tsitis97i8(fN y(N bgN n(x9bgN y(N
9i89s(ziGN
 
3.2    AGREGADOS N
N
UGOG N N IifNgHs(HgyifNy(ó(sv8N9cntb7sN9i8NbifNs(Kc7f7zifNy(NbgN1isngNDÉD1É0RN
5LLGLU4XN Kc(N f(N 9intb(n(8zgsv8N 9i8N bifN y(N (fzgN 1isngN mN bgfN
(ft(97p79g97i8(fNzj9879gfGN
N
UGOGON N IifNgHs(HgyifNKc(N8iN9cntbg8N9i8NgbHc8ifNy(NbifNs(Kc7f7zifN78y79gyifN
tiysv8N f(sN cz7b7xgyifN f7(nts(N Kc(N (bN Ri8fzsc9zisN y(nc(fzs(XN tisN
tsc(ógfN y(N bgóisgzis7iN iN ()t(s7(897gN y(N iósgfXN Kc(Ntc(yg8N tsiyc97sN
9i89s(ziNy(NbgfNtsit7(ygy(fNs(Kc(s7ygfGNIifNgHs(HgyifNf(b(997i8gyifN
y(ó(sv8Nf(sNgtsiógyifNtisN(bND8ft(9zisGN
N
UGOGUN N IifNgHs(HgyifNKc(N8iN9c(8z(8N9i8Nc8Ns(H7fzsiNy(Nf(s=797ifNy(nifzsgób(XN
iN gKc(bbifN tsi=(87(8z(fN y(N 9g8z(sgfN ()tbizgygfN y7s(9zgn(8z(N tisN (bN
Ri8zsgz7fzgXNtiysv8Nf(sNgtsiógyifNtisN(bND8ft(9zisNf7N9cntb(8N9i8NbifN
(8fgmifN8isngb7xgyifNKc(N9i8f7y(s(N9i8=(87(8z(fGN
N N 0fz(N tsi9(y7n7(8ziN 8iN 78=gb7ygN bifN (8fgmifN y(N 9i8zsibN y(N biz(fN y(N
gHs(HgyifN(8NiósgGN
N
UGOG5N N IifNgHs(HgyifNp78iNmNHsc(fiNy(ó(sv8Nf(sNng8(/gyifN9iniNngz(s7gb(fN
78y(t(8y7(8z(fGN RgygN c8gN y(N (bbifN y(ó(svN f(sN 9gygN c8iN y(N (bbifN
tsi9(fgyiXNzsg8ftiszgyiXNng87tcbgyiXNgbng9(8gyiNmNt(fgyiNy(Nng8(sgN
zgbNKc(NbgNtjsy7ygNy(Np78ifNf(gNnÁ87ngXNKc(Nng8z(8Hg8NfcNc87pisn7ygyXN
Kc(N8iNf(Ntsiycx9gN9i8zgn78g97–8NtisNfcfzg897gfN()zsg:gfNmNKc(N8iNf(N
ts(f(8z(NsizcsgNiNf(Hs(Hg97–8N7ntiszg8z(N(8N(bbifGN
N
UGOGSN N IifN gHs(HgyifN gN f(sN (ntb(gyifN (8N 9i89s(zifN Kc(N =gmg8N gN N (fzgsN
fin(z7yifN gN tsi9(fifN y(N 9i8H(bg97–8N mN y(fh7(biN mN 8iN 9cntbg8N9i8N(bN
g9vt7z(NSGOGONy(NbgN1isngNDÉD1É0RN5LLGLU4Ntiysv8Nf(sNcz7b7xgyifNf7Nc8N
9i89s(ziN y(N tsit7(ygy(fN 9intgsgób(fXN ts(tgsgyiN 9i8NgHs(HgyiN y(bN
n7fniN is7H(8XN hgN y(nifzsgyiN c8N 9intiszgn7(8ziN fgz7fpg9zis7iN 9cg8yiN
(fzc=iNfin(z7yiNgN9i8y797i8(fNy(N78z(nt(s7fniNf7n7bgs(fNgNbgfNKc(Nf(N
(ft(sgGN
N
UGOGVN N 0bNgHs(HgyiNy(Ntsi9(y(897gNngs78gNy(ó(svNf(sNzsgzgyiNtisNbg=gyiN9i8N
gHcgNtizgób(Ng8z(fNy(Ncz7b7xgsbiN(8NbgNts(tgsg97–8Ny(bN9i89s(ziGN
N
UGOG4N N 0bNgHs(HgyiNNNp78iNtiysvN9i8f7fz7sNy(Ngs(8gN8gzcsgbNiNng8cpg9zcsgygXNiN
c8gN 9inó78g97–8N y(N gnógfGN ÍcfN tgszÁ9cbgfN f(sv8N b7nt7gfXN y(N t(sp7bN
ts(p(s(8z(n(8z(N g8HcbgsXN ycsiXN 9intg9ziN mN s(f7fz(8z(PN y(ó7(8yiN (fzgsN
b7ós(N y(N tgszÁ9cbgfN (f9gnifgfXN ngz(s7gN isHv879gN cN izsgfN fcfzg897gfN

17.    4N
yg:78gfGN
N
UGOGQN N 0bN gHs(HgyiN Hsc(fiN tiysvN 9i8f7fz7sN y(N Hsg=gN8gzcsgbN iN zs7zcsgygGN ÍcfN
tgszÁ9cbgfN f(sv8N b7nt7gfXN y(N t(sp7bN ts(p(s(8z(n(8z(N g8HcbgsN iN f(n7k
g8HcbgsXN ycsgfXN 9intg9zgfXN s(f7fz(8z(fN mN y(N z()zcsgN ts(p(s(8z(n(8z(N
scHifgPNy(ó(svN(fzgsNb7ós(Ny(NtgszÁ9cbgfN(f9gnifgfXNngz(s7gNisHv879gNcN
izsgfNfcfzg897gfNyg:78gfGN
N
UGOGJN N IgNHsg8cbin(zsÁgNf(b(997i8gygNtgsgN(bNgHs(HgyiNy(ó(svNt(sn7z7sNióz(8(sN
bgN nv)7ngN y(8f7ygyN y(bN 9i89s(ziN 9i8N c8gN gy(9cgygN zsgóg/gó7b7ygyN (8N
pc897–8Ny(NbgfN9i8y797i8(fNy(N9ibi9g97–8Ny(NbgNn(x9bgGN
N
UGOG LNN 0bNzgng:iNnv)7niN8in78gbNy(bNgHs(HgyiNHsc(fiN8iNy(ó(svNf(sNngmisN
y(NN
N
N N geN C8NKc78ziNy(NbgNn(8isNy7n(8f7–8N(8zs(NbgfN9gsg fNy(bN(89ipsgyiXNiN
N N óeN C8Nz(s97iNy(bNt(sgbz(Ny(NbgNbifgXNiN
N N 9eN És(fN 9cgszifN y(bN n(8isN (ftg97iN b7ós(N (8zs(N ógssgfN y(N s(pc(sxiNN
78y7=7ycgb(fNiN(8NtgKc(z(fNiNz(8yi8(fNiNyc9zifNy(Nts(fpc(sxiGN
N
N N 0fzgfN b7n7zg97i8(fN tc(y(8N f(sN ió=7gygfN f7XN gN 9s7z(s7iN y(bN D8ft(9zisXN bgN
zsgóg/gó7b7ygyNmNbifNtsi9(y7n7(8zifNy(N9intg9zg97–8Nt(sn7z(8N9ibi9gsN(bN
9i89s(ziNf78Npisng97–8Ny(N=g9ÁifNiN9g8Hs(/(sgfGN
N
UGOG  NN 0bN bg=gyiN y(N bgfN tgszÁ9cbgfN y(N gHs(HgyiN Hsc(fiN f(N y(ó(svN hg9(sN 9i8N
gHcgN tizgób(N iN gHcgN b7ós(N y(N ngz(s7gN isHv879gXN fgb(fN mN f–b7yifN (8N
fcft(8f7–8GN
N
UGOG ONN 0bNgHs(HgyiNy(8in78gyiNShisn7H–8SN9iss(fti8y(NgNc8gNn(x9bgN8gzcsgbN
y(NHsg=gNmNgs(8gGNÍ–biNtiysvN(ntb(gsf(N(8NbgN(bgóisg97–8Ny(N9i89s(zifN
9i8Ns(f7fz(897gN(8N9ints(f7–8NhgfzgNy(N LLNaHá9nONgNbifNOQNyÁgfGN
N N 0bN9i8z(87yiNnÁ87niNy(N9(n(8ziNf(svNy(NOSSNaHánUG N
N N N
0bN hisn7H–8N y(ó(svN (fzgsN b7ós(N y(N 9g8z7ygy(fN t(s/cy797gb(fN y(N tib=iXN
z(ssi8(fXN tgszÁ9cbgfN óbg8ygfN iN (f9gnifgfXN fgb(fXN vb9gb7fXN ngz(s7gN
isHv879gNmNizsgfNfcfzg897gfNyg:78gfNtgsgN(bN9i89s(ziGN
N N N
08N biN Kc(N f(gN gtb79gób(XN f(N f(Hc7sv8N tgsgN (bN hisn7H–8N bgfN
s(9in(8yg97i8(fN78y79gygfNtgsgNbifNgHs(HgyifNp78iNmNHsc(fiGN
N
3.3    AGUA N
N
UGUG N N 0bNgHcgN(ntb(gygN(8NbgNts(tgsg97–8NmN9csgyiNy(bN9i89s(ziNy(ó(svNf(sXN
y(Nts(p(s(897gXNtizgób(GN
N
UGUGON N Í(Ncz7b7xgsvNgHcgfN8iNtizgób(fNf–biNf7NN
N
N N geN 0fzv8N b7nt7gfN mN b7ós(fN y(N 9g8z7ygy(fN t(s/cy797gb(fN y(N g9(7z(fXN
v97yifXN vb9gb7fXN fgb(fXN ngz(s7gN isHv879gN cN izsgfN fcfzg897gfN Kc(N
tc(yg8Nf(sNyg:78gfNgbN9i89s(ziXNg9(siNy(Ns(pc(sxiNiN(b(n(8zifN

18.    QN
(nó(ó7yifGN
N N óeN IgN f(b(997–8N y(N bgfN tsitis97i8(fN y(N bgN n(x9bgNy(N 9i89s(ziN f(N
ógfgN (8N (8fgmifN (8N bifN Kc(N f(N hgN cz7b7xgyiN gHcgN y(NbgN pc(8z(N
(b(H7ygGN
N N 9eN IifN9cóifNy(Ntsc(ógNy(Nnisz(siNts(tgsgyifN9i8N gHcgN8iNtizgób(N
mN(8fgmgyifNy(Ng9c(syiNgNbgN1isngNMÍÉÓNR LJXNz7(8(8NgNbifN4NmN
OQNyÁgfNs(f7fz(897gfN(8N9ints(f7–8N8iNn(8is(fNy(bNJLRNy(NbgNy(N
nc(fzsgfNf7n7bgs(fNts(tgsgygfN9i8NgHcgNtizgób(GN
N
UGUGUN N IgfN fgb(fN cN izsgfN fcfzg897gfN 8i97=gfN ts(f(8z(fN (8N bifN gHs(HgyifN máiN
gy7z7=ifNy(ó(sv8Nfcngsf(NgNbgfNKc(Ntc(ygNgtiszgsN(bNgHcgNy(Nn(x9bgyiN
tgsgN(=gbcgsN(bN9i8z(87yiNzizgbNy(Nfcfzg897gfN789i8=(87(8z(fGN
N
UGUG5N N IgNfcngNy(NbifN9i8z(87yifNy(N7i8N9biscsiNts(f(8z(fN(8N(bNgHcgNmN(8NbifN
y(nvfN 9inti8(8z(fN y(N bgN n(x9bgN ugHs(HgyifN mN gy7z7=ifeN 8iN y(ó(sv8N
()9(y(sNbifN=gbis(fN78y79gyifN(8NbgNÉgóbgN5G5G5Ny(bNRgtÁzcbiN5GN
NNNNN
UGUGSN N 0bNgHcgNy(NngsNf–biNtiysvN(ntb(gsf(N(8NbgNts(tgsg97–8Ny(bN9i89s(ziNf7N
f(N9c(8zgN9i8NbgNgczis7xg97–8Ny(bND8H(87(siNAsim(9z7fzgNmNy(bND8ft(9zisGN
1iNf(Ncz7b7xgsvN(8NbifNf7Hc7(8z(fN9gfifNN
N
N N kN Ri89s(ziNts(fpisxgyiGN
N N kN Ri89s(zifN9i8Ns(f7fz(897gfNngmis(fNy(N 4SNQHá9n ONgNbifNOQNyÁgfGN
N N kN Ri89s(zifN 9i8N (b(n(8zifN (nó(ó7yifN y(N p7(ssiN Hgb =g87xgyiN iN
gbcn787iGN
N N kN Ri89s(zifN9i8Nc8Ng9gógyiNfct(sp797gbNy(N7ntiszg 897gGN
N
UGUGVN N 1iNf(Ncz7b7xgsvN(8NbgNts(tgsg97–8Ny(bN9i89s(ziXN(8N(bN9csgyiNy(bNn7fniXNiN
(8N (bN bg=gyiN y(bN (Kc7tiXN gKc(bbgfN gHcgfN Kc(N 8iN 9cntbg8N 9i8N bifN
s(Kc7f7zifNg8z(s7is(fGN
N
3.4    ACERO DE REFUERZO N
N
UG5G N N IgfNógssgfNy(Ns(pc(sxiNy(Ny7vn(zsiNngmisNiN7HcgbNgNQNnnNy(ó(sv8Nf(sN
9isscHgygfXNbgfNy(Ny7vn(zsifNn(8is(fNtiysv8Nf(sNb7fgfGN
N
3.4.2    Soldadura del refuerzoN
N
UG5GOG NNN 0bN s(pc(sxiN Kc(N =gN gN f(sN fibygyiN gfÁN 9iniN (bN tsi9(y7n7(8ziN y(N
fibygycsgXN (bN 9cgbN y(ó(svN f(sN 9intgz7ób(N 9i8N bifN s(Kc7f7zifN y(N
fibygó7b7ygyNy(bNg9(siNKc(Nf(N(ntb(gsvXNy(ó(sv8N(fzgsN78y79gyifN(8NbifN
tbg8ifGN
N N N
08N(fz(N9gfiXNbgfN(ft(97p79g97i8(fNtgsgNbgfNógssgfNy(Ns(pc(sxiNy(ó(sv8N
()7H7sN gy797i8gbn(8z(N (bN g8vb7f7fN KcÁn79iN y(bN ngz(s7gbN 9i8N bgN
y(z(sn78g97–8Ny(bN9i8z(87yiNy(N9gsói8iN(Kc7=gb(8z(NuR0eXN()9(tziNtgsgN
ógssgfN Kc(N 9cntb(8N 9i8N bgN (ft(97p79g97–8N MÍÉÓN M4LVXN gN p78N y(N
gy(9cgsbiN gN bifN tsi9(y7n7(8zifN y(N fibygycsgN (ft(97p79gyifN (8N (bN
SÍzsc9zcsgbN Z(by78HN Riy(N .(78pis978HN Íz((bSN uM1ÍDáMZÍN 2 G5eN y(N bgN
Mn(s79g8NZ(by78HNÍi97(zmGN

19.    JN
N
3.4.3    Refuerzo CorrugadoN
N
UG5GUG N IgfN ógssgfN 9isscHgygfN y(Ns(pc(sxiNy(ó(sv8N9cntb7sN9i8NgbHc8gNy(NbgfN
f7Hc7(8z(fN(ft(97p79g97i8(fNN
N
N N geN 0ft(97p79g97–8N tgsgN ógssgfN y(N g9(siN 9i8N s(fgbz(fN tgsgN 9i89s(ziN
gsngyiNuDÉD1É0RNU5 GLU eGN
N N óeN 0ft(97p79g97–8N tgsgN ógssgfN y(N g9(siN y(N óg/gN gb(g97–8N MÍÉÓN
M4LVGN
N
UG5GUGON My797i8gbn(8z(NbgfNógssgfN9isscHgygfNy(Ns(pc(sxiNy(ó(sv8N9cntb7sN9i8NN
N
N N geN IgNs(f7fz(897gNgNbgNpbc(897gNy(ó(N9iss(fti8y(s NgNbgNy(z(sn78gygN
tisNbgfNtsc(ógfNy(NógssgfNy(Nf(997–8Nzsg8f=(sfgbN9intb(zgGN N
N N óeN IifNs(Kc7f7zifNtgsgNbgNtsc(ógNy(NyióbgyiNy(Nbg fNógssgfXNy(fy(N(bN
y7vn(zsiNVNnnNhgfzgN(bNy7vn(zsiNUSNnnXNy(ó(8Nhg9(sf(N(8Nógf(N
gN yiób(9(fN y(N  QLON (8N ógssgfNy(Nf(997–8Nzsg8f=(sfgbN9intb(zgXN
gbs(y(yisN y(N ng8ys7b(fN 9cmifN y7vn(zsifN f(N (ft(97p79g8N (8N bgN
ÉgóbgNUG5GUGOGN
N
TABLA 3.4.3.2   
REQUISITOS PARA LA PRUEBA DE DOBLADO 
N
N
2DMÓ0É.EN1EÓD1MIN20NIMN
ÑM..MN
N
nnN
N
N
tcbHgygfN
N
N
2DMÓ0É.EN20IN
ÓM12.DINAM.MN0IN
P.M2ENM.1N5OLN
NNNNNNNNNNNNNNNNNNNNNNNN
NNNNNVXNQXN LXNN
NNNNN ONmN VN
NNNNNOLXNOONXNOSN
NNNNNULXNUSN
N
N
 á5XNUáQX áON
NNNNNNNNNNNSáQN
NNNNNNNNNNNUá5XN N
NNNNNNNNNNN NUáQN
N
5yóN
N
SyóN
4yóN
NN
UG5GUGUN IgfNógssgfNy(Ns(pc(sxiN9isscHgygfN9i8Nc8gNs(f7fz(897gN(ft(97p79gygNgNbgN
pbc(897gNpmXNfct(s7isNgbNHsgyiNM.1N5OLNy(NbgN1isngNDÉD1É0RNU5 GLU N8iN
tiysv8Nf(sNcfgygfN(8N(b(n(8zifNKc(Npisng8Ntgsz(Ny(bN(fKc(b(ziNf7fnik
s(f7fz(8z(GN
N N AgsgN9gb7ygy(fNy(Ng9(siNfct(s7is(fNgNbgN78y79gygN(8N(bNtvssgpiNg8z(s7isXN
(bN (fpc(sxiN y(N pbc(897gN pmN f(svN (bN 9iss(fti8y7(8z(NgN c8gN y(pisng97–8N
c87zgs7gN y(bN LXUSRN mN y(ó(svN 9cntb7sN 9i8N c8gN y(N bgfN(ft(97p79g97i8(fN
78y79gygfN (8N bgN Í(997–8N UG5GUG N mN 9i8N bifN s(Kc7f7zifN y(N bgN Í(997–8N
UG5GUGOGN
N
UG5GUG5N IgfNngbbgfNy(NógssgfNy(ó(sv8N9cntb7sN9i8NbgN(ft(97p79g97–8NMÍÉÓNM Q5GN
N
UG5GUGSN 0bN gbgnós(N 9isscHgyiN tgsgN (fpc(sxiN y(bN 9i89s(ziN y(ó(N 9cntb7sN 9i8N bgN

20.   OLN
1isngNDÉD1É0RNU5 GLVQXN()9(tziNKc(N(bNy7vn(zsiNy(bNgbgnós(N8iNf(svN
n(8isNgNSXSNnnNmNtgsgNgbgnós(N9i8Nc8gNs(f7fz(897gN(ft(97p79gygNgNbgN
pbc(897gNpmNfct(s7isNgN5OLLNaHá9nOXNpmNf(svN(bN(fpc(sxiN9iss(fti8y7(8z(N
gNc8gNy(pisng97–8Nc87zgs7gNy(bNLXUSRGN
N
UG5GUGVN IgN ngbbgN fibygygN y(N gbgnós(N b7fiN tgsgN s(pc(sxiN y(bN 9i89s(ziN y(ó(N
9cntb7sN 9i8N bgN (ft(97p79g97–8N DÉD1É0RN USLGLLOXN ()9(tziN Kc(N tgsgN
gbgnós(N9i8Nc8gNs(f7fz(897gN(ft(97p79gygNgNbgNpbc(897gNpmNfct(s7isNgN5OLLN
aHá9nOXNpmNf(svN(bN(fpc(sxiN9iss(fti8y7(8z(NgNc8gNy(pisng97–8Nc87zgs7gN
y(bNLXUSRGN
N N IgfN78z(sf(997i8(fNfibygygfN8iNy(ó(sv8N(ftg97gsf( NnvfNy(NULN9nN(8NbgN
y7s(997–8Ny(bNs(pc(sxiNts7897tgbNy(Npb()7–8GN
N N N
UG5GUG4N IgNngbbgNfibygygNy(Ngbgnós(N9isscHgyiNtgsgNs(pc(sxiNy(bN9i89s(ziNy(ó(N
9cntb7sN9i8NbgN1isngNDÉD1É0RNUSLGLLOXN()9(tziNKc(NtgsgNgbgnós(N9i8N
c8gNs(f7fz(897gN(ft(97p79gygNgNbgNpbc(897gNpmNfct(s7isNgN5OLLNaHá9nOXNpmN
f(svN(bN(fpc(sxiN9iss(fti8y7(8z(NgNc8gNy(pisng97–8Nc87zgs7gNy(bNLXUSRGN
N N IgfN78z(sf(997i8(fNfibygygfN8iNy(ó(sv8N(ftg97gsf( NnvfNy(N5LN9nN(8NbgN
y7s(997–8Ny(bNs(pc(sxiNts7897tgbNy(Npb()7–8GN
N
3.4.3.    Refuerzo lisoN
N
UG5G5G N IgfN ógssgfN b7fgfN tgsgN s(pc(sxiN y(ó(8N 9cntb7sN 9i8N bgfN (ft(97p79g97i8(fN
78y79gygfN (8N bgN Í(997–8N UG5GUG N mN 9i8N bifN s(Kc7f7zifN y(N bgN Í(997–8N
UG5GUGOGN1iNf(Ncfgsv8NógssgfNb7fgfN9i8Ny7vn(zsifNngmis(fNy(NVX5NnnGNN
N
UG5G5GON 0bN gbgnós(N b7fiN tgsgN s(pc(sxiN (8N (ft7sgbN y(ó(N 9cntb7sN 9i8N bgN 1isngN
DÉD1É0RN U5 GLU XN ()9(tziN Kc(N tgsgN gbgnós(N 9i8N c8gN s(f7fz(897gN
(ft(97p79gygNgNbgNpbc(897gNpmNfct(s7isNgN5OLLNaHá9nOXNpmNf(svN(bN(fpc(sxiN
9iss(fti8y7(8z(NgNc8gNy(pisng97–8Nc87zgs7gNy(bNLXUSRGN
N
3.4.5    Tendones de presfuerzoN
N
UG5GSG N IifNgbgnós(fXNzisi8(fNmNógssgfNtgsgNz(8yi8(fN(8N9i89s(ziNts(fpisxgyiN
y(ó(8N9cntb7sN9i8Nc8gNy(NbgfNf7Hc7(8z(fN(ft(97p79g97i8(fNzj9879gfNN
N N geN 0ft(97p79g97i8(fN tgsgN gbgnós(N f78N s(9cós7n7(8z iN s(b(=gyiN y(N
(fpc(sxifXNtgsgN9i89s(ziNts(fpisxgyiNuMÍÉÓNM5O eGN
N N óeN 0ft(97p79g97i8(fN tgsgN zis–8N f78N s(9cós7n7(8ziXN y(N 4N gbgnós(fXN
s(b(=gyiNy(N(fpc(sxifXNtgsgN9i89s(ziNts(fpisxgyiNuMÍÉÓNM5 VeGN
N N 9eN 0ft(97p79g97i8(fN tgsgN ógssgN f78N s(9cós7n7(8ziNy(N g9(siN y(N gbzgN
s(f7fz(897gXNtgsgN9i89s(ziNts(fpisxgyiNuMÍÉÓNM4OOeGN
N
UG5GSGON IifN gbgnós(fXN zisi8(fN mN ógssgfN 8iN y(zgbbgyifN (ft(9Áp79gn(8z(N (8N bgfN
8isngfN 78y79gygfN f(N tiysv8N cfgsN f7(nts(N Kc(N f(N y(nc(fzs(N Kc(N
9cntb(8N9i8NbifNs(Kc7f7zifNnÁ87nifNy(N(fzgfN(ft(97p79g97i8(fNzj9879gfNmN
Kc(N8iNz7(8(8Ntsit7(ygy(fNKc(NbifNhgHg8Nn(8ifNfgz7fpg9zis7ifNKc(NbifN
78y79gyifN(8NMÍÉÓNM5 VXNM5O NmNM4OOGN
N
3.5    ADITIVOS 
N

21.   O N
UGSG N N IifN gy7z7=ifN Kc(N f(N (ntb((8N (8N (bN 9i89s(ziN 9cntb7sv8N 9i8N bgfN
(ft(97p79g97i8(fNy(NbgN1isngNDÉD1É0RNUJGLQVGNÍcN(ntb(iN(fzgsvNfc/(ziN
gNgtsióg97–8Nts(=7gNy(bND8ft(9zisNmN8iNgczis7xgNgNniy7p79gsN(bN9i8z(87yiN
y(N9(n(8ziNy(NbgNn(x9bgGN
N
UGSGON N 0bNRi8fzsc9zisNy(ó(svNy(nifzsgsNgbND8ft(9zisNKc(NbifNgy7z7=ifN(ntb(gyifN
fi8N9gtg9(fNy(Nng8z(8(sN(f(897gbn(8z(NbgNn7fngN9gb7ygyXN9intif797–8N
mN9intiszgn7(8ziN(8NziygNbgNiósgGN
N
UGSGUN N 0bN9biscsiNy(N9gb97iNiNbifNgy7z7=ifNKc(N9i8z(8Hg8N9biscsifNKc(N8iNf(g8Ny(N
7ntcs(xgfN y(N bifN 9inti8(8z(fN y(bN gy7z7=iN 8iN y(ó(sv8N (ntb(gsf(N (8N
9i89s(ziNts(fpisxgyiXN(8N9i89s(ziNKc(Nz(8HgN(nó(ó7yifN(b(n(8zifNy(N
gbcn787iN iN y(N p7(ssiN Hgb=g87xgyiXN 9i89s(ziN 9ibi9gyiN (8N (89ipsgyifN y(N
n(zgbNHgb=g87xgyiXN9i89s(zifNngf7=ifNiN9i89s(zifN9ibi9gyifN(8N9b7ngfN
9vb7yifGN
N N 08NbifN9gfifNKc(N(bND8H(87(siNAsim(9z7fzgNgczis79(N(bN(ntb(iNy(N9biscsiN
y(N9gb97iNiNy(Ngy7z7=ifN9i8N9i8z(87yiNy(N9biscsifXNy(ó(svN9(sz7p79gsf(NKc(N
(bN9i8z(87yiNzizgbNy(N7i8N9biscsiN(8NbgNn(x9bgNy(N9i89s(ziN8iN()9(ygNbifN
bÁn7z(fN78y79gyifN(8NbgNÉgóbgN5G5G5Ny(bNRgtÁzcbiN5GN
N
UGSG5N N IgfN tcxibg8gfN Kc(N f(N (ntb((8N 9iniN gy7z7=iN y(ó(sv8N 9cntb7sN 9i8N bgN
1isngNMÍÉÓNRV QGN
N
UGSGSN N IifNgy7z7=ifN789istisgyis(fNy(Ng7s(Ny(ó(8N9cntb7sN9i8NbgN1isngNMÍÉÓN
ROVLGN
N
UGSGVN N IifNgy7z7=ifNs(yc9zis(fNy(NgHcgXNs(zgsyg8z(fXNg9(b(sg8z(fXNs(yc9zis(fNy(N
gHcgNmNs(zgsyg8z(fXNs(yc9zis(fNy(NgHcgNmNg9(b(sg8z(fNy(ó(sv8N9cntb7sN
9i8NbgN1isngNMÍÉÓNR5J5GN
N
UGSG4N N 0bNRi8fzsc9zisNtsitis97i8gsvNgbND8ft(9zisNbgNyif7p79g97–8Ns(9in(8ygób(N
y(bNgy7z7=iN(N78y79gsvNbifN(p(9zifNt(s/cy797gb(fNy(ó7yifNgN=gs7g97i8(fNy(NbgN
n7fngXN bgN 9intif797–8N KcÁn79gN y(bN gy7z7=iXN (bN 9i8z(87yiN y(N 9biscsifN
()ts(fgyifN9iniNtis9(8zg/(N(8Nt(fiNy(N7i8N9biscsiNmNbgNs(9in(8yg97–8N
y(bNpgós79g8z(NtgsgNbgNyif7p79g97–8Nf7Nf(N(ntb(gNgy7z7=ifN789istisgyis(fN
y(Ng7s(GNN
N
UGSGQN N MN p78N y(N Hgsg8z7xgsN c8gN 9c7ygyifgN y7fzs7óc97–8N y(N bifN 78Hs(y7(8z(fN f(N
(ntb(gsvN(Kc7tiNy(NgH7zgyiN9cg8yiNbifNgy7z7=ifN=gmg8NgNf(sN(ntb(gyifN
(8NpisngNy(Nfcft(8f7–8NiNy(Nfibc97i8(fN8iN(fzgób(fGN
N
UGSGJN N IifN gy7z7=ifN (ntb(gyifN (8N iósgN y(ó(8N f(sN y(NbgN n7fngN 9intif797–8XN
z7tiNmNngs9gNKc(NbifNcz7b7xgyifNtgsgNbgNf(b(997–8Ny(NbgfNtsitis97i8(fNy(N
bgNn(x9bgNy(N9i89s(ziGN
N
3.6.    ALMACENAMIENTO DE LOS MATERIALES EN OBRA N
N
UGVG N N IifN ngz(s7gb(fN y(ó(sv8N gbng9(8gsf(N (8N iósgN y(N ng8(sgN y(N (=7zgsN fcN
y(z(s7isiN iN 9i8zgn78g97–8GN 1iN f(N cz7b7xgsv8N ngz(s7gb(fN y(z(s7isgyifN iN
9i8zgn78gyifGN

22.   OON
N
UGVGON N 08N s(bg97–8N 9i8N (bN gbng9(8gn7(8ziN y(bN 9(n(8ziN f(N z(8ysv8N bgfN
f7Hc7(8z(fNts(9gc97i8(fNN
N N geN 1iN f(N g9(tzgsvN (8N iósgN óibfgfN y(N 9(n(8ziN 9cmgfN (8=ibzcsgfN
(fzj8Ny(z(s7isgygfNiNt(spisgygfGN
N N óeN 0bN 9(n(8ziN (8N óibfgfN f(N gbng9(8gsvN (8N iósgN (8N c8N bcHgsN
z(9hgyiXNps(f9iXNb7ós(Ny(Nhcn(ygyXNf78N9i8zg9ziN9i8N(bNfc(biGNÍ(N
gbng9(8gsvN(8Nt7bgfNy(NhgfzgN LNóibfgfNmNf(N9cós7svN9i8Nngz(s7gbN
tbvfz79iNcNizsifNn(y7ifNy(Ntsiz(997–8GN
N N 9eN 0bN9(n(8ziNgNHsg8(bNf(Ngbng9(8gsvN(8Nf7bifNn(z vb79ifXNgtsiógyifN
tisNbgND8ft(997–8NXN9cmgfN9gsg9z(sÁfz79gfN7nt(y7sv8N(bN78Hs(fiNy(N
hcn(ygyNiN(b(n(8zifN9i8zgn78g8z(fGN
N
UGVGUN N IifN gHs(HgyifN f(N gbng9(8gsv8N iN gt7bgsv8N y(N ng8(sgN y(N 7nt(y7sN bgN
f(Hs(Hg97–8Ny(NbifNn7fnifXNfcN9i8zgn78g97–8N9i8NizsifNngz(s7gb(fNiNfcN
n(x9bgyiN9i8NgHs(HgyifNy(N9gsg9z(sÁfz79gfNy7p(s(8z(fGN
N
UGVG5N N IgfNógssgfNy(Ng9(siNy(Ns(pc(sxiXNgbgnós(XNz(8yi8(fNmNyc9zifNn(zvb79ifN
f(N gbng9(8gsv8N (8N c8N bcHgsN f(9iXN g7fbgyiN y(bN fc(biNmNtsiz(H7yiNy(NbgN
hcn(ygyXNz7(ssgXNfgb(fXNg9(7z(NmNHsgfgfGN
N
UGVGSN N IifN gy7z7=ifN f(sv8N gbng9(8gyifN f7Hc7(8yiN bgfN s(9in(8yg97i8(fN y(bN
pgós79g8z(GNÍ(Nts(=(8ysvNbgN9i8zgn78g97–8XN(=gtisg97–8NiNy(z(s7isiNy(N
bifNn7fnifGNIifNgy7z7=ifNbÁKc7yifNf(sv8Ntsiz(H7yifNy(Nz(nt(sgzcsgfNy(N
9i8H(bg97–8N mN y(N 9gnó7ifN y(N z(nt(sgzcsgN Kc(N tc(yg8Ngp(9zgsN fcfN
9gsg9z(sÁfz79gfGN
N N IifNgy7z7=ifN8iNy(ó(sv8Nf(sNgbng9(8gyifN(8NiósgNt isNc8Nt(sÁiyiNngmisN
y(N f(7fN n(f(fN y(fy(N bgN p(9hgN y(bN Mbz7niN (8fgmiGN 08N9gfiN 9i8zsgs7iXN
y(ó(sv8Ns((8fgmgsf(NtgsgN(=gbcgsNfcN9gb7ygyNg8z(fNy(NfcN(ntb(iGN
N N IifN gy7z7=ifN 9cmgN p(9hgN y(N =(897n7(8ziN f(N hgN 9cntb7yiN 8iN f(sv8N
cz7b7xgyifGN
N
3.7    ENSAYO DE LOS MATERIALES N
N
UG4G N N 0bN D8ft(9zisN tiysvN isy(8gsXN (8N 9cgbKc7(sN (zgtgN y(N bgN (/(9c97–8N y(bN
tsim(9ziXN (8fgmifN y(N 9(sz7p79g97–8N y(N bgN 9gb7ygyN y(N bifN ngz(s7gb(fN
(ntb(gyifGN
N N 0bNnc(fzs(iNmN(8fgmiNy(NbifNngz(s7gb(fNf(Ns(gb7xg svNy(Ng9c(syiNgNbgfN
1isngfNDÉD1É0RN9iss(fti8y7(8z(fGN
UG4GON IifNs(fcbzgyifNy(N9(sz7p79g97–8Ny(N9gb7ygyNy(NbifNngz(s7gb(fNcz7b7xgyifNf(N
s(H7fzsgsv8Ny(Ng9c(syiNgNbiN78y79gyiN(8NbgNÍ(997–8N GUGUG5GN
 
 
 
 
 

23.   OUN
PARTE 3 - REQUISITOS DE CONSTRUCCIÓN 
 
CAPÍTULO 4 - REQUISITOS DE CONSTRUCCIÓN 
 
4.1.    CONSIDERACIONES GENERALES N
N
NN 5G G N N IgNf(b(997–8Ny(NbgfNtsitis97i8(fNy(NbifNngz(s7gb(fNKc(N78z(s=7(8(8N(8NbgN
n(x9bgN y(ó(svN t(sn7z7sN Kc(N (bN 9i89s(ziN gb9g89(N bgN s(f7fz(897gN (8N
9ints(f7–8Ntsin(y7iNy(z(sn78gygN(8NbgNÍ(997–8N5GUGOGN0bN9i89s(ziNf(svN
pgós79gyiN y(N ng8(sgN y(N s(yc97sN gbN nÁ87niN (bN 8Mn(siNy(N =gbis(fN y(N
s(f7fz(897gN tisN y(óg/iN y(bN pW9N (ft(97p79gyiXN 9iniN f(N (fzgób(9(N (8N N bgN
Í(997–8N5GVG5GOGN
N
NN 5G GON N IgN=(s7p79g97–8Ny(bN9cntb7n7(8ziNy(NbifNs(Kc7f7zifNtgsgNpW9Nf(NógfgsvN(8N
bifN s(fcbzgyifN y(N tsió(zgfN y(N 9i89s(ziN ts(tgsgygfN mN (8fgmgygfN y(N
g9c(syiNgNbgfN1isngfNDÉD1É0RNUUJGLUUXNUUJGLU5NmNUUJGLUVGN
N
NN 5G GUN N 0bN=gbisNy(NpW9Nf(NzingsvNy(Ns(fcbzgyifNy(N(8fgmifNs(gb7xgyifNgNbifNOQN
yÁgfNy(Nniby(gygfNbgfNtsió(zgfGN
NN N N Í7Nf(Ns(Kc7(s(Ns(fcbzgyifNgNizsgN(ygyXN(fziNy(ó (svNf(sN78y79gyiN(8NbifN
tbg8ifNmN(8NbgfN(ft(97p79g97i8(fNzj9879gfGN
N
NN 5G G5N N IifNs(fcbzgyifNy(NbifN(8fgmifNy(Ns(f7fz(897gNgNbgNpb()7–8NiNgNbgNzsg997–8N
tisN9ints(f7–8Ny7gn(zsgbNy(bN9i89s(ziN8iNy(ó(sv8Nf(sNcz7b7xgyifN9iniN
9s7z(s7iNtgsgNbgNg9(tzg97–8Ny(bNn7fniGN
N
5G GSN Í(N 9i8f7y(sgN 9iniN c8N (8fgmiN y(N s(f7fz(897gN gbN tsin(y7iN y(N bifN
s(fcbzgyifNy(NyifNtsió(zgfN97bÁ8ys79gfNts(tgsgygfNy(NbgNn7fngNnc(fzsgN
y(N 9i89s(ziN mN (8fgmgygfN gN bifN OQN yÁgfN iN gN bgN (ygyN (b(H7ygN tgsgN bgN
y(z(sn78g97–8Ny(NbgNs(f7fz(897gNy(bN9i89s(ziGN
N
4.2.    SELECCION DE LAS PROPORCIONES DEL CONCRETO N
N
NN 5GOG N N IgN f(b(997–8N y(N bgfN tsitis97i8(fN y(N bifN ngz(s7gb(fN 78z(Hsg8z(fN y(bN
9i89s(ziNy(ó(sv8Nt(sn7z7sNKc(NN
N
geN Í(N biHs(8N bgN zsgóg/gó7b7ygyN mN bgN 9i8f7fz(897gN Kc(N t(sn7zg8N Kc(N (bN
9i89s(ziNf(gN9ibi9gyiNpv97bn(8z(N(8NbifN(89ipsgyifNmNgbs(y(yisNy(bN
g9(siN y(N s(pc(sxiN óg/iN bgfN 9i8y797i8(fN y(N 9ibi9g97–8N gN f(sN
(ntb(gygfXNf78Nf(Hs(Hg97–8N87N()cyg97–8N()9(f7=gfGN
óeN Í(NbiHs(Ns(f7fz(897gNgNbgfN9i8y797i8(fN(ft(97gb(fNy(N()tif797–8NgN
Kc(Ntc(ygN(fzgsNfin(z7yiN(bN9i89s(ziXN9iniNf(N()7H(N(8NbgNÍ(997–8N
5G5GN
9eN Í(N9cntbgN9i8NbifNs(Kc7f7zifN(ft(97p79gyifNtgsgNbgNs(f7fz(897gN(8N
9ints(f7–8NcNizsgfNtsit7(ygy(fGN
N
NN 5GOGON N Rcg8yiN f(N (ntb((N ngz(s7gb(fN y7p(s(8z(fN tgsgN tgsz(fN y7fz78zgfN y(N c8gN
iósgXN9gygN9inó78g97–8Ny(N(bbifNy(ó(svNf(sN(=gbcgygGN
N

24.   O5N
NN 5GOGUN N IgfNtsitis97i8(fNy(NbgNn(x9bgNy(N9i89s(ziXN789bc7ygNbgNs(bg97–8NgHcgNkN
9(n(8ziXNy(ó(sv8Nf(sNf(b(997i8gygfNfiós(NbgNógf(Ny(NbgN()t(s7(897gNy(N
iósgN máiN y(N n(x9bgfN y(N tsc(ógN ts(tgsgygfN 9i8N bifN ngz(s7gb(fN gN f(sN
(ntb(gyifXN9i8N()9(t97–8Ny(NbiN78y79gyiN(8NbgNÍ(997–8N5G5GN
N
4.3    PROPORCIONAMIENTO EN BASE A EXPERIENCIA DE CAM PO Y/O  
MEZCLAS DE PRUEBA N
N
5GUG     RBIRCIEN20NIMN20ÍoDMRDd1N0ÍÉB12M.  
N
5GUG G N ÓjziyiN N 
NN N N Í7Nf(Ntif((Nc8Ns(H7fzsiNy(Ns(fcbzgyifNy(N(8fgmi fNy(NiósgfNg8z(s7is(fXN
y(ó(svN9gb9cbgsf(NbgNy(f=7g97–8N(fzv8ygsGN
NN N N N
0bNs(H7fzsiNy(ó(svNN
N
geN .(ts(f(8zgsN N N ngz(s7gb(fXN N N tsi9(y7n7(8zifN N N y(NN N 9i8zsibN y(N
9gb7ygyNmN9i8y797i8(fNf7n7bgs(fNgNgKc(bbgfNKc(Nf(N(ft(sg8N(8NbgN
iósgNKc(Nf(N=gNgN78797gsGN
óeN .(ts(f(8zgsN gN 9i89s(zifN ts(tgsgyifN tgsgN gb9g8xgsN c8gN
s(f7fz(897gN y(N y7f(:iN pW9N Kc(N (fzjN y(8zsiN y(bN sg8HiN y(N [N 4LN
aHá9nONy(NbgN(ft(97p79gygNtgsgN(bNzsgóg/iNgN78797gsGN
9eN Ri8f7fz7sN y(N tisN biN n(8ifN ULN (8fgmifN 9i8f(9cz7=ifN iN y(N yifN
HsctifN y(N (8fgmifN 9i8f(9cz7=ifN Kc(N zizgb79(8N tisN biNn(8ifNULN
(8fgmifGN IifN (8fgmifN f(N (p(9zcgsv8N f(HM8N biN 78y79gyiN (8N bgN
Í(997–8N5G GSGN
N N N
5GUG GO    ÓjziyiNONN
NN N N N
Í7N f–biN f(N tif((N c8N s(H7fzsiN y(N  SN gN OJN (8fgmifN 9i8f(9cz7=ifXN f(N
9gb9cbgsvNbgNy(f=7g97–8N(fzv8ygsNSfSN9iss(fti8y7(8z(NgNy79hifN(8fgmifNmN
f(N ncbz7tb79gsvNtisN(bNpg9zisNy(N9iss(997–8N78y79gyiN(8NbgNÉgóbgN5GUG GON
tgsgNióz(8(sN(bN8c(=iN=gbisNy(NSfSGN
NN N N N
0bNs(H7fzsiNy(N(8fgmifNgNKc(Nf(Nhg9(Ns(p(s(897gN(8N(fz(NnjziyiNy(ó(svN
9cntb7sN9i8NbifNs(Kc7f7zifNgeNmNóeNy(bNnjziyiN NmNs(ts(f(8zgsNc8Ns(H7fzsiN
y(N(8fgmifN9i8f(9cz7=ifNKc(N9ints(8ygNc8Nt(sÁiyiNy(N8iNn(8ifNy(N5SN
yÁgfN9gb(8ygs7ifGN
 
TABLA 4.3.1.2 
 
ÓC0ÍÉ.MÍN 3MRÉE.N20NRE..0RRDd1N
Ó(8ifNy(N SN
 SN
OLN
OSN
ULN
CfgsNÉgóbgN5GUGOóN
 X VN
 XLQN
 XLUN
 XLLN
N

25.   OSN
5GUGON N RMIRCIEN20NIMN.0ÍDÍÉ01RDMNA.EÓ02DEN.06C0.D2M N
N
N N IgNs(f7fz(897gN(8N9ints(f7–8Ntsin(y7iNs(Kc(s7ygNu pW9seXN(ntb(gygN9iniN
ógf(N(8NbgNf(b(997–8Ny(NbgfNtsitis97i8(fNy(bN9i89s(ziXNf(N9gb9cbgsvNy(N
g9c(syiNgNbifNf7Hc7(8z(fN9s7z(s7ifNN
N
geN Í7N bgN y(f=7g97–8N (fzv8ygsN f(N hgN 9gb9cbgyiN y(N g9c(syiN gN biN
78y79gyiN (8N (bN ÓjziyiN  N –N (8N (bN ÓjziyiN OXN bgN s(f7fz(897gN
tsin(y7iNs(Kc(s7ygNf(svN(bNngmisNy(NbifN=gbis(fNy(z(sn78gyifN
tisN bgfN p–sncbgfN f7Hc7(8z(fXN cfg8yiN bgN y(f=7g97–8N (fzv8ygsN SfSN
9gb9cbgygN y(N g9c(syiN gN biN 78y79gyiN (8N bgN Í(997–8N 5GUG G N –N
5GUG GOGN
N
N N N  GN NpW9sNN\NNpW9N]N XU5fN
N
N N N OGNNNpW9sNN\NNpW9N]NOXUUfNkNUSN
N
N N N yi8y(NN
N N N fN\N2(f=7g97–8N(fzv8ygsN(8NaHá9nON
N
óeN Í7Nf(Ny(f9i8i9(N(bN=gbisNy(NbgNy(f=7g97–8N(fzv8ygsXNf(Ncz7b7xgsvNbgN
ÉgóbgN 5GUGOóN tgsgN bgN y(z(sn78g97–8N y(N bgN s(f7fz(897gN tsin(y7iN
s(Kc(s7ygGN
 
         TABLA 4.3.2b 
RESISTENCIA A LA COMPRESION PROMEDIO REQUERIDA 
(Kg/cm2) 
 
N
pW9N
N
N
pW9sN
N
n(8ifNy(NO LN
O LNgNUSLN
fiós(NUSLN
N
N
pW9N]N4LN
pW9N]NQ5N
pW9N]NJQN
N
5GUGUN N Í0I0RRDE1N20NIMÍNA.EAE.RDE10ÍNAE.NÓ0,RIMÍN20 NA.C0ÑMN
N
5GUGUG N Í7N8iNf(Nzc=7(sg8NbifNs(Kc7f7zifNiNjfzifN8iN9cntb7(sg8N9i8NbiN78y79gyiN(8N
bgN f(997–8N g8z(s7isXN f(N tiysvN tsitis97i8gsN bgN n(x9bgN n(y7g8z(N bgN
(bgóisg97–8Ny(Nn(x9bgfNy(Ntsc(ógGN08NjfzgfNf(Nz(8ysvN(8N9i8f7y(sg97–8N
bgfNf7Hc7(8z(fNb7n7zg97i8(fNN
N
geN IifN ngz(s7gb(fN cz7b7xgyifN mN bgfN 9inó78g97i8(fN y(N bifN n7fnifN
f(sv8NgKc(bbifNgNcz7b7xgsf(N(8NiósgGN
óeN IgfNn(x9bgfNy(Ntsc(ógNy(ó(sv8Nts(tgsgsf(N(ntb(g8yiN8iNn(8ifN
y(N zs(fN y7p(s(8z(fN s(bg97i8(fN gHcgk9(n(8ziN iN 9i8z(87yifN y(N
9(n(8ziXNgNp78Ny(Nióz(8(sNc8Nsg8HiNy(Ns(f7fz(897gfNy(8zsiNy(bN9cgbN
f(N(89c(8zs(NbgNs(f7fz(897gNtsin(y7iNy(f(gygGN

26.   OVN
9eN 0bN gf(8zgn7(8ziN y(N n(x9bgfN y(N tsc(ógN y(ó(svN (fzgsN y(8zsiN y(bN
sg8HiNy(NnvfNiNn(8ifNOLNnnNy(bNnv)7niNt(sn7z7yiGN
yeN AgsgN9gygNn(x9bgNy(Ntsc(ógNy(ó(sv8Nts(tgsgsf(NmN9csgsf(NtisNbiN
n(8ifN UN tsió(zgfN tgsgN 9gygN (ygyN y(N (8fgmiGN Í(N f(Hc7svN biN
78y79gyiN(8NbgN1isngNMÍÉÓNR JOGN
(eN 08Nógf(NgNbifNs(fcbzgyifNy(NbifN(8fgmifNy(NbgfNtsió(zgfXNy(ó(sv8N
9i8fzsc7sf(N9cs=gfNKc(Nnc(fzs(8NbgN78z(ss(bg97–8N(8zs(NbgNs(bg97–8N
gHcgk9(n(8ziN iN (bN 9i8z(87yiN y(N 9(n(8ziN mN bgN s(f7fz(897gN (8N
9ints(f7–8GNIgNs(bg97–8NgHcgk9(n(8ziNnv)7ngNiN(bN9i8z(87yiNy(N
9(n(8ziNnÁ87niNf(b(997i8gyiNy(ó(svNf(sNgKc(bNKc(N(8NbgN9cs=gN
nc(fzs(NKc(Nf(NhgNy(Nz(8(sNbgNs(f7fz(897gNtsin(y7iNs(Kc(s7ygGNÍ(N
z(8ysvN(8N9i8f7y(sg97–8NbiN78y79gyiN(8NbgNÍ(997–8N5G5GN
N
4.4    CONDICIONES ESPECIALES DE EXPOSICIÓN N
N
NN 5G5G N N IifN9i89s(zifNfin(z7yifNgNtsi9(fifNy(N9i8H (bg97–8NmNy(fh7(biNy(ó(sv8N
z(8(sN g7s(N 789istisgyiGN 0bN 9i8z(87yiN y(N g7s(N zizgbN9iniN fcngN y(N g7s(N
789istisgyiNnvfNg7s(NgzsgtgyiNf(svN(bN78y79gyiN(8NbgNÉgóbgN5G5G XNy(8zsiN
y(N c8gN zib(sg897gN y(N [N  XSGN N AgsgN s(f7fz(897gfN gN bgN 9ints(f7–8N pW9N
ngmis(fNy(NUSLNaHá9nOXNf(Ntc(y(Ns(yc97sN(8N XLN(bNtis9(8zg/(Ny(Ng7s(N
zizgbN78y79gyiN(8NbgNÉgóbgN5G5G GN
N
NN 5G5GON N Í7Nf(Ns(Kc7(s(Nc8N9i89s(ziNy(Nóg/gNt(sn(gó7b7ygyXNiNf7N(bN9i89s(ziNhgNy(N
(fzgsN fin(z7yiN gN tsi9(fifN y(N 9i8H(bg97–8N mN y(fh7(biN (8N 9i8y797–8N
hMn(ygXN f(N y(ó(svN 9cntb7sN 9i8N bifN s(Kc7f7zifN 78y79gyifN (8N bgN ÉgóbgN
5G5GOGN
N
5G5GUN N 0bN 9i89s(ziN Kc(N =gN gN (fzgsN ()tc(fziN gN bgN g997–8N y(N N fibc97i8(fN Kc(N
9i8z7(8(8N fcbpgzifXN y(ó(svN 9cntb7sN 9i8N bifN s(Kc7f7zifN 78y79gyifN (8N bgN
ÉgóbgN5G5GUGN1iNf(N(ntb(gsvN9biscsiNy(N9gb97iN9iniNgy7z7=iN(8N(fz(Nz7tiN
y(N9i89s(ziGN
N
5G5G5N N IgN nv)7ngN 9i89(8zsg97–8N y(N 7i8N 9biscsiN fibcób(N (8N gHcgN Kc(N y(ó(N
hgó(sN(8Nc8N9i89s(ziNgNbgfN(ygy(fNy(NOQNgN5ONyÁgfXN()ts(fgygN9iniNbgN
fcngNy(NbifNgtisz(fNy(NziyifNbifN78Hs(y7(8z(fNy(NbgNn(x9bgXN8iNy(ó(svN
()9(y(sN bifN b7n7z(fN 78y79gyifN (8N bgN ÉgóbgN 5G5G5GN 0bN (8fgmiN tgsgN
y(z(sn78gsN(bN9i8z(87yiNy(N7i8N9biscsiNy(ó(svN9cntb7sN9i8NbiN78y79gyiNtisN
bgN 3(y(sgbN T7HhXgmN Myn787fzsgz7i8N .(tiszN 1ON 3TZMk.2k44kQSN
SÍgntb78HNg8yNÉ(fz78HN3isNRhbis7y(NDi8N78NRi89s(z(SGN
N
5G5GSN N Í7N (bN 9i89s(ziN gsngyiN hgN y(N (fzgsN ()tc(fziN gN bgN g997–8N y(N gHcgfN
fgbiós(fXNgHcgNy(NngsNiNsi9ÁiNiN8(ób78gNtsi=(87(8z(Ny(NjfzgfXNy(ó(sv8N
9cntb7sf(NbifNs(Kc7f7zifNy(NbgNÉgóbgN5G5GONtgsgNbgNf(b(997–8Ny(NbgNs(bg97–8N
gHcgk9(n(8ziGNIgN(b(997–8Ny(Ns(9cós7n7(8zifNnÁ87nifNtgsgN(bNs(pc(sxiN
y(ó(svNf(sN9intgz7ób(N9i8N(bNz7tiNy(N()tif797–8GN
N
4.5    REDUCCIÓN DE LA RESISTENCIA PROMEDIO N
N
5GSG N N 2csg8z(N(bNtsi9(fiNy(N9i8fzsc997–8Ny(NbgNiósgXNf(NtiysvNs(yc97sN(bN=gbisNN
N(8N (bN Kc(N bgN s(f7fz(897gN tsin(y7iN ()9(y(N gN bgN s(f7fz(897gN y(N y7f(:iN

27.   O4N
f7(nts(NKc(NN
geN Í(N y7fti8HgN ycsg8z(N (bN tsi9(fiN 9i8fzsc9z7=iN y(N ULN –N nvfN
s(fcbzgyifNy(N(8fgmifNy(Ntsió(zgfN9csgygfNóg/iN9i8y797i8(fNy(N
bgóisgzis7iN mN (bN tsin(y7iN y(N jfzifN ()9(ygN gN bgN s(f7fz(897gN
tsin(y7iN f(b(997i8gygN y(N g9c(syiN gN biN 78y79gyiN (8N bgN Í(997–8NN
5GUGOgeGN
óeN Í(Ny7fti8HgNycsg8z(N(bNtsi9(fiN9i8fzsc9z7=iNy(NbifNs(fcbzgyifNy(N
 SN gN OJN (8fgmifN y(N tsió(zgfN 9csgygfN óg/iN 9i8y797i8(fN y(N
bgóisgzis7iN mN (bN tsin(y7iN y(N jfzifN ()9(ygN gN bgN s(f7fz(897gN
tsin(y7iN f(b(997i8gygN y(N g9c(syiN gN biN 78y79gyiN (8N bgN Í(997–8N
5GUGOóeGN
N N 9eN Í(N9cntbg8NbifNs(Kc7f7zifN78y79gyifN(8NbgNÍ(99 7–8N5G5GN
N
4.6    EVALUACIÓN Y ACEPTACIÓN DEL CONCRETO N
N
5GVG G N RIMÍ0N20NRE1R.0ÉEN
N
5GVG G N N AgsgN bgN f(b(997–8N y(bN 8Mn(siN y(N nc(fzsgfN y(N (8fgmiXN f(N
9i8f7y(sgsvN9iniNS9bgf(Ny(N9i89s(ziSNgNN
N
geN IgfN y7p(s(8z(fN 9gb7ygy(fN y(N 9i89s(ziN s(Kc(s7ygfNtisN s(f7fz(897gN
(8N9ints(f7–8GN
óeN AgsgN c8gN n7fngN s(f7fz(897gN (8N 9ints(f7–8XN bgfN y7p(s(8z(fNNN
9gb7ygy(fN y(N 9i89s(ziN ióz(87ygfN tisN =gs7g97i8(fN (8N(bN zgng:iN
nv)7niNy(bNgHs(HgyiNHsc(fiXNniy7p79g97i8(fN(8NbgNHsg8cbin(zsÁgN
y(bNgHs(HgyiNp78iNiNcz7b7xg97–8Ny(N9cgbKc7(sNz7tiNy(Ngy7z7=iGN
9eN 0bN9i89s(ziNtsiyc97yiNtisN9gygNc8iNy(NbifN(Kc7tifNy(Nn(x9bgyiN
cz7b7xgyifN(8NbgNiósgGN
N
5GVGON N 3.0RC01RDMN20NIEÍN01ÍM-EÍN
N
NN 5GVGOG N IgfNnc(fzsgfNtgsgN(8fgmifNy(Ns(f7fz(897gN(8N9ints(f7–8Ny(N9gygN9bgf(N
y(N9i89s(ziN9ibi9gyiN9gygNyÁgNy(ó(sv8Nf(sNzingygfNN
N
geN 1iNn(8ifNy(Nc8gNnc(fzsgNy(N(8fgmiNtisNyÁgGN
óeN 1iNn(8ifNy(Nc8gNnc(fzsgNy(N(8fgmiNtisN9gygNSLNn(zsifN9Mó79ifN
y(N9i89s(ziN9ibi9gyiGN
9eN 1iN n(8ifN y(N c8gN nc(fzsgN y(N (8fgmiN tisN 9gygN ULLN n(zsifN
9cgysgyifNy(Nvs(gNfct(sp797gbNtgsgNtg=7n(8zifNiNbifgfGN
yeN 1iNn(8ifNy(Nc8gNnc(fzsgNy(N(8fgmiNtisN9gygN9789iN9gn7i8(fN
9cg8yiNf(Nzsgz(Ny(N9i89s(ziNts(n(x9bgyiGN
N
5GVGOGON Í7N(bN=ibcn(8NzizgbNy(N9i89s(ziNy(Nc8gN9bgf(NygygN(fNzgbNKc(NbgN9g8z7ygyN
y(N(8fgmifNy(Ns(f7fz(897gN(8N9ints(f7–8NhgNy(Nf(sNn(8isNy(N9789iXN(bN
D8ft(9zisNisy(8gsvN(8fgmifNy(NtisNbiNn(8ifN9789iNzg8ygfNzingygfNgbN
gxgsXNiNy(N9gygNzg8ygNf7N=gNgNhgó(sNn(8ifNy(N9789iGN
N
5GVGOGUN 08N(b(n(8zifNKc(N8iNs(f7fzg8Npc(sxgfNy(Nf7fniXNf7N(bN=ibcn(8NzizgbNy(N
9i89s(ziNy(Nc8gN9bgf(NygygN(fNn(8isNy(N5LNn(zsifN9Mó79ifXN(bND8ft(9zisN
tiysvN N y7fti8(sN bgN fcts(f7–8N y(N bifN (8fgmifN y(N s(f7fz(897gN (8N

28.   OQN
9ints(f7–8Nf7XNgNfcN/c797iXN(fzvNNNHgsg8z7xgygNbgN9gb7ygyNy(bN9i89s(ziGN
5GVGUN N A.0AM.MRDd1N20NIMÍNA.EÑ0ÉMÍN20N01ÍM-EN
N
5GVGUG N NIgfN nc(fzsgfN y(N 9i89s(ziN gN f(sN cz7b7xgygfNf(N zingsv8N y(N g9c(syiN gbN
tsi9(y7n7(8ziN 78y79gyiN (8N bgN 1isngN DÉD1É0RN UUJGLUVGN IgfN tsió(zgfN
f(sv8Nniby(gygfNy(Ng9c(syiNgNbgN1isngNDÉD1É0RNUUJGLUUGN
 
5GVG5N N 01ÍM-EN20NA.EÑ0ÉMÍNRC.M2MÍN01NIMÑE.MÉE.DEN
N
NN 5GVG5G N IgfNtsió(zgfN9csgygfN(8N(bNbgóisgzis7iNf(Hc7sv8NbgfNs(9in(8yg97i8(fNy(N
bgN 1isngN MÍÉÓN R JON mN f(sv8N (8fgmgygfN y(N g9c(syiN gN bgN 1isngN
DÉD1É0RNUUJGLU5GN
N
5GVG5GON Í(N 9i8f7y(sgsv8N fgz7fpg9zis7ifN bifN s(fcbzgyifN y(N bifN (8fgmifN y(N
s(f7fz(897gNgNbgN9ints(f7–8NgNbifNOQNyÁgfNy(Nc8gN9bgf(Ny(N9i89s(ziNf7Nf(N
9cntb(8NbgfNyifN9i8y797i8(fNf7Hc7(8z(fNN
N
geN 0bNtsin(y7iNy(NziygfNbgfNf(s7(fNy(Nzs(fN(8fgmifN9i8f(9cz7=ifN(fN
7HcgbNiNngmisNKc(NbgNs(f7fz(897gNy(Ny7f(:iGN
óeN 178HM8N (8fgmiN 78y7=7ycgbN y(N s(f7fz(897gN (fzvN tisN y(óg/iN y(N bgN
s(f7fz(897gNy(Ny7f(:iNtisNnvfNy(NUSNaHá9nOGN
N
5GVG5GUN NNN Í7N 8iN f(N 9cntb7(sg8N bifN s(Kc7f7zifN y(N bgN f(997–8N g8z(s7isXN (bN
D8ft(9zisNy7fti8ysvNbgfNn(y7ygfNKc(Nt(sn7zg8N789s(n(8zgsN(bNtsin(y7iN
y(N bifN f7Hc7(8z(fN s(fcbzgyifGN My797i8gbn(8z(XN y(N 8iN 9cntb7sf(N bifN
s(Kc7f7zifN y(N bgN Í(997–8N 5GVG5GOóeXN y(ó(svN gtb79gsf(N biN 78y79gyiN (8N bgN
Í(997–8N5GVGVGN
N
5GVGSN N 01ÍM-EN20NA.EÑ0ÉMÍNRC.M2MÍN01NEÑ.MN
N
5GVGSG N 0bN D8ft(9zisN tiysvN fib797zgsN s(fcbzgyifN y(N(8fgmifN y(N s(f7fz(897gN (8N
9ints(f7–8N y(N tsió(zgfN 9csgygfN óg/iN 9i8y797i8(fN y(NiósgXN 9i8N bgN
p78gb7ygyNy(N=(s7p79gsNbgN9gb7ygyNy(NbifNtsi9(fifNy(N9csgyiNmNtsiz(997–8N
y(bN9i89s(ziGN
N
5GVGSGON 0bN9csgyiNy(NbgfNtsió(zgfNóg/iN9i8y797i8(fNy(NiósgNy(ó(svNs(gb7xgsf(N(8N
9i8y797i8(fN f7n7bgs(fN gN bgfN y(bN (b(n(8ziN (fzsc9zcsgbN gbN 9cgbN (bbgfN
s(ts(f(8zg8GN
N
5GVGSGUN IgfNtsió(zgfNKc(Nhg8Ny(Nf(sN9csgygfNóg/iN9i8y797i8(fNy(NiósgNy(ó(sv8N
f(sNniby(gygfNgbNn7fniNz7(ntiNmNy(NbgNn7fngNnc(fzsgNy(N9i89s(ziN9i8N
bgNKc(Nf(Nts(tgsg8NbgfNtsió(zgfNgNf(sN9csgygfN(8N(bNbgóisgzis7iGN
N
5GVGSG5N 2(ó(svNtsi9(y(sf(NgNn(/isgsNbifNtsi9(fifNy(Ntsiz(997–8NmN9csgyiNy(bN
9i89s(ziN (8N ziyifN gKc(bbifN 9gfifN (8N bifN Kc(N bgN s(f7fz(897gN (8N
9ints(f7–8Ny(NbgfNtsió(zgfN9csgygfNóg/iN9i8y797i8(fNy(NiósgXNgNbgN(ygyN
(b(H7ygNtgsgNbgNy(z(sn78g97–8Ny(NbgNs(f7fz(897gNtsin(y7iXNf(gN78p(s7isNgbN
QSRN y(N bgN y(N bgfN tsió(zgfN 9intg:(sgfN 9csgygfN (8N bgóisgzis7iGN 0fz(N
s(Kc7f7ziN f(N ió=7gsvN f7N bgN s(f7fz(897gN (8N 9ints(f7–8N y(N bgfN tsió(zgfN
9csgygfN óg/iN 9i8y797i8(fN y(N iósgN (fN ngmisN (8N USN aHá9nON gN bgN

29.   OJN
s(f7fz(897gNy(Ny7f(:iGN
5GVGVN N D1o0ÍÉDPMRDd1N20NIEÍN.0ÍCIÉM2EÍN2C2EÍEÍN
N
5GVGVG N Í7N9cgbKc7(sN(8fgmiNy(Ns(f7fz(897gN(8N9ints(f7–8Ny(Ntsió(zgfN9csgygfN
(8N(bNbgóisgzis7iN(fzvNtisNy(óg/iNy(NbgNs(f7fz(897gNy(Ny7f(:iN(8NnvfNy(NN
USNQHá9nONiNf7NbifNs(fcbzgyifNy(NbifN(8fgmifNy(NbgfNtsió(zgfN9csgygfN
óg/iN 9i8y797i8(fN y(N iósgN 78y79g8N y(p797(897gfN (8N bgN tsiz(997–8N iN (bN
9csgyiXN(bND8ft(9zisNy7fti8ysvNn(y7ygfNKc(NHgsg8z79(8NKc(NbgN9gtg97ygyN
y(N9gsHgNy(NbgN(fzsc9zcsgN8iN(fzvN9intsin(z7ygGN
N
5GVGVGON Í7N f(N 9i8p7sngN Kc(N (bN 9i89s(ziN z7(8(N c8gN s(f7fz(897gN (8N 9ints(f7–8N
n(8isN Kc(N bgN (ft(97p79gygN mN bifN 9vb9cbifN 78y79g8N Kc(N bgN 9gtg97ygyN y(N
9gsHgN y(N bgN (fzsc9zcsgN tc(y(N (fzgsN 9intsin(z7ygXN y(ó(sv8N s(gb7xgsf(N
(8fgmifN (8N z(fz7HifN ()zsgÁyifN y(bN vs(gN 9c(fz7i8gygGN 08N (fz(N 9gfiN f(N
zingsv8Nzs(fNz(fz7HifNtisN9gygN(8fgmiNy(Ns(f7fz(897gN(8N9ints(f7–8NKc(N
(fzvNtisNy(óg/iNy(NbgNs(f7fz(897gNy(Ny7f(:iN(8NnvfNy(NUSNQHá9nOGNIifN
z(fz7HifNf(N()zsg(sv8Ny(Ng9c(syiNgNbgN1isngNDÉD1É0RNUUJGLSJGNN
N
5GVGVGUN Í7N (bN 9i89s(ziN y(N bgN (fzsc9zcsgN =gN gN (fzgsNf(9iN (8N 9i8y797i8(fN y(N
f(s=797iXNbifNz(fz7HifNy(ó(sv8Nf(9gsf(NgbNg7s(NtisNf7(z(NyÁgfNg8z(fNy(Nf(sN
(8fgmgyifN (8N (fzgyiN f(9iGN Í7N (bN 9i89s(ziN y(N bgN (fzsc9zcsgN =gN gN (fzgsN
hMn(yiN (8N 9i8y797i8(fN y(N f(s=797iXN bifN z(fz7HifN y(ó(sv8N (fzgsN
fcn(sH7yifN(8NgHcgN8iNn(8ifNy(N5LNhisgfNmN(8fgmgsf(NhMn(yifGN
N
5GVGVG5N 0bN 9i89s(ziN y(bN vs(gN s(ts(f(8zgygN tisN bifN z(fz7HifN f(N 9i8f7y(sgsvN
(fzsc9zcsgbn(8z(Ngy(9cgyiNf7N(bNtsin(y7iNy(NbifNzs(fNz(fz7HifN(fN7HcgbNgN
tisN biN n(8ifN (bN QSRN y(N bgN s(f7fz(897gN y(N y7f(:iN mN 878HM8N z(fz7HiN (fN
n(8isNy(bN4SRNy(NbgNn7fngGN0bND8ft(9zisNtiysvNisy(8gsN8c(=gfNtsc(ógfN
gNp78Ny(N9intsiógsNbgNts(97f7–8Ny(NbgfNn7fngfN(8Nxi8gfNy(Ns(fcbzgyifN
y7ft(sfifGN
N
5GVGVGSN Í7N8iNf(N9cntb(8NbifNs(Kc7f7zifNy(NbgNf(997–8Ng8z(s7isNmNbgfN9i8y797i8(fN
(fzsc9zcsgb(fN t(sng8(9(8N (8N ycygXN (bN D8ft(9zisN y7fti8ysvN Kc(N f(N
s(gb79(8Ntsc(ógfNy(N9gsHgNtgsgNbgNtgsz(N9c(fz7i8gygNy(NbgN(fzsc9zcsgNiN
zingsvN izsgN y(97f7–8N gy(9cgygN gN bgfN 97s9c8fzg897gfXN y(N g9c(syiN gN biN
78y79gyiN(8N(bNRgtÁzcbiNOUGN
 
 
 
 
 
 

30.   ULN
TABLA 4.4.1 
 
  CONCRETO RESISTENTE A LAS HELADAS 
 
          AIRE TOTAL 
 
N
RE1É01D2EN20NMD.0XN01NRN
N
0lAEÍDRDd1NÍ0o0.MN
N
0lAEÍDRDd1NÓE20.M2M N
N
N
N
ÉMÓMFENÓBlDÓEN
1EÓD1MINNuUeN
N
ÉEÉMINNNNNNMÉ.MAM2EN
N
ÉEÉMINNNNNMÉ.MAM2EN
N
UáQSN
 áOSN
Uá5SN
 SN
 N áO^N
OSNNuUUeN
USNNuUUeN
VSNNuUUeN
N
4XSNNNNNNNNNNNNNNNNUXLN
4XLN NNNNNNNNNNOXSN
VXLNNNNNNN NNNNNNNNNOXLN
VXLN NNNNNNNNN XSN
SXSNN NNNNNNNNN XLN
SXLNNNNNNNNNNNNNNNLXSN
5XSNNNNNNNNNNNNNNNLXUN
5XLNNN NNNNNNNNNLXONNN
N
VXLNNNNNNNNNNNNNNUXLN
SXSNNNNNNNNNNNNNNOXSN
SXLNNNNNNNNNNNNNNOXLN
NNNNNNNNNNN5XSNNNNNNNNNNNNNN XSN
5XSN NNNNNNNN XLNN
NNNNNNNNNNN5XLNNNNNNNNNNNNNNLXSN
UXSN NNNNNNNNLXUN
UXLN NNNNNNNNLXON
N
N NN
N N uUeN N N N N N N o(sN bgN 1isngN MÍÉÓN RUUN tgsgN zib(sg897gfN(8N bifN y7=(sfifN
zgng:ifNNNNNNNNNNNNnv)7nifN8in78gb(fGN
N uUUeN ÉiyifNbifN=gbis(fNy(NbgNzgóbgN9iss(fti8y(8NgbNzizgbNy(NbgNn(x9bgGN
N N Rcg8yiN f(N (8fgmgN (fzifN 9i89s(zifXN f78N (nógsHiXN (bN gHs(HgyiN
ngmisNy(N N áOSN(fNs(ni=7yiNng8cgbn(8z(NiNtisN9(s87yiNhMn(yiN
mN(bN9i8z(87yiNy(Ng7s(N(fNy(z(sn78gyiNtgsgNbgNpsg997–8Nn(8isNy(N N
 áOSXN gtb79v8yif(N bgfN zib(sg897gfN (8N (bN 9i8z(87yiN y(N g7s(N gN(fz(N
=gbisGN
N N N
0bN9i8z(87yiNzizgbNy(Ng7s(Ny(NbgNn(x9bgN(fN9gb9cbgyiNgNtgsz7sNy(bN
=gbisNy(NbgNpsg997–8Nn(8isNy(N N áOSGN
N
 
 
 
 
 
 
 
 
 
 
 
 
 

31.   U N
          TABLA  4.4.2 
   
CONDICIONES ESPECIALES DE EXPOSICION 
N
 
RE12DRDE10ÍN20N0lAEÍDRDd1N
.0IMRDd1N
MPCMáR0Ó01ÉEN
ÓBlDÓMN
Ri89s(ziNy(Nóg/gNt(sn(gó7b7ygyNN
N
geN 0)tc(fziNgNgHcgNycb9(NN N
N N N N
óeN 0)tc(fziNgNgHcgNy(NngsNiNN
N gHcgfNfgbiós(fNN
N
9eN 0)tc(fziNgNbgNg997–8Ny(NgHcgfN
N 9big9gb(fNuUeNN
N
N
LXSLN
N
LX5SN
N
N
LX5SN
Ri89s(ziN ()tc(fziN gN tsi9(fifN y(N
9i8H(bg97–8NmNy(fh7(biN(8N9i8y797–8NhMn(ygN
NN
N
geN Ígsy78(b(fXN9c8(zgfXNf(997i8(fN
N y(bHgygfNN
N
óeN EzsifN(b(n(8zifNN
N
N
N
N
LX5SN
N
LXSLN
Asiz(997–8N 9i8zsgN bgN 9issif7–8N y(N 9i89s(ziN
()tc(fziNgNbgNg997–8Ny(NgHcgNy(NngsXNgHcgfN
fgbiós(fNiN8(ób78gNiNsi9ÁiNy(N(fzgNgHcgNN
N
Í7N(bNs(9cós7n7(8ziNnÁ87niNf(N789s(n(8zgN(8N
 SNnnNN
N
N
LX5LN
N
N
LX5SN
 
uUeNNIgNs(f7fz(897gNp_9N8iNy(ó(svNf(sNNn(8isNy(NO5SNaHá9nOXN
tisNsgxi8(fNy(Nycsgó7b7ygyGN
N
N
N
 
 
 
 
 
 
 
 
 
 
 
 
 

32.   UON
  TABLA 4.4.3 
 
  CONCRETO EXPUESTO A SOLUCIONES DE SULFATOS 
 
 
 
0)tif797–8N
gNfcbpgzif 
 
N
ÍcbpgziNfibcób(N
(8NNgHcgNuÍE
5Ne
 
N
NXNNts(f(8z(N(8N(bN
fc(biXNRN(8Nt(fi
N
N
ÍcbpgziNuÍE
5eN
N08NgHcgNtGtGnG
 
N
N
É7tiNy(N9(n(8zi 
Ri89s(ziN9i8N
gHs(HgyiNy(N
t(fiN8isngbN
.(bg97–8N
nv)7ngN
gHcgá9(n(8ziN
(8Nt(fiN
 N
Ri89s(ziN
9i8N
gHs(HgyifN
y(Nt(fiN
8isngbNmN
b7H(siN
.(f7fz(897gN
nÁ87ngNgN
?13A28J
f7–8XNpY9NN
ÓAgN
  
 
2(fts(97gób
8 
N
Óiy(sgyiN
ON
N
N
Í(=(siN
 
ÓcmNÍ(=(si
 
 
N
LXLL`NÍE
5NaLX L
N
N
LX L`NÍE
5NaLXOL
N
N
N
LXOL`NÍE
5NaOXLL
N
N
ÍE
5NbOXLLN
 
N
LXLL`NÍE
5Na SL
N
N
 SL`NÍE
5N
a SLLN
N
N
 SLL`NÍE
5N
a LLLLN
N
ÍE
5Nb LLLN
 
N
kGkN
N
DDXN
DAuÓÍeXDÍuÓÍeXAuÓ
ÍeXN
DuAÓeuÓÍeXDuÍÓeuÓ
ÍeN
 
oN
N
oNnvfNtcxibg8g 
3 
N
kGkN
N
LXSLN
N
N
LX5SN
N
LX5SN
N
kGkN
 
OQN
N
N
U N
N
U  
N N N N
 N Ac(y(Ns(Kc(s7sf(Nc8gNs(bg97–8NgHcgk9(n(8ziNn(8isNiNc8gNs(f7fz(897gNnvfN
gbzgN tgsgN biHsgsN óg/gN t(sn(gó7b7ygyXN tsiz(997–8N 9i8zsgN bgN 9issif7–8N y(N
(b(n(8zifNn(zvb79ifN(nó(ó7yifXNiN9i8zsgN9i8H(bgn7(8ziNmNy(fh7(biNuÉgóbgN
5G5GOeGN
ON MHcgNy(NngsGN
UN Acxibg8gNKc(Nf(NhgNy(z(sn78gyiNtisNn(y7iNy(N(8fgmifNiNtisN()t(s7(897gN
Kc(N n(/isgN bgN s(f7fz(897gN gN fcbpgzifN 9cg8yiN f(N cfgN(8N 9i89s(zifN Kc(N
9i8z7(8(8NR(n(8zifNÉ7tiNoGN
N N
   

33.   UUN
TABLA  4.4.4 
N
  CONTENIDO MAXIMO DE ION CLORURO 
 
 
 
 
ÉDAEN20N0I0Ó01ÉEN
Ri8z(87yiNnv)7niNy(N7–8N
9biscsiNfibcób(N(8NgHcgN
(8N(bN9i89s(ziXN()ts(fgyiN
9iniNRN(8Nt(fiNy(bN
9(n(8ziN
N
Ri89s(ziNts(z(8fgyiNN
N
Ri89s(ziNgsngyiN()tc(fziNgNbgNg997–8Ny(N9biscsifNN
N
Ri89s(ziN gsngyiN N 8iN N tsiz(H7yiN Kc(N tc(y(N (fzgsN
fin(z7yiNgNNc8Ngnó7(8z(NhMn(yiNt(siN8iN()tc(fziNgN
9biscsifN u789bcm(N N có79g97i8(fN yi8y(N (bN 9i89s(ziN
tc(y(N (fzgsN i9gf7i8gbn(8z(N hMn(yiN zgb(fN 9iniN
9i978gfXN Hgsg/(fXN (fzsc9zcsgfN s7ó(s(:gfN mN vs(gfN 9i8N
hcn(ygyNtiz(897gbNtisNN9i8y(8fg97–8eNN
NN
Ri89s(ziNgsngyiNKc(Ny(ó(svN(fzgsNf(9iNiNtsiz(H7yiN
y(N bgN hcn(ygyN ycsg8z(N fcN =7ygN tisN n(y7iN y(N
s(9cós7n7(8zifN7nt(sn(gób(fNN
N
N
LXLVN
N
LX LN
N
N
N
N
N
N
LX SN
N
N
N
LXQLN
N
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
CAPÍTULO  5 - CONCRETO EN OBRA 
N
5.1    PREPARACIÓN PARA LA COLOCACIÓN DEL CONCRETO N
N

34.   U5N
SG G N NN M8z(fNy(N78797gsN(bNtsi9(fiNy(Nts(tgsg97–8NmN9ibi9g97–8Ny(bN9i89s(ziNf(N
y(ó(svN=(s7p79gsNKc(NN
N
geN IgfN 9izgfN mN y7n(8f7i8(fN y(N bifN (89ipsgyifN mN bifN(b(n(8zifN
(fzsc9zcsgb(fN9iss(fti8yg8N9i8NbgfNy(NbifNtbg8ifGN
óeN IgfNógssgfNy(Ns(pc(sxiXN(bNngz(s7gbNy(NbgfN/c8zgfXNbifNg89bg/(fNmNbifN
(b(n(8zifN(nó(ó7yifN(fzj8N9iss(9zgn(8z(Ncó79gyifGN
9eN IgNfct(sp797(N78z(s8gNy(NbifN(89ipsgyifXNbgfNógssgfNy(Ns(pc(sxiNmN
bifN (b(n(8zifN (nó(ó7yifN (fzj8N b7nt7ifN mN b7ós(fN y(N s(fzifN y(N
nisz(siXN 9i89s(ziXN 87(=(XN h7(biXN (f9gngfN y(N –)7yifXN g9(7z(XN
HsgfgfXN t78zcsgfXN (f9inósifN mN 9cgbKc7(sN (b(n(8ziN iNfcfzg897gN
t(s/cy797gbNtgsgN(bN9i89s(ziGN
yeN IifN (89ipsgyifN (fzj8N z(sn78gyifXN gy(9cgygn(8z(N gss7ifzsgyifXN
hcn(y(97yifNmáiNg9(7zgyifGN
(eN Í(NhgNs(z7sgyiNziygN(bNgHcgXN87(=(NmNh7(biNy(NbifNbcHgs(fNKc(N=g8NgN
f(sNi9ctgyifNtisN(bN9i89s(ziGN
peN IgNfct(sp797(Ny(NbgfNc87ygy(fNy(Ngbóg:7b(sÁgNKc(N=gmg8NgN(fzgsN(8N
9i8zg9ziN9i8N(bN9i89s(ziN(fzj8Ngy(9cgygn(8z(NzsgzgygGN
HeN Í(N9c(8z(N(8NiósgN9i8NziyifNbifNngz(s7gb(fN8(9(fgs7ifNmN9i8N(bN
8Mn(siNfcp797(8z(Ny(NbifN(Kc7tifNgNf(sN(ntb(gyifN(8N(bNtsi9(fiN
y(N9ibi9g97–8GN0fzifNy(ó(sv8N(89i8zsgsf(Nb7nt7ifNmN(8Nt(sp(9zgfN
9i8y797i8(fNy(NcfiGN
heN Í(N hgmgN (b7n78gyiN bgN b(9hgygN (8ycs(97ygN mN ziyiN izsiN ngz(s7gbN
y(p(9zcifiN iN fc(bziN g8z(fN y(N 9ibi9gsN c8N8c(=iN9i89s(ziN9i8zsgN
9i89s(ziN(8ycs(97yiGN
N
5.2    MEDIDA DE LOS MATERIALES N
N
SGOG N NN IgN n(y7ygN y(N bifN ngz(s7gb(fN (8N bgN iósgN y(ó(svN s(gb7xgsf(N tisN n(y7ifN
Kc(NHgsg8z79(8NbgNióz(897–8Ny(NbgfNtsitis97i8(fN(ft(97p79gygfGN
N
5.3    MEZCLADO N
N
SGUG N NN RgygNzg8ygNy(ó(Nf(sN9gsHgygN(8NbgNn(x9bgyisgNy(Nng8(sgNzgbNKc(N(bN
gHcgN 9in7(89(N gN 78Hs(fgsN g8z(fN Kc(N (bN 9(n(8ziN mN bifN gHs(HgyifGN 0bN
gHcgN 9i8z78cgsvN pbcm(8yiN tisN c8N t(sÁiyiXN (bN 9cgbN tc(y(N tsibi8Hgsf(N
hgfzgN p78gb7xgsN bgN ts7n(sgN 9cgszgN tgsz(N y(bN z7(ntiNy(N n(x9bgyiN
(ft(97p79gyiGN
N
SGUGON NN 0bNngz(s7gbNy(Nc8gNzg8ygN8iNy(ó(svN9in(8xgsNgN78Hs(fgsNgNbgNn(x9bgyisgN
g8z(fNy(NKc(NbgNzizgb7ygyNy(NbgNg8z(s7isNhgmgNf7yiNy(f9gsHgygGN
N
SGUGUN NN 0bN 9i89s(ziN y(ó(svN f(sN n(x9bgyiN (8N c8gN n(x9bgyisgN 9gtgxN y(N biHsgsN
c8gN9inó78g97–8NzizgbNy(NbifNngz(s7gb(fXNpisng8yiNc8gNngfgNc87pisn(N
y(8zsiN y(bN z7(ntiN (ft(97p79gyiN mN y(f9gsHg8yiN (bN 9i89s(ziN f78N
f(Hs(Hg97–8GN
SGUG5N N 08N(bNtsi9(fiNy(Nn(x9bgyiNf(Ny(ó(svN9cntb7sNbiNf7Hc7(8z(NN
N
geN 0bN(Kc7tiNy(Nn(x9bgyiNy(ó(svNf(sNgtsiógyiNtisN(bND8ft(9zisGN
óeN IgNn(x9bgyisgNy(ó(svNf(sNit(sgygNgNbgN9gtg97ygyNmNgbN8Mn(siNy(N

35.   USN
s(=ibc97i8(fNtisNn78cziNs(9in(8ygyifNtisN(bNpgós79g8z(GN
9eN IgN zg8ygN 8iN y(ó(svN f(sN y(f9gsHgygN hgfzgN Kc(N (bN z7(ntiN y(N
n(x9bgyiN f(N hgmgN 9cntb7yiGN 0fz(N z7(ntiN 8iNf(svNn(8isNy(NJLN
f(Hc8yifN y(ftcjfN y(bN nin(8ziN (8N Kc(N ziyifN bifN ngz(s7gb(fN
(fzj8N(8N(bNzgnóisGN
N
SGUGSN 08N bgN 789istisg97–8N y(N gy7z7=ifN gN bgN n(x9bgyisgN f(N z(8ysvN (8N
9i8f7y(sg97–8NbiNf7Hc7(8z(NN
geN IifNgy7z7=ifNKcÁn79ifNy(ó(sv8Nf(sN789istisgyifNgNbgNn(x9bgyisgN
(8N pisngN y(N fibc97–8N (ntb(g8yiXN y(N ts(p(s(897gXN (Kc7tiN
y7ft(sfg8z(Nn(9v879iGNIgNfibc97–8Ny(ó(svNf(sN9i8f7y(sgygN9iniN
tgsz(Ny(bNgHcgNy(Nn(x9bgyiGN
óeN IifN gy7z7=ifN n78(sgb(fN tiysv8N f(sN t(fgyifN iN n(y7yifN tisN
=ibcn(8XNy(Ng9c(syiNgNbgfNs(9in(8yg97i8(fNy(bNpgós79g8z(GN
9eN Í7N f(N =g8N gN (ntb(gsN yifN iN nvfN gy7z7=ifN (8N (bN 9i89s(ziXN (bbifN
y(ó(sv8N f(sN 789istisgyifN f(tgsgygn(8z(N gN p78N y(N (=7zgsN
s(g997i8(fNKcÁn79gfNKc(Ntc(yg8Ngp(9zgsNbgN(p797(897gNy(N9gygNc8iN
y(N(bbifNiNbgfNtsit7(ygy(fNy(bN9i89s(ziGN
N
SGUGVN NN 0bN 9i89s(ziN y(ó(svN f(sN n(x9bgyiN (8N 9g8z7ygy(fN gy(9cgygfN tgsgN fcN
(ntb(iN 78n(y7gziGN 0bN 9i89s(ziN 9cmiN psgHcgyiN mgN f(N hgN 78797gyiN (8N bgN
n(x9bgyisgN 8iN y(ó(svN f(sN s(n(x9bgyiN 87N cz7b7xgyiGN AisN 878HM8N niz7=iN
y(ó(svNgHs(Hgsf(NgHcgNgy797i8gbNgNbgNn(x9bgGN
N
SGUG4N NN 0bN9i89s(ziNts(n(x9bgyiNy(ó(svNf(sNyif7p79gyiXNn(x9bgyiXNzsg8ftiszgyiXN
(8zs(HgyiNmN9i8zsibgyiNy(Ng9c(syiNgNbgN1isngNMÍÉÓNRJ5GN1iNf(NtiysvN
(ntb(gsN9i89s(ziNKc(Nz(8HgNnvfNy(N N áONhisgfNn(x9bv8yif(Ny(fy(N(bN
nin(8ziN (8N Kc(N bifN ngz(s7gb(fN 9in(8xgsi8N gN 78Hs(fgsN gbN zgnóisN
n(x9bgyisGN
N
SGUGQN N Í(Ny(ó(svNg8izgsN(8N(bN.(H7fzsiNy(NEósgNN
N
geN 0bN8Mn(siNy(Nzg8ygfNtsiyc97ygfGN
óeN IgfNtsitis97i8(fNy(NbifNngz(s7gb(fN(ntb(gyifGN
9eN IgN p(9hgN mN hisgN mN bgN có79g97–8N (8N (bN (b(n(8ziN (fzsc9zcsgbN y(bN
9i89s(ziNtsiyc97yiGN
yeN RcgbKc7(sN 9i8y797–8N (ft(97gbN y(N bifN tsi9(fiN y(N n(x9bgyiN mN
9ibi9g97–8GN
N
5.4    TRANSPORTE N
N
SG5G N NN 0bN 9i89s(ziN y(ó(svN f(sN zsg8ftiszgyiN y(fy(N bgN n(x9bgyisgN hgfzgN fcN
có79g97–8Np78gbN(8NbgN(fzsc9zcsgNzg8Nsvt7yiN9iniNf(gNtif7ób(NmN(ntb(g8yiN
tsi9(y7n7(8zifNKc(Nts(=(8Hg8NbgNf(Hs(Hg97–8NmNbgNtjsy7ygNy(Nngz(s7gb(fN
mNHgsg8z79(8NbgN9gb7ygyNy(f(gygNtgsgN(bN9i89s(ziGN
N
SG5GON NN 0bN (Kc7tiN y(ó(svN f(sN 9gtgxN y(N tsitis97i8gsXN f78N 78z(ssct97i8(fXN c8N
gógfz(97n7(8ziNy(N9i89s(ziN(8N(bNtc8ziNy(N9ibi9g97–8GN
N
SG5GUN NN IifN9gn7i8(fNn(x9bgyis(fNmNbgfNc87ygy(fNgH7zgyisgfNmN8iNgH7zgyisgfXN

36.   UVN
gfÁN 9iniN fcN tsi9(y7n7(8ziN y(N it(sg97–8XN y(ó(sv8N 9cntb7sN 9i8N biN
78y79gyiN(8NbgN1isngNMÍÉÓNRJ5GN
N
5.5    COLOCACION N
N
SGSG N NN 0bN 9i89s(ziN y(ó(svN f(sN 9ibi9gyiN zg8N 9(s9gN 9iniN f(gN tif7ób(N y(N fcN
có79g97–8Np78gbXNgNp78Ny(N(=7zgsNf(Hs(Hg97–8Ny(ó7ygNgNs(ng87tcb(iNiNpbc/iGN
N
SGSGON NN 0bN9i89s(ziN8iNy(ó(svNf(sNfin(z7yiNgN878HM8Ntsi9(y7n7(8ziNKc(Ntc(ygN
is7H78gsNf(Hs(Hg97–8GN
N
SGSGUN NN 0bNtsi9(fiNy(N9ibi9g97–8Ny(ó(svN(p(9zcgsf(N(8Nc8gNit(sg97–8N9i8z78cgN
iN(8N9gtgfNy(N(ft(fisNzgbNKc(N(bN9i89s(ziN8iNf(gNy(tif7zgyiNfiós(NizsiN
Kc(NmgNhgmgN(8ycs(97yiNbiNfcp797(8z(NtgsgNis7H78gsNbgNpisng97–8Ny(N/c8zgfN
iNtbg8ifNy(N=g97gyiNy(8zsiNy(NbgNf(997–8GN
N
SGSG5N NN IgNit(sg97–8Ny(N9ibi9g97–8Ny(ó(svN9i8z78cgsNhgfzgNKc(Nf(N9intb(z(Nc8N
tg:iNiNf(997–8Ny(p787yiNtisNfcfNbÁn7z(fNiN/c8zgfNts(y(z(sn78gygfGNÍ7NbgN
f(997–8N8iNtc(y7(sgNf(sNz(sn78gygN(8Nc8N=g97gyiN9i8z78ciXNbgfN/c8zgfNy(N
9i8fzsc997–8Ny(ó(sv8Nhg9(sf(Ny(Ng9c(syiNgNbiN78y79gyiN(8NbgNÍ(997–8N
VG5GN
N
SGSGSN NN 0bN9i89s(ziNKc(NhgN(8ycs(97yiNtgs97gbn(8z(NiNhgmgNf7yiN9i8zgn78gyiN
tisN fcfzg897gfN ()zsg:gfN 8iN y(ó(svN f(sN 9ibi9gyiGN DHcgbn(8z(N 8iN f(svN
9ibi9gyiN (bN 9i89s(ziN s(z(ntbgyiN iN gKc(bN Kc(N hgmgN f7yiN s(n(x9bgyiN
y(ftcjfNy(N78797gyiN(bNpsgHcgyiGN
N
SGSGVN NN IifN f(tgsgyis(fN z(ntisgb(fN 78z(s8ifN y(N bifN(89ipsgyifN tiysv8N f(sN
s(z7sgyifN9cg8yiN(bN9i89s(ziN9ibi9gyiNhgmgNgb9g8xgyiN(bN87=(bNKc(NhgHgN
NfcN t(sng8(897gN 788(9(fgs7gGN Ac(y(8N t(sng8(9(sN (nó(ó7yifN (8N (bN
9i89s(ziN M879gn(8z(N f7N 8iN fi8N yg:78ifN gN jfz(N mN f(N 9c(8z(N 9i8N bgN
gczis7xg97–8Ny(bND8ft(9zisGN
N
SGSG4N NN 0bN=g97gyiNy(NbgfN=7HgfNmNbifgfN8iNf(N(p(9zcgsvNg8z(fNKc(N(bN9i89s(ziNy(N
bifN(b(n(8zifNKc(Nb(Nf7s=(8Ny(NgtimiNhgmgNtgfgyiNy(bN(fzgyiNtbvfz79iNgbN
f–b7yiGN0bNz7(ntiNnÁ87niNf(svNy(NUNhisgfNy(ftcjfNy(bN=g97gyiNy(N(fzifN
Mbz7nifGN
 
5.6    CONSOLIDACION N
N
SGVG N NN 0bN 9i89s(ziN y(ó(svN f(sN 9c7ygyifgn(8z(N 9i8fib7ygyiN ycsg8z(N fcN
9ibi9g97–8XNy(ó7(8yiNg9iniygsf(Ngbs(y(yisNy(NbgfNógssgfNy(Ns(pc(sxiNmN
bifN(b(n(8zifN(nó(ó7yifNmN(8NbgfN(fKc78gfNy(NbifN(89ipsgyifGN
N
SGVGON NN IifN =7ósgyis(fN 8iN y(ó(sv8N cfgsf(N tgsgN y(ftbgxgsN bgz(sgbn(8z(N (bN
9i89s(ziN(8NbifN(89ipsgyifGN
N
5.7    PROTECCION N
N
SG4G N NN MNn(8ifNKc(Nf(N(ntb((NnjziyifNy(Ntsiz(997–8Ngy(9cgyifNgczis7xgyifN

37.   U4N
tisN (bN D8ft(9zisXN (bN 9i89s(ziN 8iN y(ó(svN f(sN 9ibi9gyiN ycsg8z(N bbc=7gfXN
8(=gygfNiNHsg87xgygfGN
N
SG4GON NN 1iNf(Nt(sn7z7svNKc(N(bNgHcgNy(Nbbc=7gN789s(n(8z(N(bNgHcgNy(Nn(x9bgyiNiN
yg:(N(bNg9gógyiNfct(sp797gbNy(bN9i89s(ziGN
N
SG4GUN NN Í(N y(ó(svN 9i8f7y(sgsN biN 78y79gyiN (8N bgN Í(997–8N SGJN 9cg8yiN bgN
z(nt(sgzcsgNgnó7(8z(Nn(y7gN(fzjNtisNy(óg/iNy(NSORNmNbiN78y79gyiN(8NbgN
Í(997–8NSG LN9cg8yiN(fzjNtisN(897ngNy(NOQORGN
N
SG4G5N NN IgNz(nt(sgzcsgNy(bN9i89s(ziNgbNf(sN9ibi9gyiN8iNy(ó(svNf(sNzg8NgbzgN9iniN
tgsgN 9gcfgsN y7p79cbzgy(fN y(ó7ygfN gN tjsy7ygN y(N gf(8zgn7(8ziXN psgHcgN
78fzg8zv8(gNiN/c8zgfNpsÁgfGNMy(nvfXN8iNy(ó(svNf(sNngmisNy(NUOORGN
N
SG4GSN NN Rcg8yiN bgN z(nt(sgzcsgN 78z(s8gN y(bN 9i89s(ziNycsg8z(N (bN tsi9(fiN y(N
h7ysgzg97–8N ()9(ygN (bN =gbisN y(N UOOXN y(ó(sv8N zingsf(N n(y7ygfN tgsgN
tsiz(H(sN gbN 9i89s(ziXN bgfN n7fngfN Kc(N y(ó(sv8N f(sN gtsiógygfN tisN (bN
D8ft(9zisGN
N
SG4GVN NN IgNz(nt(sgzcsgNy(NbifN(89ipsgyifNn(zvb79ifNmN(bNg9(siNy(Ns(pc(sxiN8iN
y(ó(svNf(sNngmisNy(NSLORGN
N
5.8    CURADO N
N
SGQG N NN 0bN9i89s(ziNy(ó(svNf(sN9csgyiNmNng8z(87yiNfiós(NbifN LORNtisNbiNn(8ifN
ycsg8z(NbifN4Nts7n(sifNyÁgfNy(ftcjfNy(NfcN9ibi9g97–8XNz7(ntiNKc(NtiysvN
s(yc97sf(NgNUNyÁgfN(8N(bN9gfiNy(N9i89s(ziNy(NgbzgNs(f7fz(897gN78797gbGNÍ7Nf(N
cfgN 9(n(8ziN z7tiN  AXN  AÓN iN tcxibv879iN (bN 9csgyiN y(ó(N ng8z(8(sf(N
9iniNnÁ87niNbifNts7n(sifN LNyÁgfGN
0bN 9csgyiN tiysvN fcft(8y(sf(N f7N (bN 9i89s(ziN y(N tsió(zgfN 9csgygfN óg/iN
9i8y797i8(fNy(NiósgNhcó7(sgNgb9g8xgyiNc8N=gbisN(Kc7=gb(8z(NiNngmisNgbN
4LRNy(NbgNs(f7fz(897gNy(Ny7f(:iN(ft(97p79gygGN
N
SGQGON N IifNf7fz(ngfNy(N9csgyiNy(ó(sv8N(fzgsN78y79gyifN(8NbgfN(ft(97p79g97i8(fN
zj9879gfGN
N
SGQGUN N C8N f7fz(ngN y(N 9csgyiN tiysvN f(sN s((ntbgxgyiN tisN 9cgbKc7(sN izsiN
y(ftcjfN y(N c8N yÁgN y(N gtb79g97–8N y(bN ts7n(siXN 9i8N gtsióg97–8N y(bN
D8ft(9zisXN9c7yg8yiNy(N(=7zgsN(bNf(9gyiNfct(sp797gbNycsg8z(NbgNzsg8f797–8GN
N
SGQG5N NN Í(Nng8z(8ysv8NbifN(89ipsgyifNhMn(yifNhgfzgNKc(Ntc(yg8Nf(sNs(z7sgyifN
f78N t(b7HsiN tgsgN (bN 9i89s(ziGN 2(ftcjfN y(N s(z7sgsN bifN (89ipsgyifXN (bN
9i89s(ziNy(ó(svNf(sN9csgyiNhgfzgNbgNp78gb7xg97–8Ny(bNz7(ntiN78y79gyiN(8N
bgNÍ(997–8NSGQG GN
N
SGQGSN NN 0bN9csgyiN(ntb(g8yiN=gtisNgNgbzgNts(f7–8XN=gtisNgNts(f7–8Ngznifpjs79gXN
9gbisNmNhcn(ygyNcNizsifNtsi9(y7n7(8zifNg9(tzgyifNtiysvNf(sN(ntb(gyiN
tgsgNg9(b(sgsN(bNy(fgssibbiNy(Ns(f7fz(897gNmNs(yc97sN(bNz7(ntiNy(N9csgyiGN
N
SGQGVN N 2csg8z(N(bNt(sÁiyiNy(N9csgyiN(bN9i89s(ziNy(ó(svNf(sNtsiz(H7yiNy(Nyg:ifN

38.   UQN
tisN g997i8(fN n(9v879gfN zgb(fN 9iniN (fpc(sxifN is7H78gyifN tisN 9gsHgfXN
7ntg9zifNiN()9(f7=gfN=7ósg97i8(fGNÉiygfNbgfNfct(sp797(fNy(bN9i89s(ziNmgN
z(sn78gygfNy(ó(sv8Nf(sNtsiz(H7ygfNy(Nyg:ifNis7H78gyifNtisN(bN(Kc7tiNy(N
9i8fzsc997–8XNngz(s7gb(fNiNtsi9(y7n7(8zifN9i8fzsc9z7=ifXNtsi9(y7n7(8zifN
y(N 9csgyiN iN y(N bgN g997–8N y(N bbc=7gfN iN gHcgfN y(N (f9iss(8zÁgGN IgfN
(fzsc9zcsgfN 8iN y(ó(sv8N f(sN 9gsHgygfN y(N ng8(sgN y(N fiós(N (fpisxgsN (bN
9i89s(ziGNNNNNNNNNNNNNNNNNNNNNN
N
SGQG4NN NNNNNNNNNNN0bN D8ft(9zisN tiysvN fib797zgsN (8fgmifN y(N s(f7fz(897gN (8N 9ints(f7–8N
gy797i8gb(fN tgsgN 9(sz7p79gsN Kc(N (bN tsi9(y7n7(8ziN y(N 9csgyiN (ntb(gyiN
hgmgNt(sn7z7yiNióz(8(sNbifNs(fcbzgyifNy(f(gyifGN
N
5.9    REQUISITOS GENERALES EN CLIMAS FRIOS N
N
SGJG N NN AgsgNbifNp78(fNy(N(fzgN1isngNf(N9i8f7y(sgN9iniN9b7ngNpsÁiNgNgKc(bN(8N
Kc(XN(8N9cgbKc7(sNjti9gNy(bNg:iXNbgNz(nt(sgzcsgNgnó7(8z(Ntc(ygN(fzgsN
tisNy(óg/iNy(NSORGN
N
SGJGON NN 2csg8z(N (bN tsi9(fiN y(N 9ibi9g97–8XN gy(nvfN y(N biN 78y79gyiN (8N bgfN
f(997i8(fN 9iss(fti8y7(8z(fNy(N(fzgN1isngXNf(Nzingsv8NbgfNf7Hc7(8z(fN
ts(9gc97i8(fGN
N
geN 0bN9i89s(ziNy(ó(svNpgós79gsf(N9i8Ng7s(N789istisgyiGN
óeN 2(ó(svNz(8(sf(N(8NiósgN(Kc7tiNgy(9cgyiNtgsgN9gb(8zgsN(bNgHcgN
máiN (bN gHs(HgyiXN gfÁN 9iniN tgsgN tsiz(H(sN (bN 9i89s(ziN 9cg8yiN bgN
z(nt(sgzcsgNgnó7(8z(N(fzjNtisNy(óg/iNy(NSORGN
9eN 08N (bN 9gfiN y(N cfgsN 9i89s(zifN y(N gbzgN s(f7fz(897gXN (bN z7(ntiN y(N
tsiz(997–8N8iNf(svNn(8isNy(N5NyÁgfGN
yeN ÉiyifN bifN ngz(s7gb(fN 78z(Hsg8z(fN y(bN 9i89s(ziXN gfÁN 9iniN bgfN
ógssgfN y(N s(pc(sxiXN ngz(s7gbN y(N s(bb(8iN mN fc(biN 9i8N (bN 9cgbN (bN
9i89s(ziNhgNy(N(fzgsN(8N9i8zg9ziNy(ó(sv8N(fzgsNb7ós(fNy(N87(=(XN
Hsg87xiNmNh7(biGN
(eN IifN ngz(s7gb(fN9i8H(bgyifXNgfÁN9iniNgKc(bbifNKc(Nz7(8(8Nh7(biXN
8iNy(ó(sv8Nf(sN(ntb(gyifGN
N
SGJGUN NN 08N 9b7ngfN psÁifXN bgN z(nt(sgzcsgN y(bN 9i89s(ziN gbN nin(8ziN y(N f(sN
(8zs(HgyiN (8N (bN tc8ziN y(N 9ibi9g97–8XN y(ó(svN (fzgsN y(8zsiN y(N bifN
f7Hc7(8z(fNbÁn7z(fNN
N
N
N
N
N
N
N
É0ÓA0.MÉC.MNÓT1DÓMN20INRE1R.0ÉENuOReN
N
É0ÓA0.MÉC.MN
MÓÑD01É0NNuNOReN
Í(997i8(fN9cmgNn(8isN
y7n(8f7–8N(fNn(8isNy(N
ULN9nN
Í(997i8(fN9cmgNn(8isN
y7n(8f7–8N(fNngmisNy(N
ULN9nN

39.   UJN
SNNNgNNNk NNN
k NNNgNNk QN
óg/iNNNk QN
 VN
 QN
O N
 LN
 UN
 VN
N N
SGJG5N NN Í7N(bNgHcgNiN(bNgHs(HgyiNfi8N9gb(8zgyifXN(bNgHcgNy(ó(svNf(sN9inó78gygN
9i8N(bNgHs(HgyiN(8NbgNn(x9bgyisgNg8z(fNy(Ng:gy7sN(bN9(n(8ziGN
N
SGJGSN NN Rcg8yiN bgN z(nt(sgzcsgN y(bN n(y7iN gnó7(8z(N (fN n(8isN y(N SORXN bgN
z(nt(sgzcsgNy(bN9i89s(ziNmgN9ibi9gyiNy(ó(svNf(sNng8z(87ygNfiós(N LORN
ycsg8z(N(bNt(sÁiyiNy(N9csgyiGN
N
SGJGVN NN Í(N zingsv8N ts(9gc97i8(fN tgsgN ng8z(8(sN gbN 9i89s(ziN y(8zsiN y(N bgN
z(nt(sgzcsgN s(Kc(s7ygN f78N Kc(N f(N tsiycx9g8N yg:ifN y(ó7yifN gN bgN
9i89(8zsg97–8N y(N 9gbisGN 1iN f(N cz7b7xgsvN y7ftif7z7=ifN y(N 9inócfz7–8N
ycsg8z(N bgfN ts7n(sgfN O5N hisgfXN gN n(8ifN Kc(N f(N zin(8N ts(9gc97i8(fN
tgsgN(=7zgsNbgN()tif797–8Ny(bN9i89s(ziNgNHgf(fNKc(N9i8z(8Hg8Nó7–)7yiNy(N
9gsói8iGN
N
5.10    REQUISITOS GENERALES EN CLIMAS CALIDOS N
N
SG LG NNN AgsgN bifN p78(fN y(N (fzgN 1isngN f(N 9i8f7y(sgN9b7ngN 9vb7yiN 9cgbKc7(sN
9inó78g97–8N y(N gbzgN z(nt(sgzcsgN gnó7(8z(N uOQOReXN óg/gN hcn(ygyN
s(bgz7=gNmNgbzgN=(bi97ygyNy(bN=7(8ziXNKc(Nz7(8ygNgNt(s/cy79gsNbgN9gb7ygyNy(bN
9i89s(ziNps(f9iNiN(8ycs(97yiNiNKc(Ny(N9cgbKc7(sNizsgNng8(sgNtsi=iKc(N
(bNy(fgssibbiNy(Nniy7p79g97i8(fN(8NbgfNtsit7(ygy(fNy(Njfz(GN
N
SG LGONNN 2csg8z(N(bNtsi9(fiNy(N9ibi9g97–8Ny(bN9i89s(ziN(8N9b7ngfN9vb7yifXNy(ó(svN
ygsf(Ngy(9cgygNgz(897–8NgNbgNz(nt(sgzcsgNy(NbifN78Hs(y7(8z(fXNgfÁN9iniN
gNbifNtsi9(fifNy(Ntsiyc997–8XNng8(/iXN9ibi9g97–8XNtsiz(997–8NmN9csgyiNgN
p78N y(N ts(=(87sN (8N (bN 9i89s(ziN z(nt(sgzcsgfN ()9(f7=gfN Kc(N tcy7(sg8N
7nt(y7sNgb9g8xgsNbgNs(f7fz(897gNs(Kc(s7ygNiN(bNgy(9cgyiN9intiszgn7(8ziN
y(bN(b(n(8ziN(fzsc9zcsgbGN
N
SG LGUNNN MN p78N y(N (=7zgsN gbzgfN z(nt(sgzcsgfN (8N (bN 9i89s(ziXN tjsy7ygfN y(N
gf(8zgn7(8ziXN psgHcgN 78fzg8zv8(gN iN pisng97–8N y(N /c8zgfXN tiysv8N
(8ps7gsf(N bifN 78Hs(y7(8z(fN y(bN 9i89s(ziN g8z(fN y(bN n(x9bgyiN iN cz7b7xgsN
h7(biXN (8N pisngN y(N t(Kc(:ifN Hsv8cbifN iN (f9gngfXN 9iniN fcfz7zcziN y(N
tgsz(Ny(bNgHcgNy(bNn(x9bgyiGN
N
SG LG5NNN 08N 9b7ngfN 9vb7yifN f(N y(ó(sv8N zingsN ts(9gc97i8(fN (ft(97gb(fN (8N (bN
9csgyiNtgsgN(=7zgsNbgN(=gtisg97–8Ny(bNgHcgNy(NbgNn(x9bgGN
 
 
 
 
CAPÍTULO 6 - ENCOFRADOS, ELEMENTOS EMBEBIDOS Y JUNT ASN
N
6.1    ENCOFRADOS N
N
VG G N NN IifN(89ipsgyifNy(ó(sv8Nt(sn7z7sNióz(8(sNc8gN(fzsc9zcsgNKc(N9cntbgN9i8N

40.   5LN
bifN t(sp7b(fXN 87=(b(fXN gb78(gn7(8ziN mN y7n(8f7i8(fN s(Kc(s7yifN tisN bifN
tbg8ifN mN bgfN (ft(97p79g97i8(fN zj9879gfGN IifN(89ipsgyifNmNfcfNfitisz(fN
y(ó(sv8N(fzgsNgy(9cgygn(8z(Ngss7ifzsgyifGN
N
VG GON NN IifN (89ipsgyifN y(ó(sv8N f(sN biN fcp797(8z(n(8z(N 7nt(sn(gób(fN 9iniN
tgsgN7nt(y7sNtjsy7ygfNy(Nb(9hgygNiNnisz(siGN
N
VG GUN NN IifN(89ipsgyifNmNfcfNfitisz(fNy(ó(sv8Nf(sNy7f(:gyifNmNN9i8fzsc7yifNy(N
pisngN zgbN Kc(N 8iN 9gcf(8N yg:ifN gN bgfN (fzsc9zcsgfN 9ibi9gygfGN 08N fcN
y7f(:iNf(Nz(8ysvN(8N9i8f7y(sg97–8NbiNf7Hc7(8z(NN
N
geN o(bi97ygyNmNtsi9(y7n7(8ziNy(N9ibi9g97–8Ny(bN9i89s(ziGN
óeN RgsHgfNy(N9i8fzsc997–8XN=(sz79gb(fNNhis7xi8zgb(fXNmNy(N7ntg9ziGN
9eN .(Kc7f7zifN y(N bifN (89ipsgyifN (ft(97gb(fN (ntb(gyifN (8N bgN
9i8fzsc997–8N y(N 9vf9gsgfXN 9MtcbgfXN 9i89s(ziN gsKc7z(9z–879iN iN
(b(n(8zifNf7n7bgs(fGN
yeN 2(pb()7–8XN9i8zsgpb(9hgXN()9(8zs797ygyNmNfcóts(f7–8GN
(eN IgNc87–8Ny(NbifNtc8zgb(fNmNfcfNgtimifGN
peN IifN(89ipsgyifNtgsgN(b(n(8zifNts(fpisxgyifNy(ó(sv8Ny7f(:gsf(N
mN9i8fzsc7sf(Ny(Nng8(sgNzgbNKc(Nt(sn7zg8NbgfNy(pisng97i8(fNy(bN
(b(n(8ziNf78N9gcfgsb(Nyg:iNycsg8z(NbgNgtb79g97–8Ny(NbgNpc(sxgNy(N
ts(fpc(sxiGN
N
6.2    REMOCION DE ENCOFRADOS Y PUNTALES N
N
VGOG N NNNNNNNNNNN178Hc8gN 9gsHgN y(N 9i8fzsc997–8N y(ó(svN f(sN gtb79gygN mN 878HM8N tc8zgbN iN
(b(n(8ziN y(N fifzj8N y(ó(svN f(sN s(z7sgyiN y(N 9cgbKc7(sN tgsz(N y(N bgN
(fzsc9zcsgN(8Ntsi9(fiNy(N9i8fzsc997–8XN()9(tziN9cg8yiNbgNtis97–8Ny(NbgN
(fzsc9zcsgN(8N9inó78g97–8N9i8N(bNf7fz(ngNy(N(89ipsgyifNmNtc8zgb(fNKc(N
t(sng8(9(N z7(8(N fcp797(8z(N s(f7fz(897gN 9iniN tgsgN fitiszgsN 9i8N
f(Hcs7ygyNfcNtsit7iNt(fiNmNbgfN9gsHgfN9ibi9gygfNfiós(N(bbgGN
N
VGOGON NN 08Ng8vb7f7fN(fzsc9zcsgbNy(NbifN(89ipsgyifNmNbifNs(fcbzgyifNy(NbifN(8fgmifN
y(N s(f7fz(897gN y(ó(sv8N f(sN tsitis97i8gyifN gbN D8ft(9zisN 9cg8yiN jbN biN
s(Kc7(sgGN
N
VGOGUN NNNNNNNNNNN178Hc8gN9gsHgNy(N9i8fzsc997–8NKc(N()9(ygNbgN9inó78g97–8Ny(NbgfN9gsHgfN
nc(szgfNfiós(7ntc(fzgfNnvfNbgfN9gsHgfN=7=gfN(ft(97p79gygfNy(ó(svNf(sN
gtb79gygN gN gbHc8gN tis97–8N 8iN gtc8zgbgygN y(N bgN (fzsc9zcsgN (8N
9i8fzsc997–8XNgNn(8ifNKc(N(bNg8vb7f7fN78y7Kc(NNKc(N()7fz(Nc8gNs(f7fz(897gN
gy(9cgygNtgsgNfitiszgsNzgb(fN9gsHgfNgy797i8gb(fGN
N
VGOG5N NNNNNNNNNNN08NbifN(b(n(8zifNy(N9i89s(ziNts(fpisxgyiXNbifNfitisz(fNy(bN(89ipsgyiN
tiysv8N f(sN s(ni=7yifN 9cg8yiN f(N hgmgN gtb79gyiN fcp797(8z(N ts(fpc(sxiN
tgsgN Kc(N y79hifN (b(n(8zifN fitisz(8N fcN t(fiN tsit7iN mN bgfN 9gsHgfN y(N
9i8fzsc997–8Nts(=7fzgfGN
 
6.3  CONDUCTOS Y TUBERIAS EMBEBIDOS EN EL CONCRETO 
N
VGUG N NN 2(8zsiNy(NbgfNb7n7zg97i8(fNy(NbgNÍ(997–8NVGUXNtiysv8Nf(sN(nó(ó7yifN(8N(bN

41.   F
?1>?28/1 ?1>C:?/1. /:H82@0. ; 30>=:5/1. C8 ?:079:582F 30/82507F >1F
C0D5>1 A020 G./8 A28L50 0A21H0?5E> C87 I>.A8?/12 ;F .583A28F 9:8F .8F
?1>.5C828F 9:8F 8771.F >1F 2883A70F0>F 8./2:?/:20738>/8F07F ?1>?28/1F
C8.A70F0C1
F
1.8C8H82B83H8H828>87?1>?28/18./2:?/:207F?1>C:?/1.F1F/:[email protected]
C807:35>51038>1.9:8.8C5.A1>=0C8:>28?:H25358>/1F1F.5./830FC8F
A21/8??5E>F 9:8F A28L8>=0F 70F 280??5E>F 07:35>51J?1>?28/1F 1F 70F 0??5E>F
878?/217@/5?08>/288707:35>51;870?821
F
0. /:H82@0. ; ?1>C:?/1. 5>?7:5C1. .:. 0??8.1251. 9:8 8./G>
83H8H5C1.8>:>0?17:3>0>1C8H82B>C8.A70F023B.C87RC87B280
C8F70F.8??5E>F/20>.L82.07F9:8F.8F:/575F0FA020F87F?B7?:71FC8F70F28.5./8>?50F1F
9:8.8289:5820?131A21/8??5E>?1>/205>?8>C51.
F
<?8A/1 8> 87 ?0.1 9:8 70 :H5?0?5E> C8 ?1>C:?/1.F ;F /:[email protected] .80F
0A21H0C0 A12 87 I>=8>5821 21;8?/5./0 ?:0>C1 G./1.F .8F 8>?:8>/28>F
83H8H5C1.8>:>071.03:211L5=0C8H82B>.0/5.40?82F70.F.5=:58>/8.F
?1>C5?51>8.NF
F
0- 7C5B38/218</82512>1C8H82B.8230;12C8:>/82?51FC87F8.A8.12F
/1/07C87071.03:211L5=08>709:88./G>83H8H5C1.
H- 0C5./0>?5075H288>/2887838>/1.>1C8H82B.82F38>12FC8F/28.F
C5B38/21.10>?I18>/28?8>/21.
?- : A28.8>?50 8> 87 87838>/1 8./2:?/:207 >1 C8H82BF C5.35>:52F
.5=>545?0/5L038>/8F70F28.5./8>?50FC8F70F?1>./2:??5E>
F
:8C8 ?1>.5C8202.8 9:8 70. /:H82@0. ?1>C:?/1.F 1F 30>=:5/1.F
2883A70F0>F 8./2:?/:20738>/8F 8>F ?13A28.5E>F 07F ?1>?28/1F C8.A70F0C1F
.583A28F9:8NF
F
0- 771.>18./G>8<A:8./1.0A21?8.1.C81<5C0?5E>F:F1/20.F41230.FC8F
C8/825121
H- 80>C845822110?821>128L8./5C11=07L0>5F0C1?1>:>8.A8.12>1
.80F38>12F9:8F09:G7F9:8F?1228.A1>C8F07FC8F70F/:H82@0F8./B>C02FC8F
0?821?I8C:78
?- 8>=0> :> C5B38/21 5>/82512 >135>07 >1 30;12 C8 33 8./G>
8.A0?50C1.F>1F38>1.FC8F/28.FC5B38/21.F8>/28F?8>/21.
F
C5?51>0738>/8071.289:5.5/1.5>C5?0C1.8>708??5E>70./:H82@0.
9:8L0>0?1>/8>827@9:5C1.=0.8.1L0A12A1C2B>.82F83H8H5C0.F8>F87F
?1>?28/1F8./2:?/:207F.583A28F9:8F.8F?:3A70>F70.F.5=:58>/8.F?1>C5?51>8.F
0C5?51>078.NF
F
0- 0./:H82@0.;:>51>8.C8H82B>.82C5.8D0C0.A020FA1C82F28.5./52F
71.848?/1.C8730/8250770A28.5E>;70/83A820/:20F0F70.F?:078.F
I0>C88./02.138/5C0.
H- 0 /83A820/:20 C87 7@9:5C1 =0. 1 L0A12 >1 C8H82BF 8<?8C82F C8F
O
?- 0 A28.5E> 3B<530 0 70 9:8 70. /:H82@0. ; :>51>8.F 8./02B>F

42.   5ON
fin(z7ygfN 8iN ()9(y(svN y(N  5N aHá9n
O
N fiós(N bgN ts(f7–8N
gznifpjs79gGN
N
VGUG4N NN M8z(fNy(NbgN9ibi9g97–8Ny(bN9i89s(ziXNf(Ngf(HcsgsvNn(y7g8z(Ntsc(ógfNKc(N
8iN ()7fzg8N tjsy7ygfN (8N bgfN zcó(sÁgfGN 0fzgfN tsc(ógfN9cntb7sv8N 9i8N biN
y7ftc(fziN(8NbgN1isngNÍGOLLND8fzgbg97i8(fNÍg87zgs7gfGN
N
VGUGQN NN 178HM8N bÁKc7yiXN HgfN iN =gtisXN gN ()9(t97–8N y(N gHcgXN 9cmgN z(nt(sgzcsgN
()9(ygNUOORNXN87NUXSNQHá9n
O
XNy(ó(svNf(sN78zsiyc97yiNgNbgfNzcó(sÁgfNhgfzgN
Kc(N(bN9i89s(ziNhgmgNgb9g8xgyiNfcNs(f7fz(897gNy(Ny7f(:iGN
N
VGUGJN NN 08NbgfNbifgfNng97xgfXNbgfNzcó(sÁgfNy(ó(sv8N9ibi9gsf(N(8zs(N(bNs(pc(sxiN
fct(s7isN mN (bN 78p(s7isGN Í(N ()9(tzMgNgNbifN9gfifNy(Nzcó(sÁgfNtgsgNsgy7gsN
9gbisNiNpc8y7sN87(=(GN
N
VGUG LNNN 0bNs(9cós7n7(8ziNy(N9i89s(ziNy(NbgfNzcó(sÁgfNmNg99(fis7ifN8iNf(svNn(8isN
y(N5N9nNtgsgN9i89s(ziN(8N9i8zg9ziN9i8N(bNz(ss(8iNiN(bNgnó7(8z(N()z(s7isN
87Ny(NON9nNtgsgN(bN9i89s(ziN8iN()tc(fziNgbN()z(s7isNiNgbN9i8zg9ziN9i8N(bN
fc(biGN
N
VGUG  NNN Í(N9ibi9gsvNs(pc(sxiNt(st(8y79cbgsNgNbgNzcó(sÁgNy(NtisNbiNn(8ifNLGLLON
=(9(fN(bNvs(gNy(NbgNf(997–8Ny(N9i89s(ziGN
N
VGUG ONNN IgN zcó(sÁgN mN bifN g99(fis7ifN f(N g9itbgsv8N n(y7g8z(N fibygycsgN cN izsiN
njziyiN7Hcgbn(8z(Nfgz7fpg9zis7iGN1iNf(Nt(sn7z7sv8Nc87i8(fNsif9gygfGNIgN
zcó(sÁgNf(svNzsgóg/gygN(N78fzgbgygNy(NzgbNng8(sgNKc(N8iNf(Ns(Kc7(sgNKc(N
bgfN ógssgfN y(N s(pc(sxiN f(N 9isz(8XN yiób(8N iN y(ftbg9(8N pc(sgN y(N fcN
có79g97–8Ngy(9cgygGN
N
6.4    JUNTAS DE CONSTRUCCION N
N
VG5G N NN IgfNfct(sp797(fNy(NbgfN/c8zgfNy(N9i8fzsc997–8Ny(ó(sv8Nf(sNb7nt7gygfNmNf(N
(b7n78gsvNbgNb(9hgygNfct(sp797gbGN
N
VG5GON NN D8n(y7gzgn(8z(Ng8z(fNy(NbgN9ibi9g97–8Ny(bN8c(=iN9i89s(ziXNbgfN/c8zgfNy(N
9i8fzsc997–8N y(ó(sv8N f(sN hcn(y(97ygfN mN (bN ()9(fiN y(N gHcgN y(ó(svN
(b7n78gyiGN
N
VG5GUN NN IgfN/c8zgfNy(N9i8fzsc997–8Ny(ó(sv8Nf(sNh(9hgfNmN(fzgsNcó79gygfNy(NzgbN
ng8(sgN Kc(N 8iN y7fn78cmg8N bgN s(f7fz(897gN y(bN (b(n(8ziN (fzsc9zcsgbGN
2(ó(sv8N zingsf(N n(y7ygfN tgsgN bgN zsg8fp(s(897gN y(bN 9iszg8z(N mN izsgfN
pc(sxgfGN
N
VG5G5N NN IgfN/c8zgfNy(N9i8fzsc997–8N(8N(8zs(t7fifNy(ó(sv8N(fzgsNcó79gygfN(8N(bN
z(s97iN9(8zsgbNy(NbgNbcxNy(NbifgfNmN=7HgfGNIgfN/c8zgfN(8N=7HgfNts7897tgb(fXN
(8N9gfiN()7fzg8N=7HgfNzsg8f=(sfgb(fNy(8zsiNy(Nc8Nn7fniNtg:iXNy(ó(sv8N
(fzgsN gN c8gN y7fzg897gN nÁ87ngN y(N yifN =(9(fN (bN g89hiNy(N bgfN =7HgfN
zsg8f=(sfgb(fN78y79gygfGN
N
VG5GSN NN IgfN =7HgfN ts7897tgb(fN mN f(9c8ygs7gfXN bgfN nj8fcbgfN mN bifN 9gt7z(b(fXN

43.   5UN
y(ó(sv8Nf(sN=g97gygfNni8ibÁz79gn(8z(N9iniNtgsz(Ny(bNf7fz(ngNy(NbifgfXN
gN n(8ifN Kc(N izsiN tsi9(y7n7(8ziN f(gN 78y79gyiN (8N bifNtbg8ifN iN
(ft(97p79g97i8(fNy(NiósgGN
N
6.5    TOLERANCIAS N
N
VGSG N NN 08N bgfN p–sncbgfN Kc(N f7Hc(8XN c7^N (fN bgN zib(sg897gN (8N 9nN mN cyÑ^N (fN bgN
y7n(8f7–8N9i8f7y(sgygNtgsgN(fzgób(9(sNfcNzib(sg897gN(8N9nGN
N
VGSGON NN IgfNzib(sg897gfNtgsgNbgfNy7n(8f7i8(fNy(NbgNf(997–8Nzsg8f=(sfgbNy(N=7HgfXN
9ibcn8gfXNxgtgzgfNmN(ft(fisNy(NbifgfXNncsifNmNxgtgzgfN(fzgsv8NygygfN
tisNN
NN N N NNNNNNNNNNNNNNNNNNNNNNN
N N N N N
NN NNNNNNNNNNNNNNNNNNNNNN7NN\NN[NLXOSNuyÑe
 áUN
N
VGSGUN NN IgNzib(sg897gNtgsgNbgNtif797–8Ny(NbifN(/(fNy(N9ibcn8gfXNncsifNmNzgó7Kc(fN
s(ft(9ziNgNbifN(/(fN78y79gyifN(8NbifNtbg8ifNy(N9i8fzsc997–8Nf(svNN
N
08Nc8Ntg:iN–NVNnNiNn(8ifNNNNNNNNNNNNNNN7NN\NN[N XUN9nN
08Nc8Ntg:iNy(N ONnNiNnvfNNNNNNNNNNNNNNN7NN\NN[NOXSN9nN
N
08zs(NVNnNmN ONnXNf(N78z(stibgsv8NbifN=gbis(fNy(Nc7^GN
N
VGSG5N NN IgN zib(sg897gN gyn7f7ób(N (8N (bN 87=(bN y(N bgfNbifgfN (8zs(N yifN t7fifN
9i8f(9cz7=ifN8iNf(svN(8N878HM8Ntc8ziNy(NngmisNy(NN
N
NNNNNNNNNNNNNNNNNNNNNNNN
N N N NNNNNNNNNNNNNNNNNNNNNNNNNNNN
N7N\NN[NLXOSNuyÑe
 áUN
N
N NNNNNNNNNNNs(ft(9ziNgbN87=(bN78y79gyiN(8NbifNtbg8ifNy(N9i8fzsc997–8GN
N
VGSGSN N IgNzib(sg897gNgyn7f7ób(N(8NbgNbcxNy(Nc8gN=7HgNf(svNngmisNy(NN
N
NNNNNNNNNNNNNNNNNNNNNNNN
N N N NNNNNNNNNNNNNNNNNNNNNNNNNNNN
N7N\NN[NLXOSNuyÑe
 áUN
N
 
 
 
 
 
 
 
 
 
CAPITULO 7 - DETALLES DEL REFUERZO N
N
7.1    GANCHO ESTANDAR N
N
0bNzjsn78iNHg89hiN(fzv8ygsNf(N(ntb(gN(8N(fzgN1isngNtgsgNy(f7H8gsNN
N

44.   <<α
0-α  >αH0220.α71>=5/:C5>078.Nα
-α μ1H78FαC8αργ]Oα3B.α:>0α8</8>.5E>α3@>530αC8α<αCH0αA821α
>1α38>12αC8α=)(α?30α07α8</2831α75H28αC8α70αH0220)α
-α μ1H78Fα C8α ]Oα 3B.α :>0α 8</8>.5E>α 3@>530α C8α ρβα CHα 07α
8</2831α75H28αC8α70αH0220)α
H-α  >α8./25H1.αNα
-α μ1H78Fα C8α ρ1(Oα 3B.α :>0α 8</8>.5E>α 3@>530α C8α ρ]α CHα 07α
8</2831α 75H28α C8α 70α H0220)α  >α 87838>/1.α 9:8α >1α 28.5./8>α
0??51>8.α[email protected]?0.0α?:0>C1α71.α8./25H1.α>1α.8α289:5820>αA12α
?1>45>0358>/10α87αC1H78FαA1C2Bα.82αC8α]OαEαρ1(Oα3B.α:>0α
8</8>.5E>αC8α=CH)α
α
7.2    DIAMETROS MINIMOS DE DOBLADO α
α
0-α  >αH0220.α71>=5/:C5>078.Nα
 7α C5B38/21α C87α C1H78Fα 38C5C1α 0α 70α ?020α 5>/82512α C8α 70α H0220α >1α
C8H82Bα.82α38>12α0Nα
+0220.ααΦ1KγSαα0ααΦρSαNααααααααααααααααα=CHα
+0220.ααΦραρKγSαα0ααΦαρα1KγSαNαααααααγCHαα
H-α  >α8./25H1.Nα
 7α C5B38/21α C87α C1H78Fα 38C5C1α 0α 70α ?020α 5>/82512α C8α 70α H0220α >1α
C8H82Bα.82α38>12α0Nα
 ./25H1.ααΦ1KγSαα0ααΦα(KγαNαααααααααααα<CHα
 ./25H1.ααΦ1K<Sαα;αα30;128.Nααααααα=CHα
?-α  >α8./25H1.αC8α30770α.17C0C0α+?122:=0C0α1α75.0-αNαα
 7αC5B38/21α5>/82512αC8α71.αC1H78?8.α>1αC8H82Bα.82α38>12α0Nα
±020α0703H28α?122:=0C1αΦ=33α1α30;12Nααααααααααα<CHαα
±020α87α28./1NααααααααααααααααααααααααααααααααααααααααααααααααααααααααβCHα
Φα38>1.αC8α<αCHαC8α:>0α5>/82.8??5E>α.17C0C0NαααγCHα
α
7.3    DOBLADO DEL REFUERZO α
α
×)1)ρα αα ≥1C1α 87α 284:82F1α C8H82Bα C1H702.8α 8>α 42@1)α  7α 284:82F1α A02?50738>/8α
83H8H5C1αC8>/21αC87α?1>?28/1α>1αC8H82BαC1H702.80α8<?8A/1α?:0>C1α0.@αα
.8α5>C59:8α8>α71.αA70>1.αC8αC5.8D1αEα71α0:/125?8α87α2>=8>5821α±21;8?/5./0)α
α
×)1)βα α [1α.8αA8235/52Bα87α28C1H70C1αC87α284:82F1)α
α
7.4    CONDICIONES DE LA SUPERFICIE DEL REFUERZO α
α
×)<)ρα αα  >α87α3138>/1αC8α?171?02α87α?1>?28/10α87α284:82F1αC8H8α8./02α75H28αC8α
70C10α0?85/8α:α1/21.α28?:H25358>/1.α9:8αA:8C0>α048?/02α0CL82.038>/8α.:α
?0A0?5C0CαC8α0CI828>?50)α
α
×)<)βα αα  7α 284:82F1α 38/B75?1α 8<?8A/:0>C1α 87α 0?821α C8α A28.4:82F10α 87α 284:82F1α
38/B75?1α ?1>α E<5C10α 8.?030.α 1α :>0α ?13H5>0?5E>α C8α 03H0.α C8H82Bα
?1>.5C8202.8α .0/5.40?/1251α .5α 70.α C538>.51>8.α 3@>530.0α 5>?7:;8>C1α 70α
07/:20α C8α 70.α ?122:=0?51>8.α 1α 28.07/8.α ;α 87α A8.1α C8α :>α 8.AG?538>α C8α
A2:8H0α?8A5770C1α0α30>10α>1α.1>α38>128.α9:8α70.α8.A8?545?0C0.α8>α70α
[1230α2≥2[≥ φα1<ρ)]1ρ)α

45.   5SN
N
7.5    COLOCACION DEL REFUERZO N
N
4GSG N NN 0bNs(pc(sxiNf(N9ibi9gsvNs(ft(zg8yiNbifNs(9cós7n7(8zifN(ft(97p79gyifN(8N
bifN tbg8ifGN 0bN s(pc(sxiN y(ó(svN gf(Hcsgsf(N y(N ng8(sgN Kc(N ycsg8z(N (bN
=g97gyiN 8iN f(N tsiycx9g8N y(ftbgxgn7(8zifN Kc(N fiós(tgf(8N bgfN
zib(sg897gfNt(sn7f7ób(fGN
N
4GSGON NN MNn(8ifNKc(N(bND8H(87(siNAsim(9z7fzgN78y7Kc(NizsifNN=gbis(fXN(bNs(pc(sxiN
f(N 9ibi9gsvN (8N bgfN tif797i8(fN (ft(97p79gygfN y(8zsiNy(N bgfN f7Hc7(8z(fN
zib(sg897gfNN
Éib(sg897gN(8N(bN
Éib(sg897gN (8N yNN N N N N N s(9cós7n7(8ziN
nÁ87niNN
AgsgNNyNaNOLN9nNNNNNNNNNNNNNNN[N XLN9nNNNNNNNNNNNNNNNNNNNNNNNkN XLN9nN
AgsgNNyNbNOLN9nNNNNNNNNNNNNNNN[N XON9nNNNNNNNNNNNNNNNNNNNNNNNkN XON9nN
N
y(ó7(8yiN gy(nvfXN bgN zib(sg897gN tgsgN (bN s(9cós7n7(8ziN nÁ87niN 8iN
()9(y(svNy(N áUNy(bN(ft(97p79gyiN(8NbifNtbg8ifGN
IgN zib(sg897gN (8N bgN có79g97–8N y(N bifNtc8zifNy(NyióbgyiNiN9isz(Ny(NbgfN
ógssgfNNf(svNy(N[NSN9nGN
 
7.6    LIMITES PARA EL ESPACIAMIENTO DEL REFUERZO N
N
4GVG N NN 0bN(ftg97gn7(8ziNb7ós(N(8zs(NógssgfNtgsgb(bgfNy(Nc8gNn7fngN9gtgNy(ó(svN
f(sN ngmisN iN 7HcgbN gN fcN y7vn(zsiXN gN OXSN 9nN mN gN  XUN =(9(fN (bN zgng:iN
nv)7niN8in78gbNy(bNgHs(HgyiNHsc(fiGN
N
4GVGON NN 08N9gfiNKc(Nf(Nz(8Hg8N=gs7gfN9gtgfNtgsgb(bgfNy(Ns(pc(sxiXNbgfNógssgfNy(N
bgfN9gtgfNfct(s7is(fNy(ó(sv8Ngb78(gsf(N(8NbiNtif7ób(N9i8NbgfN78p(s7is(fXN
y(Nng8(sgNy(Npg97b7zgsN(bN=g97gyiGNIgNf(tgsg97–8Nb7ós(N(8zs(N9gtgNmN9gtgN
y(Ns(pc(sxiNf(svNngmisNiN7HcgbNgNOXSN9nGN
N
4GVGUN NN 08N9ibcn8gfXNbgNy7fzg897gNb7ós(N(8zs(NógssgfNbi8H7zcy78gb(fNf(svNngmisN–N
7HcgbNgN XSN=(9(fNfcNy7vn(zsiXNgN5N9nNmNgN XUN=(9(fN(bNzgng:iNnv)7niN
8in78gbNy(bNgHs(HgyiNHsc(fiGN
N
4GVG5N NN IgNb7n7zg97–8Ny(NbgNy7fzg897gNb7ós(N(8zs(NógssgfNzgnó7j8Nf(Ngtb79gsvNgNbgN
y7fzg897gNb7ós(N(8zs(Nc8Nzsgfbgt(NmNbifNzsgfbgt(fNiNógssgfNgymg9(8z(fGN
4GVGSN NN 08N ncsifN mN bifgfXN ()9(tzcg8yiN bgfN bifgfN 8(s=gygfXN (bN (ftg97gn7(8ziN
(8zs(N(/(fNy(bNs(pc(sxiNts7897tgbNtisNpb()7–8Nf(svNn(8isNiN7HcgbNgNUN=(9(fN
(bN(ft(fisNy(bN(b(n(8ziN(fzsc9zcsgbXNf78N()9(y(sN5SN9nGN
N
4GVGVN NN 0bN s(pc(sxiN tisN 9i8zsg997–8N mN z(nt(sgzcsgN y(ó(svN 9ibi9gsf(N 9i8N c8N
(ftg97gn7(8ziN(8zs(N(/(fNn(8isN–N7HcgbNgNSN=(9(fN(bN(ft(fisNy(NbgNbifgXN
f78N()9(y(sNy(N5SN9nGN
N
7.7    PAQUETES DE BARRAS N
N
4G4G N NN IgfN ógssgfN bi8H7zcy78gb(fN tiysv8N gHsctgsf(Npisng8yiN tgKc(z(fN Kc(N

46.   <=α
0?/M8>α?131α:>0α:>5C0C0αC8H58>C1α7535/02.8α0α:>α3B<531αC8α<αH0220.α
A12αA09:8/8)α
α
×)×)βα αα Σ1.α A09:8/8.α C8H82B>α 071602.8α C8>/21α C8α 8./25H1.α ?8220C1.0α C8H58>C1α
0C83B.α0302202.8α/1C0.α70.αH0220.α8>/28α.@)α
α
×)×)1α α  >α87838>/1.α.:68/1.α0α478<5E>0α70.αH0220.αC8α71.αA09:8/8.α9:8α.8α?12/8>α
C8>/21αC87α/2031αC8H82B>α/8235>02α8>αA:>/1.αC5./5>/1.α;α.8A020C1.αA12α71α
38>1.α:>0αC5./0>?50αC8α<]αL8?8.α.:αC5B38/21)α
α
×)×)<α αα ±020αC8/8235>02α87α8.A0?50358>/1α3@>531α8>/28αA09:8/8.0α?0C0α:>1α.8α
/20/02Bα ?131α :>0α H0220α .53A78α C8α 5=:07α B280α /20>.L82.07α 9:8α 70α C87α
A09:8/8)α
α
×)×)(α αα  7α28?:H25358>/1α3@>531αA020α71.αA09:8/8.αC8αH0220.αC8H82Bα.82α5=:07α07α
C87αC5B38/21α89:5L078>/8αC87αA09:8/80αA821α>1α>8?8.5/0α.82α30;12αC8α(α
?3)α±020α?1>?28/1αL0?50C1α?1>/20α87α.:871α;αA8230>8>/838>/8α8<A:8./1α
0αG70α87α28?:H25358>/1α3@>531αC8H82Bα.82αC8α×α?3)α
α
7.8    DUCTOS Y TENDONES DE PRESFUERZO α
α
αΣ0α C5./0>?50α 75H28α 8>/28α /8>C1>8.α C8α A28.4:82F1α 8>α ?0C0α 8</2831α C87α
87838>/1α >1α .82Bα 38>12α 9:8α <α CHα A020α 0703H28.0α >5α 38>12α 9:8α 1αCHα
A020α/121>8.)α
α >α87α/2031α?8>/207αC8α70α7:FαA:8C8αA8235/52.8α:>α38>12α8.A0?50358>/1)α
Σ1.αC:?/1.αA020α/8>C1>8.αA1./8>.0C1.αA1C2B>α8./02α8>αA09:8/8.α.5α.8α
C83:8./20α9:8α.8ααA:8C8αI0?82α:>αL0?50C1α.0/5.40?/1251αC87α?1>?28/1α;α
.583A28α9:8α.8αI0;0>α/130C1α70.αA28?0:?51>8.α>8?8.0250.αA020α9:8α71.α
/8>C1>8.α>1α.8α213A0>α07α.82αα/8>.0C1.)α
α
7.9    RECUBRIMIENTO PARA EL REFUERZO α
α
×))ρ    φδ[φπ ≥δαΦφ2Φμδα [αδ+πΦ  
α
μ8H82BαA21A12?51>02.8α87α.5=:58>/8α28?:H25358>/1α3@>531αC8α?1>?28/1α07α
284:82F1Nα
0-α φ1>?28/1αL0?50C1α?1>/20α87α.:871α1α8>α?1>/0?/1α?1>α0=:0αα
C8α302Nαααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααα×α?3α
H-αααφ1>?28/1α8>α?1>/0?/1α?1>α87α.:871α1α8<A:8./1α07α03H58>/8Nα
Jα +0220.αC8ααφ(KγSαα1α38>128.Nαααααααααααααα<α?3α
Jα +0220.αC8ααφ1K<Sαα1α30;128.Nαααααααααααααα(α?3α
?-αααφ1>?28/1α>1α8<A:8./1α07α03H58>/8α+A21/8=5C1αA12α:>α28L8./5358>/1-α
>5α8>α?1>/0?/1α?1>α87α.:871α+L0?50C1α?1>α8>?1420C1α;K1α.170C1-Nα
Jα Σ1.0.α1α075=820C1.Nααααααααααααααααααααααααααααβα?3α
Jα ,:21.α1α3:21.αC8α?12/8Nααααααααααααααααααααβα?3α
Jα 5=0.α;α?17:3>0.Nαααααααααααααααααααααααααααααα<α?3α+U-α
Jα φB.?020.α;α7B35>0.αA78=0C0.Nαααααααααααβα?3α
+U-α 7α28?:H25358>/1αC8H82Bα38C52.8α07α8./25H1)α
α
×))β    φδ[φπ ≥δα±π σΦ+π2φΦμδ  +σ0H25?0C1αH061α?1>C5?51>8.αC8α?1>/217α

47.   <×α
8>αA70>/0-)  
 
    °8αC8H82BαA21A12?51>02α87α.5=:58>/8α28?:H25358>/1α3@>531αC8α?1>?28/1α
07α284:82F1Nα
0-α φ1>?28/1α8>α?1>/0?/1α?1>α87α.:871α1α8<A:8./1α07α03H58>/8Nα
Jα ±0>878.αA020α3:21.α;α71.0.Nααααααααααααααβα?3α
Jα δ/21.α87838>/1.Nα
+0220.α30;128.αC8ααφ(KγSNαααααααααα<α?3α
+0220.αC8ααφ(Kγ^αα1α38>128.Nαααααα1α?3α
H-α φ1>?28/1α>1α8<A:8./1α07α03H58>/8α>5α8>α?1>/0?/1α?1>α87α.:871Nα
Jα ±0>878.αA020α3:21.α;α71.0.Nααααααααααααρ0(α?3α
Jαααααααααα5=:8/0.Nααααααααααααααααααααααααααααααααααααααααααααρ0(α?3α
Jα 5=0.α;α?17:3>0.Nααααααααααααααααααααααααααααααβα?3α+U-α
Jα φB.?020.α;α7B35>0.αA78=0C0.Nααααααααααρ0(?3α
+U-α 7α28?:H25358>/1αC8H82Bα38C52.8α0α70α?020α8</82512αC87α8./25H1)αα
α α
×))1    π φ≤+π2,2 [≥δ°α °± φ2ΦΣ °α
α
α >α03H58>/8.α?1221.5L1.α;α8>α1/20.α?1>C5?51>8.α.8L820.αC8α8<A1.5?5E>α
C8H82Bα 0:38>/02.8α 0C8?:0C038>/8α 87α 8.A8.12α C8α 71.α 28?:H25358>/1.0α
/130>C1α 0C83B.α 8>α ?1>.5C820?5E>α 9:8α C8H82Bα A21A12?51>02.8α :>α
?1>?28/1αC8>.1)α
α
×))<α α  °± °δπαμ αμ °√Φ°≥ α
α
 >α.:A8245?58.α8<A:8./0.α0α0H20.5E>0α/07α?131α70α9:8αA21C:?8α87α/2B>.5/1α
5>/8>.10α>1α.8α/1302Bα8>α?:8>/0α?131αA02/8αC8α70α.8??5E>α28.5./8>/8α87α
8.A8.12α9:8αA:8C0αC8.=0./02.8)αΦαG./8α.8α78α0.5=>02Bα:>0αC538>.5E>α>1α
38>12α9:8αρ0(α?3)α
α
×))(α α π  °≥2,2 [≥δ°α
α
Σ1.α28L8./5358>/1.α>1α.8α/1302B>α8>α?:8>/0α?131αA02/8αC8α70α.8??5E>α
28.5./8>/8αC8α>5>=M>α87838>/1)α
α
7.10    REFUERZO POR CONTRACCIÓN Y TEMPERATURA α
α
×)ρ])ρααα  >α71.0.α8./2:?/:2078.αC1>C8α87α284:82F1αA12α478<5E>α.8α8</58>C0α8>α:>0α
C528??5E>0α .8α C8H82Bα A21A12?51>02α 284:82F1α A82A8>C5?:702α 0α G./8α A020α
28.5./52α71.α8.4:82F1.αA12α?1>/20??5E>α;α/83A820/:20)α
α
×)ρ])βααα  ./0α 0230C:20α C8H82Bα A21A12?51>02α 70.α .5=:58>/8.α 2870?51>8.α 3@>530.α
C8αB280αC8α70α0230C:20α0αB280αC8α70α.8??5E>α/1/07αC8α?1>?28/10α.8=M>α87α
/5A1αC8α0?821αC8α284:82F1α9:8α.8α:.8Nα
-α Σ1.0.αC1>C8α.8α:.0>αH0220.α75.0.Nααααααααααααααααααααααααααααα]0]]β(α
-α Σ1.0.αC1>C8α.8α:.0>αH0220.αα
α ?122:=0C0.α?1>α7@35/8.αC8α8.Jα
α 4:82F1αC8α47:8>?50α38>128.αα
α C8α<β]]α*=K?3
β
Nαααααααααααααααααααααααααααααααααααααααααααααααααααααααααα]0]]β]α
-α Σ1.0.αC1>C8α.8α:.0>αH0220.αα

48.   5QN
N 9isscHgygfNiNngbbgNy(NgbgnkN
N ós(NKc(Nz(8Hg8N78z(sf(9kN
N 97i8(fNfibygygfXN9i8NbÁn7z(fN
N y(N(fpc(sxiNy(Npbc(897gNy(N
NNNNNN5OLLNaHá9n
O
NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNLXLL QN
-N IifgfNyi8y(Nf(Ncfg8NógssgfN
N RisscHgygfN9i8NbÁn7z(fNy(N(fkN
N pc(sxiNy(Npbc(897gNngmis(fNN
N Kc(N5OLLNaHá9n
ONN
n(y7ygfNgNN
N c8gNy(pisng97–8Nc87zgs7gNy(NN
NNNNNNpbc(897gNy(NLXUSRNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNLXLL QN
NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNu5OLLápmeXN 8iN n(kNNN
NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN8isN y(N LXLL 5N
NNNN
N
4G LGUNNN 0bNs(pc(sxiNtisN9i8zsg997–8NmNz(nt(sgzcsgNtiysvN9ibi9gsf(N(8Nc8gNiN(8N
bgfNyifN9gsgfNy(bN(b(n(8ziXNy(t(8y7(8yiNy(bN(ft(fisNy(Njfz(NmNzing8yiN
(8N9c(8zgNbiN78y79gyiN(8NbgNÍ(997–8N4GVGN
N
7.11    DETALLES PARA EL REFUERZO DE COLUMNAS N
N
4G  G NN 2EÑIM2EN-NÉ.MÍIMA0N20NÑM..MÍN
N
4G  G G N IgfNógssgfNbi8H7zcy78gb(fNyióbgygfNy(ó7yiNgNc8N9gnó7iNy(Nf(997–8N(8NbgN
9ibcn8gN y(ó(sv8N z(8(sXN 9iniN nv)7niXN c8gN t(8y7(8z(N y(N  N (8N VN u N
t(st(8y79cbgsNmNVNtgsgb(bgNgbN(/(Ny(NbgN9ibcn8geXN9i8z78cg8yiNbc(HiN9i8N
bgNy7s(997–8Ny(bN(/(Ny(NbgN9ibcn8gGN
N
4G  G GON 2(ó(svN tsitis97i8gsf(N fitisz(N his7xi8zgbN gy(9cgyiN tgsgN c8gN ógssgN
yióbgygNtisN9gnó7iNy(Nf(997–8XNtisNn(y7iNy(N(fzs7óifNiN(ft7sgb(fNiNtisN
tgsz(fNy(Nf7fz(ngNy(N(8zs(t7fiGN0bNfitisz(Nhis7xi8zgbNy(ó(svNs(f7fz7sNc8gN
=(xNmNn(y7gN(bN=gbisNy(NbgN9inti8(8z(Nhis7xi8zgbNy(NbgNpc(sxgN8in78gXN
(8NbgNtis97–8N789b78gygNy(NbgNógssgNKc(Nf(Nfcti8(Nzsgóg/gNgNfcNnv)7ngN
9gtg97ygyGN
N
4G  G GUN Rcg8yiNbgfN9gsgfNy(NbgfN9ibcn8gfNz(8Hg8Nc8Ny(fgb78(gn7(8ziN=(sz79gbN
y(N4XSN9nNiNnvfNmNbgfNógssgfNbi8H7zcy78gb(fN8iNf(Ntc(yg8NyióbgsN(8NbgN
pisngN78y79gygN(8NbifNtvssgpifNg8z(s7is(fXNjfzgfNy(ó(sv8Nzsgfbgtgsf(N9i8N
(bNs(pc(sxiNbi8H7zcy78gbNy(NbgN9ibcn8gNfct(s7isGN
N
4G  G G5N IgfN ógssgfN bi8H7zcy78gb(fN y(N 9ibcn8gN f(N (ntgbngsv8N y(N ts(p(s(897gN
y(8zsiN y(N bifN OáUN 9(8zsgb(fN y(N bgN gbzcsgN y(bN (b(n(8ziXN (8N bi8H7zcy(fN
f(HM8NbiN78y79gyiN(8NbgNÍ(997–8NQG OGN
N
4G  GONN .03C0.,ENÉ.M1Ío0.ÍMIN
N2(ó(svN9cntb7sN9i8NbifNs(Kc(s7n7(8zifNy(Ny7f(:iNtisNpc(sxgN9iszg8z(NmN
tisN9i8p78gn7(8ziXN(bNs(pc(sxiNzsg8f=(sfgbNy(ó(svN9cntb7sN9i8NbiN78y79gyiN
gN9i8z78cg97–8NN
N
4G  GOG N 0ÍAD.MI0ÍN

49.   5JN
N
geN IifN(ft7sgb(fNy(ó(sv8N9i8f7fz7sNy(NógssgfN9i8z78cgfXN(ftg97gygfN
c87pisn(n(8z(XN9i8Nc8Ny7vn(zsiNnÁ87niNy(NUáQSGN0bN(ftg97iNb7ós(N
(8zs(N(ft7sgb(fNf(svN9iniNnÁ87niNOXSN9nNmN9iniNnv)7niN4XSN9nGN
óeN 0bNg89bg/(Ny(bNs(pc(sxiN(8N(ft7sgbNf(NhgsvNgcn(8zg8yiN XSN=c(bzgfN
y(NbgNógssgN(8N9gygN()zs(niGN
9eN IifN(ntgbn(fN(8N(bNs(pc(sxiN(8N(ft7sgbNf(sv8NtisNzsgfbgt(XN9i8N
c8gNbi8H7zcyNnÁ87ngNy(N5QNyóGN
yeN 0bNs(pc(sxiN(8N(ft7sgbNy(ó(svN()z(8y(sf(Ny(fy(NbgNtgsz(Nfct(s7isN
y(NbgNxgtgzgNiNbifgN(8N9cgbKc7(sN87=(bXNhgfzgNbgNgbzcsgNy(bNs(pc(sxiN
his7xi8zgbNnvfNóg/iNy(bN(b(n(8ziNfitiszgyiGN
(eN Í7(nts(Ny(ó(sv8N9ibi9gsf(N(fzs7óifNtisN(897ngNy(NbgNz(sn78g97–8N
y(bN(ft7sgbNhgfzgNbgNtgsz(N78p(s7isNy(NbgNbifgNiNvóg9iGN
peN 08N 9ibcn8gfN 9i8N 9gt7zgb(fXN (bN s(pc(sxiN (8N (ft7sgbN f(N ()z(8y(svN
hgfzgN(bN87=(bN(8N(bN9cgbN(bNy7vn(zsiNiNg89hiNy(bN9gt7z(bN(fN(bNyiób(N
y(NbgN9ibcn8gGN
HeN 0bNs(pc(sxiN(8N(ft7sgbNf(svNfc/(zgyiNp7sn(n(8z(N(8NfcNbcHgsNmNf(N
cfgsv8N(ftg97gyis(fN=(sz79gb(fNtgsgNng8z(8(sNbgNgb78(g97–8GN
 
4G  GOGON 0ÍÉ.DÑEÍN
N
geN ÉiygfN bgfN ógssgfN bi8H7zcy78gb(fN y(ó(sv8N (fzgsN 9i8p78gygfN tisN
(fzs7óifN9(ssgyifGNo(sNbgNÍ(997–8N4G GN
óeN 08N 9ibcn8gfXN f(N cfgsv8N (fzs7óifN y(N UáQSN y(N y7vn(zsiXN 9iniN
nÁ87niXN tgsgN (bN 9gfiN y(N ógssgfN bi8H7zcy78gb(fN hgfzgN y(N  SN mN
(fzs7óifN y(N  áOSN y(N y7vn(zsiXN 9iniN nÁ87niXN tgsgN (bN9gfiN y(N
ógssgfNy(Ny7vn(zsifNngmis(fGN
9eN 0bN (ftg97gn7(8ziN nv)7niN (8zs(N (fzs7óifN 8iN y(ó(svN ()9(y(sN
878Hc8iNy(NbifNf7Hc7(8z(fN=gbis(fN VN=(9(fN(bNy7vn(zsiNy(NbgNógssgN
bi8H7zcy78gbXN bgN n(8isN y7n(8f7–8N y(bN (b(n(8ziN fc/(ziN gN
9ints(f7–8NiNULN9nGN
yeN IifN (fzs7óifN y(ó(sv8N y7fti8(sf(N y(N zgbN pisngN Kc(N 9gygN ógssgN
bi8H7zcy78gbNy(N(fKc78gNz(8HgNgtimiNbgz(sgbNtsitis97i8gyiNtisN(bN
yiób(xNy(Nc8N(fzs7óiN9i8Nc8Nv8HcbiN9ints(8y7yiNn(8isNiN7HcgbNgN
 USONmNKc(N878Hc8gNógssgN(fzjNf(tgsgygNnvfNy(N SN9nNy(NizsgN
ógssgNbgz(sgbn(8z(NgtimgygGN
(eN 08N(fzsc9zcsgfNy(NncsifNtiszg8z(fNy(Ngbóg:7b(sÁgN9cmgNs7H7y(xNmN
s(f7fz(897gN (8N gnógfN y7s(997i8(fN g8z(N g997i8(fN bgz(sgb(fN (fzjN
ygygN ts7897tgbn(8z(N tisN (fzifXN f(N tiysv8N cfgsN (fzs7óifN y(N
y7vn(zsiN á5SN(8NN
-N Ribcn8gfN g7fbgygfN 9cmgN n(8isN y7n(8f7–8N 8iN ()9(ygN y(N
OSN9nGN
-N Ribcn8gfN Kc(N z(8Hg8N 9iniN pc897–8N ts7897tgbN tsi=((sN
9i8p78gn7(8ziNgNncsifNy(Ngbóg:7b(sÁgNuo(sNbgN1isngN0GL4LN
Mbóg:7b(sÁgeGN
peN 08N 9ibcn8gfN 9cmgfN ógssgfN bi8H7zcy78gb(fN (fzj8N y7ftc(fzgfN gN biN
bgsHiN y(N c8gN 97s9c8p(s(897gXN f(N tiysv8N (ntb(gsN (fzs7óifN
97s9cbgs(fGN
N
7.12     DETALLES PARA EL REFUERZO TRANSVERSAL DE ELE MENTOS 

50.   SLN
EN FLEXIÓN 
N
4G OG NNN 0bN s(pc(sxiN (8N 9ints(f7–8N (8N =7HgfN y(ó(N 9i8p78gsf(N 9i8N (fzs7óifN Kc(N
fgz7fpgHg8N bgfN b7n7zg97i8(fN y(N zgng:iN mN (ftg97gn7(8ziN (8N bgN Í(997–8N
4G  GOGOXNiNó7(8N9i8Nc8gNngbbgN(b(9zsifibygygNy(Nc8Nvs(gN(Kc7=gb(8z(GN
Égb(fN(fzs7óifNy(ó(sv8N(ntb(gsf(N(8NziygNbgNbi8H7zcyNyi8y(Nf(Ns(Kc7(sgN
s(pc(sxiN(8N9ints(f7–8GN
N
4G OGONNN 0bN s(pc(sxiN bgz(sgbN tgsgN (b(n(8zifN y(N t–sz79ifN (8N pb()7–8N fc/(zifN gN
(fpc(sxifNs(=(sf7ób(fNiNgNzisf7–8N(8NbifNgtimifXN9i8f7fz7svN(8N(fzs7óifNiN
(ft7sgb(fNKc(Nf(N()z7(8yg8Ngbs(y(yisNy(bNs(pc(sxiN(8Npb()7–8GN
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
CAPÍTULO 8 - DESARROLLO Y EMPALMES DEL REFUERZO 
N
8.1    DESARROLLO DEL REFUERZO-GENERALIDADES N
N
QG G N NN IgNzsg997–8NiN9ints(f7–8N9gb9cbgygN(8N(bNs(pc(sxiN(8N9gygNf(997–8Ny(N
(b(n(8zifN y(N 9i89s(ziN gsngyiXN y(ó(svN y(fgssibbgsf(NgN 9gygN bgyiN y(N
y79hgNf(997–8Nn(y7g8z(Nc8gNbi8H7zcyNy(Ny(fgssibbiXNHg89hiXNy7ftif7z7=iN
n(9v879iN–Nc8gN9inó78g97–8Ny(N(bbifGN
N
QG GON N IifN Hg89hifN f(N tiysv8N (ntb(gsN f–biN (8N (bN y(fgssibbiN y(N ógssgfN (8N

51.   S N
zsg997–8GN
N
8.2    DESARROLLO DE BARRAS CORRUGADAS SUJETAS A TRAC CIONN
N
QGOG N N IgNbi8H7zcyNy(Ny(fgssibbiNóvf79gNbyóXN(8N9(8zÁn(zsifXNf(svN(bNngmisNy(N
bifNf7Hc7(8z(fN=gbis(fNN
N N
byóNN\NNLXLVNMóNpmNáNuNpW9Ne
 áON
N
byóNN\NNLXLLVNyóNpmN
N
IgNbi8H7zcyNy(Ny(fgssibbiNbyNf(svNbgNióz(87ygNy(Nncbz7tb79gsNbyóNtisNc8iNy(N
bifNf7Hc7(8z(fNpg9zis(fNNN
N
geN AgsgNógssgfNhis7xi8zgb(fNKc(Nz(8Hg8NtisNy(óg/iNnvfNy(NULN9nNy(N
9i89s(ziNps(f9iNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN X5N
óeN Rcg8yiN(bNs(pc(sxiN(fzjN(ftg97gyiNbgz(sgbn(8z(NtisNbiNn(8ifN SN
9nN(8zs(N(/(fNmNz(8HgNc8Ns(9cós7n7(8ziNbgz(sgbNy(NtisNbiNn(8ifN4XSN
9nNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNLXQNNN
N
IgN bi8H7zcyN y(N y(fgssibbiN byN 8iN f(svN n(8isN y(N ULN 9nN ()9(tziN (8N
zsgfbgt(fXNtgsgNbiNKc(Ns(H7svNbiN78y79gyiN(8NbgNÍ(997–8NQGJGN
N N N N N
8.3    DESARROLLO  DE  BARRAS  CORRUGADAS  SUJETAS  A 
COMPRESION 
N
QGUG N N IgN bi8H7zcyN y(N y(fgssibbiN byXN (8N 9(8zÁn(zsifXN f(svN (bN ngmisN y(N bifN
f7Hc7(8z(fN=gbis(fNN
N
byNN\NNLXLQNyóNNpmNáNuNpW9Ne
 áON
byNN\NNLXLL5NyóNNpmN
N
N N bgNbi8H7zcyNy(Ny(fgssibbiNbyN8iNf(svNn(8isNy(NOLN9nGN
 
8.4    DESARROLLO DE BARRAS EN PAQUETES N
N
IgNbi8H7zcyNy(Ny(fgssibbiNy(N9gygNógssgNy(8zsiNy(Nc8NtgKc(z(Ny(NógssgfN
fc/(zgfN gN zsg997–8N iN 9ints(f7–8XN y(ó(svN f(sN gKc(bbgN y(N bgN ógssgN
78y7=7ycgbXNgcn(8zgygN(8NOLRNtgsgNtgKc(z(fNy(NUNógssgfNmN(8NUURNtgsgN
tgKc(z(fNy(N5NógssgfGN
8.5    DESARROLLO DE GANCHOS ESTÁNDAR EN TRACCIÓN N
N
QGSG N NN AgsgNógssgfNy(Ns(pc(sxiNKc(Nz(sn78(8N(8NHg89hifN(fzv8ygsXNbgNbi8H7zcyN
y(Ny(fgssibbiN(8Nzsg997–8NbyHXN(8N9nXNf(svNN
 áON
byHNN\NNU QNyóNáNuNpW9NeNNNNXN
N
t(siN8iNn(8isNKc(NQN=(9(fN(bNy7vn(zsiNy(NbgNógssgN87NKc(N SN9nGN
N
N0fzgNy7fzg897gNf(Nn(y7svNy(fy(NbgNf(997–8N9sÁz79gNhgfzgN(bNóisy(N()z(s7isN

52.   SON
y(bNyiób(xXNfiós(Nc8gNb78(gNs(9zgNKc(N9i7897y(N(bN(/(Nbi8H7zcy78gbNy(NbgN
ógssgGN
N
QGSGON NN Rcg8yiN(bNs(9cós7n7(8ziNbgz(sgbNy(NbgNógssgNu8isngbN(bNtbg8iNy(bNHg89hieN
(fN 7HcgbN iN ngmisN gN VSN nnN N mN (8N (bN 9gfiN y(N Hg89hifN JLdN f(N z(8HgN
gy(nvfN Kc(N (bN s(9cós7n7(8ziN (8N bgN ()z(8f7–8N y(N bgN ógssgN (fN ngmisN iN
7HcgbNgNSLNnnXN(bN=gbisNy(NbyHNf(NtiysvNncbz7tb79gsNtisNLX4LXN9cg8yiNbgN
ógssgN f(N hgbbgN y(8zsiN y(N (fzs7óifN 9(ssgyifXN =(sz79gb(fN iN his7xi8zgb(fXN
(ftg97gyifN8iNnvfNy(NUNyóN(8NziygNbgNbi8H7zcyNbyHXN(bN=gbisNy(NbyHNf(N
tiysvNncbz7tb79gsNtisNLXQGN
0fzifNyifNpg9zis(fN8iNfi8N()9bcm(8z(fGN
N
8.6     DESARROLLO  DEL  REFUERZO  CORRUGADO  DE  MALLA 
ELECTROSOLDADA 
N
QGVG N NN IgN bi8H7zcyN y(N y(fgssibbiN byXN (8N 9(8zÁn(zsifXN y(N ngbbgN y(N gbgnós(N
9isscHgyiN fibygyiXN n(y7yiN y(fy(N (bN tc8ziN y(N f(997–8N 9sÁz79gN hgfzgN (bN
()zs(niNy(bNgbgnós(XNf(Ny(ó(svN9gb9cbgsN9iniN(bNtsiyc9ziNy(NbgNbi8H7zcyN
y(Ny(fgssibbiNóvf79gNbyóNy(NbgNÍ(997–8NQGVGON–NQGVGUNmN(bNpg9zisNiNpg9zis(fN
y(Nniy7p79g97–8Ngtb79gób(fNy(NbgfNÍ(997i8(fNQGOG NgeNmNóePNt(siNbyN8iNf(svN
n(8isNy(NOLN9nGN
N
QGVGON NN IgN bi8H7zcyN y(N y(fgssibbiN óvf79gN byóXN (8N 9(8zÁn(zsifXN y(N ngbbgN y(N
gbgnós(N 9isscHgyiN fibygyiXN 9i8N tisN biN n(8ifN c8N gbgnós(N zsg8f=(sfgbN
y(8zsiNy(NbgNbi8H7zcyNy(Ny(fgssibbiNmNgN8iNn(8ifNy(NSN9nNy(fy(N(bNtc8ziN
y(Nf(997–8N9sÁz79gXNy(ó(Nf(sNN
 áON
LX  NyóNupmNe 5LVeNáNuNpW9NeNNUNNXN
N
N N UNIgN97psgN 5LVN(8NQHá9n
ON
N
t(siN8iNn(8isNy(NN
N
LX4SNuNMXNáNÍXNeNfpmNáNuNpY9Ne
 áO
gN
N
yi8y(NNN
MXN N \N N N Bs(gN y(N c8N gbgnós(N 78y7=7ycgbN Kc(N f(N y(ó(N y(fgssibbgsN iN
zsgfbgtgsXN9n
ONN
ÍXN\NÍ(tgsg97–8Ny(NbifNgbgnós(fNKc(Ny(ó(8Ny(fgssibbgsf(NiNzsgfbgtgsf(XN
9nN
N
QGVGUN NN IgN bi8H7zcyN y(N y(fgssibbiN óvf79gN byóN y(N ngbbgN y(N gbgnós(N 9isscHgyiN
fibygyiNf78Ngbgnós(fNzsg8f=(sfgb(fNy(8zsiNy(NbgNbi8H7zcyNy(Ny(fgssibbiXN
f(Ny(ó(Ny(z(sn78gsNy(N7HcgbNng8(sgNKc(NtgsgNgbgnós(N9isscHgyiGN
N
8.7    ANCLAJE MECANICO N
N
N N Í(NtiysvNcz7b7xgsN9iniNg89bg/(N9cgbKc7(sNy7ftif7z7=iNn(9v879iN9gtgxNy(N
y(fgssibbgsN bgN s(f7fz(897gN y(bN s(pc(sxiN f78N Kc(N (fz(N yg:(N (bN 9i89s(ziN mN
ts(=7gNts(f(8zg97–8Ny(Ntsc(ógfXNbgfNKc(NNy(ó(sv8Nf(sNgtsiógygfNtisN(bN

53.   SUN
D8H(87(siNAsim(9z7fzgNmN(bND8ft(9zisGN
N
8.8                CORTE O DOBLADO DEL REFUERZO PARA MIEMBROS SUJETOS 
A FLEXIÓN 
N
QGQG N N P010.MID2M20ÍN
N
QGQG G N NNNNNNNNNNN0bN s(pc(sxiN f(N tc(y(N y(fgssibbgsN yióbv8yibiN (8N (bN gbngXN tgsgN
g89bgsbiN iN hg9(sbiN 9i8z78ciN 9i8N (bN s(pc(sxiN y(N bgN 9gsgN itc(fzgXN iN
f7ntb(n(8z(Ny(/v8yibiN9iniNógssgNs(9zgN9i8NfcNy(ó7yiNg89bg/(GN
N
QGQG GON NNNNNNNNNNN08N(b(n(8zifNgNpb()7–8NKc(Ns(f7fzg8Nnin(8zifNy(Nf7fniNy(ó(svN
()7fz7sN s(pc(sxiN 9i8z78ciN gN ziyiN biN bgsHiN y(N bgN =7HgXN 9i8fz7zc7yiN tisN ON
ógssgfNzg8ziN(8NbgN9gsgNfct(s7isN9iniN(8NbgN9gsgN78p(s7isXN9i8Nc8Nvs(gNy(N
g9(siN8iNn(8isNgNhNy(NbgNnv)7ngNs(Kc(s7ygN(8NbifN8cyifXN87Nn(8isNy(NN
N
LX4NNfuNpY9Ne
 áO
NáNpmgNóXNyNN
N
My797i8gbn(8z(Ny(ó(svN9i8f7y(sgsf(NN
N
geN ÉiygfN bgfN ógssgfN Kc(N g89b(8N (8N 9ibcn8gfN ()zs(ngfN y(ó(sv8N
z(sn78gsN(8NHg89hiN(fzv8ygsGN
óeN IgfNógssgfNKc(Nf(N9isz(8N(8NgtimifN78z(sn(y7ifNf78NcfgsNHg89hiXN
y(ó(sv8Ntsibi8Hgsf(NgNzsg=jfNy(NbgN9ibcn8gN78z(s7isGNIgNtgsz(Ny(N
byN Kc(N 8iN f(N hgbb(N y(8zsiN y(bN 8M9b(iN 9i8p78gyiN y(ó(svN
789s(n(8zgsf(Nncbz7tb79v8yibgNtisNc8Npg9zisN XVGN
N
QGQG GUN NNNNNNNNNNNIgfNxi8gfN9sÁz79gfNtgsgN(bNy(fgssibbiNy(bNs(pc(sxiN(8N(b(n(8zifN(8N
pb()7–8XN f(sv8N bgfN f(997i8(fN y(N nv)7niN (fpc(sxiN mN bgfN f(997i8(fN y(bN
zsgniNyi8y(Nz(sn78gNiNf(NyióbgN(bNs(pc(sxiNgymg9(8z(GN
N
QGQG G5N NNNNNNNNNN0bNs(pc(sxiNy(ó(svN()z(8y(sf(XNnvfNgbbvNy(NbgNf(997–8Nyi8y(NmgN
8iN(fN8(9(fgs7iNtisN9vb9cbiXNc8gNy7fzg897gN7HcgbNgbNt(sgbz(N(p(9z7=iNy(bN
(b(n(8ziN–N ONyóXNbgNKc(Nf(gNngmisXNf7(nts(NKc(Ny(fgssibb(NbyNy(fy(N(bN
tc8ziNy(Nnv)7niN(fpc(sxiGNÍ(N()9(tzMg8NbifNgtimifNgsz79cbgyifNmNbifN
()zs(nifNy(N=ibgy7xifGN
N
QGQG GSN NNNNNNNNNNNRcg8yiN f(N cf(N c8N s(pc(sxiN 9i8z78ciN mN izsiN gy797i8gbN y(N n(8isN
bi8H7zcyNXNf(Ny(ó(svN9cntb7sNN
N
geN 0bNs(pc(sxiN9i8z78ciNy(ó(svNz(8(sNc8gNbi8H7zcyNy(Ng89bg/(NngmisNiN
7HcgbN gN bgN bi8H7zcyN y(N y(fgssibbiN byN nvfN gbbvN y(bN tc8ziN yi8y(N(bN
s(pc(sxiN Kc(N f(N hgN 9iszgyiN iN yióbgyiN 8iN (fN 8(9(fgs7iN tisN
9vb9cbiGN
óeN 0bN s(pc(sxiN tisN pb()7–8N 8iN y(ó(svN z(sn78gsf(N (8Nc8gN xi8gN y(N
zsg997–8XN gN n(8ifN Kc(N (8N (bN tc8ziN y(N 9isz(N (bN s(pc(sxiN Kc(N
9i8z78MgNtsitis97i8(N(bNyiób(Ny(bNvs(gNs(Kc(s7ygNtisNpb()7–8NmNKc(N
(bN9iszg8z(N8iN()9(ygNbgfNUá5Ntgsz(fNy(NbiNt(sn7z7yiGN
 
QGQGON N 2DÍAEÍDRDd1N20IN.03C0.,ENAM.MNÓEÓ01ÉENAEÍDÉD oEN

54.   S5N
N
QGQGOG N NNNNNNNNNNNAisNbiNn(8ifNbgNz(s9(sgNtgsz(Ny(bNs(pc(sxiNtisNnin(8ziNtif7z7=iN
y(ó(svN tsibi8Hgsf(N y(8zsiN y(bN gtimiXN 9cntb7(8yiN 9i8N (bN g89bg/(N
s(Kc(s7yiGN
N
QGQGOGON NNNNNNNNNNN08N(b(n(8zifNKc(Ns(f7fzg8Nnin(8zifNy(Nf7fniXNy(ó(svN9cntb7sf(N
Kc(NbgNs(f7fz(897gNgNnin(8ziNtif7z7=iN(8NbgN9gsgNy(bN8cyiN8iNf(gNn(8isN
Kc(N  áUN y(N bgN s(f7fz(897gN gN nin(8ziN 8(Hgz7=iN (8N bgNn7fngN 9gsgN y(bN
8cyiGN
N
QGQGOGUN NNNNNNNNNNN08N gtimifN f7ntb(fN mN (8N tc8zifN y(N 78pb()7–8XN (bN s(pc(sxiN tisN
nin(8ziN tif7z7=iN (fzgsvN b7n7zgyiN gN c8N y7vn(zsiN zgbNKc(N (bN =gbisN y(N byN
9gb9cbgyiNf(HM8NbgNÍ(997–8NQGOG Nf(gNn(8isNiN7HcgbNgNN
N
byN`NuÓ8NáNoceNNN]NNNbgN
N
0fzgN9i8y797–8N8iN8(9(f7zgNf(sNfgz7fp(9hgXNf7N(bNs(pc(sxiN(8NbifNgtimifN
z(sn78gNnvfNgbbgNy(NbgNbÁ8(gN9(8zsgbNy(bNgtimiN9i8Nc8NHg89hiN(fzg8ygsNiN
c8Ng89bg/(Nn(9v879iGN
N
08NbgN(9cg97–8Ng8z(s7isNNN
Ó8N \N Óin(8ziN 8in78gbN tsi=7fziN tisN(bNs(pc(sxiNtif7z7=iNy(NbgNf(997–8N
9i8f7y(sgygGNN
ocNN\NN3c(sxgN9iszg8z(Ny(Ny7f(:iN(8NbgNf(997–8N9i8f7y(sgygGN
bgNNN\NN0bN=gbisNngmisN(8zs(NyN–N ONyóGN
N N N N N N N
NN N
QGQGUN N 2DÍAEÍDRDd1N20IN.03C0.,ENAM.MNÓEÓ01ÉEN10PMÉD oEN
N
QGQGUG N NNNNNNNNNNN0bNs(pc(sxiNtisNnin(8ziN8(Hgz7=iN(8Nc8N(b(n(8ziN9i8z78ciNiN(8N
=ibgy7xiNiN(8N9cgbKc7(sN(b(n(8ziNy(Nc8Nt–sz79iXNy(ó(svNg89bgsf(N(8XNiNgN
zsg=jfNy(NbifN(b(n(8zifNy(NgtimiNtisNbi8H7zcy(fNy(Ng89bg/(XNHg89hifNiN
g89bg/(fNn(9v879ifGN0bNs(pc(sxiNKc(Nbb(HgNhgfzgN(bN()zs(niNy(Nc8N=ibgyiN
z(sn78gsvN(8NHg89hiN(fzv8ygsGN
QGQGUGON NNNNNNNNNNN0bN s(pc(sxiN tisN nin(8ziN 8(Hgz7=iN z(8ysvN c8gN bi8H7zcyN y(N
y(fgssibbiNy(8zsiNy(bNzsgniXN9cntb7(8yiN9i8NbgfNÍ(997i8(fNQG NmNQGQG G5GN
N
QGQGUGUN NNNNNNNNNNNAisNbiNn(8ifNc8Nz(s97iNy(bNs(pc(sxiNzizgbNtisNpb()7–8N(8N(bNgtimiN
f(N()z(8y(svNc8gNbi8H7zcyXNnvfNgbbvNy(bNtc8ziNy(N78pb()7–8XNngmisNiN7HcgbN
gbNt(sgbz(N(p(9z7=iXN ONyóN–N á VNy(NbgNbcxNy(bNzsgniXN(bNKc(Nf(gNngmisGN
N
8.9    EMPALMES EN EL REFUERZO N
N
QGJG N NN IifN s(pc(sxifN f(N y(ó(sv8N (ntgbngsN ts(p(s(8z(n(8z(N (8N xi8gfN y(N
(fpc(sxifNóg/ifGNo(sNÍ(997i8(fN4G  G G5NmN  GUGOGN
N
QGJGON NN IifN(ntgbn(fNy(ó(sv8Nhg9(sf(Nf–biN9iniNbiNs(Kc7(sg8NiNt(sn7zg8NbifN
tbg8ifNy(Ny7f(:iNiNbgfN(ft(97p79g97i8(fNzj9879gfNiN9iniNbiNgczis79(N(bN
D8ft(9zisGN
N

55.   SSN
QGJGUN N IifN(ntgbn(fNtiysv8Nf(sNy(Ny7p(s(8z(fNz7tifNNN
geN AisNzsgfbgt(GN
óeN AisNfibygycsgGN
9eN AisNc87i8(fNn(9v879gfGN
 
8.10    EMPALME POR TRASLAPE N
N
QG LG NNN IgfN ógssgfN (ntgbngygfN tisN n(y7iN y(N zsgfbgt(fN f78N 9i8zg9ziN (8N
(b(n(8zifN fc/(zifN gN pb()7–8XN 8iN y(ó(sv8N (fzgsN f(tgsgygfN
zsg8f=(sfgbn(8z(NnvfNy(N áSNy(NbgNbi8H7zcyNy(Nzsgfbgt(Ns(Kc(s7ygXN87NnvfN
y(N SN9nGN
N
QG LGONNN IifN zsgfbgt(fN y(N ógssgfN Kc(N pisng8N tgKc(z(fN y(ó(sv8N ógfgsf(N (8N bgN
bi8H7zcyNy(Nzsgfbgt(Ns(Kc(s7ygNtgsgNbgfNógssgfN78y7=7ycgb(fXNgcn(8zgygN
(8NOLRNtgsgNtgKc(z(fNy(NUNógssgfNmN(8NUURNtgsgNtgKc(z(fNy(N5NógssgfGN
IifN zsgfbgt(fN y(N bgfN ógssgfN 78y7=7ycgb(fN y(8zsiN y(Nc8N tgKc(z(N 8iN
y(ó(sv8N9i7897y7sNy(8zsiNy(Nc8gNn7fngNbi8H7zcyNy(Nzsgfbgt(GN
N
8.11     EMPALMES TRASLAPADOS DE BARRAS CORRUGADAS SU JETAS 
A TRACCIÓN 
N
QG  G NNN IgNbi8H7zcyNnÁ87ngNy(bNzsgfbgt(N(8NbifN(ntgbn(fNzsgfbgtgyifN(8Nzsg997–8N
f(svN9i8pisn(NgNbifNs(Kc7f7zifNy(NbifN(ntgbn(fNy(8in78gyifNz7tiNÑNiN
z7tiNRXNt(siN8c89gNn(8isNgNULN9nNN
0ntgbn(Nz7tiNNÑNNNNNNNNNb(NN\NN XUNbyN
0ntgbn(Nz7tiNNRNNNNNNNNNb(NN\NN X4NbyN
yi8y(Nb(N(fNbgNbi8H7zcyNy(bN(ntgbn(NmNbyN(fNbgNbi8H7zcyNy(Ny(fgssibbiN(8N
zsg997–8GN
N
QG  GONNNNNNNNNNNNNIifN (ntgbn(fN (8N xi8gfN y(N (fpc(sxifN gbzifN y(ó(8N ts(p(s(8z(n(8z(N
(=7zgsf(PN f78N (nógsHiXN f7N pc(sg8N (fzs79zgn(8z(N 8(9(fgs7ifN mN f(N
(ntgbngsgNn(8ifNy(NbgNn7zgyNy(NbgfNógssgfNy(8zsiNy(Nc8gNbi8H7zcyNb(XN
f(Ny(ó(sv8NcfgsN(ntgbn(fNÉ7tiNÑGNÍ7Nf(N(ntgbngsgNnvfNy(NbgNn7zgyN
y(NbgfNógssgfNy(8zsiNy(Nc8gNbi8H7zcyNb(XNf(Ny(ó(svNcfgsN(ntgbn(fNÉ7tiN
RGN
 
8.12     EMPALMES TRASLAPADOS DE BARRAS CORRUGADAS SU JETAS 
A COMPRESIÓN 
 
NIgN bi8H7zcyN nÁ87ngN y(N c8N (ntgbn(N zsgfbgtgyiN (8N 9ints(f7–8N f(svN bgN
bi8H7zcyN y(N y(fgssibbiN (8N 9ints(f7–8N 78y79gygN g8z(s7isn(8z(XN t(siN 8iN
f(svNn(8isNgNLXLL4NpmNyóN87NgNULN9nGNAgsgN9i89s(zifN9i8NpW9Nn(8isNy(N
O LNaHá9n
O
XNbgNbi8H7zcyNy(N(ntgbn(Nf(svN789s(n(8zgygN(8Nc8Nz(s97iGN
N
8.13    EMPALMES POR SOLDADURA N
N
QG UG NNN IifN(ntgbn(fNfibygyifNy(ó(sv8Ny(fgssibbgsNtisNbiNn(8ifN(bN OSRNy(NbgN
s(f7fz(897gNgNbgNpbc(897gNupmeNy(NbgfNógssgfGN
N
QG UGONNN IifN(ntgbn(fNfibygyifNy(ó(sv8N9cntb7sN9i8NbiN78y79gyiN(8NbgNÍ(997–8N

56.   SVN
UG5GONmNy(ó(sv8N9i8zgsN9i8NbgNgtsióg97–8Ny(bND8H(87(siNAsim(9z7fzgNmNy(bN
D8ft(9zisGN
N
8.14    EMPALMES POR UNIONES MECANICAS N
N
QG 5G NNN C8N (ntgbn(N tisN c87–8N n(9v879gN y(ó(svN y(fgssibbgsN (8N zsg997–8N iN
9ints(f7–8XNf(HM8Nf(Ns(Kc7(sgXNtisNbiNn(8ifNc8N OSRNy(NbgNs(f7fz(897gN
gNbgNpbc(897gNupmeNy(NbgNógssgGN
N
QG 5GONNN IifN(ntgbn(fNtisNc87i8(fNn(9v879gfNy(ó(sv8Ncfgsf(Nf–biN9cg8yiNf(N
(ntb((8Ny7ftif7z7=ifN9i8Ntgz(8z(fNy(ó7ygn(8z(NtsiógygfNiN9cg8yiNf(N
ióz(8Hg8Ns(fcbzgyifNfgz7fpg9zis7ifN(8Ntsc(ógfNy(ó7ygn(8z(N=(s7p79gygfN
tisN(bND8ft(9zisNmNgtsiógygfNtisN(bND8H(87(siNAsim(9z7fzgGN
N
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
PARTE 4 - REQUISITOS GENERALES 
 
CAPÍTULO 9 - REQUISITOS GENERALES PARA EL ANÁLISIS  Y DISEÑO 
 
9.1    MÉTODOS DE DISEÑO N
N
JG G N NN 08N(bNy7f(:iNy(N9i89s(ziNgsngyiXNbifN(b(n(8zifNy(ó(sv8Ntsitis97i8gsf(N
tgsgNc8gNs(f7fz(897gNgy(9cgygNy(Ng9c(syiNgNbgfNy7ftif797i8(fNy(N(fzgN
1isngXNcz7b7xg8yiNbifNpg9zis(fNy(N9gsHgNmNbifNpg9zis(fNy(Ns(yc997–8Ny(N
s(f7fz(897gN(ft(97p79gyifN(8NbgfNÍ(997i8(fN LGONmN LGUGN
N
9.2    CARGAS N
N

57.   S4N
JGOG N NN IgfN9gsHgfNy(Nf(s=797iN9cntb7sv8N9i8NbiN(fz7tcbgyiN(8NbgN1isngN0GLOLN
RgsHgfNmNbgN1isngN0GLULN27f(:iNÍ7fniss(f7fz(8z(GN
N
JGOGON N IgfN9gsHgfNy(NHsg=(ygyNf(Ntiysv8N9inó78gsNy(Ng9c(syiNgNbiNf7Hc7(8z(NN
N
geN IgN9gsHgNnc(szgNgtb79gygNfiós(NziyifNbifNzsgnifXN9i8NbgNzizgb7ygyN
y(NbgN9gsHgN=7=gNgtb79gygNf7ncbzv8(gn(8z(N(8NziyifNbifNzsgnifGN
óeN IgN9gsHgNnc(szgNgtb79gygNfiós(NziyifNbifNzsgnifN9i8NbgNzizgb7ygyN
y(NbgN9gsHgN=7=gNgtb79gygN(8NyifNzsgnifNgymg9(8z(fGN
9eN IgN9gsHgNnc(szgNgtb79gygNfiós(NziyifNbifNzsgnifN9i8NbgNzizgb7ygyN
y(NbgN9gsHgN=7=gN(8NzsgnifNgbz(s8ifGN
N
9.3  MÉTODOS DE ANÁLISIS 
 
JGUG N N N N N N N ÉiyifN bifN (b(n(8zifN y(N t–sz79ifN iN 9i8fzsc997i8(fN 9i8z78cgfN y(ó(sv8N
y7f(:gsf(N (8N ógf(N gN bifN (p(9zifN upc(sxgfN mN nin(8zifeN Kc(N f(N
y(z(sn78(8NtisNn(y7iNy(bNg8vb7f7fNfcti87(8yiN9intiszgn7(8ziN(bvfz79iN
y(bNngz(s7gbXNfgb=iNKc(Nf(Ncf(8NnjziyifNf7ntb7p79gyifNy(Ng8vb7f7fNiNf(N
niy7p7Kc(8NbifNnin(8zifNy(Npb()7–8Ny(Ng9c(syiNgNbgNf(997–8NJGVG 
N
JGUGON N ÓrÉE2EN20NIEÍNRE03DRD01É0ÍN
 
AgsgN(bNy7f(:iNy(N=7HgfN9i8z78cgfNmNy(NbifgfNgsngygfN(8Nc8gNy7s(997–8N
u8iN ts(fpisxgygfeXN f(N tiysv8N cz7b7xgsN tgsgN (bN g8vb7f7fN y(N 9gsHgfN tisN
Hsg=(ygyN bifN nin(8zifN mN pc(sxgfN 9iszg8z(N Kc(N f(N ióz7(8(8N 9i8N bgN
gtb79g97–8Ny(bNÓjziyiNÍ7ntb7p79gyiNy(NRi(p797(8z(fNf7(nts(NmN9cg8yiNf(N
9cntbg8NbgfNf7Hc7(8z(fN9i8y797i8(fNN
N
geN 0)7fz(8NyifNiNnvfNzsgnifN
óeN IifN zsgnifN fi8N gtsi)7ngygn(8z(N 7Hcgb(fXN f78N Kc(NbgN ngmisNy(N
yifNbc9(fNgymg9(8z(fN()9(ygN(8NnvfNy(NOLRNgNbgNn(8isGN
9eN IgfN9gsHgfN(fzv8Nc87pisn(n(8z(Ny7fzs7óc7ygfGN
yeN IgN9gsHgN=7=gN8iN()9(y(NgNzs(fN=(9(fNbgN9gsHgNnc(szgGN
(eN IifN(b(n(8zifNfi8Nts7fnvz79ifGN
N
N
N
Óin(8ziNtif7z7=iNN
N
08NzsgnifN()zs(nifNN
N
0)zs(niNy7f9i8z78ciN8iN(ntizsgyiNNNNNNNNNNNNNNNNNNNNNXcNNb8
O
NNáN  N
N
0)zs(niNy7f9i8z78ciNni8ibÁz79iN9i8N(bNgtimiNNNNNXcNNb8
O
NNáN 5N
N
NNNNN08NzsgnifN78z(s7is(fNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNXcNNb8
O
NNáN VN
N
N
Óin(8ziN8(Hgz7=iN(8NbgN9gsgN()z(s7isNy(bNts7n(sNgtimiN78z(s7isNN
N

58.   SQN
2ifNzsgnifNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNXcNNb8
O
NNáNNJN
N
ÓvfNy(NyifNzsgnifNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNXcNNb8
O
NNáN LN
N
Óin(8ziN8(Hgz7=iN(8NbgfNy(nvfN9gsgfNy(NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN
gtimifN78z(s7is(fNNNNNNNNNNNNNNNNNNNNNNNNNNNNNXcNNb>
O
NNáN  N
N
N N N
Momento negativo en las cara de todos los apoyos para: 
N
IifgfN9i8Nbc9(fNKc(N8iN()9(yg8Ny(NUNnNiN=7HgfN(8N
Kc(NbgNsgx–8Ny(NbgNfcngNy(Ns7H7y(9(fNy(NbgfN9ibcnkN
8gfNgNbgNs7H7y(xNy(NbgN=7HgNf(gNngmisNgNQN(8N9gygN
()zs(niNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN NNXcNNb8
O
NNáN ON
N
Óin(8ziN8(Hgz7=iN(8NbgN9gsgN78z(s7isNy(bNgtimiN()z(s7isNtgsgN(b(n(8zifN
9i8fzsc7yifNni8ibÁz79gn(8z(N9i8NfcfNgtimifNN
N
Rcg8yiN(bNgtimiN(fNc8gN=7HgNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNXcNNb8
O
NNáNO5N
N
Rcg8yiN(bNgtimiN(fNc8gN9ibcn8gNNNNNNNNNNNNNNNNNNNNNNNNNNNXcNNb8
O
NNáN VN
N
3c(sxgN9iszg8z(NN
N
RgsgN()z(s7isNy(bNts7n(sNgtimiN78z(s7isNNNNNNNNNNNNNNNN X SNNXcNNb8NNáNONN
N
RgsgfNy(NziyifNbifNy(nvfNgtimifNNNNNNNNNNNNNNNNNNNNNNNNNNNXcNNb8NNáNON
N
N
N
N0bN =gbisN y(N b8N bgN bcxN b7ós(N tgsgN (bN 9vb9cbiN y(N bifN nin(8zifN tif7z7=ifN mN
pc(sxgfN 9iszg8z(fXN mN (bN tsin(y7iN y(N bgfN bc9(fN b7ós(fN y(N bifN zsgnifN
gymg9(8z(fNtgsgN(bN9vb9cbiNy(NbifNnin(8zifN8(Hgz7=ifGN
N
N
N
N
9.4N N RIGIDEZ Y MÓDULO DE ELASTICIDAD 
N
JG5G N N N N N N N N AiysvN gyitzgsf(N 9cgbKc7(sN fctif797–8N sgxi8gób(N tgsgN (bN 9vb9cbiN y(N bgfN
s7H7y(9(fNs(bgz7=gfNgNpb()7–8NmNgNzisf7–8Ny(N9ibcn8gfXNncsifNmNf7fz(ngfN
y(N t7fifN mN z(9hifGN IgfN fctif797i8(fN Kc(N f(N hgHg8N y(ó(sv8N f(sN
9i8f7fz(8z(fN(8NziyiN(bNg8vb7f7fGN
N
JG5GON N AgsgN9i89s(zifNy(Nt(fiN8isngbXN(bNn–ycbiNy(N(bgfz797ygyNtiysvNzingsf(N
9iniNN
N
N N N N N N 09N\N SNLLLNNuNpW9Ne
 áONN
NNuaHá9n
O
-
N N
N N
JG5GUN N 0bNn–ycbiNy(N(bgfz797ygyNy(bNg9(siNf(NtiysvN9i8f7y(sgsN9iniNN

59.   (α
α
α α α α α α  .α\αβα<αρ]
=
ααααα+*=K?3
β
-α
α
)<)<α α  7α 3EC:71α C8α 870./5?5C0Cα  .α A020α /8>C1>8.α C8α A28.4:82F1α .82Bα
C8/8235>0C1α38C50>/8α8>.0;1.α1α.82Bα.:35>5./20C1αA12α87α40H25?0>/8)α
 
9.5    LUCES PARA EL CÁLCULO Y MOMENTOS PARA EL DISEÑ O 
α
)()ρα α  7α?B7?:71αC8α71.α3138>/1.0α?12/0>/8.0α25=5C8?8.α;αC8478<51>8.α.8αI02Bα
?1>α70.α.5=:58>/8.α7:?8.Nα
α
0-α ±020α87838>/1.α>1α?1>./2:5C1.α31>17@/5?038>/8α?1>α71.α0A1;1.0α
.8α?1>.5C8202Bα70α7:Fα75H28α3B.α87αA8207/8αC87α87838>/10αA821α>1α
3B.α9:8α70αC5./0>?50α8>/28α?8>/21.αC8α71.α0A1;1.)α
H-α ±020α 87838>/1.α C8α AE2/5?1.α 1α ?1>./2:??51>8.α ?1>/5>:0.0α .8α
?1>.5C8202Bα70α7:Fα?8>/21α0α?8>/21αC8α71.α0A1;1.)α
α α α
)()βα α  >αAE2/5?1.α1α8>α=8>8207α8>α87838>/1.α?1>./2:5C1.α31>17@/5?038>/8α?1>α
71.α0A1;1.0α.8αA1C2B>α:.02α71.α3138>/1.α8>α70.α?020.αC8α71.α0A1;1.)α
α
)()1α α Σ0.α 71.0.α .E75C0.α 1α >82L0C0.α 31>17@/5?0.α ?1>α .:.α 0A1;1.0α ?1>α 7:?8.α
75H28.α 38>128.α 1α 5=:078.α 0α 1α 3α A1C2B>α .82α 0>075F0C0.α ?131α 71.0.α
?1>/5>:0.α?1>α7:?8.α5=:078.α0α70.α7:?8.α75H28.0αC8.A28?50>C1α87α0>?I1αC8α
70.αL5=0.)α
α
9.6  REDISTRIBUCIÓN  DE  MOMENTOS  NEGATIVOS  EN  ELEMENT OS 
CONTINUOS SUJETOS A FLEXIÓN 
 
)=)ρα  <?8A/1α ?:0>C1α.8α83A788>αL07128.α0A21<530C1.αA020α71.α3138>/1.0α
71.α3138>/1.α>8=0/5L1.α?07?:70C1.αA12α38C51αC8α70α/81250α87B./5?0α8>α71.α
0A1;1.α C8α 87838>/1.α ?1>/5>:1.α .:68/1.α 0α 478<5E>0α A020α ?:079:582α
C5./25H:?5E>α.:A:8./0αC8α?02=0.0α.8αA:8C8>α0:38>/02α1αC5.35>:52α8>α>1α
3B.αC8αNα
α
β]αiραeαf+ρeαρYα-αKαρHgαjααα+8>αA12?8>/068-α
α α α α α
)=)βα Σ1.α3138>/1.α>8=0/5L1.α0.@α31C545?0C1.αC8H82B>α:.02.8αA020α?07?:702α
71.α3138>/1.α8>α1/20.α.8??51>8.αC87α87838>/1)α
α
)=)1α Σ0α28C5./25H:?5E>αC8α71.α3138>/1.α>8=0/5L1.αA1C2BαI0?82.8α.E71α?:0>C1α
70α.8??5E>α8>α70α?:07α.8α28C:?8α87α3138>/10α.8αC5.8D8αC8α/07α30>820α
9:8αρααEαα+ρJρW-αα.80α38>12α1α5=:07α0αα]0(αρH0αC1>C8Nα
α
Hαα\ααf+])γ(αβρα4Y?-αKα4;αgα<αf=]]]αKα+α=]]]α]α4;α-gαα
α α
9.7  CONSIDERACIONES PARA EL ANÁLISIS DE COLUMNAS 
α
)×)ρα Σ0.α?17:3>0.αC8H82B>α.82αC5.8D0C0.αA020α28.5./52α70.α4:82F0.α0<5078.αC8α
/1C1.α71.αA5.1.α;α/8?I1α;α87α3138>/1α3B<531αC8H5C1α0α70α?02=0α0?/:0>/8α
8>α .E71α :>1α C8α 71.α /2031.α 0C;0?8>/8.α 8>α 87α A5.1α 1α /8?I1α 8>α

60.   VLN
9i8f7y(sg97–8GNÉgnó7j8Ny(ó(svN9i8f7y(sgsf(NbgN9i8y797–8Ny(N9gsHgNKc(N
tsitis97i8(NbgNnv)7ngNs(bg97–8Ny(Nnin(8ziNgN9gsHgNg)7gbGN
N
JG4GON 08Nt–sz79ifNmN(b(n(8zifN9i8z78cifXNy(ó(svNzingsf(N(8N9c(8zgN(bN(p(9ziN
y(NbgfN9gsHgfN8iNógbg89(gygfN(8NbifN8cyifNmNbgN9gsHgN()9j8zs79gNy(ó7ygN
gNizsgfN9gcfgfXNzg8ziN(8NbgfN9ibcn8gfN()z(s7is(fN9iniN(8NbgfN78z(s7is(fGN
N
JG4GUN MbN 9gb9cbgsf(N bifN nin(8zifN (8N bgfN 9ibcn8gfN y(ó7yiN gN 9gsHgfN y(N
Hsg=(ygyXN bifN ()zs(nifN b(/g8ifN y(N bgfN 9ibcn8gfN 9i8fzsc7yifN
ni8ibÁz79gn(8z(N9i8NbgN(fzsc9zcsgNtiysv8N9i8f7y(sgsf(N(ntizsgyifGN
N
JG4G5N 0bN nin(8ziN (8N 9cgbKc7(sN 8cyiN y(ó(svN y7fzs7óc7sf(N (8zs(N bgfN 9ibcn8gfN
78n(y7gzgn(8z(Ngss7ógNmNgóg/iNy(bN(8zs(t7fiN(8NpisngNtsitis97i8gbNgNbgfN
s7H7y(9(fNs(bgz7=gfNy(NbgN9ibcn8gGN
 
9.8    CONSIDERACIONES PARA EL ANALISIS DE VIGAS T 
N
JGQG N 08NbgN9i8fzsc997–8Ny(N=7HgfNÉXN(bNgbgNmN(bNgbngNy(ó(sv8Nf(sN9i8fzsc7ygfN
ni8ibÁz79gn(8z(NiNz(8(sNc8gN9i8()7–8N(p(9z7=gGN
N
JGQGON 0bNg89hiN(p(9z7=iNy(NbgNbifgNKc(Ng9zMgN9iniNgbgNy(Nc8gN=7HgNÉNf(svNN
geN Ó(8isNiN7HcgbNgNbgN9cgszgNtgsz(Ny(NbgNbi8H7zcyNy(NbgN=7HgGN
óeN Ó(8isNiN7HcgbNgbNg89hiNy(bNgbngNnvfNi9hiN=(9(fN(bN(ft(fisNy(NbgN
bifgXNgN9gygNbgyiNy(bNgbngGN
9eN Ó(8isN iN 7HcgbN gbN g89hiN y(bN gbngN nvfN bgN y7fzg897gN b7ós(N gN bgN
f7Hc7(8z(NgbngXNgN9gygNbgyiNy(bNgbngGN
N
JGQGUN N AgsgN=7HgfNKc(Nz(8Hg8NbifgNgNc8NfibiNbgyiXN(bNg89hiN(p(9z7=iNy(NbgNbifgN
Kc(Ng9zMgN9iniNgbgNy(ó(svN(=gbcgsf(N(8Nógf(NgNbifNf7Hc7(8z(fNbÁn7z(fNN
geN Ó(8isN iN 7HcgbN gbN g89hiN y(bN gbngN nvfN bgN yi9(g=gN tgsz(N y(N bgN
bi8H7zcyNy(NbgN=7HgGN
óeN Ó(8isNiN7HcgbNgbNg89hiNy(bNgbngNnvfNf(7fN=(9(fN(bN(ft(fisNy(NbgN
bifgGN
9eN Ó(8isNiN7HcgbNgbNg89hiNy(bNgbngNnvfNbgNn7zgyNy(NbgNy7fzg897gNb7ós(N
gNbgNf7Hc7(8z(NgbngGN
N
JGQG5N NNNNNNNNNNN08N=7HgfNg7fbgygfN(8NKc(Nf(Ncz7b79(NbgNpisngNÉNtgsgNtsitis97i8gsNc8Nvs(gN
gy797i8gbN(8N9ints(f7–8XN(bNgbgNy(ó(svNz(8(sNc8N(ft(fisNngmisNiN7HcgbNgN
bgNn7zgyNy(bNg89hiNy(bNgbngNmN(bNg89hiN(p(9z7=iN8iN()9(y(svNy(N9cgzsiN
=(9(fN(bNg89hiNy(bNgbngGN
N N
JGQGSNNNNNNNNN Rcg8yiN (bN s(pc(sxiN ts7897tgbN tisN pb()7–8N y(Nc8gNbifgNKc(Nf(N9i8f7y(s(N
9iniNgbgNy(Nc8gN=7HgNÉNu()9bcm(8yiNbgfNbifgfN8(s=gygfeNf(gNtgsgb(biNgN
bgN =7HgXN y(ó(svN tsitis97i8gsf(N s(pc(sxiN t(st(8y79cbgsN gN bgN =7HgN (8N bgN
tgsz(Nfct(s7isNy(NbgNbifgNy(Ng9c(syiNgNbiNf7Hc7(8z(NN
N
geN 0bNs(pc(sxiNzsg8f=(sfgbNy(ó(svNy7f(:gsf(NtgsgNs(f7fz7sNbgN9gsHgNKc(N
g9zMgN fiós(N bgN tis97–8N 9i8f7y(sgygN 9iniN gbgN fcti87(8yiN Kc(N
zsgóg/gN9iniN=ibgy7xiGN
AgsgN =7HgfN g7fbgygfN y(ó(svN 9i8f7y(sgsf(N (bN g89hiN zizgbN y(bN gbgGN

61.   V N
AgsgNizsifNz7tifNy(N=7HgfNÉNf–biN(fN8(9(fgs7iN9i8f7y(sgsN(bNg89hiN
(p(9z7=iNy(bNgbgGN
óeN 0bN(ftg97gn7(8ziNy(bNs(pc(sxiNzsg8f=(sfgbN8iNy(ó(svN()9(y(sNy(NSN
=(9(fN(bNt(sgbz(Ny(NbgNbifgN87Ny(N5SN9nGN
N
9.9    CONSIDERACIONES PARA EL ANÁLISIS DE LOSAS NERV ADAS 
N
JGJG N IgNbifgN8(s=gygNf(N9inti8(Ny(Nc8gN9inó78g97–8 Nni8ibÁz79gNy(N8(s=7ifN
iN =7Hc(zgfN (ftg97gyifN s(Hcbgsn(8z(N (8N c8gN iN yifN y7s(997i8(fN
t(st(8y79cbgs(fXNmNy(Nc8gNbifgN(8NbgNtgsz(Nfct(s7isGN
N
JGJGON 0bNg89hiNy(NbifN8(s=7ifNiN=7Hc(zgfNf(svN LN9nN9iniNnÁ87niNmN(bNt(sgbz(N
8iN f(svN ngmisN gN zs(fN mN n(y7gN =(9(fN (bN n(8isN g89hiN y(bN 8(s=7iN iN bgN
=7Hc(zgGN
N
JGJGUN 0bN(ftg97gn7(8ziNb7ós(N(8zs(NbifN8(s=7ifNiN=7Hc(zgfNf(svN9iniNnv)7niN4SN
9nGN
N
JGJG5N IgfN bifgfN 8(s=gygfN Kc(N 8iN fgz7fpgHg8N bgfN b7n7zg97i8(fN g8z(s7is(fN
y(ó(sv8Ny7f(:gsf(N9iniNbifgfNmN=7HgfGN
N
JGJGSN 08NbgfNbifgfN8(s=gygfN(8Nc8gNy7s(997–8XN(bNs(pc(sxiNt(st(8y79cbgsNgNbifN
8(s=7ifN iN =7Hc(zgfN y(ó(svN 9cntb7sN 9i8N bifN s(Kc(s7n7(8zifN y(N pb()7–8XN
9i8f7y(sg8yiN9gsHgfN9i89(8zsgygfNf7NbgfNhcó7(sgXNt(siN8iNf(svNn(8isN
Kc(N(bNs(pc(sxiNs(Kc(s7yiNtisNz(nt(sgzcsgNmN9i8zsg997–8GN
N
JGJGVN 0bN(ft(fisNy(NbgNbifgN(8zs(N=7Hc(zgfN8iNf(svNn(8isNgNbgNyi9(g=gNtgsz(N
y(NbgNy7fzg897gNb7ós(N(8zs(N=7Hc(zgfXN87Nn(8isNy(NSN9nGN
N
JGJG4N Rcg8yiN(8NbgNbifgNf(Ns(Kc7(sg8Nyc9zifNiNzcó(sÁgfN(nó(ó7ygfXN(bN(ft(fisN
(8N9cgbKc7(sNtc8ziNy(NjfzgNy(ó(Nf(sXN9cg8yiNn(8ifNOXSN9nNngmisNKc(N
bgN gbzcsgN y(bN yc9ziN iN zcó(sÁgGN Í(N y(ó(sv8N 9i8f7y(sgsN s(pc(sxifN iN
(8fg89h(fN y(N bifN 8(s=7ifN iN =7Hc(zgfN (8N 9gfiN Kc(N (fzifN yc9zifN iN
zcó(sÁgfNgp(9z(8NgNbgNs(f7fz(897gNy(bNf7fz(ngGN
N
JGJGQN IgNs(f7fz(897gNgNbgNpc(sxgN9iszg8z(No9Ntsitis97i8gygNtisN(bN9i89s(ziNy(N
bgfN 8(s=gycsgfN tiysvN f(sN 9i8f7y(sgsN  LRN ngmisN gN bgNts(=7fzgN (8N (bN
RgtÁzcbiN  UN y(N (fzgN 1isngGN My797i8gbn(8z(XN f7N f(N s(Kc7(s(sgXN tiysvN
y7fti8(sf(N gsngycsgN tisN 9isz(N iN hg9(sf(N (8fg89h(fN y(N bifN 8(s=7ifNiN
=7Hc(zgfN(8NbgfNxi8gfN9sÁz79gfGN
 
 
 
 
 
 
 
 
 
 
 

62.   VON
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
CAPÍTULO 10 - REQUISITOS GENERALES DE RESISTENCIA Y  DE SERVICIO 
 
10.1    GENERALIDADES 
N
 LG G N IgfN (fzsc9zcsgfN mN bifN (b(n(8zifN (fzsc9zcsgb(fN y(ó(sv8N y7f(:gsf(N tgsgN
ióz(8(sXN(8NziygfNfcfNf(997i8(fNs(f7fz(897gfNtisNbiNn(8ifN7Hcgb(fNgNbgfN
s(Kc(s7ygfXN 9gb9cbgygfN tgsgN bgfN 9gsHgfN gntb7p79gygfN (8N bgfN
9inó78g97i8(fNKc(Nf(N(fz7tcbg8N(8N(fzgN1isngGN
N
 LG GON IgfN(fzsc9zcsgfNmNbifN(b(n(8zifN(fzsc9zcsgb(fNy(ó(sv8N9cntb7sN9i8NziyifN
bifNy(nvfNs(Kc7f7zifNy(N(fzgN1isngXNtgsgNHgsg8z7xgsNc8N9intiszgn7(8ziN
gy(9cgyiN(8NbifN87=(b(fNy(N9gsHgfNy(Nf(s=797iGN
N
10.2    RESISTENCIA REQUERIDA 
N
 LGOG NN IgN s(f7fz(897gN s(Kc(s7ygN uCeN tgsgN 9gsHgfN nc(szgfN uRÓeXN 9gsHgfN =7=gfN
uRoeNmN9gsHgfNy(Nf7fniNuRÍeXNf(svN9iniNnÁ87niNN
N

63.   =1α
≤αα\ααρ0(αφ,αα]ααρ0γαφα
α
≤αα\ααρ0β(α+αφ,α]αφα±αφ°α-α
α
≤αα\αα]0αφ,αα±ααρ0β(αφ°α
α
 >α70.α?13H5>0?51>8.αC1>C8α.8α5>?7:;0α?02=0.αC8α1αC8α.5.310αC8H82Bα
?1>.5C8202.8α87αL0712α/1/07α;α?821αC8α70α?02=0αL5L0α+φ-αA020αC8/8235>02α70α
3B.α.8L820αC8α70.α?1>C5?51>8.)α
α
ρ])β)βα °5α 8>α 87α C5.8D1α .8α C8H5820>α ?1>.5C8202α ?02=0.α C8α L58>/1α +φ5-0α .8α
2883A70F02Bα8./8αL0712αA12α71.α848?/1.αC87α.5.31α+φ°-α8>α70.α4123:70.α
0>/825128.0α>1α.58>C1α>8?8.0251α?1>.5C820270.α.53:7/B>8038>/8)α
α  >α70.α?13H5>0?51>8.α0>/825128.0αC1>C8α.8α5>?7:;8α?02=0.αC8αL58>/1α1αC8α
.5.310α C8H82Bα ?1>.5C8202.8α 87α L0712α /1/07α ;α ?821α C8α 70α ?02=0α L5L0α +φ-α
A020αC8/8235>02α70α3B.α.8L820αC8α70.α?1>C5?51>8.)α
α α α
ρ])β)1αα °5α 4:820α >8?8.0251α 5>?7:52α 8>α 87α C5.8D1α 87α848?/1α C87α 83A:68α70/8207αC87α
/8228>1α+φ -0α70α28.5./8>?50α289:825C0α+≤-α.82Bα?131α3@>531Nα
α
≤αα\ααρ0(αφ,αα]ααρ0γαφαα]ααρ0γαφ α
α
≤αα\ααρ0(αφ,αα]ααρ0γαφα
α
 >α87α?0.1α8>α9:8α70α?02=0α3:82/0α;K1α?02=0αL5L0α28C:F?0>α87α848?/1αC87α
83A:68α70/82070α.8α:.02BNα
α
≤αα\αα]0αφ,αα]ααρ0γαφ α
α
ρ])β)<α °5α 4:820α >8?8.0251α 5>?7:52α 8>α 87α C5.8D1α 87α 848?/1α C8α ?02=0.α C8H5C0.α 0α
A8.1α ;α A28.5E>α C8α 7@9:5C1.α ?1>α C8>.5C0C8.α H58>α C845>5C0.α ;α 07/:20.α
?1>/2170C0.0αC5?I0.α?02=0.αA1C2B>α/8>82α:>α40?/12αC8αρ0(α;α0=28=02.8α8>α
/1C0.α70.α?13H5>0?51>8.α9:8α5>?7:;8>α?02=0αL5L0)α
α
ρ])β)(α °5α4:820α>8?8.0251α5>?7:52α8>α87αC5.8D1α87α848?/1αC8α?02=0.αC8α53A0?/10α
G./0.αC8H82B>α5>?7:52.8α8>α70α?02=0αL5L0α+φ-)α
α
ρ])β)=α °5α 4:820α >8?8.0251α 5>?7:52α 87α 848?/1α +φ≥-α C8α 71.α 0.8>/0358>/1.α
C54828>?5078.0α 47:8>?500α ?1>/20??5E>α 1α ?03H51.α C8α /83A820/:200α 70α
28.5./8>?50α289:825C0αC8H82Bα.82Bα?131α3@>531Nα
α
≤αα\ααρ0β(α+αφ,α]αφ≥α]αφα-α
α
≤αα\ααρ0(αφ,αα]ααρ0(αφ≥α
α
αΣ0.α 8./530?51>8.α C8α 71.α 0.8>/0358>/1.α C54828>?5078.0α 70α 47:8>?500α 70αα
47:8>?500α70α?1>/20??5E>α1α71.α?03H51.αC8α/83A820/:20αC8H8>αH0.02.8α8>α
:>0α C8/8235>0?5E>α 28075./0α C8α /078.α 848?/1.α C:20>/8α 87α .82L5?51α C8α 70α
8./2:?/:20)α
α

64.   =<α
10.3    RESISTENCIA DE DISEÑO 
α
ρ])1)ραα Σ0α 28.5./8>?50α C8α C5.8D1α A21A12?51>0C0α A12α:>α 87838>/10α .:.α
?1>8<51>8.α ?1>α 1/21.α 87838>/1.α ;α .:.α .8??51>8.α /20>.L82.078.0α 8>α
/G235>1.αC8α478<5E>0α?02=0α0<5070α?12/8α;α/12.5E>αC8H82Bα/1302.8α?131α70α
28.5./8>?50α>135>07α+28.5./8>?50αA21A12?51>0C0α?1>.5C820>C1α87α284:82F1α
280738>/8α ?171?0C1-0α ?07?:70C0α C8α 0?:82C1α ?1>α 71.α 289:5.5/1.α ;α
.:A1.5?51>8.αC8α8./0α[12300α3:7/5A75?0C0αA12α:>α40?/12αC8α28C:??5E>αC8α
28.5./8>?50αφ)α
α
ρ])1)βαα  7α40?/12αC8α28C:??5E>αC8α28.5./8>?50αFα.82BN 
ρ-α ±020α478<5E>α.5>α?02=0α0<507Nαααααααααααααααααααααααααααααφα\α]0]α
β-α ±020α478<5E>α?1>α?02=0α0<507αC8α/20??5E>Nαααααααααφα\α]0]ααααααααα
1-α ±020α478<5E>α?1>α?02=0α0<507α C8α ?13A28.5E>α ;α A02 0α
?13A28.5E>α.5>α478<5E>Nα
0-α  7838>/1.α?1>α284:82F1α8>α8.A5207Nα αααααφα\α]0×(α
H-α δ/21.α87838>/1.Nααααααααααααααααααααααααααααααααααφα\α]0×]ααα
8<?8A/1α 9:8α A020α L07128.α 28C:?5C1.α C8α ?02=0α 0<5070αFα A:8C8α
5>?2838>/02.8α 75>80738>/8α I0./0αφα \α ]0]0α ?1>41238α 87α L0712α C8α
φ±>αC5.35>:;8αC8.C8α]0ρ]α4W?αΦ=α0α?821)α
φ:0>C1α87αL0712αC8α]0×]α±HαA020α87838>/1.α?1>α8./25H1.αEα]0×(±Hα
A020α 87838>/1.α ?1>α 284:82F1α 8>α 8.A5207α .80α 38>12α 9:8α ]0ρ]α 4Y?α
Φ=-0α8./8αL0712α.82Bα2883A70F0C1αA12α87αC8α]0×]α±HαEα]0×(α±Hα8>α
71α5>C5?0C1α8>α87αAB22041α0>/82512)α
<-α ±020α?12/0>/8α.5>α1α?1>α/12.5E>Nαααααααααααααααααααααααφα\α]0γ(α
(-α ±020α0A70./0358>/1α8>α87α?1>?28/1Nαααααααααααααααααφα\α]0×]α
α
ρ])1)1α Σ0.α71>=5/:C8.αC8αC8.0221771α8.A8?545?0C0.α8>α87αφ0A@/:71αγα>1α289:5828>α
C8α:>α40?/12αφ)α
α
α
10.4    CONTROL DE DEFLEXIONES EN ELEMENTOS ARMADOS E N UNA 
DIRECCIÓN SOMETIDOS A FLEXIÓN 
α
ρ])<)ρ   ± πΦΣ≥ °α,τ[2,δ°α±ΦπΦα[δα π2σ2φΦπαμ σΣ 2δ[ °  
α
ρ])<)ρ)ρα  >α 71.0.α 075=820C0.α ?1>/5>:0.α ?1>41230C0.αA12α L5=:8/0.αC8αρ]α?3αC8α
0>?I10αH719:8.αC8α70C25771αC8α1]α?3αC8α0>?I1α;α71.0α.:A82512αC8α(α?30α
?1>α.1H28?02=0.α38>128.α0α1]]αQ=K3βα;α7:?8.α38>128.αC8α×0(α30αA1C2Bα
C8602αC8αL82545?02.8α70.αC8478<51>8.α?:0>C1α.8α?:3A70α9:8Nα
α
Iαααkααα7αKαβ(α
α
ρ])<)ρ)βα  >α 71.0.α 30?5F0.α ?1>/5>:0.α ?1>α .1H28?02=0.α 38>128.α 0α 1]]α Q=K3βα;α
7:?8.α 38>128.α C8α ×0(α 30α A1C2Bα C8602α C8α L82545?02.8α70.α C8478<51>8.α
?:0>C1α.8α?:3A70α9:8Nα
α
Iαααkααα7αKα1]α
α α α α α α α
ρ])<)ρ)1α  >αL5=0.α9:8α41230>αAE2/5?1.0αA1C2BαC8602αC8αL82545?02.8α70.αC8478<51>8.α

65.   I
?:0>C1I.8I?:3A78I9:8NI
I
Ik7K
I
5 70 L5=0 71.0 075=820C0 1 71.0 30?5F0.8 8>?:8>/20 8> L170C5F1 1
.1H28I 8770I .8I 0A1;0>I 87838>/1.I 9:8I A:8C0>I .82I C0D0C1.I A12I
C8478<51>8.8<?8.5L0..82B>8?8.0251L82545?0270.C8478<51>8.>1.58>C1
0A75?0H78I70.I8<?8A?51>8.I0>/825128.8I
I
$ (III
I
0.C8478<51>8.9:81?:228>5>38C50/038>/8IC8.A:G.IC8I70I0A75?0?5E>I
C870.?02=0.A1C2B>?07?:702.8A1271.3G/1C1.14E23:70.I:.:078.IC87I
0>B75.5.87B./5?1?1>.5C820>C171.848?/1.9:8/58>8>I70I45.:20?5E>I;I87I
284:82F1I.1H28I70I25=5C8FIC87I87838>/18I
I
38>1.9:8.8I0=0:>0>B75.5.3B.?13A78/1I1I9:8I.8IC5.A1>=0IC8I
C0/1.I8<A82538>/078.IA020I8L07:02I70I25=5C8FI0I478<5E>IC87I87838>/1I+´I-
70I C8478<5E>I 5>38C50/0I A020I 87838>/1.I C8I ?1>?28/1I C8I A8.1I >12307I
A1C2BI?07?:702.8I?1>I87I3EC:71IC8I870./5?5C0CIC87I?1>?28/1I8.A8?545?0C1I
8> 70 8??5E> # ; ?1> 87 3138>/1 C8 5>82?50 C8 70I .8??5E>I
/20>.41230C0I 0=258/0C0I +I8- 8<?8A/1 ?:0>C1 87 3138>/1 478?/12 A020
?1>C5?51>8.IC8I.82L5?51I8>I?:079:582I.8??5E>IC87I87838>/1I>1I8<?8C0IC87I
3138>/1C80=258/0358>/1+?2-A1C2B:.02.8873138>/1IC8I5>82?50I
C8I70I.8??5E>I>1I0=258/0C0I+I=-8I
I
7 3138>/1 C8 0=258/0358>/1 .8 ?07?:702B ?131I .8I 5>C5?0I 0I
?1>/5>:0?5E>NI
?2\42I=IIKII /I
I
=1C2BI/1302.8INIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
42II\IIlI+I4W?I-
-Kl
IIIIIIIIII
73138>/1C85>82?50C870.8??5E>/20>.41230C0I0=258/0C0I+I8-IA1C2BI
?07?:702.8I?131I.8I5>C5?0I0I?1>/5>:0?5E>NI
I
0-I =020I 87838>/1.I C8I .8??5E>I 28?/0>=:702I .5>I 284:82F1I 8>I
?13A28.5E>NI
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
I8III\III+HI?

K-]>.+CJ?-
lI
I I I I
IC1>C8I?I8.I70IC5./0>?50IC8I70I45H20I3B.I?13A2535C0I07I868I>8:/21I;I
A:8C8I8L07:02.8I?1>.5C820>C1I9:8NI
I I I I I IIIIIII
+HI?
l
IIKIl-III\III>I .I+CIJI?-I
I I I I
I I H-I =020I:>0I.8??5E>I28?/0>=:702IC1H7838>/8I28412F 0C0NI
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
I8III\III+HI?

K-]>.+CJ?-
l
II]II+l>IeI--I Y.I+?IeICY-
lI
I
I I I C1>C8I?IA:8C8I8L07:02.8I?1>.5C820>C1I9:8INI

66.   ==α
α α α α α ααααααα
+Hα?
β
ααKαβ-αα]αα+β>αJαρ-αΦY.α+?αeαCY-αα\αα>αΦ.α+CαJα?-α
α α α
α α ?-α  >α 87838>/1.α ?1>/5>:1.α C8α .8??5E>α ?1>./0>/80α 87α 3138>/1α C8α
5>82?50α9:8α.8α:/575?8αA020α?07?:702α70.αC8478<51>8.α.82Bα:>αL0712α
A2138C51α?07?:70C1αC8α0?:82C1α0αNα
α
I8αA2138C51αα\ααα+ααI8ραα]ααI8βαα]ααβαI81αα-ααKαα<α
α α α α α
C1>C8αI8ρα ;αI8βα .1>α 71.α 3138>/1.α C8α 5>82?50α 8>α 70.α .8??51>8.α
8</2830.αC87α/2031α;αI81α8.α87α3138>/1αC8α5>82?50αC8α70α.8??5E>α
?8>/207αC87α/2031)α
α
°5α87α/2031α.E71α8.α?1>/5>:1α8>α:>α8</28310α87α3138>/1αC8α5>82?50α
A2138C51α.8α?07?:702Bα?1>Nα
α
I8αA2138C51αα\ααα+ααI8βαα]ααβαI81αα-ααKαα1α
α α α α
α α C-α ±020α87838>/1.α.53A7838>/8α0A1;0C1.α8>α03H1.α8 </2831.0α.8α
:.02Bα87α3138>/1αC8α5>82?50α?07?:70C1αA020α70α.8??5E>α?8>/207)α
α
α α 8-α ±020α 87838>/1.α 8>α L170C5F1α .8α :.02Bα 87α 3138>/1 α C8α 5>82?50α
?07?:70C1αA020α70α.8??5E>α8>α87α0A1;1αC87αL170C5F1)α
α
ρ])<)1αα φΣφ≤Σδαμ αΣΦ°αμ σΣ 2δ[ °αμ2σ π2μΦ°α
α
ρ])<)1)ρα Σ0αC8478<5E>αC54825C0α1α0C5?51>07α8>α87α/583A10α28.:7/0>/8αC87α47:61αA7B./5?1α
C87α?1>?28/1α;αC8α70α?1>/20??5E>αC8α420=:0C1αC8α71.α87838>/1.α8>α478<5E>0α
A1C2Bα 8./5302.8α 3:7/5A75?0>C1α 70α C8478<5E>α 5>38C50/0α ?0:.0C0α A12α 70.α
?02=0.α.1./8>5C0.α+?02=0α3:82/0α;α70αA12?5E>αC8α?02=0αL5L0α9:8α.8αA28LGα
0?/:02BαA8230>8>/838>/8-αA12α87α40?/12ατα9:8α.8α1H/58>8αA12Nα
α
τααα\ααασααKαα+ρα]α(]αρY-α
α
C1>C8αρWα8.α70α?:0>/@0αC87α0?821α8>α?13A28.5E>α+Aα\αΦY.KHC-α8>α87α?8>/21α
C87α/2031αA020α87838>/1.α.53A78.α1α?1>/5>:1.α;α8>α70α.8??5E>αC8α0A1;1α
A020α87838>/1.α8>αL170C5F1)α
 7α 40?/12α σα C8A8>C8α C87α /583A1α 8>α 9:8α .8α C8.88α 8L07:02α 70α C8478<5E>α
C54825C0α;αA1C2Bα/1302.8Nα
σαα\ααρ0]ααααααααα+α1α38.8.α-α
σαα\ααρ0βααααααααα+α=α38.8.α-α
σαα\ααρ0<αααααααα+αρβα38.8.α-α
σαα\ααβ0]ααααα+α(α0D1.α1α3B.α-α
α
ρ])<)<   μ σΣ 2δ[ °α,2,Φ°α± π,2°2+Σ °  
α
ρ])<)<)ρα Σ0αC8478<5E>α/1/07α.82Bα70α.:30αC8α70αC8478<5E>α5>38C50/0α;α70αC8478<5E>α
C54825C0)α
α
ρ])<)<)βα α α α α α α α Σ0α C8478<5E>α ?07?:70C0α C8α 0?:82C1α ?1>α 70.α .8??51>8.α 0>/825128.α >1α

67.   =×α
C8H82Bα8<?8C82α71.αL07128.α5>C5?0C1.α8>α70α≥0H70αρ])<)<)β) 
 
10.5  CONTROL DE DEFLEXIONES EN ELEMENTOS ARMADOS EN  DOS 
DIRECCIONES SOMETIDOS A FLEXIÓN (NO PRESFORZADOS) 
 
 7αA8207/8α3@>531αC8α71.0.α0230C0.α8>αC1.αC528??51>8.α9:8α/8>=0>α:>0α
2870?5E>αC8α/2031α702=1α0α/2031α?12/1α>1α30;12αC8αβαC8H82Bα?07?:702.8α
?1>α70.α.5=:58>/8.α8?:0?51>8.αNα
ρ-ααα
I\αf7>αα+αγ]]α]α]0]×ρα4;α-gααKαi1=]]]α]α(]]]αβ[α3αeα]0(α+ραJαβ.-α+ρα]αρKβ-gjα
α
α α A821α>1α38>12α9:8Nα
α
α α β-ααα
α α Iα\ααf7>αα+αγ]]α]α]0]×ρα4;α-gαKαf1=]]]α]α(]]]αβ+ρα]αβ.-gα
α
ΦC83B.0α87αA8207/8α>1α>8?8.5/02Bα.82α30;12α9:8αNα
α α 1-α
α α I\αf7>αα+αγ]]α]α]0]×ρα4;α-gαKα1=]]]α
α
C1>C8αNα
β  \ααααπ870?5E>αC8α7:Fα75H28α30;12α0α7:Fα75H28α38>12)α
β.α α\α α π870?5E>α C8α 70α 71>=5/:Cα C8α 71.α H12C8.α ?1>/5>:1.α 07α
A82@38/21α/1/07αC8α:>αA0D1αC8α71.0)α
α α α\ααααπ870?5E>αC8α70α25=5C8Fα0α478<5E>αC8α70α.8??5E>αC8α70αL5=0α
0α 70α 25=5C8Fα 0α 478<5E>α C8α :>α 0>?I1α C8α 71.0α 7535/0C1α
70/820738>/8α A12α 70.α 7@>80.α ?8>/2078.α C8α 71.α A0D1.α
0C;0?8>/8.α8>α?0C0α70C1αC8α70αL5=0)α
α3α \ααααα±2138C51αC8α71.αL07128.αC8αaα8>α/1C1α87αA82@38/21αC87α
A0D1)α±020α71.0.α.5>αL5=0.0α/1302αα3\])α
α
ΦC5?51>0738>/8αC8H82B>α?:3A752.8α71.α.5=:58>/8.α3@>531.Nα
α
0-α Σ1.0.α.5>αL5=0.α>5αBH0?1.NααααααααααααααααααααααααααIα≥αρβ0(α?3α
α
H-α Σ1.0.α.5>αL5=0.α?1>αBH0?1.NααααααααααααααααααααααααIα≥ααρ]αα?3α
α
?-α Σ1.0.α?1>αL5=0.α8>α<αH12C8.0α?1>αα3≥βNαααααIαkααα?3α
α
0α 38>1.α 9:8α .8α C83:8./28α A12α 87α ?B7?:71α 9:8α 70.α C8478<51>8.α >1α
8<?8C8>α 71.α 7@35/8.α 8./5A:70C1.α 8>α 70α ≥0H70α ρ])<)<)βα 5>C5?0C0α A020α
87838>/1.α8>α:>0αC528??5E>)α
α
TABLA 10.4.4.2 
 DEFLEXIONES MÁXIMAS PERMISIBLES 
 
≥2±δαμ α Σ , [≥δα
α
μ σΣ 2>[α
φδ[°2μ πΦμΦα
μ σΣ 2>[αΣτ,2≥ α
α
≥8?I1.αA70>1.α9:8α>1α.1A12/8>α
α
α
α
α

68.   F
>5F8./G>F75=0C1.F0F87838>/1.F>1F
8./2:?/:2078.F.:.?8A/5H78.FC8F
.:4252FC0D1.FA12FC8478<51>8.F
8<?8.5L0.F
F
F
8478<5E>5>./0>/B>80C8H5C0070
?02=0L5L0
F
K+UU-
F
l5.1.F9:8F>1F.1A12/8>F>5FF8./G>F
75=0C1.F0F87838>/1.F>1F
8./2:?/:2078.F.:.?8A/5H78.FC8F
.:4252FFC0D1.FA12FC8478<51>8.F
8<?8.5L0.
F
F
F
8478<5E>5>./0>/B>80C8H5C0070
?02=0L5L0
F
F
F
K
F
l5.1F1F/8?I1.F9:8F.1A12/8>F1F
8./G>F75=0C1.F0F87838>/1.F>1F
8./2:?/:2078.F.:.?8A/5H78.FC8FF
.:4252FC0D1.FA12FC8478<51>8.F
8<?8.5L0.F
F
F
F
K+UUU-
F
l5.1.F1F/8?I1.F9:8F.1A12/8>F1F
8./G>F75=0C1.F0F87838>/1.F>1F
8./2:?/:2078.F>1F.:.?8A/5H78.FC8F
.:4252FC0D1.FA12FC8478<51>8.F
8<?8.5L0.
F
F
F
F
0FA02/8FC8F70FC8478<5E>F/1/07F9:8F
1?:228FC8.A:G.FC8F70F:>5E>FC8FFF
71.F87838>/1.F>1F8./2:?/:2078.F+70F
.:30FC8F70FC8478<5E>FC54825C0F
C8H5C0F0F/1C0.F70.F?02=0.F
.1./8>5C0.F;F70FC8478<5E>F
5>38C50/0FC8H5C0F0F?:079:582F
?02=0L5L00C5?51>07-
+FUF-F
F
F
F
K+UUUU-
F
C1>C8FF\F:FFC8F?B7?:71F/07F?131F.8F78FC845>8F8>F708??5E>#
F
+U- 0. C8478<51>8. C54825C0. .8 A1C2B> 28C:?52 .8=M>F 70F ?0>/5C0CF C8F 70F
C8478<5E>F9:8F1?:220F0>/8.FC8F:>52F71.F87838>/1.F>18./2:?/:2078../0
?0>/5C0C .8 C8/8235>02B H0.B>C1.8 8> 71. C0/1. C8 I>=8>582@0F
0?8A/0H78.F ?1>F 2870?5E>F 0F 70.F ?020?/82@./5?0.F /583A1JC841230?5E>F C8F
87838>/1.F.5357028.F0F71.F9:8F.8F8./B>F?1>.5C820>C1
+UU- ./8 7@35/8 >1 /58>8 A12 1H68/1 ?1>./5/:52.8 8>F :>F 28.=:02C1F ?1>/20F 87F
8./0>?0358>/1C80=:0.719:8.8C8H8L82545?0238C50>/8F?B7?:71.FC8F
C8478<51>8. 0C8?:0C1. 5>?7:;8>C170.C8478<51>8.0C5?51>078.FC8H5C0.F
07FFA8.1FC87F0=:0F8./0>?0C0F;F?1>.5C820>C1F71.F848?/1.F0F702=1FA70F1FC8F
/1C0. 70. ?02=0. .1./8>5C0. 70 ?1>/20478?I0 70. /17820>?50.F C8F
?1>./2:??5E>F;F70F?1>450H575C0CF8>F70.FA28L5.51>8.FA02087C28>068
F
+UUU- ./8 7@35/8 .8 A1C2B 8<?8C82 .5 .8 /130> 38C5C0.F 0C8?:0C0.F A020F
A28L8>52C0D1.8>87838>/1.0A1;0C1.1:>5C1.
F
+UUUU-F l821F >1F 30;12F 9:8F 70F /17820>?50F 8./0H78?5C0FA020F 71.F 87838>/1.F >1F
8./2:?/:2078. ./8 7@35/8 .8 A1C2B 8<?8C82 .5 .8 A21A12?51>0F :>0F
?1>/20478?I0F C8F 31C1F 9:8F 70F C8478<5E>F /1/07F 38>1.F 70F ?1>/20478?I0F >1F
8<?8C0C5?I17@35/8
 
 

69.   =α
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
PARTE 5 - DISEÑO 
 
CAPÍTULO 11 – FLEXIÓN 
α
11.1    ALCANCE 
α
Σ0.αC5.A1.5?51>8.αC8α8./8α?0A@/:71α.8α0A75?02B>α07αC5.8D1αC8α87838>/1.α
?131α L5=0.0α 71.0.0α 3:21.α C8α ?1>/8>?5E>0α 8.?07820.α ;0α 8>α =8>82070α
?:079:582α87838>/1α.138/5C1α0α478<5E>0α8<?8A/1α9:8αA020αL5=0.αC8α=20>α
A8207/80αF0A0/0.α;α71.0.α0230C0.α8>αC1.αC528??51>8.α.8αC8H82Bα?:3A752α
?1>α71α8./5A:70C1α8>α71.αφ0A@/:71.α28.A8?/5L1.)α
α
 7α C5.8D1α C8α 70.α .8??51>8.α /20>.L82.078.α C8α 71.α 87838>/1.α .:68/1.α 0α
478<5E>αC8H82BαH0.02.8α8>α70α8<A28.5E>Nα
α
,:αα≤ααφα,>α
C1>C8αNα
,:αα8.α70α28.5./8>?50α289:825C0αA12α478<5E>α8>α70α.8??5E>α0>075F0C0)α
,>αα8.α70α28.5./8>?50α>135>07α0α70α478<5E>αC8α70α.8??5E>)α
 
11.2    HIPÓTESIS DE DISEÑO 

70.   ×]α
α
ρρ)β)ραα  7α C5.8D1α A12α 28.5./8>?50α C8α 87838>/1.α .:68/1.α 0α 478<5E>α C8H82Bα
.0/5.40?82α 70.α ?1>C5?51>8.α C8α 89:575H251α ;α ?13A0/5H575C0Cα C8α
C841230?51>8.)αΦC83B.αC8H82BαH0.02.8α8>α70.α.5=:58>/8.αI5AE/8.5.Nα
α
0-α Σ0.αC841230?51>8.α8>α87α284:82F1α;α8>α87α?1>?28/1α.8α.:A1>C2B>α
C528?/038>/8αA21A12?51>078.α0α70αC5./0>?50α07α868α>8:/21)α
H-α  <5./8α0CI828>?50α8>/28α87α0?821α;α87α?1>?28/1α9:8α70αC841230?5E>α
C87α0?821α8.α5=:07α0α70αC87α?1>?28/1α0C;0?8>/8)α
?-α Σ0α3B<530αC841230?5E>α:/575F0H78αC87α?1>?28/1α8>α70α45H20α8</2830α
0α?13A28.5E>α.8α.:A1>C2Bα5=:07α0α]0]]1)α
C-α  7α 8.4:82F1α 8>α 87α 284:82F1α C8H82Bα /1302.8α ?131α  .α L8?8.α 70α
C841230?5E>α C87α 0?8210α A821α A020α C841230?51>8.α 30;128.α 0α 70.α
?1228.A1>C58>/8.α0α4;0α87α8.4:82F1α.8α?1>.5C8202Bα5>C8A8>C58>/8α
C8α70αC841230?5E>α8α5=:07α0α4;)α
8-α Σ0α28.5./8>?50α0α/20??5E>αC87α?1>?28/1α>1α.82Bα?1>.5C820C0α8>α71.α
?B7?:71.)α
4-α  7αC50=2030α8.4:82F1JC841230?5E>αA020α70αF1>0αC8α8.4:82F1.αC8α
?13A28.5E>αC87α?1>?28/1α.8αA:8C8αC845>52α?131Nα
Jα ≤>α8.4:82F1αC8α]0γ(α4W?0α9:8α.8α.:A1>C2Bα:>54123838>/8α
C5./25H:5C1α 8>α :>0α F1>0α89:5L078>/8αC8α?13A28.5E>α8>α87α
?1>?28/10α7535/0C0αA12α71.αH12C8.αC8α70α.8??5E>α/20>.L82.07α
;α:>0α7@>80α28?/0αA0207870α07α868α>8:/210α0α:>0αC5./0>?50αα0α\α
βρ?α C8α 70α 45H20α C8α C841230?5E>α :>5/0250α 3B<530α 8>α
?13A28.5E>)α
Jα Σ0α C5./0>?50α ?0α C8.C8α 70α 45H20α C8α C841230?5E>α :>5/0250α
3B<530α07α868α>8:/21α.8α38C52Bα8>αC528??5E>αA82A8>C5?:702α
0αC5?I1α868)α
Jα  7α40?/12αβραC8H82Bα/1302.8α?131α]0γ(αA020α28.5./8>?50.α
C8α ?1>?28/1α 4W?α I0./0α C8α βγ]α *=K?3
β
)α ±020α 28.5./8>?50.α
.:A825128.α 0α βγ]α *=K?3
β
0αβρα C5.35>:52Bα 0α 20FE>α C8α ]0](α
A12α ?0C0α ×]α *=K?3
β
α C8α 0:38>/1α C8α 4W?0α ?1>α :>α L0712α
3@>531αC8α]0=()α
 
11.3    DISPOSICIONES ESPECIALES PARA ELEMENTOS RESIS TENTES A 
FUERZAS DE SISMO 
α
ρρ)1)ραα Σ0.α C5.A1.5?51>8.α C8α 8./0α °8??5E>α .1>α 0A75?0H78.α 0α 87838>/1.α
.138/5C1.α0α478<5E>α9:8αC8H0>α28.5./52α4:82F0.αC8α.5.310α;α8>α70.α?:078.α
70.α 4:82F0.α C8α C5.8D1α 2870?51>0C0.α ?1>α 71.α 848?/1.α[email protected]?1.α I0>α .5C1α
C8/8235>0C0.α8>αH0.8α0α70α?0A0?5C0CαC8α70α8./2:?/:20αC8αC5.5A02α8>82=@0α
8>α87α20>=1α5>87B./5?1αC8α28.A:8./0α+28C:??5E>αA12αC:?/575C0C-)α >α8./8α
=2:A1α .8α 8>?:8>/20>α 70.α L5=0.α 9:8α 41230>α AE2/5?1.α ?1>α ?17:3>0.α 1α
A70?0.)α
α
ρρ)1)βαα Σ0.αL5=0.α9:8αC8H0>α28.5./52α4:82F0.αC8α.5.31α?:3A752B>α?1>α71α5>C5?0C1α
8>α8./0α.8??5E>αA020α71α284828>/8α07α284:82F1α71>=5/:C5>070α8>α87αφ0A@/:71α
ρ1α A020α 71α 284828>/8α 07α 284:82F1α /20>.L82.07α ;α 8>α 87α φ0A@/:71α γα A020α 71α
284828>/8α07αC8.0221771α;α83A0738.αC87α284:82F1)α
α

71.   4 N
kN IgNs(f7fz(897gN(ft(97p79gygNy(bN9i89s(ziNupW9eN8iNf(svNn(8isNKc(N
O LNaHá9n
O
NGN
kN IgN9gb7ygyNy(bNg9(siNy(Ns(pc(sxiN8iN()9(y(svNy(NbiN(ft(97p79gyiN
tgsgNg9(siNHsgyiNM.1N5OLNu5 5NÓAgNiN5OLLNaHá9n
O
eGN
kN IgNs(bg97–8Ng89hiNgNt(sgbz(Ny(NbgfN=7HgfN8iNy(ó(svNf(sNn(8isNKc(N
LXUGN
kN 0bNt(sgbz(N(p(9z7=iNuyeNy(ó(svNf(sNn(8isNiN7HcgbNKc(Nc8N9cgsziNy(N
bgNbcxNb7ós(GN
kN 0bNg89hiNy(NbgfN=7HgfN8iNf(svNn(8isNKc(NOSN9nXN87NngmisNKc(N(bN
g89hiN y(N bgN 9ibcn8gN y(N gtimiN un(y7ygN (8N c8N tbg8iN
t(st(8y79cbgsNgbN(/(Ny(NbgN=7HgeNnvfNUá5Ny(bNt(sgbz(Ny(NbgN=7HgNgN
9gygNbgyiGN
kN IgN 9gsHgN g)7gbN uAceN 8iN y(ó(svN ()9(y(sN y(N LX N pW9NMHGN 08N 9gfiN
9i8zsgs7iXN (bN (b(n(8ziN y(ó(svN zsgzgsf(N 9iniN (b(n(8ziN (8N
pb()i9ints(f7–8GN
kN 1iN y(ó(sv8N hg9(sf(N (ntgbn(fN zsgfbgtgyifN iN fibygyifN (8N (bN
s(pc(sxiNgNc8gNy7fzg897gNSySNiNn(8isNy(NbgfN9gsgfNy(NbifN8cyifGN
kN IifN(ntgbn(fNzsgfbgtgyifNy(bNs(pc(sxiN(8Nxi8gfNy(N78=(sf7–8Ny(N
(fpc(sxifN y(ó(sv8N Kc(ygsN 9i8p78gyifN tisN (fzs7óifN 9(ssgyifN
(ftg97gyifN gN 8iN nvfN y(N  VN =(9(fN (bN y7vn(zsiN y(N bgfNógssgfN
bi8H7zcy78gb(fXNf78N()9(y(sNULN9nGN
 
11.4    REFUERZO MÁXIMO EN ELEMENTOS SUJETOS A FLEXIÓ N 
N
08N (b(n(8zifN fc/(zifN gN pb()7–8XN (bN tis9(8zg/(N y(N s(pc(sxiN tNN
tsitis97i8gyiN8iNy(ó(svN()9(y(sNy(NLX4SNtóXNyi8y(NtóN(fN(bNtis9(8zg/(N
y(Ns(pc(sxiNKc(Ntsiyc9(NbgN9i8y797–8Nógbg89(gygXN=(sNbgNÍ(997–8NJGVGUGN
08N(b(n(8zifN9i8Ns(pc(sxiN(8N9ints(f7–8XNbgNtis97–8Ny(NtóN(Kc7b7ósgygN
tisN (bN s(pc(sxiN (8N 9ints(f7–8N 8iN y(ó(svN s(yc97sf(N n(y7g8z(N (bN pg9zisN
LX4SGN
N
AgsgNbgNs(y7fzs7óc97–8Ny(Nnin(8zifXNNt –NutNeNtYeN8iNy(ó(svN()9(y(sNy(N
LXSNtóGN
 
11.5    REFUERZO MÍNIMO EN ELEMENTOS SUJETOS A FLEXIÓ N 
N
  GSG N 08N 9cgbKc7(sN f(997–8N y(N c8N (b(n(8ziN fin(z7yiN gN pb()7–8XN ()9(tziN
xgtgzgfNmNbifgfXNyi8y(NtisN(bNg8vb7f7fNf(Ns(Kc7(sgNs(pc(sxiNy(Ng9(siXN(bN
vs(gN y(N g9(siN Kc(N f(N tsitis97i8(N f(svN bgN 8(9(fgs7gNtgsgN Kc(N (bN
nin(8ziN s(f7fz(8z(N y(N bgN f(997–8N f(gN tisN biN n(8ifN  XSN =(9(fN (bN
nin(8ziNy(NgHs7(zgn7(8ziNy(NbgNf(997–8N8iNgHs7(zgygNÓ9sXNyi8y(NN
N
Ó9sNN\NNpsNDHNáN-zNNNNNNNNNNXNNNNNNNNNNNpsN\NONuNpY9Ne
 áO
NN
NN
  GSGONN 0bN vs(gN nÁ87ngN y(N s(pc(sxiN y(N f(997i8(fN s(9zg8Hcbgs(fXN tiysvN
9gb9cbgsf(N9i8NN
N
Mf
3@>NN\NiNfNLX4NuNpY9e
 áON
gNNáNNpmNjNuóNyeN
N N NNNNNNNNNNNNNNN N N NNNNN
  GSGUNNNNNNNNNNNMbz(s8gz7=gn(8z(XN(bNvs(gNy(Ns(pc(sxiNtif7z7=iNiN8(Hgz7=iN(8N9gygNf(997–8N

72.   4ON
y(bN(b(n(8ziXNy(ó(svNf(sNtisNbiNn(8ifNc8Nz(s97iNngmisNKc(NbgNs(Kc(s7ygN
tisN(bNg8vb7f7fGN
N
  GSG5NN N 08NbifgfXN(bNvs(gNnÁ87ngNy(bNs(pc(sxiN9cntb7svNbiN78y79gyiN(8NbgNÍ(997–8N
4G LXNz(87(8yiN(8N9c(8zgNgy797i8gbn(8z(N(bNs(pc(sxiN(8NbgN9gsgN78p(s7isNy(N
bifgfN gsngygfN (8N yifN y7s(997i8(fN unin(8ziN tif7z7=ieN mN (8N bgN 9gsgN
fct(s7isN (8N (bN 9gfiN y(N =ibgy7xifN f(svN 9iniN nÁ87niN LXLL ON óN hXN (fz(N
s(pc(sxiN f(N y7fti8ysvN 9i8N (bN (ftg97gn7(8ziN nv)7niN 78y79gyiN (8N bgN
Í(997–8N4GVGNN
 
11.6    DISTANCIA  ENTRE  APOYOS  LATERALES  DE  ELEMENTOS  
SUJETOS A FLEXIÓN (PANDEO LATERAL) 
N
IgNf(tgsg97–8N(8zs(NgtimifNbgz(sgb(fNy(Nc8gN=7HgN8iNy(ó(svN()9(y(sNy(N
SLN=(9(fN(bNg89hiNn(8isNóNy(bNgbgNiNbgN9gsgN(8N9ints(f7–8GN
N
11.7    DISTRIBUCIÓN DEL REFUERZO POR FLEXIÓN EN VIGA S Y LOSAS 
EN UNA DIRECCIÓN. CONTROL DE FISURACIÓN 
N
  G4G N  P010.MID2M20Í 
N
N N 0fzgNÍ(997–8N(fzgób(9(NbifNs(Kc7f7zifNtgsgNbgNy7fzs7óc97–8Ny(bNs(pc(sxiNy(N
pb()7–8XN9i8N(bNp78Ny(Nb7n7zgsN(bNgHs7(zgn7(8ziNtisNpb()7–8N(8N=7HgfNmNbifgfN
gsngygfN(8Nc8gNy7s(997–8GN
N N N
IgfN y7ftif797i8(fN y(N (fzgN f(997–8N fi8N gtb79gób(fN gN(b(n(8zifN 8iN
()tc(fzifNgNc8Ngnó7(8z(NgHs(f7=iNmN8iN7nt(sn(gób(fGN08N9gfiN9i8zsgs7iN
y(ó(sv8Nzingsf(Nts(9gc97i8(fN(ft(97gb(fNtgsgN9i8zsibgsNbgNp7fcsg97–8GN
N
N
N
  G4GO   2DÍÉ.DÑCRDd1N20IN.03C0.,E  
N
  G4GOG N 0bNs(pc(sxiNy(Nzsg997–8NtisNpb()7–8Ny(ó(svNy7fzs7óc7sf(Ngy(9cgygn(8z(N(8N
bgfN xi8gfN y(N zsg997i8(fN nv)7ngfN y(N c8N (b(n(8ziXN y(NzgbN niyiN y(N
ióz(8(sNc8N=gbisN,Nn(8isNiN7HcgbNgNU NLLLNaHá9nNtgsgN9i8y797i8(fNy(N
()tif797–8N78z(s7isNmNn(8isNiN7HcgbNgNOVNLLLNaHá9nNtgsgN9i8y797i8(fNy(N
()tif797–8N()z(s7isGN
0bN=gbisN,Nf(N9gb9cbgsvNn(y7g8z(NbgN()ts(f7–8NN
N
,NN\NNpfNNuNy9NMYNe
 áUN
NNNNNNNNNNNNNNNNNNNNNNNNNN N NNNN N NNNN
N N 0bN(fpc(sxiN(8N(bNg9(siNpfNtc(y(N(fz7ngsf(N9i8NbgN()ts(f7–8NÓNáNuLGJNyN
MfeXNuÓN(fN(bNnin(8ziNpb(9zisN(8N9i8y797i8(fNy(Nf(s=797ieNiNfcti8(sf(N
7HcgbNgNLXVNpmGN
N
  G4GOGON Rcg8yiN bgfN gbgfN y(N bgfN =7HgfN ÉN (fzj8N fc/(zgfN gN zsg997–8XN tgsz(N y(bN
s(pc(sxiN y(N zsg997–8N tisN pb()7–8N y(ó(svN y7fzs7óc7sf(N fiós(N (bN g89hiN
(p(9z7=iNy(bNgbgNy(Ng9c(syiNgNbiN(ft(97p79gyiN(8NbgNÍ(997–8NJGQN–N(8Nc8N
g89hiN7HcgbNgN á LNy(NbgNbcxNy(bNzsgniXN(bNKc(Nf(gNn(8isGN

73.   ×1α
α
ρρ)×)β)1α °5α87αA8207/8αC87α0730α8<?8C8αC8α]α?30α.8αC8H82Bα?171?02α?82?0αC8α70.α
?020.αC87α0730α:>α284:82F1α71>=5/:C5>07α?:;0αB280α.80αA12α71α38>1.α5=:07α
0α ρ]Rα C87α B280α C8α 284:82F1α C8α /20??5E>α A12α 478<5E>)α  ./8α 284:82F1α .8α
C5./25H:52Bα8>α70αF1>0αC8α/20??5E>αA12α478<5E>α?1>α:>α8.A0?50358>/1α9:8α
>1α8<?8C0αC8α1]α?3α1α87α0>?I1αC87α0730)α
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
CAPÍTULO 12 - FLEXOCOMPRESIÓN 
 
12.1    ALCANCES 
α
α α Σ0.αC5.A1.5?51>8.αC8α8./8αφ0A@/:71α.8α0A75?02B>α07αC5.8D1αC8α87838>/1.α
.138/5C1.α0α478<5E>α;α?02=0.α0<5070α?131α.1>α?17:3>0.0α3:21.αC8α?12/80α
3:21.α C8α .E/0>10α ;α 8>α =8>8207α ?:079:582α 87838>/1α .138/5C1α 0α
478<1?13A28.5E>)α
α
12.2    HIPOTESIS DE DISEÑO 
α
Σ0.α I5AE/8.5.α C8α C5.8D1α A020α 87838>/1.α 8>α 478<1?13A28.5E>α .1>α 70.α
5>C5?0C0.α8>α87αφ0A@/:71αρραJασ78<5E>)α
α
12.3    PRINCIPIOS Y REQUISITOS GENERALES 
α
ρβ)1)ραα  >α 87838>/1.α .:68/1.α 0α 478<1?13A28.5E>α ?1>α?02=0.α C8α C5.8D1α αφα ±>α
38>128.α0αα]0ρ]α4W?αΦ=ααEααφα±Hαα+70α38>12-0α87αA12?8>/068αC8α284:82F1α
3B<531αA21A12?51>0C1αC8H82Bα?:3A752α?1>α71α5>C5?0C1α8>α87αφ0A@/:71αρρα
Jαασ78<5E>)α
α
ρβ)1)βαα Σ0α 28.5./8>?50α C8α C5.8D1α +φ±>-α C8α 87838>/1.α 8>α ?13A28.5E>α >1α .8α
/1302Bα30;12α9:8Nα
α

74.   ×<α
±020α87838>/1.α?1>α8.A52078.Nα
φ±>α+3B<-αα\αα]0γ(αφαfα]0γ(α4W?α+αΦ=αeαΦ./α-α]αΦ./α4;αgα
±020α87838>/1.α?1>α8./25H1.Nα
φ±>α+3B<-αα\αα]0γ]αφαfα]0γ(α4W?α+αΦ=αeαΦ./α-α]αΦ./α4;αgα
α
ρβ)1)1αα ≥1C0α .8??5E>α .:68/0α 0α 478<1?13A28.5E>α .8α C5.8D02Bα A020α 87α 3138>/1α
3B<531α9:8αA:8C8α0?/:02α?1>αC5?I0α?02=0)α
α α α α α α α α α α
ρβ)1)<αα Σ0α?02=0α0<507αM7/530α±:αA020α:>0α8<?8>/25?5C0CαC0C0α>1αC8H82Bα8<?8C82α
C8αφ±>α+3B<-)αα 7α3138>/1α,:αC8H82Bα03A7545?02.8αA020α?1>/83A702α71.α
848?/1.αC8α8.H87/8F)α
α
ρβ)1)(αα ±020α87αC5.8D1αC8α?17:3>0.αC8H82Bα0C83B.α?:3A752.8α?1>α71α8./5A:70C1α
8>α87αφ0A@/:71α×αJαμ8/0778αC87απ84:82F1)α
 
12.4    DISPOSICIONES  ESPECIALES  PARA  COLUMNAS  SUJETA S  A 
FLEXOCOMPRESIÓN QUE RESISTAN FUERZAS DE SISMO 
α
ρβ)<)ραα Σ0.αC5.A1.5?51>8.αC8α8./0α°8??5E>α.1>α0A75?0H78.α07αC5.8D1αC8α?17:3>0.α
.138/5C0.α0α478<1?13A28.5E>α9:8αC8H0>α28.5./52α4:82F0.αC8α.5.31α;α8>α
70.α?:078.α70.α4:82F0.αC8αC5.8D1α2870?51>0C0.α?1>α71.α848?/1.α[email protected]?1.α
.8αI0>αC8/8235>0C1α8>αH0.8α0α70α?0A0?5C0CαC8α70α8./2:?/:20αC8αC5.5A02α
8>82=@0α8>α87α20>=1α5>87B./5?1αC8α28.A:8./0α+28C:??5E>αA12αC:?/575C0C-)α
α
ρβ)<)βαα Σ1.α289:5.5/1.αC8α8./0α°8??5E>α.1>α0A75?0H78.α.5α70α?02=0αC8αC5.8D1αφ±>α
8<?8C8αC8α]0ρα4_?αΦ=αEαφ±Hα+70α38>12-)α >α?0.1α?1>/202510α87α87838>/1α
C8H82Bα?:3A752α71.α289:5.5/1.αA020α87838>/1.α8>α478<5E>Nα
α
Jα Σ0α28.5./8>?50α8.A8?545?0C0αC87α?1>?28/1α+4W?-α>1α.82Bα38>12α9:8α
βρ]αQ=K?3β)α
Jα Σ0α?075C0CαC87α0?821αC8α284:82F1α>1α8<?8C82BαC8α71α8.A8?545?0C1α
A020α0?821α=20C1αΦπ[α<β]α+<ρ<α,±0αEα<β]]αQ=K?3β-)α
Jα  7α0>?I1α3@>531αC8α70.α?17:3>0.α.82BαC8αβ(α?3)α
Jα Σ0α 2870?5E>α C8α 70α C538>.5E>α 38>12α 0α 70α 30;12α C8α 70α .8??5E>α
/20>.L82.07αC8α70α?17:3>0α>1α.82Bα38>12α9:8α]0<)α
Jα Σ0α?:0>/@0αC8α284:82F1α71>=5/:C5>07α+r-α>1α.82Bα38>12α9:8α]0]ρα>5α
30;12α9:8α]0]=)αφ:0>C1α70α?:0>/@0α8<?8C0αC8α]0]<0α71.αA70>1.α
C8H82B>α5>?7:52αC8/0778.α?1>./2:?/5L1.αC8α70α0230C:20α8>α70α:>5E>α
L5=0J?17:3>0)α
α
ρβ)<)1αα Σ0α28.5./8>?50α0α70α478<5E>αC8α70.α?17:3>0.αC8H82Bα.0/5.40?82α70α8?:0?5E>Nα
α
Σα+,>?-ααbααρ0<ααΣα+,>L-α
C1>C8αNα
Σ+,>?-α 8.α 70α .:30α C8α 3138>/1.0α 07α ?8>/21α C87α >:C10α
?1228.A1>C58>/8α 0α 70α 28.5./8>?50α >135>07α 8>α 478<5E>α C8α
70.α ?17:3>0.α 9:8α 41230>α C5?I1α >:C1Pα 8./0α 28.5./8>?50α
8>α478<5E>α.8α?07?:702BαA020α70α4:82F0α0<507α0?/:0>/8α8>α70α
I5AE/8.5.α 9:8α ?1>.5C820α 70.α 4:82F0.α C8α =20L8C0Cα ;α C8α
.5.31α 8>α 70α C528??5E>α ?1>.5C820C00α L82545?0>C1α 70α

75.   ×(α
?1>C5?5E>α9:8αCGα?131α28.:7/0C1α70α28.5./8>?50α0α478<5E>α
3B.αH060)α
α
Σ+,>L-α 8.α 70α .:30α C8α 3138>/1.0α 07α ?8>/21α C87α >:C10α
?1228.A1>C58>/8α0α70.α28.5./8>?50.α>135>078.α8>α478<5E>α
C8α70.αL5=0.α9:8α41230>α87α>:C1)ααΣ0.α28.5./8>?50.α0α70α
478<5E>αC8H82B>α.:302.8αC8α30>820α9:8α71.α3138>/1.α
C8α70α?17:3>0α.8α1A1>=0>α0α71.α3138>/1.αC8α70.αL5=0.)α
α
 ./0α ?1>C5?5E>α C8H82Bα .0/5.40?82.8α 8>α 70.α C1.α C528??51>8.α C8α ?0C0α
?17:3>0)α
α
ρβ)<)<αα Σ1.α 83A0738.α C8α 70α 0230C:20α 71>=5/:C5>07α C8H82B>α ?:3A752α ?1>α 71α
8.A8?545?0C1α8>α70α°8??5E>αγ)ρ])α
α
ρβ)(    DIMENSIONES  DE  DISEÑO  PARA  ELEMENTOS  SUJETOS  A 
COMPRESIÓN  CON  AREA  TRANSVERSAL  MAYOR  A  LA 
REQUERIDA 
α
φ:0>C1α:>α87838>/1α.:68/1α0α?13A28.5E>α/8>=0α:>0α.8??5E>α/20>.L82.07α
30;12α 9:8α 70α 289:825C0α A12α 70.α ?1>.5C820?51>8.α C8α ?02=00α 87α 284:82F1α
3@>531α ;α 70α 28.5./8>?50α M7/5300α A1C2B>α H0.02.8α 8>α :>0α B280α 848?/5L0α
28C:?5C0α+Φ=-α30;12α1α5=:07α0αρKβαC87αB280α/1/07)α
α
α
ρβ)=)ρ)ραLIMITES DEL REFUERZO PARA ELEMENTOS EN COMPRESIÓN 
 
ρβ)=)ραα  7α B280α C8α 284:82F1α 71>=5/:C5>07α A020α 87838>/1.α .:68/1.α 0α ?13A28.5E>α
+?17:3>0.-0α>1αC8H82Bα.82α38>12α9:8α]0]ρα>5α30;12α9:8α]0]=αL8?8.α87α
B280α/1/07αC8α70α.8??5E>)α
α
ρβ)=)βαα  7α 284:82F1α 71>=5/:C5>07α 3@>531α C8H82Bα .82αC8α <α H0220.α C8>/21α C8α
8./25H1.α 28?/0>=:7028.α 1α ?52?:7028.0α 1α H0220.α C8>/21α C8α 8./25H1.α
/250>=:7028.α;α=αH0220.α8>α?0.1α9:8α.8α:.8>α8.A52078.)α
α
ρβ)=)1αα Σ0α?:0>/@0αC87α284:82F1α8>α8.A5207α+r.-α>1αC8H82Bα.82α38>12α9:8α87αL0712α
C0C1αA12Nα
r.αα\αα]0<(α+αΦ=αKαΦ?αeαρα-α4Y?αKα4;α
>5α38>12α9:8αNα
r.αα\αα]0ρβαα4Y?αKα4;αα α α α
α
C1>C8α4;α8.α87α8.4:82F1αC8α47:8>?50α8.A8?545?0C1αC87α0?821αC8α70α8.A52070α
>1α30;12αC8α<β]]αQ=K?3β)α
α
12.7    TRANSMISIÓN  DE  CARGAS  DE  LAS  COLUMNAS  A  TRAVÉ S  DEL 
SISTEMA DE PISOS 
α
α α φ:0>C1α70α28.5./8>?50α0α70α?13A28.5E>α8.A8?545?0C0αC87α?1>?28/1α8>α:>0α
?17:3>0α 8.α ρ0<α L8?8.α 30;12α 9:8α 70α 8.A8?545?0C0α A020α 87α .5./830α C8α
A5.10α 70α /20>.35.5E>α C8α 70α ?02=0α 0α /20LG.α C87α .5./830α C8α A5.1α C8H82Bα

76.   ×=α
71=202.8αC8α:>0αC8α70.α.5=:58>/8.α41230.Nα
α
0-α  7α ?1>?28/1αC8α28.5./8>?50α8.A8?545?0C0αA020α70α?17:3>0αC8H82Bα
L0?502.8α8>α87αA5.1α8>α70α:H5?0?5E>αC8α70α?17:3>0α;α8>α:>αB280α
41230C0α A12α =]α ?3α 0C5?51>078.α 0α ?0C0α 70C1α C8α 70α ?020α C8α 70α
?17:3>0)α
H-α Σ0α28.5./8>?50αC8α70α?17:3>0α0α/20LG.αC87α.5./830αC8αA5.1αC8H82Bα
H0.02.8α 8>α 87α 38>12α L0712α C8α 70α 28.5./8>?50α C87α ?1>?28/10α ?1>α
H0220.αC8α/20>.35.5E>αL82/5?078.α;α8.A52078.α.8=M>α.8α289:5820)α
?-α ±020α?17:3>0.α02251./20C0.α70/820738>/8αA12α71.α<α70C1.α?1>αL5=0.α
C8α:>αA8207/8α?0.5α:>541238α1αA12α71.0.α30?5F0.0α70α28.5./8>?50αC8α
70α ?17:3>0α .8α A:8C8α H0.02α 8>α :>0α 28.5./8>?50α .:A:8./0α C87α
?1>?28/1α8>α70.α6:>/0.αC8α70.α?17:3>0.0α9:8α8.α5=:07α07α×(RαC8α70α
28.5./8>?50α C87α ?1>?28/1α C8α 70α ?17:3>0α 3B.α 87α 1(Rα C8α 70α
28.5./8>?50αC87α?1>?28/1αC87αA5.1)ααααααααααα
 
12.8    RESISTENCIA AL APLASTAMIENTO 
α
ρβ)γ)ρα Σ0α28.5./8>?50αM7/530α07α0A70./0358>/1α>1αC8H82Bα8<?8C82αC8α]0γ(αφα4W?α
Φρ)αφ:0>C1α70α.:A8245?58αC8α0A1;1α.80α3B.α0>?I0α8>α/1C1.α71.α70C1.α
9:8α 87α B280α ?02=0C00α 70α 28.5./8>?50α M7/530α 07α 0A70./0358>/1α 8>α 87α B280α
?02=0C0αA1C2Bα3:7/5A75?02.8αA12NαlΦβαKαΦρ0α.5α8<?8C82αβ)α
α
α
C1>C8αNα
Φρααα\ααΦ280α?02=0C0α
Φβαα\αΦ280αC8α70αH0.8α5>482512αC87α30;12α/21>?1αC8αA52B35C8α1α
?1>1α28?/10α?1>/8>5C1α/1/0738>/8α8>α87α0A1;10α9:8α/8>=0α
?131α H0.8α .:A82512α 87α B280α ?02=0C0α ;α 8>α 87α 9:8α 70α
A8>C58>/8α70/8207α8./Gα8>α20FE>αC8αραL82/5?07α;αβαI125F1>/07)α
α
 ./0α°8??5E>α>1α.8α0A75?0α0α0>?7068.αC8α/8>C1>8.αA1./8>.0C1.)α
α
12.9    FLEXION BIAXIAL 
α
φ:0>C1α 70.α ?17:3>0.α 8./G>α .:68/0.α .53:7/B>8038>/8α 0α 3138>/1.α
478?/128.α8>α.:.αC1.α868.αA25>?5A078.0α87αC5.8D1αC8H82BαI0?82.8α0αA02/52α
C8α70.αI5AE/8.5.αC8α70α°8??5E>αρβ)β)αΦ7/82>0/5L038>/8α.8αA1C2Bα:.02α87α
.5=:58>/8α 3G/1C1α 0A2E<530C1α A020α ?17:3>0.α ?:0C20C0.α Eα
28?/0>=:7028.)α
α
ραKα±:αααα`ααααραKαφ±><ααα]αααραKαφ±>;ααα]αααραKαφ±>1α
C1>C8Nα
±:α 8.α70α28.5./8>?50αM7/530α8>α478<5E>αH50<507)α
φ±><α 8.αα70α28.5./8>?50αC8αC5.8D1αC8α70α?17:3>0αH061α70α0??5E>α
C8α3138>/1αM>5?038>/8α8>ααα+8;α\α]-)α
φ±>;α 8.α70α28.5./8>?50αC8αC5.8D1αC8α70α?17:3>0αH061α70α0??5E>αC8α
3138>/1αM>5?038>/8α8>α8αα+8<α\α]-)α
φ±>1α 8.α70α28.5./8>?50αC8αC5.8D1αA020α70α35.30α?17:3>0αH061α70α
0??5E>αC8α?02=0α0<507αM>5?038>/8αα+8<α\α8;α\α]-)α

77.   ××α
α α α
 ./0α8?:0?5E>α8.αLB75C0αA020αL07128.αC8α±:αKαφα±>1α30;128.α1α5=:078.α0α
]0ρ)α±020αL07128.α38>128.0α.8α:.02Bα70α.5=:58>/8α8<A28.5E>αNα
α
,:<αKαφ,><ααα]ααα,:;αKαφ,>;αααα`ααααρα
α
C1>C8Nα
α
φ,><αα8.α70α28.5./8>?50α8>α478<5E>αC8αC5.8D1α8>αC8α70α.8??5E>α?1>α
28.A8?/1α07α868α)α
φ,>;α 8.α 70α 28.5./8>?50α 8>α 478<5E>α C8α C5.8D1α C8α 70α .8??5E>α ?1>α
28.A8?/1α07α868α8)α
α
12.10  EFECTOS DE ESBELTEZ DE ELEMENTOS A COMPRESION  
α
ρβ)ρ])ρ  √ [ πΦΣ2μΦμ °α
α
ρβ)ρ])ρ)ρα  7α C5.8D1α C8α 87838>/1.α .:68/1.α 0α ?13A28.5E>α C8H82Bα H0.02.8α 8>α :>α
SΦ>B75.5.α C8α °8=:>C1α δ2C8>S0α 8>α 87α ?:07α 70.α 4:82F0.α ;α 71.α 3138>/1.α
5>/82>1.α .8α 1H/8>C2B>α /130>C1α 8>α ?:8>/0α 87α 848?/1α C8α 70.α
C841230?51>8.α.1H28α70.α4:82F0.α5>/82>0.0α70α5>47:8>?50αC8α70α?02=0α0<507α
;α87α3138>/1αC8α5>82?50αL0250H780α70α25=5C8FαC87α87838>/1α;α71.α848?/1.αC8α
70αC:20?5E>αC8α70.α?02=0.)α
α
ρβ)ρ])ρ)βα  >α 7:=02α C87α A21?8C5358>/1α 8./0H78?5C1α 8>α 70α °8??5E>α ρβ)ρ])ρ)ρ0α 71.α
848?/1.αC8α8.H87/8FαA1C2B>α8L07:02.8αC8α0?:82C1α?1>α87αA21?8C5358>/1α
0A21<530C1α9:8α.8αA28.8>/0α8>α70α°8??5E>αρβ)ρ])β)α
α
ρβ)ρ])β   ΦΣ≤Φφ2>[αΦ±πδ2,ΦμΦαμ αΣδ°α σ φ≥δ°αμ α °+ Σ≥ .  
α
±020α/1302α8>α?:8>/0α71.α848?/1.αC8α8.H87/8F0αC8H82B>α?1>.5C8202.8αNα
0-α Σ1.α 848?/1.α =71H078.α +δ=-α 9:8α 048?/8>α 0α 70α 8./2:?/:20α ?131α
?1>6:>/1)α
H-α Σ1.α848?/1.α71?078.α+δl-α9:8α048?/8>α0α?0C0α:>1αC8α71.α87838>/1.α
5>C5L5C:078.)α
 7α3138>/1αC8αC5.8D1αA020α87α87838>/1α.82BNα
α
,?ααα\αααδlα,:Lαα]ααδ=α,:.α
C1>C8Nα
,:LNα α ,138>/1α 8>α 87α 87838>/1α C8H5C1α 0α ?02=0.α L82/5?078.α
03A7545?0C0.0αA21L8>58>/8αC8α:>α0>B75.5.αC8α±25382αδ2C8>)α
,:.Nα α ,138>/1α 8>α 87α 87838>/1α C8H5C1α 0α 70.α ?02=0.α 70/82078.α
03A7545?0C0.0αA21L8>58>/8αC8α:>α0>B75.5.αC8α±25382αδ2C8>)α
α
ρβ)ρ])β)ρα  σ φ≥δ°αΣδφΦΣ °αμ α °+ Σ≥ .  
α
±020α /1302α 8>α ?:8>/0α 71.α 848?/1.α 71?078.α C8α 8.H87/8Fα C8>/21α C8α ?0C0α
?17:3>0α:α1/21α87838>/1α8>α?13A28.5E>α8>α87α?:07α.:.α8</2831.α8./G>α
02251./20C1.α 70/820738>/80α 71.α 3138>/1.α 03A7545?0C1.α 1H/8>5C1.α C8α :>α
0>B75.5.αα87B./5?1αC8α±25382αδ2C8>0αC8H82B>α3:7/5A75?02.8αA12α87α40?/12αδρα

78.   ×γα
?07?:70C1α?1>Nα
α α α α α α
δlααα\αααφ3ααKαα+αραeα±:αKαφ±?α-αααkααρ0]α
C1>C8Nα
βααααααααααααααααααβα
±?ααα\αααπααα αIααKααl>α
α
°5α8<5./8>α?02=0.α70/82078.α8>/28α71.α0A1;1.αC87α87838>/10αφ3α\αρ)α >α
?0.1α?1>/20251αNα
φ3ααα\ααα]0=αα]αα]0<α,ραKα,βαααbααα]0<α
α
ΦC83B.Nα
Iααα\ααα+α ?αI=αKα(αα]αα .αI.8α-ααKαα+αρα]αβCα-α
α
α α 1α?1>.82L0C12038>/8Nα
α
Iααα\ααα ?αI=ααKααKαααfαβ0(α+αρα]αβCα-αgα
α
°5α 71.α ?B7?:71.α 3:8./20>α 9:8α >1α 8<5./8α 3138>/1α 478?/12α 8>α 03H1.α
8</2831.αC8α:>α87838>/10α1α9:8α70.α8<?8>/25?5C0C8.α?07?:70C0.α8>α71.α
8</2831.αC87α87838>/1α.1>α38>128.α9:8α+ρ0(α]α]0]1αI-α8>α?30α,ρα;α,βα
8>α87α?B7?:71αC8αφ3αC8H82B>αH0.02.8α8>α:>0α8<?8>/25?5C0Cα3@>530αC8α
+ρ0(α]α]0]1I-α8>α?30α0728C8C12αC8α?0C0α868αA25>?5A07αA12α.8A020C1)α
α
Σ1.α848?/1.α71?078.αC8α8.H87/8FαA1C2B>α.82αC8.A28?50C1.α.5Nα
α
l>αKα2αααaααα1<ααJααρβα,ραKα,βαα
α
C1>C8Nα
l>Nα Σ1>=5/:Cα>1α0A1;0C0αC87α87838>/1α8>α?13A28.5E>)α±:8C8α
/1302.8α?131α70αC5./0>?50α75H28α8>/28α71.0.αC8α8>/28A5.1.0α
L5=0.α:α1/21.α87838>/1.α?0A0?8.αC8αA21A12?51>02α:>α0A1;1α
70/8207α07α87838>/1α8>α?13A28.5E>)α
φ:0>C1α 8<5./0>α ?02/870.α 1α ?0A5/878.α C8α ?17:3>0.0α 70α
71>=5/:Cαl>α C8H82Bα 38C52.8α 8>α 87α 8</2831α 5>482512α C87α
?0A5/87α1α?02/870α8>α87αA70>1α?1>.5C820C1)α
2Nα π0C51α C8α =521α C8α 70α .8??5E>α /20>.L82.07α C87α 87838>/1α 8>α
?13A28.5E>)α±:8C8α.82α?07?:70C1α0αA02/52αC8α70α.8??5E>α/1/07α
C8α?1>?28/1)α
α
ρβ)ρ])β)β  σ φ≥δ°α√Σδ+ΦΣ °αμ α °+ Σ≥ .  
α
Σ1.α848?/1.α=71H078.αC8α8.H87/8Fα.8αC8H82B>α8L07:02αC8α0?:82C1α0α:>0α
C8α70.α8<A28.51>8.α.5=:58>/8.Nα
α
Φ-ααααααααααααααααααααααααααααααααδ=ααα\αααρααKαα+αραeα∆α-α
α
+-ααααααααααααααααααααααδ=ααα\αααφ3ααKααfαρααJααΣ+±:-αKαφΣ+±?-αg 
α
μ8α0?:82C1α0α71α.5=:58>/8Nα

79.   ×α
α
Φ-α °5α .8α ?1>1?8>α 70.α C841230?51>8.α 70/82078.α C8α 71.α 8>/28A5.1.0α .8α
?07?:702Bαδ=α?1>α70α8<A28.5E>αρβ)ρ])β)βαΦ0αC1>C8Nα
α
∆ααα\αααΣ+±:-α∆:ααKαα+α:αIα-α
α α
∆αNααααααααααατ>C5?8αC8α8./0H575C0CαC87α8>/28A5.1)α
Σ+±:-α Nα α °:30α C8α 70.α ?02=0.α C8α C5.8D10α 3:82/0.α ;α L5L0.α
+?02=0.α C8α .82L5?51α 3:7/5A75?0C0.α A12α 87α 40?/12α C8α
?02=0α ?1228.A1>C58>/8-α 0?:3:70C0.α C8.C8α 87α
8</2831α .:A82512α C87α 8C545?51α I0./0α 87α 8>/28A5.1α
?1>.5C820C1)α
∆:Nα α α α α α α α α μ841230?5E>α 2870/5L0α 8>/28α 87α >5L87α .:A82512α ;α 87α
5>482512α C87α 8>/28A5.1α ?1>.5C820C10α C8H5C1α 0α 70.α
4:82F0.α 70/82078.α 03A7545?0C0.α ;α ?07?:70C0α C8α
0?:82C1α 0α :>α 0>B75.5.α 87B./5?1α C8α ±25382α δ2C8>)α
±020α 87α ?0.1α C8α 4:82F0.α 70/82078.α C8α .5.310α∆:α
C8H82Bα 3:7/5A75?02.8α A12α 87α 40?/12α C8α 28C:??5E>α A12α
C:?/575C0Cα?1>.5C820C1α8>α70αC8/8235>0?5E>αC8α8./0.α
4:82F0.)α
:αNα σ:82F0α?12/0>/8α03A7545?0C0α8>α87α8>/28A5.10αC8H5C0α
0α70.α?02=0.α70/82078.)α
Iα Nα Φ7/:20αC87α8>/28A5.1α?1>.5C820C1)α
α
αμ8α0?:82C1α07α@>C5?8αC8α8./0H575C0C0α71.α8>/28A5.1.α.8α?70.545?02B>α8>Nα
α
0-α °5α 87α @>C5?8α C8α 8./0H575C0Cα ∆α 8.α 38>12α 9:8α ])]=0α .8α A1C2Bα
?1>.5C8202α 9:8α 87α 8>/28A5.1α 8./Bα 02251./20C1α 70/820738>/8α ;α 71.α
848?/1.αα=71H078.αC8α°8=:>C1αδ2C8>α.8αA1C2B>αC8.A28?502α+δ=\ρ-0α
A821α C8H82B>α 0>075F02.8α 71.α 848?/1.α 71?078.α C8α 8.H87/8F)α  7α
3138>/1αC8αC5.8D1αA020α87α87838>/1α.82BNα
α
,?ααα\αααδlα,:Lαα]ααα,:.α
α
αH-α °5α87α@>C5?8αC8α8./0H575C0Cα∆α8./Bα?13A28>C5C1α8>/28α])]=α;α])β(0α
71.α 848?/1.α =71H078.α C8α 8.H87/8Fα C8H82B>α ?1>.5C8202.8α
3:7/5A75?0>C1α/1C1.α71.α3138>/1.α478?/128.αC8αL5=0.α;α?17:3>0.α
A21C:?5C0.α A12α 70.α ?02=0.α 70/82078.α 03A7545?0C0.α ;α1H/8>5C1.α
38C50>/8α :>α 0>B75.5.α 87B./5?1α C8α ±25382α δ2C8>0α A12α87α 40?/12αδ=α
9:8α .8α 5>C5?0α 8>α ρβ)ρ])β)β)Φ)α  7α 3138>/1α C8α C5.8D1αA020α 87α
87838>/1α.82BNα
α
,?ααα\αααδlα,:Lαα]ααδ=α,:.α
α α
φ:0>C1α8<5./0>α4:82F0.α70/82078.αC8α?02B?/82αA8230>8>/8α?131α
83A:68αC8α/582200α87αL0712αC8α.=α.8α?07?:702Bα?1>αNα
α
δ=ααα\αααραααKαααfαραeα∆α+αρα]αβCα-αgαα
α
?-α °5α 87α @>C5?8α C8α 8./0H575C0Cα ∆α C87α 8>/28A5.1α 8.α 30;12α 9:8α ]0β(0α

80.   γ]α
C8H82Bα28075F02.8α:>α0>B75.5.αC8α°8=:>C1αδ2C8>)α
α
α±1C2B>α5=>1202.8α71.α848?/1.αC8α8.H87/8FαA21C:?5C1.α.E71αA12α70.α?02=0.α
L82/5?078.α 03A7545?0C0.α ?:0>C1α 71.α C8.A70F0358>/1.α70/82078.α 2870/5L1.α
C87α 8>/28A5.1α A21C:?5C1.α A12α 70α 0.538/2@0α C8α 70.α ?02=0.α 1α C8α 70α
8./2:?/:200αA12α0.8>/0358>/1.αC54828>?5078.α1αA12α1/20.α?0:.0.α?:3A70>α
9:8Nα
α
∆:ααKααIαααaααα]0]]ρα α α
α α αααααα
+-α°5α70.α8./2:?/:20.α8./B>α?1>41230C0.α8<?7:.5L038>/8αA12αAE2/5?1.0α.8α
A1C2Bα8L07:02α71.α848?/1.α=71H078.αC8α8.H87/8Fα1HL50>C1α87α?B7?:71αC8α
70.α C841230?51>8.α 70/82078.0α 38C50>/8α 70α 8<A28.5E>αρβ)ρ])β)βα +0α
C1>C8Nα
α
φ3α\αρα α
α
Σ+±:-Nα α α °:30/1250α C8α 70.α ?02=0.α 0<5078.α C8α /1C1.α 70.α
?17:3>0.αC87α8>/28A5.1)α
Σ±?Nαααααα°:30/1250αC8α70.α?02=0.α?2@/5?0.αC8αA0>C81αC8α/1C0.α
70.α?17:3>0.αC87α8>/28A5.1)α°8α8L07:02Bα38C50>/8Nα
α
±?ααα\αααπ
2
ααα αIααKαα+α*αl>α-
β
α
C1>C8αNα
Iααα\ααα+α ?αI=αKα(αα]αα .αI.8α-ααKαα+αρα]αβCα-α
α
1α?1>.82L0C12038>/8αNα
α
Iααα\ααα ?αI=ααKααKαααfαβ)(α+αρα]αβCα-αgα
α
*Nαααα40?/12αC8α71>=5/:Cα848?/5L0αC8α70α?17:3>0)α
α
Σ1.α848?/1.α=71H078.αC8α8.H87/8FαA1C2B>α.82αC8.A28?50C1.α?:0>C1αα*αl>α
Kα2α.80α38>12α9:8αββ)α
α
±020α/1C1.α71.α87838>/1.α.:68/1.α0α?13A28.5E>α?:;1αL0712αC8αα*αl>αKα2αα
.80α30;12α9:8αρ]]0αC8H82BαI0?82.8α:>α0>B75.5.α?131α87α9:8α.8α5>C5?0α8>α
70α°8??5E>αρβ)ρ])ρ)ρ)α
α
ρβ)ρ])1   σ φ≥δ°αμ α °+ Σ≥ .α±ΦπΦα Σ , [≥δ°α [ασΣ 2>[  
α
 7αC5.8D1αC8α71.α87838>/1.α8>α478<5E>αC8H82Bα?1>.5C8202α87α5>?2838>/1α
C8α71.α3138>/1.α8>α70α?17:3>0αA12αC8.A70F0358>/1α70/8207)α
α
ρβ)ρ])<   σ φ≥δ°αμ α °+ Σ≥ .α [α Σ , [≥δ°α°δ, ≥2μδ°αΦασΣ 2> [α
+2Φ2ΦΣ 
 
±020α 87838>/1.α 8>α ?13A28.5E>α .138/5C1.α 0α 478<5E>α 8>α 03H0.α
C528??51>8.αA25>?5A078.0αC8H82B>α03A7545?02.8α03H1.α3138>/1.α478?/128.α
?07?:70>C1αδ=α;αδlαA020α?0C0αC528??5E>αA12α.8A020C1)α

81.   γρα
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
CAPÍTULO 13 - CORTANTE Y TORSIÓN 
 
13.1    RESISTENCIA AL CORTE 
α
ρ1)ρ)ραα  7α C5.8D1α C8α 70.α .8??51>8.α /20>.L82.078.α C8α 71.α 87838>/1.α .:68/1.α 0α
4:82F0α?12/0>/8αC8H82BαH0.02.8α8>α70α8<A28.5E>Nα
α
:ααα≤αααφα>)α
C1>C8Nα
:Nααα .α70α28.5./8>?50α289:825C0αA12α?12/8α8>α70α.8??5E>α0>075F0C0)α
α α >Nααα .α70α28.5./8>?50α>135>07α07α?12/8αC8α70α.8??5E>)α
α
Σ0α 28.5./8>?50α >135>07α >α 8./02Bα ?1>41230C0α A12α 70α?1>/25H:?5E>α C87α
?1>?28/1α?α;α70α?1>/25H:?5E>αC8α0?821α.0αC8α/07α41230α9:8Nα
α
>α\α?α]α.α
α
ρ1)ρ)βαα Φ7α C8/8235>02α 70α ?1>/25H:?5E>α C87α ?1>?28/1α?0α ?:0>C1α ?1228.A1>C00α
C8H82B>α ?1>.5C8202.8α 71.α 848?/1.α C8α 70.α 4:82F0.α C8α/20??5E>α 0<507α
C8H5C0.α 0α 70α 47:8>?50α ;α ?1>/20??5E>α C8α 420=:0C1α ;α 0α ?03H51.α C8α
/83A820/:20α8>α71.α87838>/1.α9:8α8./G>α28./25>=5C1.α0<50738>/8)α
α
ρ1)ρ)1αα Σ0.α.8??51>8.α.5/:0C0.α0α:>0αC5./0>?50α38>12α9:8αSCSαC8.C8α70α?020αC87α
0A1;10αA1C2B>α.82αC5.8D0C0.αA020α70α4:82F0α:α?07?:70C0α0α:>0αC5./0>?50α
SCS0α.5α.8α?:3A78>α70.α.5=:58>/8.α?1>C5?51>8.Nα
α
0-α φ:0>C1α 70α 280??5E>α C87α 0A1;10α 8>α C528??5E>α C87α ?12/8α 0A75?0C10α
5>/21C:?8α ?13A28.5E>α 8>α 70.α 28=51>8.α ?82?0>0.α 07α 0A1;1α C87α
87838>/1)α
H-α φ:0>C1α>1α8<5./8>α?02=0.α?1>?8>/20C0.α8>/28α70α?020αC87α0A1;1α;α
70α.8??5E>α:H5?0C0α0α:>0αC5./0>?50αSCS)α

82.   γβα
α
13.2    CONTRIBUCIÓN DEL CONCRETO EN LA RESISTENCIA A L CORTE 
α
ρ1)β)ρ)ρα Σ0α?1>/25H:?5E>αC87α?1>?28/1α?αA1C2Bα8L07:02.8α?1>.5C820>C1Nα
α
α α 0-αα±020α3583H21.α.:68/1.αM>5?038>/8α0α?12/8α;α478<5E>Nα
mmmmα
?ααα\ααα]0(1αlαα4Y?ααααHXαCα α α α
α α α
°5α0?/M0>α3138>/1.αC8α/12.5E>0αL82α70α°8??5E>αρ1)<)1)β)α
α
±020α?B7?:71.α3B.αC8/0770C1.Nα
mmmααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααmmmα
?ααα\ααα+α]0(αlα4Y?ααα]ααρ×=αρXα:αCαKα,:α-αHXαCααα`ααα]0ααlα4Y?αααHXαCα
α
C1>C8α,:α8.α87α3138>/1α0?/:0>/8α.53:7/B>8038>/8α?1>α:α8>α70α
.8??5E>α?1>.5C820C0α;α87αL0712αC8αα:αCαKα,:αα>1αC8H8α?1>.5C8202.8α
30;12α0αρα8>α87α?B7?:71αC8α?)α
α
H-ααα±020α3583H21.α.:68/1.α0C5?51>0738>/8α0α?13A28.51>8.α0<5078.αNα
mmmα
?ααα\ααα]0(1αlα4Y?αααHXαCαα+αρα]αα]0]]×ρα[:αKαΦ=α-α
α
C1>C8α[:α.8α8<A28.0α8>αQ=α;αΦ=α8>α?8>/@38/21.α?:0C20C1.)α
α
±020α?B7?:71.α3B.αC8/0770C1.Nα
ααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααmmmα
?ααα\ααα+α]0(αlα4Y?ααα]ααρ×=αρXα:αCαKα,3α-αHXαCα
α
C1>C8ααααααα,3ααα\ααα,:ααJαα[:α+α<IαeαCα-αKαγα
α
;αC1>C8α87α?1?58>/8αα:αCαKα,3αα>1α8./Bα7535/0C1α0α:>αL0712α38>12α1α
5=:07α0αρ)α°5>α83H02=10α?α>1αC8H82Bα/1302.8α30;12α9:8Nα
mmmαααααααααααααmmmmmmmmmmmmmmmmα
?ααα\ααα]0ααlα4Y?αααHXαCααlααρα]α]0]βγα[:αKαΦ=α
α
C1>C8α[:α.8α8<A28.0α8>αQ=α;αΦ=α8>α?8>/@38/21.α?:0C20C1.)α
α
φ:0>C1α ,3α 28.:7/8α >8=0/5L10α ?α C8H8α ?07?:702.8α A12α70α 8<A28.5E>α
M7/530α0>/82512)α
α
?-ααα±020α3583H21.α.:68/1.α0C5?51>0738>/8α0α/20??5E>α0<507α.5=>545?0/5L00α
87α0A12/8αC8α?1>?28/1αC8H82Bα?1>.5C8202.8α>:71α+?α\α]-)α
α
ρ1)β)βαα φ:0>C1α 71.α 87838>/1.α /8>=0>α 7:?8.α ;α A8207/8.α 53A12/0>/8.0α C8H82Bα
/8>82.8α8.A8?507α?:5C0C1α?1>α71.α848?/1.α9:8α1?0.51>0>α70α?1>/20??5E>α
C8α 420=:0α ;α 71.α ?03H51.α C8α /83A820/:200α 71.α ?:078.αA:8C8>α A21C:?52α
4:82F0.αC8α/20??5E>α0<507α53A12/0>/8.α9:8αC5.35>:;0>α70α?1>/25H:?5E>αC87α
?1>?28/10α70α9:8αC8H82Bα?1>.5C8202.8α>:70α+?α\α]-)α
α

83.   γ1α
13.3    CONTRIBUCIÓN DEL REFUERZO EN LA RESISTENCIA A L CORTE 
α
ρ1)1)ρ   π σ≤ π.δα±δπαφδπ≥ α
α
ρ1)1)ρ)ρα  7α284:82F1αA12α?12/8αA1C2Bα8./02α?13A:8./1αA12Nα
α
0-α  ./25H1.α?8220C1.αA82A8>C5?:7028.α07α868αC87α87838>/1)α
H-α  ./25H1.α A82A8>C5?:7028.α 07α 868α C87α 87838>/1α ;α H0220.α C1H70C0.α
9:8α41238>α:>αB>=:71αC8α1]°α1α3B.α?1>α87α868αC87α87838>/1)α
?-α  .A52078.α
α
ρ1)1)ρ)βα  7α8.4:82F1αC8α47:8>?50αC8αC5.8D1αC87α284:82F1αA12α?12/8α>1αC8H82Bα.82α
30;12αC8α<β]]αQ=K?3β)α
α
ρ1)1)β   μ2° δαμ Σαπ σ≤ π.δα±δπαφδπ≥   
α
ρ1)1)β)ρα φ:0>C1α 70α 4:82F0α ?12/0>/8α :α 8<?8C0α C8αφα ?0α C8H82BαA21A12?51>02.8α
284:82F1αA12α?12/8αC8α30>820α9:8α.8α?:3A70α71α5>C5?0C1α8>αρ1)ρ)ρ)α°8α
/8>C2Bα8>α?:8>/0Nα
α
':≤φ>0α>\?].α
α
0-α φ:0>C1α.8α:/575?8α8./25H1.αA82A8>C5?:7028.α07α868αC87α87838>/1Nα
α
.ααα\αααΦLα4;αCαKα.α
α
C1>C8α ΦLα 8.α 87α B280α C8α 284:82F1α A12α ?12/0>/8α C8>/21α C8α :>0α
C5./0>?50α.αA21A12?51>0C0αA12α70α.:30αC8αB280.αC8α70.α2030.αC87α
1αC8α71.α8./25H1.α:H5?0C1.α8>α87α0730)α
α
H-α φ:0>C1α .8α :/575?8α 284:82F1α A12α ?12/8α ?1>.5./8>/8α 8>α :>0α H0220α
5>C5L5C:07α1α8>α:>α.171α=2:A1αC8αH0220.αA0207870.0α/1C0.αC1H70C0.α
0α70α35.30αC5./0>?50αC87α0A1;1Nα
α
.ααα\αααΦLα4;α.8>αα
mmmα
A821α.α>1αC8H82Bα8<?8C82αC8α]0γαα√α4W?αααHXαC)α
α
?-α φ:0>C1α 87α 284:82F1α A12α ?12/8α ?1>.5./0α 8>α :>0α .8258α C8α H0220.α
A0207870.α C1H70C0.α 1α =2:A1.α C8α H0220.α A0207870.α C1H70C0.α 0α
C54828>/8.αC5./0>?50.αC87α0A1;1αNα
α
.ααα\ααα[ΦLα4;α+.8>αα]α?1.α)αC]αKα.α
α
ρ1)1)β)βα V>5?038>/8α 1K<α C8α 70α A12?5E>α 5>?75>0C0α C8α?:079:582α H0220α 71>=5/:C5>07α
C1H70C0αC8H82Bα?1>.5C8202.8α848?/5L0α?131α284:82F1αA12α?12/8)α
α
ρ1)1)β)1α φ:0>C1α.8α83A788α3B.αC8α:>α/5A1αC8α284:82F1αA12α?12/8αA020α28412F02α70α
35.30α A12?5E>α C87α 07300α 70α 28.5./8>?50α 07α ?12/8α .αC8H82Bα ?07?:702.8α
?131α70α.:30αC8α71.αL07128.α.α?07?:70C1.αA020α71.αC5L82.1.α/5A1.)α

84.   γ<α
α
ρ1)1)β)<α Σ0α28.5./8>?50α07α?12/0>/8α.α>1αC8H82Bα?1>.5C8202.8α30;12α9:8Nα
αααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααmmmmα
αααααααααααβ0ραlαα4Y?ααααHXαCα α
α
ρ1)1)1αα Στ,2≥ °αμ Σα °±Φφ2Φ,2 [≥δαμ Σαπ σ≤ π.δα±δπα φδπ≥  
α
ρ1)1)1)ρα  7α8.A0?50358>/1αC87α284:82F1αA12α?12/8α?171?0C1αA82A8>C5?:70238>/8α07α
868αC87α87838>/1α>1αC8H82Bα.82α30;12αC8αα]0(αCαα>5αC8αα=]α?3)α
mmmα
ρ1)1)1)βα φ:0>C1α.α8<?8C0αC8ααρ0ραα√α4W?ααHXαC0α87α8.A0?50358>/1α3B<531αC8H82Bα
28C:?52.8α0α70α35/0C)α
α
ρ1)1)<αα π σ≤ π.δα,τ[2,δα±δπαφδπ≥ α
α
ρ1)1)<)ρα μ8H82BαA21A12?51>02.8α:>αB280α3@>530αC8α284:82F1αA12α?12/8α?:0>C1α:α
8<?8C0αC8αα]0(αφα?α0α8<?8A/1α8>Nα
α
0-α Σ1.0.α;αF0A0/0.α
H-α Σ1.0.α>82L0C0.α1α075=820C1.α
?-α 5=0.α?1>αA8207/8α/1/07α9:8α>1α8<?8C0α87α30;12αC8α71.α.5=:58>/8.α
L07128.Nαβ(α?30αC1.α;α38C50αL8?8.α87α8.A8.12αC87α0700α70α35/0CαC87α
0>?I1αC87α0730)α
α
ρ1)1)<)βα φ:0>C1α.8αC8H0α:.02α284:82F1αA12α?12/8αC8α0?:82C1α?1>α71α5>C5?0C1α8>α
70α.8??5E>α0>/825120α1α.8α289:5820αA12α0>B75.5.0α87αB280α3@>530αC8α?12/8α
.82BαNα
α
ΦLααα\ααα10(αHXα.αKα4;α
α α α α
°5α0?/M0>α3138>/1.αC8α/12.5E>0αL82α70α.8??5E>αρ1)<)<)1)α
α
13.4    RESISTENCIA  A  TORSIÓN  Y  CORTE  COMBINADOS  PARA  
ELEMENTOS DE SECCIÓN RECTANGULAR O EN FORMA T 
 
ρ1)<)ραα √ [ πΦΣ2μΦμ °α
α
ρ1)<)ρ)ρα Σ1.α848?/1.αC8α/12.5E>αC8H82B>α5>?7:52.8α?1>6:>/038>/8α?1>α70α478<5E>α;α87α
?12/8α.583A28α9:8α87α3138>/1α/12.12α+≥:-α?:3A70α9:8Nα
mmmα
≥:αααkααα]0ρ1αφα√α4W?ααΣ+n8-α
α
C8α71α?1>/202510α71.α848?/1.αC8α70α/12.5E>αA1C2B>α>1α?1>.5C8202.8)α
α
ρ1)<)ρ)βα  >α71.α87838>/1.αC8α.8??5E>α≥0α87αL0712αC8αΣ+n8-αC8H82Bα?1>.5C8202.8α
A020α /1C1.α 71.α 28?/B>=:71.α ?13A1>8>/8.α C8α 70α .8??5E>0α /130>C1α 8>α
?:8>/0α:>α0>?I1α3B<531αC8α070α5=:07α0α/28.αL8?8.α.:α8.A8.12α0α?0C0α
70C1αC87α0730)α
α
ρ1)<)ρ)1α ≤>0α .8??5E>α 28?/0>=:702α /5A1α ?06E>α A1C2Bα .82α ?1>.5C820C0α ?131α :>0α

85.   γ(α
.8??5E>α.E75C0α.583A28α9:8α87α8.A8.12αC8α70αA028Cα+8-α.80α30;12α1α5=:07α
0α]0β()α≥03H5G>αA1C2Bα?1>.5C8202.8α?131α:>0α.8??5E>α.E75C0α09:8770α
9:8α ?:3A70α 70α ?1>C5?5E>α ]0ρa8a]0β(0α 8<?8A/1α 9:8αΣ+n8-α C8H82Bα
3:7/5A75?02.8α A12α <8K)α φ:0>C1α 8α .80α 38>12α C8α ]0ρ0α C8H82Bα
?1>.5C8202.8α8>α87α0>B75.5.α70α25=5C8FαC8α70αA028C)α
α
ρ1)<)ρ)<α  >α 70.α .8??51>8.α /5A1α ?06E>α .:68/0.α 0α /12.5E>0α C8H82Bα A21L882.8α
?I0470>8.α8>α70.α8.9:5>0.α5>/825128.)α
α
ρ1)<)ρ)(α ±020α 848?/1.α C87α C5.8D1α C8α 87838>/1.α .138/5C1.α 0α /12.5E>0α C8H82B>α
C5./5>=:52.8αC1.α?1>C5?51>8.Nα
α
0-α  7α 3138>/1α /12.51>0>/8α 8.α 5>C5.A8>.0H78α A020α =020>/5F02α 87α
89:575H251α C8α 70α 8./2:?/:20)α  >α 8./8α ?0.1α C8H82Bα A21A12?51>02.8α
284:82F1αA12α/12.5E>α?1>.5C820>C10α.5>α28C:??51>8.0α87α3138>/1α
/12.12α9:8αA21L8>=0αC87α0>B75.5.)α
H-α  7α3138>/1α/12.51>0>/8α.8α125=5>0αA12α87α=521αC87α87838>/1α0α45>α
C8α30>/8>82α70α?13A0/5H575C0CαC8αC841230?51>8.)α >α8./8α?0.1α87α
3138>/1α3B<531αC8α/12.5E>αM7/531αA1C2Bα28C:?52.8α0Nα
α
mmmα
≥:ααα\αα]0ρραφαlα4Y?αααΣ+n8-K1α
α
°5α.8αI0?8α8./0α28C:??5E>0α71.αL07128.αC8α71.α?12/0>/8.α;α3138>/1.αC8α
71.α87838>/1.α0C;0?8>/8.αC8H82B>α31C545?02.8)α
αα αααααααααααααααααααααααααααααααααααααα α α α
ρ1)<)ρ)=α  >α:>0α8./2:?/:20α?1>α71.0.α;αL5=0.αC8αH12C80α8>α7:=02αC8α:>α0>B75.5.α
3B.α A28?5.10α 87α 3138>/1α /12.51>07α C8α :>0α 71.0α A1C2Bα ?1>.5C8202.8α
:>54123838>/8αC5./25H:5C1α0α71α702=1αC87α87838>/1)α
α
ρ1)<)ρ)×α Σ0.α.8??51>8.α.5/:0C0.α0α:>0αC5./0>?50α38>12α0αSCSαC8.C8α70α?020αC87α
0A1;1α A1C2B>α .82α C5.8D0C0.α ?1>α 87α 3138>/1α /12.51>07α ?07?:70C1α 0α 70α
C5./0>?50αSCS)α
α
ρ1)<)β   π °2°≥ [φ2ΦαΦαΣΦα≥δπ°2>[ 
α
ρ1)<)β)ρα  7α C5.8D1α C8α 70.α .8??51>8.α /20>.L82.078.α C8α 71.α 87838>/1.α .:68/1.α 0α
/12.5E>αC8H82BαH0.02.8α8>α70α8<A28.5E>Nα
α
≥:ααα≤αααφα≥>α
C1>C8Nα
≥:Nααα8.α70α28.5./8>?50α289:825C0α?1>α28.A8?/1α07α3138>/1α/12.12α
8>α70α.8??5E>α0>075F0C0)α
≥>Nα 8.α70α28.5./8>?50α>135>07α?1>α28.A8?/1α07α3138>/1α/12.12)α
α
 7α3138>/1α28.5./8>/8α>135>07α≥>α8./02Bα?1>41230C1αA12α70α?1>/25H:?5E>α
C87α?1>?28/1α≥?α;αA12α70α?1>/25H:?5E>αC87α0?821α≥.0αC8α/07α41230α9:8Nα
α
≥>ααα\ααα≥?αα]αα≥.α
α

86.   γ=α
ρ1)<)1α  π °2°≥ [φ2Φαμ Σαφδ[φπ ≥δα
α
ρ1)<)1)ρα Σ0α?1>/25H:?5E>αC87α?1>?28/1α0α70α/12.5E>α≥?0αA1C2Bα8L07:02.8α.8=M>Nα
mmααααααααααααααααααααmmmmmmmmmmmmmmmmmmmmmmmα
≥?ααα\ααα]0β]ααlα4Y?ααΣ(n8-ααKααlαρα]ααfα+α]0<αKαφ/α-α+α:αKα≥:α-αgnα
α α
ρ1)<)1)βα Σ0α?1>/25H:?5E>αC87α?1>?28/1α07α?12/8α8>α70.α.8??51>8.α8>α70.α?:078.α≥:α
8<?8C0αC8α])ρ1αφα√α4W?αΣ+n8-αA1C2Bα8L07:02.8α.8=M>Nα
mmmαααααααααααααααmmmmmmmmmmmmmmmmmmα
?ααα\ααα]0(1α√α4W?ααHXαCααKααlαρα]α+αβ0(αφ/α≥:αKα:α-αnα
α
 >α03H0.α8<A28.51>8.Nα
φ/αα\ααHXαCααKααΣ+n8-α
α
ρ1)<)1)1α ±020α3583H21.α.:68/1.α0C5?51>0738>/8α0α?13A28.5E>α0<5070α87αL0712α?α
C8α70α4E23:70α0>/82512α.8α3:7/5A75?02BαA12α87α.5=:58>/8α40?/12αNα
α
+αραα]αα]0]βγα[:αKαΦ=α-α
α
ρ1)<)1)<α ±020α 3583H21.α .:68/1.α 0C5?51>0738>/8α 0α /20??5E>α 0<507α .5=>545?0/5L00α 87α
0A12/8α C87α ?1>?28/1α 0α 70α 28.5./8>?50α 07α ?12/8α ;α 0α 70α /12.5E>α C8H82Bα
?1>.5C8202.8α>:71α+?\]α;α≥?\]-)α
α
ρ1)<)<   π °2°≥ [φ2Φαμ Σαπ σ≤ π.δ  
α
ρ1)<)<)ρα μ8/0778.αC87α284:82F1α
α
0-α  7α 284:82F1α A12α /12.5E>α .82Bα A21A12?51>0C1α 8>α 0C5?5E>α 07α 284:82F1α
289:825C1αA12α?12/80α478<5E>α;α4:82F0.α0<5078.)α
α
H-α  7α 284:82F1α 289:825C1α A12α /12.5E>α A1C2Bα ?13H5>02.8α ?1>α 87α 9:8α .8α
289:5820α A020α 1/20.α 4:82F0.α 5>/82>0.0α .583A28α 9:8α 87α B280α
.:35>5./20C0α .80α 38>1.α 5=:07α 0α 70α .:30α C8α 70.α B280.α 289:825C0.α
5>C5L5C:0738>/8αA020α?0C0α848?/1α;α.8α?:3A70α?1>α71.α289:5.5/1.α3B.α
8./25?/1.αA020α70α?171?0?5E>α;α87α8.A0?50358>/1)α
α
?-α  7α8.4:82F1αC8α47:8>?50αC8αC5.8D1αC87α284:82F1αA020α/12.5E>α>1αC8H82Bα
8<?8C82αC8α<β]]αQ=K?3β)α
α
C-α  7α 284:82F1α 289:825C1α A12α /12.5E>α 8./02Bα ?13A:8./1α A12α 8./25H1.α
?8220C1.α1α8.A52078.α?13H5>0C1.α?1>αH0220.α71>=5/:C5>078.)α
α
8-α  7α 284:82F1α A12α /12.5E>α C8H82Bα A2171>=02.8α A12α 71α 38>1.α :>0α
C5./0>?50α+H]C-α3B.α077BαC87αA:>/1αC1>C8α/8E25?038>/8α8.α289:825C1)α
α
4-αααΣ1.α7@35/8.αC8α.8A020?5E>α8>/28α868.αC87α284:82F1αA12α/12.5E>α.82B>α71.α
.5=:58>/8.Nα
α
±020α8./25H1.α?8220C1.Nα
,8>12α1α5=:07α0α+ρα]α8ρ-αKα<0αA821α.5>α8<?8C82αC8α1]α?3)α

87.   γ×α
α
±020αH0220.α71>=5/:C5>078.Nα
Σ0.αH0220.α71>=5/:C5>078.αA12α/12.5E>αC8H82B>α.82αC5./25H:5C0.α
0728C8C12α C87α A82@38/21α C8α 71.α 8./25H1.α ?8220C1.α ?1>α :>0α
.8A020?5E>α3B<530αC8α1]α?3)αμ8H8α?171?02.8αC8>/21αC8α?0C0α
8.9:5>0α C8α 71.α 8./25H1.α ?8220C1.α A12α 71α 38>1.α :>0α H0220α
71>=5/:C5>07)α
φ:0>C1α .8α 83A788>α .8??51>8.α ≥0α /03H5G>α C8H82B>α :.02.8α
8./25H1.α ?8220C1.α ;α H0220.α 71>=5/:C5>078.α 8>α 70.α A02/8.α
.1H28.0758>/8.α C8α 70.α 070.α 9:8α .8α I0;0>α ?1>.5C820C1α 07α
C8/8235>02αΣ+n8-)α
α
ρ1)<)<)β μ5.8D1αC87α284:82F1α
α
0-α φ:0>C1α 87α 3138>/1α /12.12α ≥:α 8<?8C0α 70α 28.5./8>?50α C87α ?1>?28/1α
φ≥?0α.8αC8H82BαA21A12?51>02α284:82F1αA12α/12.5E>0α8L07:B>C1.8α≥.αC8α
0?:82C1α0Nα
≥.ααα\αααΦ/αα/αρα8ρα4;αKα.α
α
C1>C8αΦ/α8.α87αB280αC8α:>0α2030αC87α8./25H1αC8>/21αC8α:>0αC5./0>?50α
.0α;αα/α.8α8L07:02Bα?1>.5C820>C1Nαα
α
α/ααα\ααα]0==α]α]011α+8ραKαρ-ααα≤αααρ0(α
α
C1>C8α ρα ;α 8ρα .1>α 70.α C538>.51>8.α ?8>/21α 0α ?8>/21α C87α 8./25H1α
+ρa8ρ-)α
α
H-α  7α B280α C8α 70.α H0220.α 71>=5/:C5>078.α C5./25H:5C0.α 0728C8C12α C87α
A82@38/21α C8α 71.α 8./25H1.α ?8220C1.α +Φl-α .82Bα 87α 30;12α C8α 71.α
.5=:58>/8.αL07128.Nα
α
Φlααα\αααβαΦ/α+ρα]α8ρ-αKα.α
α
Φlα\αfαβγαα.αiα≥:αKαfα≥:α]α:αKα+α1αφ/α-αgαjαKα4;αeαβαΦ/αgαfα+ρα]α8ρ-αKα.αgαα
α
70α9:8α.80α30;12)α
α
 7α L0712α C8α Φlα ?07?:70C1α ?1>α 70α 4E23:70α 0>/82512α >1α >8?8.5/0α .82α
30;12α07α9:8α.8α1H/8>C2@0α.:./5/:;8>C1α+α]01(αHXα.αKα4;α-αA12α+αβαΦ/α-)α
α
?-α Σ0α28.5./8>?50α07α3138>/1α/12.12α≥.α>1α8<?8C82Bα<αL8?8.α≥?)α >α87α
?0.1α C8α 3583H21.α .:68/1.α 0C5?51>0738>/8α 0α /20??5E>α0<507α
.5=>545?0/5L00α87αL0712αC8α≥?α9:8α.52L8α?131α7@35/8α0α≥.α+≥.αaα<α≥?-α.8α
?07?:702Bα ?1>α 70α 4E23:70α C8α 70α °8??5E>α ρ1)<)1)ρα3:7/5A75?0C0αA12α87α
40?/12Nα
α
+αραeα]0]βγα[:αKαΦ=α-α
α
C1>C8α[:α8.α70α/20??5E>α8>α*=α;αΦ=α87αB280αC8α70α.8??5E>α8>α?3β)α
α

88.   γγα
C-α  7αB280αC8α8./25H1.α289:825C1.αA12α/12.5E>α;α?12/8αC8H82Bα8L07:02.8α
?1>.5C820>C1Nα
α
Φ280αC8αβα2030.αC87α8./25H1αKα.ααα\αααΦLαKα.αα]ααβαΦ/αKα.α
α
ρ1)<)<)1 π89:5.5/1.α3@>531.αC87α284:82F1α
ααααααmmmα
φ:0>C1α ≥:α 8<?8C8α C8α ]0ρ1αφα√α 4W?α αΣ+n8-α α ;α ?:0>C1α .8α C8H8α :.02α
284:82F1αA12α?12/8αC8α0?:82C1α0α71α5>C5?0C1α8>α70α°8??5E>αρ1)1)<)ραEα87α
0>B75.5.α71α5>C59:80α87αB280α3@>530αC8α8./25H1.αA12α/12.5E>α;α?12/8α.82BNα
α
ΦLαα]ααβαΦ/ααα\ααα10(αHXα.αKα4;α
α
13.5    CORTANTE POR FRICCIÓN 
α
ρ1)()ραα Σ0.α C5.A1.5?51>8.α C8α 8./0α .8??5E>α A:8C8>α 0A75?02.8α ?:0>C1α .80α
0A21A50C1α?1>.5C8202α70α/20>.35.5E>αC8α70α4:82F0α?12/0>/8α0α/20LG.αC8α:>α
A70>1α C0C10α /07α ?131α 87α ?0.1α C8α :>0α=258/0α8<5./8>/8α1αA1/8>?5070α:>0α
.:A8245?58α C8α ?1>/0?/1α 8>/28α 30/825078.α C5./5>/1.α 1α :>0α .:A8245?58α C8α
?1>/0?/1α8>/28αC1.α?1>?28/1.αL0?50C1.α8>αC54828>/8.αα48?I0.)α
α
±:8C8α .:A1>82.8α 9:8α 0α 71α 702=1α C87α A70>1α C8α ?12/8α .8α A21C:?52Bα :>0α
=258/0α 8>α 70α ?:07α 87α C8.A70F0358>/1α 2870/5L1α 8.α 28.5./5C1α A12α 70α 425??5E>α
30>/8>5C0αA12α70α0230C:20α0α/20LG.αC8α70α=258/0α.:A:8./0)α
α
ρ1)()βαα  7αB280αC8α284:82F1αC8α?12/0>/8αA12α425??5E>α+ΦL4-α0α/20LG.αC87αA70>1αC8α
?12/0>/8αC8H82BαC5.8D02.8α.8=M>α70α4E23:70Nα
α
:ααα\αααφαΦL4αμα4;α
α
A020α?:0>C1αΦL4α8.αA82A8>C5?:702α07αA70>1αC8α?12/80α1α
α
:ααα\αααφαΦL4αα+αμα.8>α4αα]αα?1.αα4α-αα4;α
α
A020α87α?0.1α8>α9:8αΦL4α8./Gα5>?75>0C1α8>α2870?5E>α?1>α87αA70>1αC8α?12/8α
C8α30>820α9:8α70α4:82F0α?12/0>/8αA21C:F?0α/20??5E>α8>α87α284:82F1)α >α
8./0α4E23:700αα4α8.α87αB>=:71α8>/28α87α284:82F1αC8α?12/8αA12α425??5E>α;α87α
A70>1αC8α?12/8α;αμα8.α87α?1845?58>/8αC8α425??5E>)α
α
ρ1)()1αα ±020α87α?0.1αC8α?1>?28/1.αC8αA8.1α>123070α87α?1845?58>/8αC8α425??5E>αμα
.82BNα
α
Jα ±020α?1>?28/1αL0?50C1α31>17@/5?038>/8Nαααααααααααααααααααααααααααααμα\αρ0<α
-α ±020α?1>?28/1αL0?50C1α.1H28α?1>?28/1α8>C:28?5C1α
?1>α.:A8245?58α5>/8>?51>0738>/8α2:=1.0αI0./0α
:>0αA214:>C5C0CαC8α0A21<530C038>/8α=33Nαααααααααααααααααααααααμα\αρ0]α
-α ±020α?1>?28/1αL0?50C1α.1H28α?1>?28/1α8>C:28?5C1α
>1α5>/8>?51>0738>/8α2:=1.1Nαααααααααααααααααααααααααααααααααααααααααααααααααμα\α]0=α
-α ±020α?1>?28/1α0>?70C1α0α0?821α8./2:?/:207α7035>0C10α
38C50>/8αA82>1.αC8α?0H8F0α1α38C50>/8αH0220.αC8α

89.   γα
284:82F1Nααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααμα\α]0×α
α
ρ1)()<αα  7α?12/0>/8α0A75?0C1α:α>1αC8H82Bα8<?8C82αα]0βαφα4Y?αΦ?αα>5αC8αα(=αφαΦ?αα
+8>α *=-0α C1>C8α Φ?α 8.α 87α B280α C8α 70α .8??5E>α C8α ?1>?28/1α 8>α ?3nα 9:8α
28.5./8α70α/20>.4828>?50αC8α?12/0>/8)α
α
ρ1)()(αα Σ0.α4:82F0.αC8α/20??5E>α9:8αA:C5820>α8<5./52α0α/20LG.αC87αA70>1αC8α?12/80α
C8H82B>α.82α28.5./5C0.αA12α284:82F1α0C5?51>07)α
α
ρ1)()=αα  7α284:82F1αC8α?12/0>/8αA12α425??5E>αC8H82BαC5./25H:52.8α0A21<530C038>/8α
0α71α702=1αC87αA70>1αC8α?12/0>/8α;αC8H82Bα8./02α0>?70C1αA020αC8.02217702α
70α28.5./8>?50α0α70α47:8>?50α8>α03H1.α70C1.0α38C50>/8α=0>?I1.α1α0>?7068.α
8.A8?5078.)α
α
13.6    DISPOSICIONES ESPECIALES PARA BRAQUETES 
α
ρ1)=)ραα Σ0.α C5.A1.5?51>8.α C8α 8./0α .8??5E>α C8H82B>α 0A75?02.8α 0α 3G>.:70.α 1α
H209:8/8.α ?1>α :>0α 2870?5E>α 7:Fα C8α ?12/8α 0α A8207/8α 38>12α 1α 5=:07α 0α 70α
:>5C0Cα+0KC≤ρ-α;α.:68/0.α0α:>0α4:82F0αI125F1>/07αC8α/20??5E>α[:?α9:8α>1α
8<?8C0αC8α:)α
α
ρ1)=)βαα Σ0αC5./0>?50αCαC8H82Bα38C52.8α0α70α?020αC87α0A1;1)α
α
ρ1)=)1αα  7αA8207/8αC87αH12C8α8</82512αC87αB280αC8α0A1;1α>1αC8H82Bα.82α38>12αC8α
]0(αC)α
α
ρ1)=)<α Σ0α .8??5E>α C8α 70α ?020α C87α 0A1;1α C8H82Bα 8./02α C5.8D0C0α A020α 28.5./52α
.53:7/B>8038>/8α70α4:82F0αC8α?12/8α:0α70α4:82F0αI125F1>/07αC8α/20??5E>α
[:?α ;α 87α 3138>/1α A21C:?5C1α A12α 70α 4:82F0α C8α ?12/8α :α ;α 70α 4:82F0α
I125F1>/07αC8α/20??5E>α[:?Nα
α
,:ααα\ααα:α0αα]αα[:?α+αIαeαCα-α
α
ρ1)=)(αα  >α/1C1.α71.α?B7?:71.αC87αC5.8D10α87α40?/12αC8α28C:??5E>αC8α28.5./8>?50αφα
C8H82Bα.82α]0γ()α
α
ρ1)=)=αα Σ0α4:82F0α?12/0>/8α:α>1αC8H82Bα8<?8C82αC8α]0βαφα4W?αHXαCα>5αC8α(=αφαHXα
Cα+8>α*=0αHXα;αCα8>α?3-)α
α
ρ1)=)×αα  7αC5.8D1α/8>C2Bα8>α?:8>/0αNα
α
0-α 7α284:82F1αΦL40αA020α28.5./52α70α4:82F0αC8α?12/8α:0αC8H82Bα?:3A752α?1>α
70α°8??5E>αρ1)()α
α
H-α 7α284:82F1αΦ40αA020α28.5./52α87α3138>/1α,:0αC8H82Bα?:3A752α?1>α71.α
289:5.5/1.αC8αC5.8D1αA12α478<5E>αC87αφ0A@/:71αρρ)α
α
?-α 7α 284:82F1α Φ>0α A020α 28.5./52α 70α 4:82F0α C8α /20??5E>α [:?0α C8H82Bα
C8/8235>02.8α .:A1>58>C1α 9:8α 87α 284:82F1α /130α /1C0α 70α /20??5E>0α
.8=M>Nα

90.   ]α
α
Φ>ααα\ααα[:?αKα+αφα4;α-ααααααααααφαC1>C8α\α]0γ()α
α
Σ0α4:82F0αC8α/20??5E>α[:?αC8H82Bα/1302.8α?131α3@>531α5=:07α0α]0βα
:α ;α .8α C8H82Bα ?1>.5C8202α ?131α ?02=0α L5L0α 0M>α ?:0>C1α .80α
A21C:?5C0αA12α47:8>?500α?1>/20??5E>α1α?03H51.αC8α/83A820/:20)α
α
C-α 7αB280αC87α284:82F1αA25>?5A07αC8α/20??5E>αΦ.αC8H82Bα.82α87α30;12αC8α
71.αL07128.α.5=:58>/8.Nα
α
Φ.ααα\αααΦ4αα]ααΦ>αααααααααEα
α α α α α
Φ.ααα\αααβαΦL4αKα1αα]ααΦ>α
α
70α9:8α.80α30;12)α
α
8-αμ8H8>α?171?02.8α8./25H1.α?8220C1.αA0207871.α07α284:82F1αA25>?5A07αC8α
/20??5E>α Φ.α ?1>α :>α B280α /1/07α ΦI0α 30;12α 1α 5=:07α 0α ]0(α +Φ.JΦ>-0α
C5./25H:5C1.αC8>/21αC8α71.αC1.α/82?51.αC87αA8207/8α848?/5L1α0C;0?8>/8α0α
Φ.)α
α
4-α Σ0α?:0>/@0αρ\Φ.KHCαα>1α.82Bα38>12αC8α]0]<α4W?αKα4;)α
α
ρ1)=)γαα  7α 284:82F1α A25>?5A07α C8α /20??5E>α Φ.α C8H82Bα 9:8C02α 0C8?:0C038>/8α
0>?70C1α8>α70α?020αC87α428>/8αC8α70α3G>.:70αA12α:>1αC8α71.α.5=:58>/8.α
A21?8C5358>/1.Nα
α
0-α ,8C50>/8αC1H70C1αC8α70.αH0220.αΦ.αA020α412302α:>α70F1αI125F1>/07)α
H-α ,8C50>/8α07=M>α1/21α3G/1C1αC8α0>?7068α0C8?:0C1)α
α
ρ1)=)αα Σ0α .:A8245?58α C8α ?1>/0?/1α C8α 70α ?02=0α 9:8α 0?/M0α .1H28α 70α 3G>.:70α 1α
H209:8/80α >1α C8H82Bα .1H28.0752α3B.α077BαC8α70αA02/8α28?/0αC87α284:82F1α
A25>?5A07αC8α/20??5E>αΦ.)α
 
13.7    DISPOSICIONES  ESPECIALES  PARA  EL  REFUERZO 
TRANSVERSAL  EN  ELEMENTOS  QUE  RESISTAN  FUERZAS  DE 
SISMO 
α
Σ0.αC5.A1.5?51>8.αC8α8./0α.8??5E>α.1>α0A75?0H78.α07αC5.8D1αC87α284:82F1α
/20>.L82.07α C8α 87838>/1.α .138/5C1.α 0α 478<5E>α 1α 478<1?13A28.5E>α 9:8α
C8H0>α 28.5./52α 4:82F0.α C8α .5.31α ;α 8>α 70.α ?:078.α 70.α 4:82F0.α C8αC5.8D1α
2870?51>0C0.α?1>α71.α848?/1.α[email protected]?1.α.8αI0;0>αC8/8235>0C1α8>αH0.8α0α
70α?0A0?5C0CαC8α70α8./2:?/:20αC8αC5.5A02α8>82=@0α8>α87α20>=1α5>87B./5?1αC8α
28.A:8./0α+28C:??5E>αA12αC:?/575C0C-)α
α
Σ0α ?075C0Cα C87α 0?821α C8α 284:82F1α /20>.L82.07α >1α 8<?8C82Bα C8α 71α
8.A8?545?0C1αA020α=20C1αΦπ[α<β]α+<β]α,A0α+<β]]αQ=K?3β--)α
α
α α  7α 284:82F1α /20>.L82.07α ?1>.5./52Bα 8>α 8./25H1.α ?8220C1.α ?1>α =0>?I1.α
8./B>C02α0αρ1(°α/07α?131α.8αC845>8α8>α87αφ0A@/:71α×)αα

91.   J N
N
0bNs(pc(sxiNbi8H7zcy78gbN9cntb7svN9i8NbiN78y79gyiN(8N(bNRgtÁzcbiN  NtgsgN
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pb()i9ints(f7–8GN
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7HcgbN gN yifN =(9(fN (bN t(sgbz(N y(bN (b(n(8ziN uxi8gN y(N9i8p78gn7(8zieXN
9i8Nc8N(ftg97gn7(8ziNÍiNKc(N8iN()9(ygN(bNn(8isNy(NbifNf7Hc7(8z(fN
=gbis(fNN
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y7vn(zsiGN
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g8z(s7is(fNgN9gygNbgyiNy(Nc8gNf(997–8Nyi8y(Ntc(ygNts(f(8zgsf(Npbc(897gN
tisN pb()7–8N gfi97gygN 9i8N bifN y(ftbgxgn7(8zifN bgz(sgb(fN 78(bvfz79ifN y(bN
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bifN()zs(nifNy(NbgNbcxNb7ós(Ny(bN(b(n(8ziXNgfi97gygfNgNbgNpc(sxgNg)7gbNAcN
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92.   βα
ρ1)×)β)βα μ8H82B>α?171?02.8α8>α03H1.α8</2831.αC87α87838>/1α8./25H1.α?8220C1.α
.1H28α :>0α 71>=5/:Cαl1α 38C5C0α C8.C8α 70α ?020α C87α >:C1α +F1>0α C8α
?1>45>0358>/1-α9:8α>1α.80α38>12α9:8αNα
α
0-α ≤>α.8</1αC8α70α7:Fα75H28αC87α87838>/1)α
H-α Σ0α3B<530αC538>.5E>αC8α70α.8??5E>α/20>.L82.07αC87α87838>/1)α
?-α <(α?3α
α
Φα 38>1.α 9:8α 70.α 8<5=8>?50.α A12α C5.8D1α C87α 8.4:82F1α?12/0>/8α .80>α
30;128.0α87α8.A0?50358>/1αC8α8./1.α8./25H1.α>1α8<?8C82Bα87α38>12αC8α
71.α.5=:58>/8.αL07128.Nα
α
0-α Σ0α35/0CαC8α70αC538>.5E>α3B.αA89:8D0αC8α70α.8??5E>α/20>.L82.07α
C87α87838>/1)α
H-α ρ]α?3α
 7αA25382α8./25H1αC8H82Bα:H5?02.8α0α>1α3B.αC8α(α?3αC8α70α?020αC87α>:C1)α
α
ρ1)×)β)1α  7α 8.A0?50358>/1α C87α 284:82F1α /20>.L82.07α4:820α C8α 70α F1>0α C8α
?1>45>0358>/1α>1αC8H82Bα8<?8C82α87α38>12αC8α71.α.5=:58>/8.αL07128.Nα
α
0-α ρ=αL8?8.α87αC5B38/21αC8α70αH0220α71>=5/:C5>07αC8α38>12αC5B38/21)α
H-α Σ0α38>12αC538>.5E>αC87α87838>/1)α
?-α 1]α?3α
α
ρ1)×)β)<α φ:0>C1α87α284:82F1α/20>.L82.07α?1>.5./0α8>α:>α8.A52070α.8αC8H82Bα?:3A752α
?1>α71α5>C5?0C1α8>α70α°8??5E>αρβ)=)1)α
α
ρ1)×)β)(α  7α B280α 3@>530α C87α 284:82F1α /20>.L82.07α 9:8α C8H82Bα A21A12?51>02.8α
C8>/21αC87α>:C1αC8H82Bα?:3A752α?1>Nα
α
ΦLααα≥ααα]0×αHα.αKα4;α
α
C1>C8αHα8.α87α0>?I1αC87α>:C1α8>α70αC528??5E>α9:8α.8α8./Bα0>075F0>C1)α
 7α8.A0?50358>/1α.α>1αC8H82Bα8<?8C82αC8αρ(α?3)α
α
ρ1)×)β)=α ±020α87α?0.1αC8α3:21.αC8α?12/80αL82α87αφ0A@/:71αρ()α
α
α
α
α
α
α
α
α
α
α
α
α
α
α

93.   1α
α
α
α
α
α
α
α
α
α
α
α
α
α
α
α
α
α
α
CAPÍTULO 14 - VIGAS DE GRAN PERALTE 
α
14.1  GENERALIDADES 
α
ρ<)ρ)ρα °8α?1>.5C820αL5=0αC8α=20>αA8207/8α+L5=0αA028Cα1αL5=0αC50420=30-α09:8770α
L5=0α ?:;0α 2870?5E>α C8α 7:Fα 75H28α 8>/28α 0A1;1.α 0α 07/:20α /1/07α αl>KIα α >1α
8<?8C8αC8αβ0(α.5α8.α?1>/5>:0α1αC8αβα.5α8.αC8α:>α.171α/2031)α
α
ρ<)ρ)βα  >αL5=0.αC8α=20>αA8207/8α>1α8.αLB75C0α70αI5AE/8.5.αC8αC5./25H:?5E>α75>807αC8α
70.αC841230?51>8.α125=5>0C0.αA12α70α478<5E>)α
α
14.2  DISEÑO POR FLEXION 
α
ρ<)β)ρα  7αC5.8D1αA12α478<5E>αC8αL5=0.αC8α=20>αA8207/8αC8H82BαH0.02.8α8>α:>1αC8α
71.αC1.αA21?8C5358>/1.α.5=:58>/8.Nα
α
0-αΣ0α C5./25H:?5E>α C8α 8.4:82F1.α C8α 478<5E>α 8>α 70.α .8??51>8.α ?2@/5?0.α
C8H82Bα 1H/8>82.8α 38C50>/8α 07=M>α 3G/1C1α 28?1>1?5C1α C8α 0>B75.5.)α
μ8H82BαA21L882.8α70α0230C:20α>8?8.0250αA020α/1302α87α@>/8=21αC8α70.α
28.:7/0>/8.αC8α/20??5E>α8>α70α.8??5E>0α[:αC8α30>820α9:8Nα
α
[:ααα≤αααφαΦ.α4;α
α
H-αΣ1.α 3138>/1.α C8α 478<5E>α A1C2B>α ?07?:702.8α ?1>α 70.α /812@0.α:.:078.α
0A75?0H78.α0α87838>/1.αC8αA1?1αA8207/8α;α.8αA21A12?51>02Bα87αB280αC8α
284:82F1α>8?8.0250αC8α30>820α9:8α.8α?:3A70Nα
α
,:ααα≤αααφαΦ.α4;α.α
α
C1>C8α.α8.α87αH20F1αC87αA02α5>/82>1α9:8α.8αC8/8235>02Bα.8=M>Nα
α
Jα >αL5=0.αC8α:>α.171α/2031Nα

94.   <α
α
.ααα\ααα]0βα+αρα]αβαIα-ααααααααα.5αααρααα≤αααlαKαIααα≤αααβα
α
.ααα\ααα]0=αlααααααααααααααα.5ααααlαKαIαααaαααρα
α
Jα >αL5=0.α?1>/5>:0.α+3138>/1αA1.5/5L1α1α>8=0/5L1-Nα
α
.ααα\ααα]0βα+αρα]αρ0(αIα-αααααααα.5αααρααα≤αααlαKαIααα≤αααβ)(α
α
.ααα\ααα]0(αlααααααααααααααα.5ααααlαKαIαααaαααρα
α
C1>C8αlα8.α70αC5./0>?50α?8>/21α0α?8>/21α8>/28α0A1;1.0α.5>α8<?8C82α
ρ0ρ(αL8?8.α70α7:Fα75H28)α
α
ρ<)β)βα  7αB280α3@>530αC8α284:82F1α71>=5/:C5>07αA12α478<5E>α>1α.82Bα38>12α9:8α70α
1H/8>5C0α.8=M>α71α5>C5?0C1α8>α70α°8??5E>αρρ)()α
ρ<)β)1α °5α07=:>0α?020α8>α?13A28.5E>α>1α/:L5820α02251./28α70/82070αC8H82Bα/1302.8α
8>α ?:8>/0α 70α A1.5H575C0Cα C8α 9:8α 1?:220α A0>C81α 70/8207)α Σ0α .8A020?5E>α
3B<530α 8>/28α 71.α 0A1;1.α 70/82078.α >1α 8<?8C82Bα C8α <]α L8?8.α 87α0>?I1α
38>12αC87α070α1α?020α8>α?13A28.5E>)α
α
ρ<)β)<α  7α284:82F1αC8α478<5E>α.8αC5./25H:52BαC8α70α.5=:58>/8α41230Nα
α
ρ<)β)<)ρα ±020α3138>/1αA1.5/5L1Nα
α
0-α5=0.αC8α:>α/2031Nα
 7α 284:82F1α 9:8α .8α C8/8235>8α 8>α 70α .8??5E>α C8α 3138>/1α 3B<531α
A1.5/5L1αC8H82Bα?171?02.8α28?/1α;α.5>α28C:??5E>α8>α/1C0α70α71>=5/:CαC8α
70αL5=0α;αC8H82Bα0>?702.8α8>α70.αF1>0.αC8α0A1;1αC8α70αL5=0αC8α31C1α
9:8α.80α?0A0FαC8αC8.02217702α>1α38>1.αC87αγ]RαC8α.:α8.4:82F1αC8α
47:8>?50)α
α
 7α284:82F1αA12α478<5E>αC8H82BαC5./25H:52.8α8>α:>α420>60αC8α07/:20α5=:07α0α
]0β(α Iα eα ]0](αlα α 38C5C0α C8.C8α 70α ?020α 5>482512α C8α 70α L5=00α A821α >1α
30;12α9:8α]0βαl)α
α
H-α5=0.α?1>/5>:0.Nα
 7α284:82F1α9:8α.8α?07?:78α?1>α87α3138>/1αA1.5/5L1α3B<531αC8α?0C0α
/2031αC8H82BαA2171>=02.8α28?/1α8>α/1C1α87α/2031)α°5αI0;α>8?8.5C0CαC8α
I0?82α 83A0738.0α G./1.α C8H82B>α 71?075F02.8α ?82?0α C8α71.α 0A1;1.α
5>/8238C51.)α
α
 7α0>?7068αC8α8./8α284:82F1α8>α71.α0A1;1.α;α.:αC5./25H:?5E>α8>α70α07/:20α
.82B>α?131α.8α5>C5?0αA020αL5=0.αC8α:>α/2031)α
α
ρ<)β)<)βα ±020α3138>/1α>8=0/5L1Nα
α
[1α38>1.αC8α70α35/0CαC87α284:82F1α?07?:70C1αA020α3138>/1α>8=0/5L1α8>α
71.α 0A1;1.α C8H82Bα A2171>=02.8α 8>α /1C0α 70α 71>=5/:Cα C8α 71.α /2031.α

95.   JSN
gymg9(8z(fGN 0bN s(fziN y(bN s(pc(sxiN 8(Hgz7=iN (8N 9gygNzsgniN tiysvN
78z(sscnt7sf(NgNc8gNy7fzg897gNy(NbgN9gsgNy(bNgtimiN8iNn(8isNKc(NNLX5NhNN
87NKc(NNLX5NlGN
N
0bNs(pc(sxiNtgsgNnin(8ziN8(Hgz7=iNfiós(NbifNgtimifNy(ó(svNs(tgsz7sf(N
(8NyifNpsg8/gfNtgsgb(bgfNgbN(/(Ny(NbgN=7HgGNIgNts7n(sgXN9i8Nc8gNpsg997–8N
y(bNvs(gNzizgbN7HcgbNgNNLXSNuNlNáNhNeN NeNMfXNy(ó(svNs(tgsz7sf(N(8Nc8gNgbzcsgN
7HcgbNgNNLXONhNmNbgNf(Hc8ygXN9i8N(bNs(fziNy(bNvs(gXNf(Ns(tgsz7svN(8Nc8gN
psg8/gNy(NgbzcsgN7HcgbNgNNLXVNhNy(óg/iNy(NbgNts7n(sgGN
N
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his7xi8zgbN8in78gbN(8NbgNtgsz(Nfct(s7isNy(NbgN=7HgGN
N
14.3    DIMENSIONAMIENTO DE LOS APOYOS 
N
 5GUG N AgsgN(=gbcgsNbgfNs(g997i8(fN(8NbifNgtimifNy(Nc8gN=7HgN9i8z78cgXNjfzgNf(N
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t(sgbz(XN789s(n(8zg8yiN(8N LNtisN97(8ziN(bN=gbisNy(NbgfNs(g997i8(fN(8NbifN
gtimifN()zs(nifGN
N
 5GUGON Rcg8yiN bgfN s(g997i8(fN 9ints7ng8N y7s(9zgn(8z(N bgN 9gsgN 78p(s7isN y(N bgN
=7HgXN (bN (fpc(sxiN y(N 9i8zg9ziN 9i8N (bN gtimiN 8iN y(ó(svN ()9(y(sN y(N bgN
s(f7fz(897gNgbNgtbgfzgn7(8ziXNhgmgNiN8iN(b(n(8zifNzsg8f=(sfgb(fNKc(NbiN
gss7ifzs(8N(8NziygNfcNgbzcsgGN
N
 5GUGUN Rcg8yiNbgfNs(g997i8(fNy(NbifNgtimifN9ints7ng8Ny7s(9zgn(8z(NbgN9gsgN
78p(s7isNy(NbgN=7HgNmNjfzgN8iN(fzjNgss7ifzsgygN(8NziygNfcNgbzcsgNfiós(NbifN
gtimifXNy(ó(svN9ibi9gsf(Ns(pc(sxiNgy797i8gbN=(sz79gbNmNhis7xi8zgbN(8N9gygN
c8gN y(N bgfN ngbbgfN y(N s(pc(sxiN tgsgN pc(sxgN 9iszg8z(N(8N bgfN xi8gfN
ts–)7ngfNgNbifNgtimifXNy(bNn7fniNy7vn(zsiNKc(NbgfNy(N(fz(Ns(pc(sxiNmN
y(NniyiNKc(NbgNf(tgsg97–8Ny(NbgfNógssgfN(8N(fzgfNxi8gfNf(gNbgNn7zgyN
Kc(N(8N(bNs(fziNy(NbgN=7HgGN
0bN s(pc(sxiN gy797i8gbN his7xi8zgbN y(ó(svN 9ibi9gsf(N (8N c8gN psg8/gN
78n(y7gzgn(8z(Nfct(s7isNgNbgNKc(N9i8z7(8(N(bNs(pc(sxiN78p(s7isNy(Npb()7–8N
mNy(NgbzcsgN7HcgbNgbNy(N(fzgNMbz7ngGNIgNbi8H7zcyNy(N(fzgfNógssgfNn(y7ygN
y(fy(NbgN9gsgNy(bNgtimiN8iNf(svNn(8isNKc(NNLXUNhNN–NNLXUNlXNNbgNKc(Nf(gN
n(8isNmNy(ó(sv8Ng89bgsf(Ny(NniyiNKc(Ntc(yg8Ngb9g8xgsNfcN(fpc(sxiNy(N
pbc(897gGN
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bgN9gsgNy(bNgtimiNmNy(Ng89hiN7HcgbNgNNLXONhNN–NNLXONl,NNbgNKc(Nf(gNn(8isGN
0fzgfNógssgfNy(ó(sv8Ng89bgsf(N(8N(bNb(9hiN78p(s7isNy(NbgN=7HgNmNfcNgbzcsgN
8iNf(svNn(8isNKc(NNLXSNhNN–NNLXSNlXNNbgNKc(Nf(gNn(8isGN
N
14.4  DISEÑO POR FUERZA CORTANTE 
N
 5G5G N IifNs(Kc7f7zifNy(NbgNÍ(997–8N 5G5Nf(Ngtb79gsv8NgN(b(n(8zifN9cmgNs(bg97–8N
l8áyNNf(gNn(8isNKc(NSNmN(fzj8N9gsHgyifN(8Nc8gN9gsgNmNgtimgyifN(8NbgN
9gsgNitc(fzgXNy(NzgbNng8(sgNKc(Nf(Ny(fgssibb(8Ntc8zgb(fN(8N9ints(f7–8N
(8zs(N(bNtc8ziNy(Ngtb79g97–8Ny(NbgfN9gsHgfNmNbifNgtimifGN

96.   =α
α
ρ<)<)βα  7α C5.8D1α A12α ?12/8α C8α 87838>/1.α C8α =20>α A8207/8α .:68/1.α 0α 478<5E>α .8α
H0.02Bα 8>α 70.α .5=:58>/8.α 8?:0?51>8.0α C1>C8α 70α 28.5./8>?50α 07α ?12/8α C87α
?1>?28/1α?α8./02BαC8α0?:82C1α?1>α70.α°8??51>8.αρ<)<)(α;αρ<)<)=α;α70α
28.5./8>?50α 07α ?12/8α A21L5./0α A12α 87α 284:82F1α 8./02Bα C8α 0?:82C1α ?1>α 70α
°8??5E>αρ<)<Nα
:ααα≤αααφα>α
α
>ααα\ααα?αα]αα.α
α
ρ<)<)1α Σ0α28.5./8>?50α07α?12/8α>αA020α87838>/1.αC8α=20>αA8207/8α0α478<5E>α>1α
.82Bα30;12α9:8Nα
αmmα
>ααα\αααβ0ραα√α4W?ααHXαCα0αααααααααααααααααα.5ααααααl>αKαCααaααβα
α
αααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααmmα
α>ααα\ααα]0ργα+αρ]α]α7>αKαCα-αlα4Y?ααHXαCα0ααα.5ααβαα≤ααl>αKαCααaαα(α
α α α α
ρ<)<)<α Σ0α .8??5E>α ?2@/5?0α A020α C5.8D1α A12α 4:820α ?12/0>/8α 8>α L5=0.α ?1>α ?02=0α
:>54123838>/8αC5./25H:5C0αC8H82Bα?1>.5C8202.8α:H5?0C0α0α:>0αC5./0>?50αα
]0ρ(αl>α α 38C5C0α C8.C8α 70α ?020α C87α 0A1;1)α ±020α 87α ?0.1α C8α?02=0.α
?1>?8>/20C0.0α70α.8??5E>α?2@/5?0α.8α?1>.5C8202Bα:H5?0C0α0α]0(αL8?8.α70α
C5./0>?50α8>/28α70α?02=0α?1>?8>/20C0α3B.αA2E<530α;α70α?020αC87α0A1;10α
A821α8>α>5>=M>α?0.1α30;12α9:8αC)α
α
ρ<)<)(α Φα>1α.82α9:8α.8αI0=0α:>α?B7?:71α3B.αC8/0770C1αC8α0?:82C1α0α70α.8??5E>α
ρ<)<)×0α70α?1>/25H:?5E>αC87α?1>?28/1α?αA1C2Bα8L07:02.8α.8=M>Nα
αmmαααααααααααααααααααααααααααααα
?ααα\ααα]0(1α√α4W?αHXαCα
α
ρ<)<)=αα Σ0α ?1>/25H:?5E>α C87α ?1>?28/1α 0α 70α 28.5./8>?50α 07α ?12/8α ?α A1C2Bα .82α
?07?:70C0αA12α38C51αC8α70α8<A28.5E>αNα
mmα
?ααα\αααfα10(αeαβ0(α,:αKα+α:αCα-αgααfα]0(α√α4W?α]αρ×=αρXα:αCαKα,:αgααHXαCα
α
A821α>1α30;12α9:8Nαααααααααααααααααααααααmmα
ρ0=ααlα4Y?αHXαCα
C1>C8Nα
fα10(αeαβ0(α,:αKα+α:αCα-αgαα>1α8<?8C82BαC8αβ0(α
α α α
,:Nα ,138>/1α 03A7545?0C1α 9:8α 1?:228α .53:7/B>8038>/8α?1>α
:α8>α70α.8??5E>α?2@/5?0αC845>5C0α8>α70α°8??5E>αρ<)<)()α
α
ρ<)<)×α φ:0>C1α:α8<?8C0α70α28.5./8>?50α07α?12/8αφ?0αC8H82BαA21L882.8α284:82F1α
A12α?12/8αA020α.0/5.40?82α70.α8?:0?51>8.αC8α70α°8??5E>αρ<)<)β0αC1>C8α70α
28.5./8>?50α.α.8α?07?:702Bα?1>α70α8<A28.5E>Nα
α
.ααα\αααfααΦLα+αρα]αl>αKαCα-αKα°Lααα]αααΦLIα+αρραeαl>αKαCα-αKα°Iααgαα4;αCαKαρβα
αα
α

97.   J4N
yi8y(NN
M=NN Ms(gN y(N s(pc(sxiN tisN 9isz(N t(st(8y79cbgsN gbN s(pc(sxiN tisN
pb()7–8N(ftg97gyiNc8gNy7fzg897gNÍ=GN
M=hNNMs(gN y(N s(pc(sxiN tisN 9isz(Ntgsgb(biNgbNs(pc(sxiNy(Npb()7–8N
(ftg97gyiNc8gNy7fzg897gNÍhGN
N
 5G5GQN IgN9cg8zÁgNy(bNs(pc(sxiNhis7xi8zgbNtisN9isz(N8iNf(svNn(8isNy(NLXLLOSNmN
fcN(ftg97gn7(8ziN8iN()9(y(svNy(NyáUN87Ny(N5SN9nGN
IgN9cg8zÁgNy(bNs(pc(sxiN=(sz79gbNtisN9isz(N8iNf(svNn(8isNy(NLXLL SNmNfcN
(ftg97gn7(8ziN8iN()9(y(svNy(NyáSN87Ny(N5SN9nGN
N
 5G5GJN 0bN s(pc(sxiN tisN pc(sxgN 9iszg8z(N s(Kc(s7yiN (8N bgN f(997–8N 9sÁz79gN y(ó(svN
(ntb(gsf(N(8NziygNbgNbi8H7zcyNy(bNzsgniGN
N
 5G5G LN Rcg8yiNl8áyNf(gNn(8isNy(NSNmNbgfN9gsHgfNf(Ngtb7Kc(8NgNzsg=jfNy(NbifN
bgyifNiN(8NbgNtgsz(N78p(s7isNy(NbgN=7HgXN(bNy7f(:iNy(bNs(pc(sxiN=(sz79gbNtisN
pc(sxgN 9iszg8z(N f(svN 7HcgbN Kc(N tgsgN =7HgfN y(N ti9iN t(sgbz(N y(ó7(8yiN
ts(=(sf(N Kc(N (bN s(pc(sxiN =(sz79gbN f(gN 9gtgxN y(N fitiszgsN(8Nzsg997–8NbgN
9gsHgN=(sz79gbGNMy797i8gbn(8z(XNf(Nz(8ysvNs(pc(sxiNhis7xi8zgbNzgbN9iniNf(N
78y79gNtgsgN(bN9gfiNNg8z(s7isGN
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

98.   JQN
 
 
 
 
 
 
 
 
 
CAPÍTULO 15 - MUROS 
N
15.1  ALCANCES 
N
IgfNy7ftif797i8(fNy(N(fz(N9gtÁzcbiNfi8Ngtb79gób(fNgNncsifNfin(z7yifNgN
bifN(fzgyifNy(N9gsHgNf7Hc7(8z(fNN
N
geN ÓcsifN fin(z7yifN gN 9gsHgN g)7gbN 9i8N iN f78N pb()7–8Nzsg8f=(sfgbN gN fcN
tbg8iXNy(8in78gyifNncsifNy(N9gsHgGN
óeN ÓcsifN fin(z7yifN gN 9gsHgfN =(sz79gb(fN mN his7xi8zgb(fN (8N fcN tbg8iXN
y(8in78gyifNncsifNy(N9isz(GN
9eN ÓcsifN fin(z7yifN gN 9gsHgfN 8isngb(fN gN fcN tbg8iXN y(8in78gyifN
ncsifNy(N9i8z(897–8GN
N
15.2  GENERALIDADES N
N
 SGOG N IifNncsifNf(sv8Ny7f(:gyifNtgsgNbgfN9gsHgfN=(sz79gb(fXN9gsHgfNbgz(sgb(fNcN
izsgfN9gsHgfNgNbifNKc(N(fzj8Nfin(z7yifGN
N
 SGOGON IifNncsifNfin(z7yifNgN9gsHgfN=(sz79gb(fNf(Ny7f(:gsv8Ny(Ng9c(syiNgNbgN
Í(997–8N SGUGN
N
 SGOGUN IifNncsifNfin(z7yifNgNpc(sxgfNhis7xi8zgb(fNN9itbg8gs(fNf(Ny7f(:gsv8Ny(N
g9c(syiNgNbgNÍ(997–8N SG5GN
N
 SGOG5N IifN ncsifN y(N 9i8z(897–8XN (8N =ibgy7xiN iN gtimgyifXN f(N y7f(:gsv8N y(N
g9c(syiNgNbgNÍ(997–8N SGSGN
N
 SGOGSN IgN bi8H7zcyN y(bN ncsiN 9i8f7y(sgygN 9iniN (p(9z7=gN tgsgN 9gygN 9gsHgN
9i89(8zsgygN8iNy(ó(svN()9(y(sNbgNy7fzg897gN9(8zsiNgN9(8zsiN(8zs(N9gsHgfN
87NbgNbi8H7zcyNy(NbgNfct(sp797(Ny(N9i8zg9ziNnvfNyifN=(9(fN(bN(ft(fisNy(bN
ncsiNgN9gygNbgyiXNgN8iNf(sNKc(Nf(Ny(nc(fzs(NtisNc8Ng8vb7f7fNy(zgbbgyiNbgN
9i8zs7óc97–8Ny(Nc8gNbi8H7zcyNngmisGN
N
 SGOGVN IifN(b(n(8zifN(8N9ints(f7–8N9i8fzsc7yifN78z(Hsgbn(8z(N9i8NbifNncsifN
9cntb7sv8N9i8NbifNs(Kc7f7zifNy(bNRgtÁzcbiN OGN
N
 SGOG4N IgN 9g8z7ygyN y(N s(pc(sxiN mN bifN bÁn7z(fN y(N (ft(fisN 78y79gyifN (8N (fz(N
9gtÁzcbiN tiysv8N f(sN niy7p79gyifN 9cg8yiN f(N y(nc(fzs(N tisN c8N g8vb7f7fN
(fzsc9zcsgbNKc(Nf(Nz7(8(Ngy(9cgygfNs(f7fz(897gNmN(fzgó7b7ygyGN
N
 SGOGQN IgNzsg8fp(s(897gNy(NbgfNpc(sxgfNgNbgN97n(8zg97–8N(8NbgNógf(Ny(bNncsiNf(N

99.   ##α
I02BαC8α0?:82C1α07αφ0A@/:71αρ=)α
 
15.3    MUROS DISEÑADOS COMO ELEMENTOS EN COMPRENSIÓN   
α
ρ()1)ρα  <?8A/1α 71α 5>C5?0C1α 8>α 70α °8??5E>α ρ()1)β0α 71.α 3:21.α .:68/1.α 0α ?02=0α
L82/5?07α 1α 0α 478<1?13A28.5E>α .82B>α C5.8D0C1.α C8α 0?:82C1α 0α 71.α
289:825358>/1.αC87αφ0A@/:71αρβα;αC8α70α°8??5E>αρ()β)α
ρ()1)βα Σ1.α 3:21.α C8α .8??5E>α 28?/0>=:702α .E75C0α A1C2B>α .82α C5.8D0C1.α C8α
0?:82C1α 0α 71.α 289:5.5/1.α C87α C5.8D1α 83A@25?1α C8α 8./0α .8??5E>α .5α 70α
28.:7/0>/8α C8α /1C0.α 70.α ?02=0.α 03A7545?0C0.α .8α :H5?0α C8>/21α C87α /82?51α
?8>/207αC87α8.A8.12α/1/07αC8αA028C)α
α
ρ()1)1α Σ0α28.5./8>?50α0α?02=0αL82/5?07αφ±>XαC8α:>α3:21αC8α.8??5E>α28?/0>=:702α
.E75C0α?:;0α28.:7/0>/8αC8α/1C0.α70.α?02=0.α03A7545?0C0.α.8α:H59:8αC8>/21α
C87α/82?51α?8>/207αC8α.:α8.A8.12α/1/070αA1C2BαC8/8235>02.8αC8α0?:82C1α0Nα
α
φα±>Xααα\ααα]0((αφα4W?αΦ=αiαραeαfα+α*αl?α-αKα+α1βα/α-αgαnαjα
α
C1>C8Nα
φαα\αα]0×α
l?NααC5./0>?50αL82/5?07α8>/28α0A1;1.)α
*Nααα40?/12αC8α28./25??5E>0α.8=M>Nα
Jα±020α3:21.α02251./20C1.α0225H0α;α0H061α;α?1>α28./25??5E>αC8α
21/0?5E>α8>α:>1α1α03H1.α8</2831.Nαααααααααα*α\α]0γα
Jα±020α 3:21.α 02251./20C1.α 0225H0α ;α 0H061α .5>α 28./25??5E>α C8α
21/0?5E>α8>α.:.α8</2831.Nαααααααααααααααααααααααααα*α\αρ0]α
Jα±020α3:21.α.5>α02251./28α70/8207Nααααααααααααααααα*α\αβ0]α
α
 7α8.A8.12α3@>531α0α:.02.8α8>α70α4E23:70α0>/82512α.82BαC8αρKβ(αC8α.:α
07/:20α1αC8α.:α71>=5/:C0α70α9:8α.80α38>120αA821α>1α38>1.αC8αρ]α?3)α
α
ΦC5?51>0738>/80α.8αC8H82B>α?:3A752α71.α289:5.5/1.αC8α70α°8??5E>αρ()βα;α
71.αC8α284:82F1α3@>531α5>C5?0C1.α8>α70α°8??5E>αρ()=)α
α
ρ()1)<α Σ0α?:0>/@0α3@>530αC8α284:82F1αL82/5?07α284825C0α0α70α.8??5E>αH2:/0α.82BNα
0-α]0]]ρβαA020αH0220.α?122:=0C0.αC8αC5B38/21α38>12α1α5=:07α0α(KγSα?1>α
:>0α28.5./8>?50α0α70α47:8>?50α>1α38>12α0α<β]]αQ=K?3n)α
H-α]0]]ρ(αA020α1/20.αH0220.α?122:=0C0.)α
?-α]0]]ρβαA020α30770α878?/21.17C0C0α75.0α1α?122:=0C0αC8αC5B38/21α30;12α
0αρ(α33)α
α
ρ()1)(α Σ0α?:0>/@0α3@>530αC8α284:82F1αI125F1>/07α284825C0α0α70α.8??5E>αH2:/0α.82BNα
0-α]0]]β]αA020αH0220.α?122:=0C0.αC8αC5B38/21α38>12α1α5=:07α0α(KγSα?1>α
:>0α28.5./8>?50α0α70α47:8>?50α>1α38>12α0α<β]]αQ=K?3n)α
H-α]0]]β(αA020α1/20.αH0220.α?122:=0C0.)α
?-α]0]]β]αA020α30770α878?/21.17C0C0α75.0α1α?122:=0C0αC8αC5B38/21α30;12α
0αρ(α33)α
α
ρ()1)=α Σ1.α3:21.αC8α8.A8.12αC8αβ(α?3α1α3B.αC8H82B>α 778L02α284:82F1α8>α70.α
C1.α?020.)α

100.   ρ]]α
α
15.4  MUROS DE CORTE 
α
Σ1.α3:21.αC8α?12/8αC8H82B>α.82αC5.8D0C1.αA020α70α0??5E>α?13H5>0C0αC8α
?02=0α0<5070α3138>/1.α;α?12/80αC8α0?:82C1α0α70.αC5.A1.5?51>8.αC8α8./0α
.8??5E>)α
α
ρ()<)ραα  °± °δπ °α,τ[2,δ°αα
α
ρ()<)ρ)ρα Σ1.α3:21.α.82B>αC538>.51>0C1.α/8>58>C1α8.A8?507α?1>.5C820?5E>α8>α71.α
8.4:82F1.αC8α?13A28.5E>α8>α71.α8</2831.α;α.:α28.5./8>?50α07αA0>C81)α
α
ρ()<)ρ)βα  7α8.A8.12α3@>531αA020α71.α3:21.αC8α?12/8α.82BαC8αρ]α?3)α
α
ρ()<)ρ)1α  >α 87α ?0.1α C8α 3:21.α C8α ?12/8α ?15>?5C8>/8.α?1>α 3:21.α 8</825128.α C8α
.E/0>10α87α8.A8.12α3@>531α.82BαC8αβ]α?3)α
α
ρ()<)βα μ2° δα±δπασΣ 2>[   
α
ρ()<)β)ρα Σ1.α 3:21.α ?1>α 8.4:82F1.α C8α 478<5E>α C8H5C1α0α 70α 0??5E>α C8α 4:82F0.α
?1A70>028.αC8H82B>αC5.8D02.8αC8α0?:82C1α0α71α.5=:58>/8Nα
α
0-α±020α3:21.α8.H87/1.α+2870?5E>αC8α07/:20α/1/07α0α71>=5/:CNαTKΣkρ-α.82B>α
0A75?0H78.α 71.α 75>80358>/1.α =8>82078.α 8./0H78?5C1.αA020α
478<1?13A28.5E>)α°8α5>L8./5=02Bα70α28.5./8>?50α8>αH0.8α0α:>0α2870?5E>α
C8α?02=0α0<507αJα3138>/1)α
 7α 284:82F1α L82/5?07α C8H82Bα C5./25H:52.8α 0α 71α 702=1α C8α 70α 71>=5/:Cα C87α
3:210α?1>?8>/20>C1α30;12α284:82F1α8>α71.α8</2831.)α
α
H-α±020α 3:21.α C8α A1?0α 8.H87/8Fα +2870?5E>α C8α 07/:20α/1/07α 0α 71>=5/:CNα
TKΣaρ-α ;α ?1>α ?02=0.α 0<5078.α >1α .5=>545?0/5L0.0α >1α .1>α LB75C1.α 71.α
75>80358>/1.α8./0H78?5C1.αA020α478<1?13A28.5E>α;α.8αC8H82Bα?07?:702α
87αB280αC87α284:82F1αC87α8</2831α8>α/20??5E>αA020α87α?0.1αC8α.8??51>8.α
28?/0>=:7028.α?131α.5=:8Nα
α
,:ααα\αααφαΦ.α4;α.α
C1>C8αNα
.ααα\ααα]0<αΣα+αρα]αTαKαΣα-α0ααααααα.5ααα]0(ααaααTαKαΣααaααραα
α
.ααα\αααρ0βαTα0ααααααααααααααααα.5αααααααTαKαΣαα`αα]0(α
α α α α α αααα
°5α 71.α 3:21.α >1α .1>α C8α .8??5E>α 28?/0>=:702α 1α 8./B>α.:68/1.α 0α ?02=0.α
0<5078.α .5=>545?0/5L0.0α .8α C8/8235>02B>α 70.α B280.α C8α 71.α 284:82F1.α
38C50>/8α:>α0>B75.5.α20?51>07)α
α
ρ()<)β)βα ΦC5?51>0738>/80αC8H82Bα?171?02.8α284:82F1α:>54123838>/8α28A02/5C1α0α71α
702=1αC8α70α71>=5/:CαC87α3:210α?:3A758>C1αG./8α?1>α87α0?821α3@>531αC8α
284:82F1αL82/5?07αC8α3:21.α5>C5?0C1α8>α70α°8??5E>αρ()<)1)α
α
ρ()<)β)1α  7α0?821αC8α284:82F1α?1>?8>/20C1α8>α71.α8</2831.αC8α71.α3:21.αC8H82Bα

101.   ρ]ρα
?1>45>02.8α?1>α8./25H1.α?131α8>α87α?0.1αC8α?17:3>0.)αΣ1.α83A0738.α8>α
G./8α284:82F1α.8αC5.8D02B>α?131α83A0738.α8>α/20??5E>)α
α
ρ()<)β)<α  7α284:82F1αL82/5?07αC5./25H:5C1α>1α>8?8.5/02Bα8./02α?1>45>0C1αA12α8./25H1.α
0α 38>1.α 9:8α .:α ?:0>/@0α 8<?8C0α 0α ]0]ρα 1α 9:8α .80α >8?8.0251α A12α
?13A28.5E>)α
α
ρ()<)β)(α °5α 87α 8.4:82F1α 8>α 70α 45H20α 8</2830α 8>α /20??5E>α ?07?:70C1α .:A1>58>C1α
?13A12/0358>/1α75>807α87B./5?1Nα
α
σ:ααα\ααα,:α8/αKαI=ααJαα±:αKαΦ=α
αααααααααααααααααααααααααααααααααααααααααααααααααmmα
8<?8C5820αC8αβα√α4W?α0αC8H82BαL82545?02.8α9:8α87α284:82F1α8>α/20??5E>αC8α71.α
8</2831.αA21L80α:>α3138>/1α28.5./8>/8αA12α71α38>1.α5=:07α0αρ0(αL8?8.α
87α3138>/1αC8α0=258/0358>/1α,?2αC8α70α.8??5E>Nα
αααααααααααααααααααααααmmα
,?2ααα\αααI=α+αβα√α4W?αα]α±:αKαΦ=α-αKα8/α
α
ρ()<)1α μ2° δα±δπασ≤ π.Φαφδπ≥Φ[≥ α
α
ρ()<)1)ρα Σ1.α 3:21.α ?1>α 8.4:82F1.α C8α ?12/8α C8H5C1.α 0α 70α 0??5E>α C8α 4:82F0.α
?1A70>028.α.8αC5.8D02B>α?1>.5C820>C1Nα
α
:ααα≤αααφα>α
α
>ααα\ααα?αα]αα.α
C1>C8Nααααααααααααααααααααααααααααααααααααααααααααααααααmmα
α?ααα\ααα]0(1α√α4W?α/αCα
αααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααmmα
;αα>α>1αC8H82Bα8<?8C82αC8αβ0=αα√α4W?α/αCα
α α α
α α ±020α?B7?:71.α3B.αC8/0770C1.0α.8αA1C2Bα?1>.5C8202α87α38>12αC8Nα
mmα
?ααα\ααα]0γ(α√α4W?α/αCααα]ααα+α[:αCα-αKα+α<αΣα-α
αααααααααααααααααααααααααααααααααααααααααααααmmααααααααααααααααααααmmα
?αα\ααfα]0ρ(αlα4Y?αα]αααΣα+α]01αlα4Y?α]α]0βα[:αKαΣ/α-αKα+α,:αKα:αeαΣαKαβα-αgα/αCα
α α α
α α °5αα+α,:αKα:αeαΣαKαβα-αα8.α>8=0/5L10α>1αC8H82Bα:.02.8α8./0αM7/530α4E23:70)α
α
φ:0>C1α:>α3:21α8./Gα.:68/1α0α8.4:82F1.αC8α/20??5E>α0<507α.5=>545?0/5L0α1α
?:0>C1α71.α8.4:82F1.αC8α?13A28.5E>α.80>αA89:8D1.αα+[:KΦ=αaα]0ρα4W?-0α
C8H82Bα?1>.5C8202.8α?α\αα])α
α
ρ()<)1)βα Σ0αC5./0>?50αSCSαC8α70α45H20α8</2830α8>α?13A28.5E>α07α?8>/215C8αC8α70.α
4:82F0.α8>α/20??5E>αC87α284:82F10α.8α?07?:702Bα?1>α:>αα0>B75.5.αH0.0C1α8>α
70α?13A0/5H575C0CαC8αC841230?51>8.)α >α?0.1αC8α>1αI0?82.8α8./8α0>B75.5.α
SCSαC8H82Bα/1302.8α5=:07α0α]0γαΣ)α α α
α
ρ()<)1)1α Σ0.α.8??51>8.α71?075F0C0.α8>/28α70αH0.8α;α:>0α07/:20αΣKβαEαTKβα+70α9:8α
.80α38>12-0αA1C2B>αC5.8D02.8α?1>α87α35.31αL0712αC8α?α9:8α87α?07?:70C1α

102.   ρ]βα
A020α70α.8??5E>α:H5?0C0α0αΣKβαEαTKβ)α
α
αρ()<)1)<α Σ0α4:82F0α?12/0>/8αC8αC5.8D1α:α8>α/1C0α.8??5E>αC8H82Bα?:3A752α?1>Nα
α
:ααα≥ααα:0α+α,:2αKα,:0α-αXγ 
C1>C8Nα
:0Nασ:82F0α?12/0>/8αA21L8>58>/8αC87α0>B75.5.)α
,:0Nα,138>/1α478?/12αA21L8>58>/8αC87α0>B75.5.)α
,:2Nα,138>/1α478?/12α/8E25?1α0.1?50C1α0α±:α9:8α28.5./8α70α.8??5E>α
?1>α87α284:82F1α280738>/8αA21A12?51>0C1α;α.5>α?1>.5C8202α87α
40?/12αC8α28C:??5E>ααC8α?0A0?5C0Cαφ)α
XγNα σ0?/12αC8α03A7545?0?5E>αC5>B35?00α.8=M>Nα
α
Xγααα\ααα]0αα]αα>αKαρ]α0ααααααααα.5ααααααα>αα≤αα=α
α
Xγααα\αααρ01αα]αα>αKα1]α0ααααααααα.5ααα=ααaαα>αα`ααρ(α
α
α°5Nαααααα>ααbααρ(0αα:.02α>α\αρ(α
α α α α α α α α
C1>C8α>α8.α87α>M3821αC8αA5.1.α
α
ρ()<)1)(α φ:0>C1α :α 8<?8C0α 0αφ?0α C8H82Bα ?171?02.8α 284:82F1α I125F1>/07α A12α
?12/8)α 7αB280αC8α8./8α284:82F1α.8α?07?:702Bα?1>Nα
α
.ααα\αααΦLα4;αCαKα.α
αααααααααααααααααααααααααααααααααααα
Σ0α?:0>/@0αρIαC87α284:82F1αI125F1>/07αA12α?12/8α+284825C0α0α70α.8??5E>α/1/07α
L82/5?07αC8α?1>?28/1αC87α.8?/12α8>α8./:C51-0α.82Bα30;12α1α5=:07α0α]0]]β()αα
α
 7α8.A0?50358>/1αC87α284:82F1αI125F1>/07α>1α8<?8C82BαC8αΣK(0αC8α1/α>5αC8α
<(α?30αC8H5G>C1.8α0>?702α8>α71.α8</2831.α?1>45>0C1.αC87α3:21α8>α41230α
/07α9:8αA:8C0αC8.02217702α.:α8.4:82F1αC8α47:8>?50)α
α
Σ0α?:0>/@0αρLαC87α284:82F1αL82/5?07αA12α?12/8α+284825C0α0α70α.8??5E>α/1/07α
I125F1>/07αC8α?1>?28/1-0α.82Bα30;12α1α5=:07α0Nα
α
ρLααα\αααfα]0]]β(α]α]0(α+αβ0(αeαTαKαΣα-α+αρIαeα]0]]β(α-ααα≥ααα]0]]β(α
ααααααααααααααααααααααααααααααααααα α α αααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααα
α α A821α>1α>8?8.5/02Bα.82α30;12α9:8α87α284:82F1αI125F1>/07α289:825C1)α
α α  7α8.A0?50358>/1αC87α284:82F1αL82/5?07α>1α.82Bα30;12α9:8αΣK10α9:8α1/α>5α
9:8α<(α?3)α
α
φ:0>C1α:α.80α38>12α9:8αα]0(αφα?0α70.α?:0>/@0.αC8α284:82F1αI125F1>/07α
;αL82/5?07αA1C2B>α28C:?52.8α0Nα
ρIααbαα]0]]β]α
ρLααbαα]0]]ρ(α
αα
 7α8.A0?50358>/1αC8α03H1.α284:82F1.α>1α.82Bα30;12α9:8α/28.αL8?8.α87α
8.A8.12αC87α3:21αEα<(α?3)α
α

103.   ρ]1α
ρ()<)1)=α φ:0>C1α 87α 8.A8.12α C87α 3:21α .80α 5=:07α 1α 30;12α C8α β(α ?30α C8H82Bα
C5./25H:52.8α87α284:82F1αA12α?12/8αI125F1>/07α;αL82/5?07α8>α70.αC1.α?020.)α
α
ρ()<)1)×α μ8H82Bα L82545?02.8α 70α 28.5./8>?50α 8>α 70.α 6:>/0.α C8α ?1>./2:??5E>α C8α
0?:82C1α 0α 70α °8??5E>α ρ1)()α Σ0α 28.5./8>?50α C8α 70α 6:>/0αφ>α C8H82Bα .82αα
30;12α9:8α:)α
α
ρ()<)<α 2√Φ°α [≥π α,≤πδ°  
α
Σ0α4:82F0α?12/0>/8α8>α70.αL5=0.α9:8α:>8>α0α71.α3:21.0αC8H82Bα7535/02.8α0Nα
αmmα
:ααα`αααρ0=]αφα√α4W?αHXαIααα
α
;α>1α.8α?1>.5C8202Bα>5>=M>α0A12/8αC87α?1>?28/1α0α70α28.5./8>?50α+?\]-)α
α
Σ0α 4:82F0α ?12/0>/8α :α C8α C5.8D1α C8H82Bα H0.02.8α 8>α 70α ?0A0?5C0Cα
3B<530α C8α 478<5E>α C8α 70α L5=00α ?1>.5C820>C1α :>0α .1H28α 28.5./8>?50α C87α
0?821αC8αβ(R)α
α
φ:0>C1α70α2870?5E>αl>KIα.80α38>12α0αβ0α87α8.4:82F1αA12α4:82F0α?12/0>/8α
C8H82Bα.82α0H.12H5C1αA12αH0220.αC50=1>078.αC8H5C038>/8α0>?70C0.α8>α87α
3:21)α
α
ρ()(α ,≤πδ°αμ αφδ[≥ [φ2>[   
α
ρ()()ρα Σ1.α 3:21.α C8α ?1>/8>?5E>0α 8>α L170C5F1α 1α 0A1;0C1.0α .5>α ?02=0α 0<507α
.5=>545?0/5L0α.8αC5.8D02B>αC8α0?:82C1α0α70.αC5.A1.5?51>8.αA020αC5.8D1αC8α
87838>/1.α8>α478<5E>αC87αφ0A@/:71αρρ)αΦ9:8771.αC1>C8α70α?02=0α0<507α.80α
.5=>545?0/5L0α.8αC5.8D02B>αC8α0?:82C1α0α71α8.A8?545?0C1α8>α87α?0A@/:71αρβ)α
α
ρ()()βα  7α284:82F1α3@>531αA12α478<5E>α.82Bα87α3@>531α289:825C1αA12α?1>/20??5E>α;α
/83A820/:20α8.A8?545?0C1αA020α71.0.α8>α70α°8??5E>α×)ρ])α
α
α α 2>C8A8>C58>/838>/8α C8α 71α 5>C5?0C1α 8>α 70α .8??5E>α 0>/825120α 87α 284:82F1α
3@>531α I125F1>/07α C8H82Bα ?:3A752α ?1>α 70.α.5=:58>/8.α?:0>/@0.α3@>530.α
284825C0.α0α70α.8??5E>αH2:/0Nα
0-α]0]]β]αA020αH0220.α?122:=0C0.αC8αC5B38/21α38>12α1α5=:07α0α(KγSα;α?1>α
:>0α28.5./8>?50α0α70α47:8>?50α>1α38>12α9:8α<β]]αQ=K?3n)α
H-α]0]]β(ααA020α1/20.αH0220.α?122:=0C0.)α
?-α]0]]β]α A020α α 30770α 878?/21.17C0C0α 75.0α 1α ?122:=0C0α C8α C5B38/21α
5>482512α0αρ(α33)α
α α α
 ./8α 289:5.5/1α A1C2Bα 8<?8A/:02.8α ?:0>C1α 87α 2>=8>5821α ±21;8?/5./0α
C5.A1>=0α 6:>/0.α C8α ?1>/20??5E>α ;α .8D078α A21?8C5358>/1.α ?1>./2:?/5L1.α
9:8α?1>/2178>α71.α848?/1.αC8α?1>/20??5E>α;α/83A820/:20)α
α
ρ()()1α  7α 0?821α A12α /83A820/:20α ;α ?1>/20??5E>α A1C2Bα C5.A1>82.8α 8>α 30;12α
A21A12?5E>α8>α70α?020α8<A:8./0αC87α3:210αC8H58>C1α?171?02.8α8>α03H0.α
?020.αA020α3:21.αC8α8.A8.12α30;12α1α5=:07α0αβ(α?3)α
α

104.    L5N
 SGSG5N 0bNs(pc(sxiN=(sz79gbNmNhis7xi8zgbN8iNf(N9ibi9gsvNgN(ftg97gn7(8ziNngmisN
Kc(NUN=(9(fN(bN(ft(fisNy(bNncsiN87NKc(N5SN9nGN
N
 SGSGSN 1iNf(svN8(9(fgs7iN9i8p78gsN(bNs(pc(sxiN=(sz79gbN9i8N(fzs7óifNf7NfcN9cg8zÁgN
(fN 78p(s7isN gN LXL N s(ft(9ziN gN bgN f(997–8N ósczgN iN 9cg8yiN (bN s(pc(sxiN
=(sz79gbN8iNf(Ns(Kc7(sgNtisN9ints(f7–8GN
15.6  ABERTURAS  
N
 SGVG N IgfNgó(szcsgfN(8NbifNncsifNy(ó(sv8Ncó79gsf(Ny(NniyiNzgbNy(Ns(yc97sNbiN
n(8ifNtif7ób(NfcN9gtg97ygyNs(f7fz(8z(GN
N
 SGVGON IgN ts(f(897gN y(N gó(szcsgfN y(ó(svN 9i8f7y(sgsf(N (8N ziyiN 9vb9cbiN y(N
s7H7y(9(fNmNs(f7fz(897gfGN
N
 SGVGUN 2(ó(svN9ibi9gsf(NógssgfNgNbiNbgsHiNy(N9gygNbgyiNy(NbgNgó(szcsgNmNzgnó7j8N
(8NpisngNy7gHi8gbNgNbifNbgyifNy(NbgNn7fngXNtsibi8Hv8yibgfNc8gNy7fzg897gN
7HcgbNgNbgNbi8H7zcyNy(Ng89bg/(NlyN(8Nzsg997–8Ny(fy(NbgfN(fKc78gfGN
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

105.   ρ](α
CAPÍTULO 16 - ZAPATAS 
 
16.1  GENERALIDADES  
α
ρ=)ρ)ρα Σ0.α F0A0/0.α C8H82B>α C538>.51>02.8α A020α /20>.35/52α 07α .:871α C8α
?538>/0?5E>α:>0αA28.5E>α3B<530α9:8α>1α8<?8C0α0α70α8.A8?545?0C0α8>α87α
 ./:C51αC8α,8?B>5?0αC8α°:871.)αα
°8α ?1>.5C8202B>α A020α 8./8α 45>α 70.α ?02=0.α ;α 3138>/1.α C8α .82L5?51α +.5>α
03A7545?02-α8>α70αH0.8αC8α70.α?17:3>0.)α
α
ρ=)ρ)βα Σ0.α.175?5/0?51>8.α9:8α.8α/20>.45820>α07α.:871α.8αC8H82B>αL82545?02αA020α
70.αC5./5>/0.α?13H5>0?51>8.αC8α?02=0α0?/:0>/8.α.1H28α70α8./2:?/:20)α
α
ρ=)ρ)1α  >α87α?0.1αC8αF0A0/0.α?1>αA571/8.0αG./0.α.8αC538>.51>02B>αC8α0?:82C1α07α
>M3821αC8αA571/8.α289:825C1)α
α
ρ=)ρ)<α  >α87α?B7?:71αC8α70.αA28.51>8.αC8α?1>/0?/1α8>/28α70.αF0A0/0.α;α87α.:871α>1α
.8αC8H82B>α?1>.5C8202α/20??51>8.)α
α
ρ=)ρ)(α Φα38>1.α9:8α87α ./:C51αC8α,8?B>5?0αC8α°:871.α>1α71αA8235/00α.8αA1C2Bα
?1>.5C8202α:>α5>?2838>/1αC87α1]Rα8>α87αL0712αC8α70αA28.5E>α0C35.5H78αC87α
.:871αA020α71.α8./0C1.αC8α?02=0α8>α71.α5>/82L8>=0α.5.31α1αL58>/1)α
α
ρ=)ρ)=α Σ0.α ?17:3>0.α 1α A8C8./078.α C8α 41230α ?52?:702α1α C8α A17@=1>1α 28=:7020α
A1C2B>α?1>.5C8202.8α?131α?17:3>0.α?:0C20C0.α?1>α70α35.30αB280αA020α
848?/1.α C8α 70α 71?075F0?5E>α C8α 70.α .8??51>8.α ?2@/5?0.α A020α C5.8D1α A12α
478<5E>0α?12/0>/8α1α71>=5/:CαC8α0>?7068αC87α284:82F1α8>α70.αF0A0/0.)α
α
ρ=)ρ)×α  >α/8228>1.αC8αH060α?0A0?5C0CαA12/0>/80α?538>/0?51>8.α.1H28αA571/8.α;α
?:0>C1α 87α  ./:C51α C8α ,8?B>5?0α C8α °:871.α 71α 28?1358>C80α C8H82B>α
?1>8?/02.8α 70.α F0A0/0.α 38C50>/8α L5=0.0α 8L07:B>C1.8α8>α 87α C5.8D1α 87α
?13A12/0358>/1α C8α G./0.α C8α 0?:82C1α 0α .:α 25=5C8Fα ;α 70α C87α ?1>6:>/1α
.:871J?538>/0?5E>)α
 >α 71.α ?0.1.α C8α 3:21.α C8α 07H0D5782@00α .8α A1C2Bα 71=202α 8./0α ?1>8<5E>α
38C50>/8α?5358>/1.α1α.1H28?5358>/1.α0230C1.)α
α
16.2    DISEÑO  DE  ZAPATAS  POR  FUERZA  CORTANTE  Y 
PUNZONAMIENTO  
α
ρ=)β)ρα  7αC5.8D1αC8αF0A0/0.αA12α4:82F0α?12/0>/8α;αA:>F1>0358>/1α8>α70α?82?0>@0α
C8α 70α ?17:3>0α 8./02Bα 28=5C0α A12α 70α 3B.α .8L820α C8α 70.α .5=:58>/8.α C1.α
?1>C5?51>8.Nα
α
0-α σ:82F0αφ12/0>/8α
.0A0/0α9:8α0?/M0α?131αL5=00α?1>α:>0α.8??5E>α?2@/5?0α9:8α.8α8</58>C8α
8>α :>α A70>1α 0α /20LG.α C87α 0>?I1α /1/07α ;α 9:8α 8./Bα 71?075F0C0α 0α :>0α
C5./0>?50αSCSαC8α70α?020αC8α70α?17:3>0α1αA8C8./07)α
 >α8./0α?1>C5?5E>Nα
:ααα≤αααφα>αα
α

106.   ρ]=α
αmmα
?ααα\ααα]0(1α√α4W?αHαCαα
α
H-α ±:>F1>0358>/1α
.0A0/0α 9:8α 0?/M0α 8>α C1.α C528??51>8.0α ?1>α :>0α .8??5E>α ?2@/5?0α
A82A8>C5?:702α 07α A70>1α C8α 70α 71.0α ;α 71?075F0C0α C8α /07α 41230α 9:8α .:α
A82@38/21α H1α .80α 3@>5310α A821α 9:8α >1α >8?8.5/0α 0A21<5302.8α 0α
38>1.αC8αSCKβSαC87αA82@38/21αC87αB280αC8α70αα?17:3>0)α
 >α8./0α?1>C5?5E>Nα
:ααα≤αααφα>αα
αααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααmmα
?ααα\ααα+α]0(1α]αρ)ραKαβ?α-α√α4W?αHαCα
α
A821α>1α30;12α9:8Nαααααααααααααααααααααααmmα
ρ0ραα√α4W?αH1αCα
α
C1>C8αβ?α8.α70α2870?5E>αC87α70C1α702=1α0α70C1α?12/1αC8α70α.8??5E>αC8α70α
?17:3>0α;αH1α8.α87αA82@38/21αC8α70α.8??5E>α?2@/5?0)α
α
 7α A8207/8α C8α 70.α F0A0/0.α 8./02Bα ?1>/2170C1α A12α 87αC5.8D1α A12α ?12/8α ;α
A:>F1>0358>/10α C8H58>C1α L82545?02.8α 0C5?51>0738>/8α70α 71>=5/:Cα C8α
0>?7068αC8α70.αH0220.αC8α284:82F1α71>=5/:C5>07αC87α87838>/1α9:8α.1A12/0)α
α
16.3  DISEÑO DE ZAPATAS POR FLEXIÓN  
α
ρ=)1)ρα  7α 3138>/1α 8</82>1α 8>α ?:079:582α .8??5E>α C8α :>0α F0A0/0α C8H82Bα
C8/8235>02.8αI0?58>C1αA0.02α:>αA70>1αL82/5?07α0α/20LG.αC8α70αF0A0/0α;α
?07?:70>C1α87α3138>/1αA21C:?5C1αA12α70.α4:82F0.α9:8α0?/M0>α.1H28α87α
B280α/1/07αC8α70αF0A0/0α9:8α9:8C8α0α:>α70C1αC8αC5?I1αA70>1αL82/5?07)α
α
ρ=)1)βα α±020α 87α C5.8D1α A12α 478<5E>α .8α C8H82B>α ?1>.5C8202α ?131α .8??51>8.α
?2@/5?0.α70.α.5=:58>/8.Nαα
α
0-α Σ0α.8??5E>α8>α70α?020αC8α70α?17:3>00α3:21α1αA8C8./07α.5α8./1.α.1>αC8α
?1>?28/1α0230C1)α
α
H-α  >α 87α A:>/1α 38C51α 8>/28α 87α 868α ?8>/07α ;α 87α H12C8α C87α 3:21α A020α
F0A0/0.α9:8α.1A12/8>α3:21.αC8α07H0D5782@0)α
α
?-α  >α 87α A:>/1α 38C51α 8>/28α 70α ?020α C8α 70α ?17:3>0α ;α87α H12C8α C8α 70α
A70>?I0α 38/B75?0α C8α 0A1;1α A020α F0A0/0.α 9:8α .1A12/0>α ?17:3>0.α
38/B75?0.α1αC8α30C820)α
α
ρ=)1)1α  >α F0A0/0.α 0230C0.α 8>α :>0α C528??5E>α +?538>/0?51>8.α ?1225C0.-α ;α 8>α
F0A0/0.α ?:0C20C0.α 0230C0.α 8>α C1.α C528??51>8.0α 87α 284:82F1α C8H82Bα
C5./25H:52.8α:>54123838>/8α0α/20LG.αC87α0>?I1α/1/07αC8α70αF0A0/0)α
α
ρ=)1)<α  >α F0A0/0.α 28?/0>=:7028.α 0230C0.α 8>α C1.α C528??51>8.0α 87α 284:82F1α
C8H82Bα?1>.5C8202.8α?131α.8α5>C5?0α0α?1>/5>:0?5E>Nα
α

107.    L4N
geN 08N bgN y7s(997–8N bgsHgXN (bN s(pc(sxiN f(N y7fzs7óc7svN c87pisn(n(8z(N gN
zsg=jfNy(bNg89hiNzizgbGN
N
óeN 08N bgN y7s(997–8N 9iszgXN f(N 9i89(8zsgsvN c8gN tis97–8N y(bN g9(siN zizgbN
s(Kc(s7yiN(8Nc8gNpsg8/gN9(8zsgygNs(ft(9ziNgbN(/(Ny(NbgN9ibcn8gN9cmiN
g89hiNf(gN7HcgbNgNbgNbi8H7zcyNy(bNbgyiN9isziNy(NbgNxgtgzgGN
N
0fzgNtis97–8Ny(bNg9(siNzizgbNs(Kc(s7yiNf(svNNOáu.] eNN=(9(fN(bNvs(gN
zizgbXNyi8y(N.N(fNbgNs(bg97–8NbgyiNbgsHiNgNbgyiN9isziNy(NbgNxgtgzgGN0bN
s(fziN y(bN s(pc(sxiN y(ó(svN y7fzs7óc7sf(N c87pisn(n(8z(N (8N bgfN xi8gfN
Kc(NKc(y(8Npc(sgNy(NbgNpsg8/gNNgfÁNy(p787ygGN
N
16.4  TRANSMISIÓN DE FUERZAS EN LA BASE DE COLUMNAS,  MUROS 
O PEDESTALES ARMADOS  
N
 VG5G N IgfNpc(sxgfNmNnin(8zifN(8NbgNógf(Ny(N9ibcn8gfXNncsifNmNt(y(fzgb(fN
gsngyifN y(ó(sv8N zsg8fn7z7sf(N gN bgN xgtgzgN gN zsg=jfN y(bN 9i89s(ziN mN y(bN
s(pc(sxiNbi8H7zcy78gbNKc(Ng89bgN(8NbgNxgtgzgGN
N
 VG5GON 0bN(fpc(sxiNy(Ngtbgfzgn7(8ziNy(bN9i89s(ziN(8NbgNfct(sp797(Ny(N9i8zg9ziN
(8zs(N(bN(b(n(8ziNy(NgtimiNmN(bN(b(n(8ziNgtimgyiXN8iNy(ó(svN()9(y(sNbgN
s(f7fz(897gN gbN gtbgfzgn7(8ziN y(bN 9i89s(ziN tgsgN 9gygN fct(sp797(XN y(N
g9c(syiN9i8NbiNy7ftc(fziN(8NbgNÍ(997–8N OGQGN
N
 VG5GUN 0bNs(pc(sxiNy(Ng9(siNbi8H7zcy78gbNy(NbgN9ibcn8gXNncsiNiNt(y(fzgbNgsngyiN
Kc(Ntgf(NgNzsg=jfNy(NbgN/c8zgN(8zs(N(fzifNmNbgNxgtgzgNy(ó(svNf(sN9gtgxN
y(Nzsg8fn7z7sNN
N
geN ÉiygN bgN pc(sxgN y(N 9ints(f7–8N Kc(N ()9(ygN gN bgN s(f7fz(897gN gbN
gtbgfzgn7(8ziNn(8isNy(bN9i89s(ziNy(NbifN(b(n(8zifGN
N
óeN RcgbKc7(sNpc(sxgNy(Nzsg997–8N9gb9cbgygN(8NbgN/c8zgN(8zs(N(bN(b(n(8ziN
gtimgyiNmN(bN(b(n(8ziNy(NgtimiGN
N
 VG5G5N IgfNpc(sxgfNbgz(sgb(fNy(ó(sv8Nzsg8fn7z7sf(NgbNt(y(fzgbNiNgNbgNxgtgzgXNy(N
g9c(syiN 9i8N biN y7ftc(fziN (8N bgN Í(997–8N  UGSN –N n(y7g8z(N izsifN
y7ftif7z7=ifNgtsiógyifGN
N
 VG5GSN AgsgN 9ibcn8gfN mN t(y(fzgb(fN gsngyifN =g97gyifN(8N f7z7iXN (bN vs(gN y(N
s(pc(sxiNgNzsg=jfNy(NbgN/c8zgN(8zs(NjfzifNmNbgNxgtgzgNf(svN9iniNnÁ87niN
LXLLSN=(9(fN(bNvs(gNy(bN(b(n(8ziNgtimgyiGN
N N
 VG5GVN AgsgNncsifN=g97gyifN(8Nf7z7iXN(bNvs(gNnÁ87ngNy(Ns(pc(sxiNgNzsg=jfNy(NbgN
/c8zgN (8zs(N (fzifN mN bgN xgtgzgN f(svN 8iN n(8isN gbN vs(gN nÁ87ngN =(sz79gbN
(ft(97p79gygNtgsgNncsifGN
N
16.5  ZAPATAS INCLINADAS O ESCALONADAS  
 
 VGSG N IgfN xgtgzgfN tiysv8N f(sN 789b78gygfN iN (f9gbi8gygfN ut(sgbz(N =gs7gób(eXN
y(ó7j8yif(N9cntb7sN9i8NbifNs(Kc7f7zifNy(Ny7f(:iN(8NziygNf(997–8GN

108.    LQN
 VGSGON IgfNxgtgzgfN789b78gygfNiN(f9gbi8gygfNKc(Nf(Ny7f(:(8N9iniNc8gNc87ygyN
y(ó(sv8N 9i8fzsc7sf(N y(N ng8(sgN y(N gf(HcsgsN fcN 9intiszgn7(8ziN 9iniN
zgbGN
N
16.6  ZAPATAS COMBINADAS Y LOSAS DE CIMENTACIÓN 
N
 VGVG N IgfN xgtgzgfN 9inó78gygfN mN bgfN bifgfN y(N 97n(8zg97–8N y(ó(sv8N f(sN
y7f(:gygfN 9i8f7y(sg8yiN c8gN y7fzs7óc97–8N y(N bgfN ts(f7i8(fN y(bN z(ss(8iN
g9isy(N9i8NbgfNtsit7(ygy(fNy(bNfc(biNy(N97n(8zg97–8NmNbgN(fzsc9zcsgNmN
9i8NbifNts7897t7ifN(fzgób(97yifN(8NbgNÓ(9v879gNy(NÍc(bifGN
N
 VGVGON 1iNy(ó(svNcfgsf(N(bNÓjziyiN27s(9ziNy(Ny7f(:iNy(bNRgtÁzcbiN 4GN
N
16.7  DISPOSICIONES ESPECIALES PARA ZAPATAS SOBRE PI LOTES  
 
 VG4G NN 0bN 9vb9cbiN y(N bifN nin(8zifNmN9iszg8z(fNtgsgNxgtgzgfNgtimgygfNfiós(N
t7biz(fNy(ó(svNógfgsf(N(8NbgNfctif797–8Ny(NKc(NbgNs(g997–8Ny(N9cgbKc7(sN
t7biz(N(fzvN9i89(8zsgygN(8N(bN(/(Ny(bNn7fniGN
N
 VG4GONN 2(ó(svN =(s7p79gsf(N (bN (fpc(sxiN y(N tc8xi8gn7(8ziN tsiyc97yiN tisN bgN
g997–8Ny(NbgN9gsHgN9i89(8zsgygNy(bNt7biz(N(8NbgNxgtgzgGN
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
CAPÍTULO 17 - LOSAS ARMADAS EN DOS DIRECCIONES 
N
17.1     GENERALIDADES 
N

109.    LJN
 4G G NN IgfNy7ftif797i8(fNy(N(fz(NRgtÁzcbiNs7H(8N(bNy7f(:iNy(NbifgfNgsngygfN(8N
yifNy7s(997i8(fN9i8NiNf78N=7HgfNy(NgtimiGN
N
 4G GONN IgfNbifgfNtiysv8Nf(sNng97xgfXNgb7H(sgygfNiN8(s=gygfGN
N
 4G GUNN 0bNt(sgbz(NnÁ87niNy(NbgfNbifgfNgsngygfN(8NyifNy7s(997i8(fN(fzgsv8Ny(N
g9c(syiN9i8NbiN78y79gyiN(8NbgNÍ(997–8N LGSGN
N
17.2    PROCEDIMIENTO DE ANÁLISIS  
N
 4GOG NN 0bN g8vb7f7fN y(N c8gN bifgN gsngygN (8N yifN y7s(997i8(fN f(N tiysvN s(gb7xgsN
n(y7g8z(N 9cgbKc7(sN tsi9(y7n7(8ziN Kc(N fgz7fpgHgN bgfN9i8y797i8(fN y(N
(Kc7b7ós7iN mN 9intgz7ó7b7ygyXN f7N f(N y(nc(fzsgN Kc(N 9cntb(N 9i8N bifN
s(Kc7f7zifN y(N s(f7fz(897gN s(Kc(s7ygN uÍ(997i8(fN  LGON mN  LGUeN mN bgfN
9i8y797i8(fNy(Nf(s=797iNs(bgz7=gfNgNy(pb()7i8(fNmNgHs7(zgn7(8ziNuÍ(997–8N
 LG5eGN
N
 4GOGONN AgsgNbifgfNgsngygfN(8NyifNy7s(997i8(fNKc(Nz7(8(8Ntg:ifNs(9zg8Hcbgs(fN
iN 9cgysgyifXN 9i8N iN f78N =7HgfN y(N gtimiN 9i8f7y(sg8yiN9gsHgfN
c87pisn(n(8z(Ns(tgsz7ygfXN(8NbcHgsNy(Ns(gb7xgsN(bNg8vb7f7fN78y79gyiN(8NbgN
f(997–8N g8z(s7isXN f(N tiysvN cz7b7xgsN bifN njziyifN gtsi)7ngyifN y(N bgfN
Í(997i8(fN 4GQNmN 4GJGN
N
17.3    REFUERZO DE LA LOSA  
N
 4GUG NN 0bNvs(gNy(Ns(pc(sxiN(8N9gygNy7s(997–8Ny(ó(svNy(z(sn78gsf(NgNtgsz7sNy(N
bifN nin(8zifN (8N bgfN f(997i8(fN 9sÁz79gfXN t(siN 8iN f(svN n(8isN Kc(N bgN
78y79gygN(8NbgNÍ(997–8N  GSG5GN
N
 4GUGONN 0bN (ftg97gn7(8ziN y(bN s(pc(sxiN (8N bgfN f(997i8(fN 9sÁz79gfN 8iN y(ó(svN
()9(y(sNy(Nzs(fN=(9(fN(bN(ft(fisNy(NbgfNbifgfXN()9(tziN(8N(bN9gfiNy(N
bifgfN8(s=gygfNiNgb7H(sgygfGN
N
 4GUGUNN AisNbiNn(8ifN áUNy(bNs(pc(sxiNtisNnin(8ziNtif7z7=iNt(st(8y79cbgsNgNc8N
óisy(Ny7f9i8z78ciXNy(ó(svNtsibi8Hgsf(NhgfzgN(bNóisy(Ny(NbgNbifgNmNz(8(sN
c8gN bi8H7zcyN y(N g89bg/(N y(NtisNbiNn(8ifN SN9nN(8NbgfN=7HgfNiNncsifN
t(s7n(zsgb(fGN
N
 4GUG5NN 0bNs(pc(sxiNtisNnin(8ziN8(Hgz7=iXNt(st(8y79cbgsNgNc8Nóisy(Ny7f9i8z78ciXN
y(ó(svNg89bgsf(N(8NbgfN=7HgfNiNncsifNt(s7n(zsgb(fNtgsgNKc(Ny(fgssibb(N
fcN(fpc(sxiNy(Nzsg997–8XNy(Ng9c(syiNgNbiNNs(Kc(s7yiN(8N(bNRgtÁzcbiNQGN
N
 4GUGSNN Rcg8yiNbgNbifgN8iN(fzjNgtimgyiN(8Nc8gN=7HgNiNncsiNt(s7n(zsgbNuzsgniN
()z(s7iseN(bNg89bg/(Ny(bNs(pc(sxiNf(NhgsvNy(8zsiNy(NbgNtsit7gNbifgGN
N
 4GUGVNN IgfN bifgfN 9i8N =7HgfN y(N gtimiN z(8ysv8N c8N s(pc(sxiN (ft(97gbN (8N bgfN
(fKc78gfN()z(s7is(fXNzg8ziN(8NbgN9gsgN78p(s7isN9iniN(8NbgNfct(s7isNy(NbgN
bifgNy(Ng9c(syiNgNN
N
geN0bN s(pc(sxiN (ft(97gbN zg8ziN (8N bgN 9gsgN 78p(s7isN 9iniN (8N bgN fct(s7isNN

110.   ρρ]α
C8H82Bα .82α .:45?58>/8α A020α 28.5./52α :>α 3138>/1α 5=:07α 07α 3138>/1α
A1.5/5L1α3B<531α+A12α38/21αC8α0>?I1-αC8α70α71.0)α
H-αΣ0α C528??5E>α C87α 3138>/1α C8H82Bα .:A1>82.8α A0207870α 0α 70α C50=1>07α
9:8α A02/8α C8α 70α 8.9:5>0α A020α 70α ?020α .:A82512α C8α 70α 71.0α ;α
A82A8>C5?:702α0α70αC50=1>07αA020α70α?020α5>482512αC8α70α71.0)α
?-α 7α 284:82F1α 8.A8?507α C8H82Bα ?171?02.8α 0α A02/52α C8α 70α 8.9:5>0α 0α :>0α
C5./0>?50α8>α?0C0αC528??5E>α5=:07α0αρK(αC8α70α71>=5/:Cα30;12αC87αA0D1)α
C-α 7α 284:82F1α C8α 70α 71.0α .8α A1C2Bα ?171?02α A0207871α 0α 70α C528??5E>α C87α
3138>/10α1α8>αC1.αC528??51>8.αA0207870.α0α71.α70C1.αC87αA0D1)α
α
17.4    DISPOSICIONES ESPECIALES PARA LOSAS SIN VIGAS   
α
ρ×)<)ρ   √ [ πΦΣ2μΦμ ° 
α
ρ×)<)ρ)ρα Σ0.α8./2:?/:20.αC5.8D0C0.α?1>.5C820>C1α71.0.α.5>αL5=0.αC8H82B>α/8>82α
8>α?:8>/0α70α/20>.35.5E>αC8α3138>/1.α8>/28α70.α?17:3>0.α;α70.αF1>0.α
C8α 71.0α ?82?0>0.α 0α 70.α 35.30.α C8H5C1α 0α ?02=0.α C8α =20L8C0Cα
C8.H070>?80C0.α;α0α4:82F0.α70/82078.αC8α.5.31)α
α
ρ×)<)ρ)βα °8α C8H82Bα A28L82α 3:21.α C8α ?12/8α ?1>α 87α 1H68/1α C8α A21A12?51>02α
0C8?:0C0.α25=5C8Fα70/8207α;α28.5./8>?50α07α.5./830αC8α71.0.α.5>αL5=0.)α[1α
.82Bα >8?8.0250α 8./0α 8<5=8>?50α .5α .8α C83:8./20α 9:8α .8α .0/5.40?8>α 71.α
289:5.5/1.α C8α C8.A70F0358>/1α 70/8207α 3B<531α C8α 70α [1230α ≥G?>5?0α C8α
 C545?0?5E>α  )]1]α C8α μ5.8D1α °5.31228.5./8>/8α ;α .8α 0.8=:20α :>0α
0C8?:0C0α/20>.35.5E>αA12α?12/0>/8α;α478<5E>αC8α71.α3138>/1.α8>/28α70α
71.0α;α70.α?17:3>0.)α
α
ρ×)<)ρ)1α ±020α A21A12?51>02α 30;12α 28.5./8>?50α A12α ?12/0>/8α 8>α C1.α C528??51>8.α
+A:>F1>0358>/1-0α 70.α 71.0.α .5>α L5=0.α A1C2B>α C5.8D02.8α ?1>.5C820>C1α
BH0?1.α1α?0A5/878.)α
α
°E71α.8α?1>.5C8202Bα8./2:?/:20738>/8α848?/5L0α70αA02/8αC8α?0A5/87α9:8α.8α
71?075?8α C8>/21α C87α 30;12α ?1>1α ?52?:7020α A52B35C8α 28?/0α 1α ?:D0α
0?I0470>0C0α?1>α.:.αA70>1.α0α>1α3B.αC8α<(°αC87α868αC8α70α?17:3>0)α
α
ρ×)<)βα ≥πΦ[°,2°2>[αμ α,δ, [≥δα [≥π αΣδ°Φ°α8αφδΣ≤,[Φ °α±ΦπΦα
Σδ°Φ°α°2[α2√Φ°α
α
ρ×)<)β)ρα φ:0>C1α70.α?02=0.αC8α=20L8C0Cα;K1α70.α4:82F0.αC8α.5.31α:α1/20.α4:82F0.α
70/82078.α ?0:.8>α /20>.4828>?50α C8α 3138>/10α :>0α A02/8α C87α 3138>/1α
C8H82Bα.82α/20>.4825C0αA12α478<5E>α;α87α28./1αA12α?12/0>/8α8<?G>/25?1α/07α
?131α.8α5>C5?0α0α?1>/5>:0?5E>Nα
α
0-αΣ0α A02/8α C87α 3138>/1α C8.89:575H20C1α A12α 478<5E>α/20>.4825C1α .8α
?07?:702Bα8L07:0>C1αγ4Nα
mmmmmα
γ4ααα\αααρααKαα+ααρα]αβK1αlαHρKHβαα-α
α
°58>C1Nα
HρNαΦ>?I1α /1/07α C8α 70α .8??5E>α ?2@/5?00α C845>5C0α 8>α70α °8??5E>α

111.   ρρρα
ρ×)ρ])1)ρ0α38C5C0α8>α70αC528??5E>αC8α70α7:FαA020α70α?:07α.8α
I0>αC8/8235>0C1α71.α3138>/1.α+Hρ\φρ]C-)α
HβNαΦ>?I1α /1/07α C8α 70α .8??5E>α ?2@/5?00α C845>5C0α 8>α70α °8??5E>α
ρ×)ρ])1)ρ0α 38C5C0α 8>α 70α C528??5E>α A82A8>C5?:702α 0α Hρα
+Hβ\φβ]C-)α
α
H-αΣ0α A02/8α C87α 3138>/1α /20>.4825C1α A12α 478<5E>α C8H82Bα ?1>.5C8202.8α
/20>.35/5C0α .1H28α :>0α 420>60α C8α 71.0α ?:;1α 0>?I1α 848?/5L1α 8./Gα
?13A28>C5C1α8>/28α7@>80.α71?075F0C0.α0αρ0(αL8?8.α87αA8207/8αC8α70α71.0α
1αC87αBH0?1α4:820αC8α70α?020.αC8α70α?17:3>0α1αC87α?0A5/87)α
α
?-α±1C2Bα ?1>?8>/202.8α 87α 284:82F1α .1H28α 70α ?17:3>00α 28C:?58>C1α 87α
8.A0?50358>/1α 1α 0D0C58>C1α 284:82F1α 0C5?51>070α A020α28.5./52α 87α
3138>/1α/20>.4825C1αA12α478<5E>α8>α87α0>?I1α848?/5L1αC845>5C1)α
α
C-αΣ0α A02/8α C87α 3138>/1α C8.89:575H20C1α /20>.4825C1αA12α ?12/0>/8α
8<?G>/25?1α.8α?07?:702Bα8L07:0>C1αγ?Nα
α
γc   =   1  -  γ4α
α
 ./0α A02/8α C87α 3138>/1α /20>.35/5C0α A12α ?12/0>/8α .8α?1>.5C8202Bα
0A75?0C0α .1H28α :>0α .8??5E>α :H5?0C0α 0α 71α 702=1α C87α A82@38/21α H1α
1H/8>5C1α0α:>0αC5./0>?50αCKβαC8.C8α70.α?020.αC8α70α?17:3>0α1α?0A5/87)α
α
8-αΣ1.α8.4:82F1.αC8α?12/0>/8α28.:7/0>/8αC8α70α/20>.4828>?50αC8α3138>/1α
A12α 8<?8>/25?5C0Cα C87α ?12/0>/80α C8H82B>α .:A1>82.8α L0250H78.α
75>80738>/8α0728C8C12αC8α70α.8??5E>α?2@/5?0)α
α
 7α8.4:82F1α?12/0>/8α28.:7/0>/8αC8α70α?02=0α0<507α;αC8α8./8α3138>/1α
.82BNα
L:ααα\ααα:αKα+H1αC-ααα[αααγ?α,:αφαKα5?α
α
C1>C8αφα8.α70αC5./0>?50α38C5C0αC8.C8α87α?8>/215C8αC8α70α.8??5E>αC8α
?12/8α 0α 70α .8??5E>α ?2@/5?0α 8>α 8./:C51α 8>α 70α C528??5E>α C1>C8α 0?/M0α 87α
3138>/1α ;α 5?α 8.α 70α A21A58C0Cα C8α 70α .8??5E>α ?2@/5?0α0>B71=0α 07α
3138>/1αA1702αC8α5>82?50)α
α
±020α:>0α?17:3>0α5>/82512αC8α.8??5E>α28?/0>=:702αC8α70C1.αφρα;αφβ0α
C1>C8αφρα8./Bα8>α70αC528??5E>αC1>C8α0?/M0α87α3138>/10α.8α/8>C2BNα
α
H1ααα\αααβα+φρα]αC-α]αβα+φβα]αC-ααα\αααβαHραα]ααβαHβα
α
φ3B<ααα\αααHραKαβα
αααααααα α ααα α α α
5?ααα\αααHρoαCαKα=αα]ααHραCoαKα=αα]ααCαHβαHρnαKαβα
α
±020α:>0α?17:3>0α8</82512αC8α.8??5E>α28?/0>=:702αC8α70C1.αφρα;αφβα.8α
/8>C2BNα
α
H1ααα\αααβαHραα]ααHβα

112.     ON
N
peN IifN (fpc(sxifN y(N 9iszg8z(N gfÁN ióz(87yifN 8iN y(ó(sv8N ()9(y(sN (bN
(fpc(sxiNy(N9iszg8z(N(8NyifNy7s(997i8(fNutc8xi8gn7(8zieN78y79gyiN(8N
bgNf(997–8N 4G LGN
N
17.5  FRANJAS  DE  COLUMNAS  Y  FRANJAS  CENTRALES  - 
DEFINICIONES 
 
 4GSG NN Í(Ny(8in78gN3sg8/gNy(NRibcn8gNgNc8gNpsg8/gNy(Ny7f(:iN9i8Nc8NNg89hiXN
gN9gygNbgyiNy(bN(/(Ny(NbgN9ibcn8gN7HcgbNgNNLXOSNl NN–NNLXOSNlOXN(bNKc(Nf(gN
n(8isGN yi8y(Nl XN (fN bgN bi8H7zcyN y(bN tg:iN (8N bgN y7s(997–8N (8N Kc(N f(N
y(z(sn78g8NbifNnin(8zifNmNlON(fNbgNbi8H7zcyNy(bNtg:iN(8NbgNy7s(997–8N
zsg8f=(sfgbNgNl XNgnógfNNn(y7ygfN9(8zsiNgN9(8zsiNy(NbifNgtimifGN
N
 4GSGONN IgNpsg8/gNy(N9ibcn8gN789bcm(NgNbgN=7HgNf7NjfzgN()7fz(GN
N
 4GSGUNN Í(N y(8in78gN psg8/gN 9(8zsgbN gN c8gN psg8/gN y(Ny7f(:iN b7n7zgygN tisN yifN
psg8/gfNy(N9ibcn8gfGN
N
17.6    ABERTURAS EN LOSAS 
 
 4GVG NN Í(N tiysvN z(8(sN gó(szcsgfN y(N 9cgbKc7(sN zgng:iN f7N f(N y(nc(fzsgN tisN
n(y7iN y(bN g8vb7f7fN Kc(N bgN s(f7fz(897gN Mbz7ngN tsitis97i8gygN (fN tisN biN
n(8ifN7HcgbNgNbgNs(Kc(s7ygNmNKc(Nf(N9cntb(8NbgfN9i8y797i8(fNy(Nf(s=797iXN
9i8f7y(sv8yif(NbifNbÁn7z(fNy(Ny(pb()7i8(fN78y79gyifN(8NbgNÍ(997–8N LGSGN
N
 4GVGONN Í(N tiysvN in7z7sN (bN g8vb7f7fN 78y79gyiN (8N bgNÍ(997–8N  4GVG N f7(nts(N Kc(N
c8gNgó(szcsgN(8NbifgN9cntbg8NbifNf7Hc7(8z(fNs(Kc7f7zifNN
N
geNÍ7N (fzv8N bi9gb7xgygfN (8N bgN xi8gN 9inM8N y(NyifNpsg8/gfN9(8zsgb(fXNf(N
ng8z(8ysvN bgN 9g8z7ygyN zizgbN y(N s(pc(sxiN s(Kc(s7yiN tisN (bN tg:iN f78N
9i8f7y(sgsNbgNgó(szcsgGN
N
óeNIgN xi8gN 9inM8N y(N yifN psg8/gfN y(N 9ibcn8gN Kc(N f(N 78z(sf(9z(8N 8iN
y(ó(svN78z(sscnt7sf(NtisNgó(szcsgN8iNf(svNngmisNy(N áQNy(bNg89hiNy(N
bgN psg8/gN y(N 9ibcn8gN nvfN g8HifzgGN 0bN (Kc7=gb(8z(N y(bN s(pc(sxiN
78z(sscnt7yiNtisNbgNgó(szcsgNy(ó(svNg:gy7sf(N(8NbifNbgyifNy(NjfzgGN
N
9eN(8NbgNxi8gN9inM8NNy(Nc8gNpsg8/gNy(N9ibcn8gNmNc8gNpsg8/gN9(8zsgbXN8iN
y(ó(svN 78z(sscnt7sf(N tisN bgfN gó(szcsgfN nvfN y(N  á5N y(bN s(pc(sxiN (8N
9gygNpsg8/gGN0bN(Kc7=gb(8z(Ny(bNs(pc(sxiN78z(sscnt7yiNtisNc8gNgó(szcsgN
y(ó(svNg:gy7sf(N(8NbifNbgyifNy(NjfzgGN
N
yeN1iNy(ó(svN9i8f7y(sgsf(N(p(9z7=gNgKc(bbgNtgsz(Ny(bNt(sÁn(zsiNuóieNy(NbgN
f(997–8N9sÁz79gNtisN9iszg8z(N(8NyifNy7s(997i8(fNutc8xi8gn7(8zieNKc(N
(fzjN97s9c8f9s7zgNtisNbÁ8(gfNs(9zgfNKc(Nf(Ntsim(9z(8Ny(bN9(8zsi7y(Ny(NbgN
xi8gNy(Ns(g997–8Nu9ibcn8gNiN9gt7z(beNmNKc(Nfi8Nzg8H(8z(fNgNbifNbÁn7z(fN
y(NbgfNgó(szcsgfGN
AgsgN(bN9gfiNy(N9gsHgfN9i89(8zsgygfN7ntiszg8z(fNy(ó(svN9cntb7sf(NbgN
n7fngN 9i8y797–8N 9i8f7y(sg8yiN (bN 9(8zsi7y(N y(N bgN xi8gN y(N 9gsHgN

113.   ρρ1α
?1>?8>/20C0)α
α
17.7    RIGIDEZ RELATIVA VIGA - LOSA α
α
ρ×)×)ραα °8αC845>8ααα0α70α2870?5E>α8>/28α70α25=5C8Fα0α70α478<5E>αC8α70α.8??5E>αC8α70α
L5=0α;α70α25=5C8Fα0α70α478<5E>αC8α:>0α420>60αC8α71.0α7535/0C0α70/820738>/8α
A12α71.α868.α?8>/2078.αC8αC1.α/0H7821.α0C;0?8>/8.α+.5α71.αI0;-α8>α?0C0α
70C1αC8α70αL5=0Nα
αααα\αααILααKααIρα
α
.58>C1αILα87α3138>/1αC8α5>82?50αC8α70αL5=0α8αIρα87α3138>/1αC8α5>82?50αC8α
70α71.0)α
α
ρ×)×)βαα ±020α87α?B7?:71αC8αILα.8α?1>.5C8202Bα:>0αL5=0α≥α?1>α0>?I1α9:8α5>?7:;0α
:>0α A12?5E>α C8α 71.0α 0α ?0C0α 70C1α C8α 70α L5=00α 9:8α .8α8</58>C0α :>0α
C5./0>?50α5=:07α0α70αA21;8??5E>αC8α70αA02/8αC8α70αL5=0α0H061α1α0225H0αC8α70α
71.0α+L5=0α>12307α1αL5=0α5>L82/5C0-0α70α9:8α.80α30;120αA821α>1α30;12α9:8α
<αL8?8.α85α8.A8.12αC8α70α71.0)α
α
ρ×)×)1αα Σ0α 2870?5E>ααα .8α C8H82Bα 8L07:02α A020α ?0C0α L5=0α 9:8α 41238α :>α A0D10α
C8>135>B>C1.8αα3α87αA2138C51αC8α71.αL07128.αC8αααC8α/1C0.α70.αL5=0.α
C8α:>αA0D1)α
 
17.8    MÉTODO DIRECTO 
 
ρ×)γ)ρα Σ2,2≥Φφ2δ[ °α
α
 ./8α 3G/1C1α .82Bα 0A75?0H78α ?:0>C1α .8α ?:3A70>α 70.α .5=:58>/8.α
?1>C5?51>8.Nα
α
0-α <5./8>α1αEα3B.αA0D1.α8>α?0C0αC528??5E>)α
α
H-αΣ1.αA0D1.α.80>α28?/0>=:7028.0α?1>α:>0α2870?5E>αC8α7:Fα30;12α0α7:Fα
38>120α>1α30;12αC8αβ)α
α
?-αΣ0.α71>=5/:C8.αC8αC1.αA0D1.α0C;0?8>/8.α>1αC545828>α8>α3B.αC8αρK1αC8α
70α7:Fα30;12)α
α
C-αΣ0.α ?17:3>0.α 8./G>α 075>80C0.α 1α /58>8>α :>α C8.075>80358>/1α ?131α
3B<531α 5=:07α 07α ρ]Rα C8α 70α 71>=5/:Cα C87α A0D1α 8>α 70α C528??5E>α C87α
C8.075>80358>/10α 0α A02/52α C8α ?:079:582α 868α 9:8α :>0α71.α ?8>/21.α C8α
?17:3>0.α.:?8.5L0.)α
α
8-αΣ0.α ?02=0.α .80>α C8α =20L8C0Cα ;α ?1228.A1>C8>α 0α ?02=0.α C5./25H:5C0.α
:>54123838>/8α8>α/1C1.α71.αA0D1.)α
α
4-α Σ0α?02=0αL5L0α>1α8<?8C8α0α1αL8?8.α70α?02=0α3:82/0)α
α
=-αΣ0α 2870?5E>α C8α 25=5C8Fα 2870/5L0α C8α 70.α L5=0.α 8>αC1.α C528??51>8.α
A82A8>C5?:7028.α>1α8.α38>12α9:8α]0βα>5α30;12α9:8α()α

114.   ρρ<α
α
 ./0α2870?5E>αC8α25=5C8Fα.8αC8/8235>02Bα?07?:70>C1α87α?1?58>/8Nα
α
(α1 lβn-αKα+α2 lρn-α
α
C1>C8ααρα 8.α 87α A02B38/21ααα C845>5C1α 8>α 70α .8??5E>α 0>/82512α 8>α 70α
C528??5E>αlρα;ααβα8.α87αA02B38/21ααα8>α70αC528??5E>αlβ)α
α
ρ×)γ)β   ,δ, [≥δα °≥≥2φδαΦ,±Σ2σ2φΦμδα≥δ≥ΦΣαμ α≤[α±Φδ  
 
ρ×)γ)β)ρα  7α3138>/1α8./B/5?1α03A7545?0C1α/1/07α,1αC8H82BαC8/8235>02.8α8>α:>0α
420>60α7535/0C0α70/820738>/8αA12α87α868α?8>/207αC87αA0D1α8>α?0C0α70C1αC87α
868αC8α71.α0A1;1.)α
α
ρ×)γ)β)βα Σ0α .:30α 0H.17:/0α C8α 71.α 3138>/1.α A1.5/5L1α;α >8=0/5L1α A2138C51α 8>α
?0C0αC528??5E>α>1α.82Bα38>12α9:8Nα
α
,1ααα\αααX:αlβαl>nαKαγα
α
C1>C8αl>α8.α70α7:Fα75H28α8>/28α?17:3>0.0α?0A5/878.α1α3:21.0α>1αC8H58>C1α
.82α>:>?0α38>12α0α]0=(αlρα;αX:α8.α70α?02=0α:>54123838>/8α28A02/5C0αA12α
:>5C0CαC8αB280)α
α
ρ×)γ)β)1α φ:0>C1α >1α .8α /8>=0α 70α 35.30α 71>=5/:Cα /20>.L82.07α 8>α 71.α A0D1.α
0C;0?8>/8.α07α868αC8α71.α0A1;1.α?1>.5C820C1.0αlβα.8α/1302Bα?131α87α
A2138C51αC8α70.α71>=5/:C8.α/20>.L82.078.α0C;0?8>/8.)α
α
ρ×)γ)β)<α φ:0>C1α .8α ?1>.5C828α 87α A0D1α 0C;0?8>/8α ;α A0207871α 0α :>α H12C80α 70α
C5./0>?50αC87αH12C8α07α868α?8>/207αC87αA0D1αC8H82Bα?1>.5C8202.8α?131αlβ)α
α
ρ×)γ)1α ,δ, [≥δ°α[ √Φ≥2δ°α8α±δ°2≥2δ°αΦ,±Σ2σ2φΦμδ°α
 
ρ×)γ)1)ρα Σ1.α3138>/1.α>8=0/5L1.α03A7545?0C1.α8./02B>α71?075F0C1.α8>α70α?020αC8α
71.α 0A1;1.α 28?/0>=:7028.)αΣ1.α0A1;1.αC8α41230α?52?:702α1αC8αA17@=1>1α
28=:702α .82B>α ?1>.5C820C1.α ?131α 0A1;1.α ?:0C20C1.α ?1>α :>0α B280α
89:5L078>/8)α
α
ρ×)γ)1)βα Σ1.α3138>/1.α>8=0/5L1.α;αA1.5/5L1.α03A7545?0C1.α.8α1H/8>C2B>α?131α:>α
?1845?58>/8α3:7/5A75?0C1αA12α,10αC8α70α.5=:58>/8α41230Nα
 
 
        
                 α
ααα0-ααα±Φδ°α2[≥ π2δπ °α
,+J-ααα\ααα]0=(α,1α
,+]-αα\ααα]01(α,1α
αααH-ααα±Φδ°α ≥ π2δπ °α
α φ0.1αρα φ0.1αβα φ0.1α1α φ0.1α<α φ0.1α(α
,138>/1αα α α α α α

115.   ρρ(α
[8=0/5L1α
2>/82512α
]0×(α
α
]0×]α ]0×]α ]0×]α
α
]0=(α
α
α
,138>/1α
±1.5/5L1α
α
α
]0=1α
α
α
]0(×α
α
]0(βα
α
]0(]α
α
]01(α
,138>/1α
[8=0/5L1α
 </82512α
α
α
]0]]α
α
α
]0ρ=α
α
]0β=α
α
]01]α
α
]0=(α
α
C1>C8Nαα
α
φΦ°δαραNα +12C8α8</82512α>1α28./25>=5C1α
α
φΦ°δαβαNα Σ1.0α?1>αL5=0.α8>α/1C1.α71.α70C1.α
α
φΦ°δα1αNα Σ1.0α.5>αL5=0.α
α
φΦ°δα<αNα Σ1.0α .5>α L5=0.α A821α ?1>α L5=0α C8α H12C8α +.E71α 8>α 87α
H12C8α8</82512-α
α
φΦ°δα(αNα +12C8α8</82512α/1/0738>/8α28./25>=5C1α
α
ρ×)γ)1)1α Σ0α.8??5E>α.:68/0α0α3138>/1α>8=0/5L1αC8H82BαC5.8D02.8αA020α28.5./52α87α
30;12αC8α71.αC1.α3138>/1.α>8=0/5L1.α5>/825128.αC8/8235>0C1.αA020α71.α
A0D1.α?1>α:>α0A1;1α?13M>)α
α
ρ×)γ)1)<α Σ0.α L5=0.α C8α H12C8α 1α 71.α H12C8.α C8α 70α 71.0α C8H82B>α /8>82α 70.α
C538>.51>8.α 0C8?:0C0.α A020α 28.5./52α A12α /12.5E>α 70αA02/8α C8α 71.α
3138>/1.α8</825128.α>8=0/5L1.α9:8α78.α?1228.A1>C0)α
α
ρ×)γ)1)(α ±020α/20>.4828>?50αC8α3138>/1α8>/28α70α71.0α;α:>0α?17:3>0αC8αH12C80α
8>α 87α ?0.1α C8α 71.0α .5>α L5=0.0α 70α 28.5./8>?50α >135>07α 0α 3138>/1α C8α 70α
420>60αC8α0A1;1αA21A12?51>0C0αC8H82Bα83A7802.8α?131α87α3138>/1αC8α
/20>.4828>?50αA12α?02=0αC8α=20L8C0CαC8α0?:82C1α?1>α70α°8??5E>αρ×)<)β)α
 
ρ×)γ)<αα ,δ, [≥δ°αΦ,±Σ2σ2φΦμδ°α [αΣΦασπΦ[5Φαμ αφδΣ≤, [Φαα
 
ρ×)γ)<)ρα μ8/8235>0?5E>αC8α71.α±02B38/21.ααρα;αβ/α
α
0-α 7α?1845?58>/8ααρα8.α87α?1845?58>/8αααC8α70α°8??5E>αρ×)×0αC8/8235>0C1α
8>α70αC528??5E>αC8αlρ)α
H-α 7α?1845?58>/8αβ/α28A28.8>/0α70α2870?5E>αC8α25=5C8Fα/12.51>07αC8α70αL5=0α
C8αH12C8α+A82A8>C5?:702α0αlρ-α;α70α25=5C8Fα0α478<5E>αC8α70α71.0α+8>α70α
C528??5E>αlρ-)αα
β/ααα\αααφαKα+βαIlα-α
C1>C8Nααααααααααααααααααααααααααααα
ααααααααααααααααααααααααααααααααααααααααααααααααφααα\αααΣα+αραeα]0=1ααKα8α-αoα8αKα1α

116.   ρρ=α
α
 >α70α8L07:0?5E>αC8αφ0α.8α?1>.5C8202Bα70αL5=0αC8αH12C8α?131α:>0αL5=0α
≥0α ?13A:8./0α A12α 28?/B>=:71.α C8α 70C1.α α 8α 80α .58>C1α α aα 8)α Σ0α
A12?5E>αC8α71.0α9:8α.8αC8H82Bα?1>.5C8202α?131α0>?I1α848?/5L1αA020α70α
L5=0αC8αH12C8α.82Bα5=:07α0α70αA21;8??5E>αC8α70αA02/8αC8α70αL5=00α.5/:0C0α
A12α8>?530αC8α70α71.00α70α9:8α.80α30;120α>1αC8H58>C1α8<?8C82αC8α<α
L8?8.α87α8.A8.12αC8α70α71.0)α
α
Φ7α C8.?13A1>82α 70α L5=0α ≥α 8>α 28?/B>=:71.α C8α 70C1.α α8α 80α +A020α
848?/1.αC87α?B7?:71αC8αφ-0α.8αC8H82Bα?07?:702α70.αC5./5>/0.αA1.5H575C0C8.α
C8α.:HC5L5.5E>αC8α70αL5=0α≥α8>α28?/B>=:71.0αC8H5G>C1.8α?1>.5C8202α70α
.:30/1250α30;12)α
α
±020α87α?B7?:71αC8αIlα5>/828.02Bα87α0>?I1α/1/07αlβ)α
α
ρ×)γ)<)βα Σ0.α 420>60.α C8α ?17:3>0α .8α C5.8D02B>α A020α 28.5./52α 71.α .5=:58>/8.α
A12?8>/068.αC87α3138>/1α>8=0/5L1α1αA1.5/5L1α/1/07αC87αA0D1)α
α
0-  Momento Negativo Interior:α α
α
 
lβαKαlρα
α
]0(α
α
ρα
α
βα
α
αρ+lβKlρ-α\α]α
α
×(α
α
×(α
α
×(α
α
αρ+lβKlρ-αkαρα
α
]α
α
×(α
α
<(α
α
H-  Momento Negativo Exterior 
α
 
lβαKαlρα
α
]0(α
α
ρα
α
βα
αρ+lβKlρ-α\α]α
β/α\α]α
β/αkαβ0(α
α
ρ]]α
×(α
α
ρ]]α
×(α
α
ρ]]α
×(α
αρ+lβKlρ-αkαρα
β/α\α]α
β/αkαβ0(α
α
ρ]]α
]α
α
ρ]]α
×(α
α
ρ]]α
<(α
α
α
?-  Momento Positivo:αα
α
 
lβαKαlρα
α
]0(α
α
ρα
α
βα
α
αρ+lβKlρ-α\α]α
α
α
=]α
α
=]α
α
=]α

117.   ρρ×α
α
αρ+lβKlρ-αkαρα
α
α
]α
α
×(α
α
<(α
α
 >α/1C1.α71.α?0.1.α.8αA1C2B>αI0?82α5>/82A170?51>8.α75>8078.)α
α
ρ×)γ)<)1α Σ0.α A12?51>8.α C8α 70α 71.0α 71?075F0C0α C8>/21α C8α 70α 420>60α C8α ?17:3>0α
C8H82BαC5.8D02.8αA020α28.5./52α70αA02/8αC8α71.α3138>/1.α>1α28.5./5C1.αA12α
70.αL5=0.)α
α
ρ×)γ)(αα ,δ, [≥δ°αΦ,±Σ2σ2φΦμδ°α [α2√Φ°αα
 
ρ×)γ)()ρα °5ααρ+lβKlρ-α 8.α 30;12α 1α 5=:07α 9:8α :>10α 70.α L5=0.α ?1>/8>5C0.α 8>α 70.α
420>60.α C8α ?17:3>0α C8H82B>α C5.8D02.8α A020α 28.5./52α87α γ(Rα C8α 71.α
3138>/1.αC8α70α420>60αC8α?17:3>0)α
α
ρ×)γ)()βα ±020αL07128.αC8ααρ+lβKlρ-α?13A28>C5C1.α8>/28αρα;α]0α70αA21A12?5E>αC87α
3138>/1α C8α 70α 420>60α C8α ?17:3>0α 9:8α C8H8α .82α 28.5./5C1α A12α 70α L5=0α
C8H82Bα1H/8>82.8αA12α5>/82A170?5E>α75>807α8>/28αγ(Rα;α]R)α
α
ρ×)γ)()1α Σ0.αL5=0.αC8H82B>αC5.8D02.8αA020α28.5./52α71.α3138>/1.αA21C:?5C1.αA12α
?02=0.α C8α =20L8C0Cα C528?/038>/8α 0A75?0C0.α .1H28α 8770.α +/0H59:8.α 1α
?02=0.α?1>?8>/20C0.α8.A8?5078.-0α>1α?1>.5C820C0.α8>α70α8L07:0?5E>αC8α
X:α:>541238α8>α87αA0D10α;ααA12α?02=0.α70/82078.αC8α.5.31α:α1/20.)α
α
ρ×)γ)=αα ,δ, [≥δ°αΦ,±Σ2σ2φΦμδ°αμ αΣΦασπΦ[5Φαφ [≥πΦΣα α
 
Σ0.α 420>60.α ?8>/2078.α .8α C5.8D02B>α A020α 71.α 3138>/1.α A1.5/5L1.α ;α
>8=0/5L1.α >1α 28.5./5C1.α A12α 70α 420>60α C8α ?17:3>00α ?0C0α 420>60α ?8>/207α
C8H82Bα28.5./52α70α.:30αC8α71.α87838>/1.α0.5=>0C1.α0α.:.αC1.α35/0C8.)α
α
17.9    MÉTODO DE COEFICIENTES PARA LOSAS APOYADAS EN  VIGAS 
O EN MUROS 
 
ρ×))ρ   Σ2,2≥Φφ2δ[ ° 
 
°8α?1>.5C8202Bα9:8α70.α71.0.α?1>.5./8>αC8α420>60.α8>α?0C0αC528??5E>0αC8α
0?:82C1α0α71α.5=:58>/8Nα
α
ρ×))ρ)ρα °8αC8>135>0α420>60α?8>/207α0α09:8770αC8α0>?I1α5=:07α0α70α35/0CαC87αA0D1α
1α /0H78210α .53G/25?0α 28.A8?/1α 0α 70α 7@>80α ?8>/207α C87α /0H7821α ;α 9:8α .8α
8</58>C8α8>α70αC528??5E>α8>α9:8α.8α?1>.5C820>α71.α3138>/1.)α
α
ρ×))ρ)βα °8αC8>135>0α420>60αC8α?17:3>0α0α09:8770αC8α0>?I1α5=:07α0α70α35/0CαC87α
A0D1α1α/0H78210α9:8α1?:A0α70.αC1.αB280.αC8α:>0α?:02/0αA02/8αC87α/0H78210α
4:820αC8α70α420>60α?8>/207)α
α
ρ×))ρ)1α  >αH12C8.αC5.?1>/5>:1.α.8α?1>.5C8202Bα:>α3138>/1α>8=0/5L1α5=:07α0α:>α
/82?51αC87α3138>/1αA1.5/5L1)α
α

118.     QN
 4GJGONN 20É0.ÓD1MRDd1N 20N ÓEÓ01ÉEÍXN RE.É0ÍN -N Í0RRDE1 0ÍN
R.TÉDRMÍN
N
 4GJGOG N IgfNf(997i8(fN9sÁz79gfNtgsgNnin(8zifNy(Npb()7–8Nf(sv8NNN
N
geNMNbiNbgsHiNy(NbifNóisy(fNy(bNzgób(siN(8NbgfN9gsgfNy(NbgfN=7HgfNy(NgtimiN
tgsgN(bN9gfiNy(Nnin(8zifN8(Hgz7=ifGN
N
óeNMN biN bgsHiN y(N bgN bÁ8(gfN n(y7gfN y(N bifN zgób(sifN tgsgN (bN 9gfiN y(N
nin(8zifNtif7z7=ifGN
N
 4GJGOGOGN IifN nin(8zifN y(N pb()7–8N tgsgN bgfN psg8/gfN9(8zsgb(fN f(N 9gb9cbgsv8N tisN
n(y7iNy(NbgfN()ts(f7i8(fNN
N
ÓgNNN\NNNRNXcNMnNNNNNNNNNNNNNNNNmN
N
ÓóNNN\NNNRNXcNÑnN
yi8y(NN
ÓgNN 0fN(bNnin(8ziNy(Npb()7–8N(8NbgNy7s(997–8NMGN
N
ÓóNN 0fN(bNnin(8ziNy(Npb()7–8N(8NbgNy7s(997–8NÑGN
N
RNN 0fN (bN 9i(p797(8z(N y(N nin(8zifN 78y79gyiN (8N bgfN ÉgóbgfN
 4GJGOGOgXN 4GJGOGOóNmN 4GJGOGO9GN
N
XcNN 0fNbgN9gsHgNMbz7ngNc87pisn(n(8z(Ns(tgsz7ygNtisNc87ygyNy(N
vs(gNy(NbgNbifgGN
N
MNN 0fNbgNbcxNb7ós(Ny(bNzsgniN(8NbgNy7s(997–8N9iszgGN
N
ÑNN 0fNbgNbcxNb7ós(Ny(bNzsgniN(8NbgNy7s(997–8NbgsHgGN
N
 4GJGOGUN IifN nin(8zifN tgsgN bgfN psg8/gfN y(N 9ibcn8gfNf(sv8N s(yc97yifN
Hsgycgbn(8z(Ny(fy(N(bN=gbisNzizgbN(8N(bNóisy(Ny(NbgNpsg8/gN9(8zsgbNhgfzgN
c8Nz(s97iNy(N(fzifN=gbis(fN(8N(bNóisy(Ny(bNzgób(siGN
N
 4GJGOG5N Rcg8yiN (bN nin(8ziN 8(Hgz7=iN gN c8N bgyiN y(bN gtimiN f(gN n(8isN Kc(N (bN
QLRN y(bN nin(8ziN (8N (bN izsiN bgyiXN bgN y7p(s(897gN f(svN y7fzs7óc7ygN (8N
tsitis97–8NgNbgfNs7H7y(9(fNs(bgz7=gfNy(NbgfNbifgfGN
N
 4GJGOGSN IgfN pc(sxgfN 9iszg8z(fN (8N (bN zgób(siN f(sv8N9gb9cbgygfN tgsz7(8yiN y(N bgN
h7t–z(f7fN y(N Kc(N bgN 9gsHgN f(N y7fzs7ócm(N gN bifN gtimifN f(HM8N bgfN
tsitis97i8(fN78y79gygfN(8NbgNÉgóbgN 4GJGOGSGN
N
 4GJGUNN oDPMÍN20NMAE-EN
 
N N IgfN 9gsHgfN fiós(N bgfN =7HgfN y(N gtimiN f(N 9gb9cbgsv8Nn(y7g8z(NbgNÉgóbgN
 4GJGOGOgXNtgsgNbifNtis9(8zg/(fNy(N9gsHgfN(8NbgfNy7s(997i8(fNSMSNmNSÑSGN
08N878HM8N9gfiNbgN9gsHgNfiós(NbgN=7HgXNgNbiNbgsHiNy(bNzsgniN9isziXNf(svN
n(8isN Kc(N gKc(bbgN Kc(N 9iss(fti8y(N gN c8N vs(gN b7n7zgygN tisN bgN

119.   ρρα
5>/82.8??5E>αC8α7@>80.α0α<(°α/20F0C0.αC8.C8α70.α8.9:5>0.)α
α α α
Σ0α ?02=0α 89:5L078>/8α :>54123838>/8α 28A02/5C0α A12α 38/21α 75>807α .1H28α
8./0αL5=0α?12/0α8.αX:ΦK1)α
α
17.10    DISEÑO DE LOSAS POR FUERZA CORTANTE αα
α
ρ×)ρ])ρ  √ [ πΦΣ2μΦμ ° 
 
ρ×)ρ])ρ)ρα  7α C5.8D1α A12α 4:82F0α ?12/0>/8α C8α 70.α 71.0.α 8>α C1.α C528??51>8.α C8H82Bα
28075F02.8α C8α 0?:82C1α 0α 71α 5>C5?0C1α 8>α 8./0α .8??5E>α ;α /130>C1α 8>α
?:8>/0Nα
α
0-α 48?/1αC8α70α4:82F0α?12/0>/8α8>α70α71.0α0?/:0>C1α?131αL5=0α0>?I0)α
α
H-α 48?/1αC8α70α4:82F0α?12/0>/8α8>αC1.αC528??51>8.α+A:>F1>0358>/1-)α
α
ρ×)ρ])ρ)βα  7αC5.8D1αA12α4:82F0α?12/0>/8α;αA:>F1>0358>/1α.8αI02Bα?1>.5C820>C1Nα
α
0-ασ:82F0α?12/0>/8α?131αL5=0Nα
α
:ααα≥αααφα>α
α
>ααα\ααα?α
αmmα
?ααα\ααα]0(1α√α4W?αH1αCα
α α α
H-ασ:82F0α?12/0>/8α8>αC1.αC528??51>8.α+A:>F1>0358>/1-Nα
α
:ααα≤αααφα>α
α
>ααα\αααα?α
ααααααααααmmαααααααααααααααααααααααααα
αααααααααα?ααα\ααα+α]0(1αα]ααρ0ραKαβ?α-α√α4W?αH1αCαααα
mmα
αααααααααααααααααααααααα?αααaαααρ0ρα√α4W?αH1αCαααα
α
μ1>C8αβ?α8.α70α2870?5E>αC87α70C1α702=1α07α70C1α?12/1αC8α70α?17:3>0α9:8α
28?5H8α0α70α71.0α;αH1α8.α87αA82@38/21αC8α70α.8??5E>α?2@/5?0)α
α
α
α
ρ×)ρ])β  σ≤ π.Φαφδπ≥Φ[≥ α [αΣδ°Φ°αφδ[α2√Φ°α  
 
ρ×)ρ])β)ρα Σ0.α L5=0.α ?:;1α A02B38/21ααρ+lβKlρ-α .80α 30;12α 1α 5=:07α 0α ρα C8H82B>α
C538>.51>02.8αA020α28.5./52α70α4:82F0α?12/0>/8αA21C:?5C0αA12α70.α?02=0.α
0?/:0>/8.α 8>α 70.α B280.α /25H:/0250.α 7535/0C0.α A12α 7@>80.α 0α <(°0α /20F0C0.α
C8.C8α70.α8.9:5>0.αC8α71.α/0H7821.α;α71.α868.αC8α71.α35.31.α0C;0?8>/8.α
;αA0207871.α0α71.α70C1.α30;128.)α
α

120.    OLN
 4G LGOGON My(nvfNy(NbgNpc(sxgN9iszg8z(Ntsiyc97ygNtisNbgfN9gsHgfNy(NbgNbifgXNbgfN
=7HgfN y(ó(sv8N s(f7fz7sN bgN pc(sxgN 9iszg8z(N tsiyc97ygN tisN bgfN 9gsHgfN
y7s(9zgn(8z(Ngtb79gygfNfiós(N(bbgfNmNtisNpc(sxgfNbgz(sgb(fGN
N
 4G LGOGUN IgN s(f7fz(897gN gN bgN pc(sxgN 9iszg8z(N y(N bgN bifgN f(N y(ó(svN 9gb9cbgsN
fcti87(8yiNKc(NbgN9gsHgNf(Ny7fzs7ócm(NgNbgfN=7HgfNy(NgtimiNy(Ng9c(syiNgN
biN78y79gyiN(8NbgNÍ(997–8N 4G LGOG GN
N
 4G LGOG5N IgNf(997–8N9sÁz79gNf(N9i8f7y(sgsvNcó79gygNgNc8gNy7fzg897gNyNy(NbgN9gsgN
y(bNgtimiGN
N
 4G LGUN 3C0.,MNRE.ÉM1É0N01NIEÍMÍNÍD1NoDPMÍNN
 
 4G LGUG N IgfNbifgfNf78N=7HgfNy(ó(sv8Ny7n(8f7i8gsf(NtgsgN(bN(p(9ziNy(NbgNpc(sxgN
9iszg8z(N (8N yifN y7s(997i8(fN utc8xi8gn7(8zieXN y(ó7j8yif(N 9i8f7y(sgsN
c8gNf(997–8N9sÁz79gNcó79gygNgNbiNbgsHiNy(NbgNfct(sp797(NpisngygNtisNbifN
tbg8ifN zsgxgyifN =(sz79gbn(8z(N gN c8gN y7fzg897gN yáON y(N bgfN 9gsgfN y(N bgN
9ibcn8gN iN y(bN 9gt7z(bN f7N (fz(N ()7fz(N ut(sÁn(zsiN óieXN gy(nvfN y(ó(svN
=(s7p79gsf(N(8Nf(997i8(fNfc9(f7=gfNnvfNy7fzg8z(fNy(bNgtimiGN
N
 4G LGUGON Rcg8yiN bgN 9gsHgN y(N Hsg=(ygyXN =7(8ziXN f7fniN cN izsgN pc(sxgN bgz(sgbN
tsiycx9gNzsg8fn7f7–8Ny(Nnin(8zifN(8NbgfN9i8()7i8(fN(8zs(NbgfNbifgfNmN
bgfN 9ibcn8gfXN bgN pc(sxgN 9iszg8z(N Kc(N f(N y(s7=gN y(N bgN zsg8fn7f7–8N y(N
nin(8ziXNy(ó(svNgy797i8gsf(NgNbifN(fpc(sxifNtsi=(87(8z(fNy(NbgN9gsHgN
gtb79gygNtisNbgNbifgN(8NbgNf(997–8N9sÁz79gNcó79gygNgNyáONy(NbgN9ibcn8gXN
9iniNf(N78y79gN(8NbgNÍ(997–8N 4G5GOGN
N
17.11    DIMENSIONES MÍNIMAS PARA ÁBACOS 
 
N N Rcg8yiN f(N (ntb((N c8N vóg9iN tgsgN s(yc97sN bgN 9g8z7ygyNy(Ns(pc(sxiNtisN
nin(8ziN8(Hgz7=iNfiós(NbgN9ibcn8gNy(Nc8gNbifgNf78N=7HgfXN(bNzgng:iNy(bN
vóg9iNy(ó(svN(fzgsNy(Ng9c(syiN9i8NbiNf7Hc7(8z(NN
N
geN0bN vóg9iN y(ó(svN ()z(8y(sf(N (8N 9gygN y7s(997–8XN gNtgsz7sN y(bN (/(N y(bN
gtimiN gN c8gN y7fzg897gN 8iN n(8isN y(N  áVN y(N bgN bi8H7zcyN y(bN zsgniXN
n(y7ygN9(8zsiNgN9(8zsiNy(NbifNgtimifN(8N(fgNy7s(997–8GN
óeNIgN tsim(997–8N y(bN vóg9iN tisN y(óg/iN y(N bgN bifgN y(ó(svN f(sN tisN biN
n(8ifNN á5Ny(bNt(sgbz(Ny(NjfzgGN
9eN08N(bN9vb9cbiNy(bNs(pc(sxiNs(Kc(s7yiNtgsgNbgNbifgXN(bNt(sgbz(Ny(bNvóg9iN
óg/iN jfzgN 8iN y(ó(svN 9i8f7y(sgsf(N ngmisN y(N  á5N y(N bgN y7fzg897gN y(bNN
()zs(niNy(bNvóg9iNgbNóisy(Ny(NbgN9ibcn8gNiNy(bN9gt7z(bGN

121.    O N
 
 
 
 

122.    [[F
 
 
 
 
 
 

123.   F
 
 
 
 
 
 

124.    O5N
 
 
 
 
 
 
 
 
 
 
 
CAPÍTULO 18 - CONCRETO PRESFORZADO 
 
18.1    ABREVIATURAS 
 

125.   F
rF $280F C8F 70F .8??5E>F /20>.L82.07F ?13A28>C5C0F 8>/28F70F ?020F C8F
/20??5E>FA12F478<5E>F;F87F?8>/21FC8F=20L8C0CFC8F70F.8??5E>/1/07
?3n
F
rA.F $280FC87F284:82F1FA28.412F0C1F8>F70FF1>0F8>F/20??5E>?3n
F
. $280C87284:82F18>/20??5E>>1A28.412F0C1?3n
F
L $280C87284:82F1A12?12/0>/8
F
W. $280C87284:82F18>?13A28.5E>?3n
F
r F $280FC8F0A70./0358>/1FC8F70FA70>?I0FC8F0>?7068FC8F71.F/8>C1>8.F
C8A1./8>.0C1
F
r[F $280F 3B<530F C8F 70F A12?5E>F C8F 70F .:A8245?58F C8F 0>?7068F
=813G/25?038>/8F.83860>/8F;F?1>?G>/25?0F07FB280FC8F70FA70?0FC8F
0>?7068C871./8>C1>8.C8A1./8>.0C1
F
H >?I1C870?0208>?13A28.5E>C873583H21?3
F
HX >?I13@>531C870730C8:>87838>/1?1>070.?3
F
a3F a02=0.F3:82/0.F1F4:82F0.F;F3138>/1.F5>/82>1.F2870?51>0C1.
F
aLF a02=0.FL5L0.F1F4:82F0.F;F3138>/1.F5>/82>1.F2870?51>0C1.
F
C 5./0>?50 C8 70 45H20 8</82>0 8> ?13A28.5E> 07 ?8>/215C8F C87F
284:82F1F A28.412F0C1F 1F 07F ?8>/215C8F ?13H5>0C1F ?:0>C1F .8F
5>?7:;0284:82F1C8/20??5E>>1A28.412F0C1?3
F
CA 5./0>?50 C8 70 45H20 8</82>0 8> ?13A28.5E> 07 ?8>/215C8F C87F
284:82F1A28.412F0C1
F
8 0.8C871.71=025/31.>8A8250>1.
F
4H .4:82F1 C8 0A70./0358>/1 A8235.5H78 8> 87 ?1>?28/1F H061F 70F
A70?0C80>?7068C871./8>C1>8.C8A1./8>.0C1?1>F70FF1>0FC8F
0>?70688>878</28310C8?:0C038>/828412F0C0
F
4C .4:82F1 C8H5C1 0 70 ?02=0 3:82/0 >1 03A7545?0C0 8> 70 45H20
8</2830FC8F:>0F.8??5E>F8>F70F?:07F71.F8.4:82F1.FC8F/20??5E>F.8F
A21C:?8>A12?02=0.0A75?0C0.8</82>038>/8Q=K3
F
4A? .4:82F1 A2138C51 C8 ?13A28.5E> 8> 87 ?1>?28/1C8H5C1F
M>5?038>/8F0F70F4:82F0F848?/5L0FC8FA28.4:82F1F+C8.A:G.FC8F9:8F
I0>1?:225C1/1C0.70.AG2C5C0.C8A28.4:82F1-Q=K3
F
4A8 .4:82F1C8?13A28.5E>8>87?1>?28/1C8H5C1M>5?038>/8F0F70F
4:82F0F 848?/5L0F C8F A28.4:82F1F +C8.A:G.F C8F 9:8F I0>F 1?:225C1F

126.   I
/1C0.I 70.I AG2C5C0.I C8I A28.4:82F1-I 8>I 70I 45H20I 8</2830I C8I :>0I
.8??5E>I 8>I 70I ?:07I 71.I 8.4:82F1.I C8I /20??5E>I .8I I0>I A21C:?5C1I
A1270.?02=0.0A75?0C0.8</82>038>/8Q=K3
I
4A.I ´.4:82F1I 8>I 87I 284:82F1I A28.412F0C1I 0I 70I 28.5./8>?50 >135>07
Q=K3l8I
I
4A:I '8.5./8>?50I 8.A8?545?0C0I 0I 70I /20??5E>I C8I 71.I /8>C1>8.I C8I
A28.4:82F1Q=K3
I
4A;I '8.5./8>?50I 8.A8?545?0C0I 0I 70I 47:8>?50I C8I 71.I /8>C1>8.I C8I
A28.4:82F1Q=K3
I
42 EC:71C821/:20C87?1>?28/1Q=K3
I
4.8I ´.4:82F1I848?/5L1I8>I87I284:82F1IA28.412F0C1I+C8.A:G.I9:8II0>I
1?:225C1/1C0.70.AG2C5C0.C8A28.4:82F1-Q=K3
I
4;I '8.5./8>?50I 8.A8?545?0C0I 0I 70I 47:8>?50I C87I 284:82F1I >1I
A28.412F0C1Q=K3
I
4W?I '8.5./8>?50I8.A8?545?0C0I0I70I?13A28.5E>IC87I?1>?28/1Q=K3
I
4W?5II '8.5./8>?50I 0I 70I ?13A28.5E>I C87I ?1>?28/1I 07I 3138>/1I C87IIIIIIIII
A28.4:82F15>5?507Q=K3
I
I 8207/8/1/07C8787838>/1?3
I
I 138>/1 C8 5>82?50 C8 70 .8??5E> 9:8 28.5./8 70. ?02=0.I
03A7545?0C0.8I
I
*I c1845?58>/8I C8I 425??5E>I 71>=5/:C5>07I A12I 38/21I C8I /8>CE>I C8I
A28.4:82F18I
I
lI 6:FI 75H28I C8I 71.0.I A70>0.I 8>I C1.I C528??51>8.I 8>I 87I .8>/5C1I
A020787107C87284:82F19:8.88./BC8/8235>0>C1?38I'G0.8I70I
8??5E>
I
l< 1>=5/:CC87/8>CE>C8A28.4:82F1C878</28318>I87I=0/1I0I:>I
A:>/1?:079:5820<3'G0.8708??5E>
I
3B< 138>/1 3B<531 03A7545?0C1 8> 70 .8??5E> C8H5C1I 0I ?02=0.I
0A75?0C0.I8</82>038>/88I
I
? :82F0C8/20??5E>8>87?1>?28/1C8H5C0070?02=0I3:82/0I3B.I
70?02=0L5L0>103A7545?0C0.+3]L-
I
. :82F0C87/8>CE>C8A28.4:82F18>878</2831C87I=0/18I
I
< :82F0C87/8>CE>C8A28.4:82F18>?:079:582A:>/1I<8I

127.   ρβ×α
α
ρα ±12?8>/068αC8α284:82F1α8>α/20??5E>α>1αA28.412F0C10ααρ \αΦ.αKα+HαC-α
α
ρρα ±12?8>/068αC8α284:82F1αA28.412F0C10ααρρα\αΦA.αKα+HαCA-α
α
ρWα ±12?8>/068αC8α284:82F1α8>α?13A28.5E>0ααρWαα\ααΦW.αKα+HαC-α
α
.α  .A0?50358>/1α8>/28α8./25H1.)α
α
Cα σ:82F0α ?12/0>/8α 8>α 70α .8??5E>0α C8H5C0α 0α 70α ?02=0α 3:82/0α >1α
03A7545?0C0)α
α
5α σ:82F0α ?12/0>/8α 03A7545?0C0α 8>α 70α .8??5E>0α C8H5C0α 0α ?02=0.α
0A75?0C0.α8</82>038>/8α9:8α.8αA28.8>/0>α.53:7/0>8038>/8α?1>α
,30<)α
α
?5α π8.5./8>?50α >135>07α 07α ?12/0>/8α A21A12?51>0C0α A12α 87α ?1>?28/1α
?:0>C1α 87α 0=258/0358>/1α C50=1>07α 8.α 87α 28.:7/0C1α C8α 70α
?13H5>0?5E>αC8α?12/0>/8α;α3138>/1)α
α
?Xα π8.5./8>?50α >135>07α 07α ?12/0>/8α A21A12?51>0C0α A12α 87α ?1>?28/1α
?:0>C1α 87α 0=258/0358>/1α C50=1>07α 8.α 87α 28.:7/0C1α C8α 71.α
8<?8.5L1.α8.4:82F1.αA25>?5A078.αC8α/20??5E>α8>α87α0730)α
α
Aα φ13A1>8>/8α L82/5?07α C8α 70α 4:82F0α 848?/5L0α C8α A28.4:82F1α 8>α 70α
.8??5E>α?1>.5C820C0)α
α
Xα ρα4;αKα4W?α
α
Xραρρα4A.αKα4W?α
α
XWα ρWα4;αKα4W?α
α
XXααPααXρXααPα
XWXα τ>C5?8.αC8α284:82F1αA020α.8??51>8.α?1>α070.0α?07?:70C1.αC8α5=:07α
41230α9:8αX0αXρα;αXW0α8<?8A/1α9:8αHα.82Bα87α0>?I1αC87α0730α;α87α
B280α C8α 284:82F1α C8H82Bα .82α 70α 289:825C0α A020α C8.02217702α
M>5?038>/8α70α28.5./8>?50α0α70α?13A28.5E>αC87α0730)α
α
αα φ03H51α 0>=:702α /1/07α C87α A82457α C87α /8>CE>α C8α A28.4:82F10α 8>α
20C50>8.0αC8.C8α87α8</2831αC87α=0/1αI0./0αα?:079:582αA:>/1α<)α
α
βρα σ0?/12αC845>5C1α8>α70α°8??5E>αρρ)β)ρ4)α
α
μα φ1845?58>/8αC8α425??5E>αA12α?:2L0/:20)α
α
φα σ0?/12αC8α28C:??5E>αC8α28.5./8>?50)α
α
18.2    DEFINICIONES 
 

128.    OQN
Í(Ny(p78(8NbifNf7Hc7(8z(fNzjsn78ifNtgsgNfcNcfiN(8N(fz(NRgtÁzcbiNN
N
a)  Anclaje.- Ó(y7iN tisN (bN 9cgbN bgN pc(sxgN ts(z(8fisgN f(N zsg8fp7(s(N
t(sng8(8z(n(8z(NgbN9i89s(ziGN
 
b)  Concreto  Presforzado.- Ri89s(ziN gsngyiN (8N (bN 9cgbN f(N hg8N
78zsiyc97yiN(fpc(sxifN78z(s8ifNtgsgNs(yc97sNbifN(fpc(sxifNtiz(897gb(fN
y(Nzsg997–8N(8N(bN9i89s(ziNs(fcbzg8z(fNy(NbgfN9gsHgfGN
 
c)  Fricción por curvatura.- 3s7997–8NKc(Ns(fcbzgNy(Nyiób(9(fNmN9cs=gfN
(8N(bNt(sp7bN(ft(97p79gyiNy(bNz(8y–8GN
 
d)  Fricción  por  alabeo.- 3s7997–8N 9gcfgygN tisN c8gN y(f=7g97–8N 8iN
78z(897i8gbNy(bNz(8y–8N9i8Ns(bg97–8NgNfcNt(sp7bN(ft(97p79gyiGN
 
e)  Fuerza  en  el  gato.- 3c(sxgN z(ntisgbN (/(s97ygN tisN (bN gtgsgziN Kc(N
tsiyc9(NbgNzsg997–8N(8NbifNz(8yi8(fGN
 
f)  Resistencia  nominal  a  la  fluencia.- .(f7fz(897gN gN bgN pbc(897gN
(ft(97p79gygN tisN bgN 8isngN t(sz78(8z(N mN (8N 9i89isyg897gN 9i8N biN
(fzgób(97yiN(8NbgNÍ(997–8NUG5GN
 
g)  Postensionado.- ÓjziyiNy(Nts(fpc(sxiN(8N(bN9cgbNbifNz(8yi8(fNf(N
z(8fg8Ny(ftcjfNKc(N(bN9i89s(ziNhgN(8ycs(97yiGN
 
h)  Pretensionado.- ÓjziyiNy(Nts(fpc(sxiN(8N(bN9cgbNbifNz(8yi8(fNf(N
z(8fg8Ng8z(fNKc(Nf(N9ibiKc(N(bN9i89s(ziGN
 
i)  Presfuerzo efectivo.- 0bN(fpc(sxiNKc(Nt(sng8(9(N(8NbifNz(8yi8(fN
y(ftcjfN Kc(N hg8N i9css7yiN ziygfN bgfN tjsy7ygfXN ()9(tzcg8yiN bifN
(p(9zifNy(N9gsHgNnc(szgNmNy(N9gsHgfNfiós(tc(fzgfGN
 
j)  Tendón.- 0b(n(8ziNy(Ng9(siNzgbN9iniNgbgnós(XN9gób(XNógssgNiNzis–8XN
iNc8NtgKc(z(Ny(Nzgb(fN(b(n(8zifXNcfgyiNtgsgN7ntgsz7sNNts(fpc(sxiNgbN
9i89s(ziGN
 
k)  Tendones adheridos.- É(8yi8(fNKc(N(fzv8Ngyh(s7yifNgbN9i89s(ziN
mgN f(gN y7s(9zgn(8z(N iN tisN n(y7iN y(N 78m(997–8N y(N nisz(siGN IifN
z(8yi8(fN 8iN gyh(s7yifN (fzv8N b7ós(fN y(N ni=(sf(N 9i8N s(ft(ziN gbN
9i89s(ziNKc(NbifNsiy(gGN
 
l)  Transferencia.- Et(sg97–8N y(N zsg8fp(s7sN bgN pc(sxgN y(bN z(8y–8N gbN
9i89s(ziGN
N
N
18.3    ALCANCE 
 
 QGUG NN IgfNy7ftif797i8(fNy(N(fz(NRgtÁzcbiNf(Ngtb79g8NgN(b(n(8zifNy(N9i89s(ziN
fc/(zifNgNpb()7–8Nts(fpisxgyifN9i8Ng9(siNy(NgbzgNs(f7fz(897gGN
N

129.    OJN
 QGUGONN ÉiygfN bgfN y7ftif797i8(fN y(N (fzgN 1isngN Kc(N 8iN f(N ()9bcmg8N
(ft(9Áp79gn(8z(NmNKc(N8iN(fzj8N(8Nitif797–8N9i8NbgfNy7ftif797i8(fNy(N
(fz(Ng9vt7z(XNf(N9i8f7y(sgsv8Ngtb79gób(fNgN9i89s(ziNts(fpisxgyiGN
N
 QGUGUNN IgfN f7Hc7(8z(fN y7ftif797i8(fN 8iN f(N gtb79gsv8N gbN 9i89s(ziN ts(fpisxgyiNN
Í(997i8(fNN4GVGSXNNJGVXNNJGQGOXNNJGQGUXNNJGQG5XNNJGJXNN  G5XNN  GSXNN  G4XNN
 OGVG XNN OGVGOXNN OGQXNN SGUXNN SG5XNN SGVNNmNRgtÁzcbiN 4GN
N
18.4    CONSIDERACIONES GENERALES  
 
 QG5G NN Í(N 78=(fz7Hgsv8N bifN (fpc(sxifN mN bgN s(f7fz(897gN gN bgN sizcsgN (8N bgfN
9i8y797i8(fNy(Nf(s=797iNmN(8NziygfNbgfN(zgtgfNy(N9gsHgNKc(Ntc(yg8Nf(sN
9sÁz79gfN ycsg8z(N bgN =7ygN y(N bgN (fzsc9zcsgN y(fy(N Kc(N f(N gtb79gN (bN
ts(fpisxgyiGN
N
 QG5GONN Í(N zingsv8N (8N 9c(8zgN (8N (bN y7f(:iN bgfN 9i89(8zsg97i8(fN y(N (fpc(sxifN
y(ó7ygfNgbNts(fpc(sxiNiNgNizsgfN9gcfgfGN
N
 QG5GUNN Í(N zingsv8N (8N 9c(8zgN bifN (p(9zifN fiós(N bgN (fzsc9zcsgN gymg9(8z(N
tsiyc97yifN tisN y(pisng97i8(fN (bvfz79gfN mN tbvfz79gfXN y(pb()7i8(fXN
9gnó7ifNy(Nbi8H7zcyNmNsizg97i8(fN9gcfgygfNtisN(bNts(fpc(sxiPN9cg8yiNfcN
(p(9ziN (fN gy7z7=iN gN bifN (p(9zifN y(N z(nt(sgzcsgN mN 9i8zsg997–8XN f(N
9i8f7y(sgsv8Nf7ncbzv8(gn(8z(GN
N
 QG5G5NN Í(N 9i8f7y(sgsv8N bgfN tif7ó7b7ygy(fN y(N tg8y(iN (8N c8N (b(n(8ziN (8zs(N
tc8zifN y(N 9i8zg9ziN y(bN 9i89s(ziN 9i8N bifN z(8yi8(fN y(N ts(fpc(sxiGN Í(N
9i8f7y(sgsvNzgnó7j8N(bNtg8y(iNy(NgbngfNmNgbgfNy(bHgygfGN
N
 QG5GSNN MbN9gb9cbgsNbgfNtsit7(ygy(fNy(NbgNf(997–8Nts(=7gfNgNbgNgyh(s(897gNy(NbifN
z(8yi8(fNy(Nts(fpc(sxiXNy(ó(svN9i8f7y(sgsf(N(bN(p(9ziNy(NbgNtjsy7ygNy(bN
vs(gNy(ó7ygNgNbifNyc9zifN=g9ÁifGN0bNvs(gNzsg8fpisngygNy(NbifNz(8yi8(fN
gyh(s7yifN tc(y(N f(sN 789bc7ygN (8N n7(nósifN ts(z(8f7i8gyifN mN (8N
n7(nósifNtifz(8fgyifNy(ftcjfNy(NbgN78m(997–8GN
N
 QG5GVNN 0bNn–ycbiNy(N(bgfz797ygyNy(bN9i89s(ziNf(Nfcti8ysvN9iniNf(N78y79gN(8NbgN
Í(997–8NJG5GOGN
N
 QG5G4NN 0bNn–ycbiNy(N(bgfz797ygyNy(bNg9(siNy(Nts(fpc(sxiNf(svNy(z(sn78gyiNtisN
n(y7iNy(N(8fgmifNiNtsitis97i8gyiNtisN(bNpgós79g8z(GN
N
18.5    HIPÓTESIS 
 
 QGSG NN IgfN f(997i8(fN tbg8gfN g8z(fN y(N bgN y(pisng97–8N t(sng8(9(8N tbg8gfN
y(ftcjfNy(NbgNy(pisng97–8GN
N
 QGSGONN 08Nf(997i8(fNgHs7(zgygfXNf(Ny(fts(97gsvNbgN9gtg97ygyNy(bN9i89s(ziNtgsgN
s(f7fz7sNzsg997i8(fGN
N
18.6    ESFUERZOS PERMISIBLES EN EL CONCRETO 
 

130.   ρ1]α
ργ)=)ραα Σ1.α8.4:82F1.α8>α87α?1>?28/1α5>38C50/038>/8αC8.A:G.αC8α70α/20>.35.5E>α
C87α A28.4:82F1α +0>/8.α C8α 70.α AG2C5C0.α C8α A28.4:82F1α C8A8>C58>/8.α C87α
/583A1-α>1αC8H82B>α8<?8C82αC8α71α.5=:58>/8Nα
α
0-α .4:82F1αC8α70α45H20α8</2830α8>α?13A28.5E>Nα ]0=α4W?5α
α
H-α .4:82F1αC8α70α45H20α8</2830α8>α/20??5E>0α8<?8A/1ααααααααααααααααααmmmα
8>α71αA8235/5C1αA12α?-Nαα αα]0γα √α4W?5α
α
?-α .4:82F1αC8α70α45H20α8</2830α8>α/20??5E>α8>α71.ααααααααααααααααααααααmmmα
8</2831.αC8α87838>/1.α.53A7838>/8α0A1;0C1.Nα ααρ0=α√α4W?5α
α
φ:0>C1α71.α8.4:82F1.αC8α/20??5E>α?07?:70C1.α8<?8C0>αC8α8./1.αL07128.0α
C8H8αA21A12?51>02.8α284:82F1α0:<57502αC8α0CI828>?50α+>1αA28.412F0C1α1α
A28.412F0C1-α 8>α 70α F1>0α C8α /20??5E>α A020α 28.5./52α 70α 4:82F0α /1/07α C8α
/20??5E>α8>α87α?1>?28/10α?07?:70C0αH061α70α.:A1.5?5E>αC8α:>0α.8??5E>α>1α
0=258/0C0)α
α
ργ)=)βαα Σ1.α 8.4:82F1.α 8>α 87α ?1>?28/1α H061α 70.α ?02=0.α C8α .82L5?51α+C8.A:G.αC8α
9:8αA28.8>/8>α/1C0.α70.αAG2C5C0.αC8αA28.4:82F1-α>1αC8H82B>α8<?8C82αC8α
71.α.5=:58>/8.αL07128.Nα
α
0-α .4:82F1αC8α70α45H20α8</2830α8>α?13A28.5E>Nα ]0<(α4W?α
α
H-α .4:82F1αC8α70α45H20α8</2830α8>α/20??5E>0α8>α70αααααααααααααααααααααααmmα
F1>0αA28?13A2535C0Nαα ααρ0=α √α4W?α
α
?-α .4:82F1αC8α70α45H20α8</2830α8>α/20??5E>α8>α70α
F1>0αA28?13A2535C0αC8α71.α87838>/1.α+8<?8A/1α
8>α.5./830.αC8α71.0.α8>αC1.αC528??51>8.-α8>α71.α
?:078.α87α0>B75.5.αH0.0C1α8>α70.α.8??51>8.α
/20>.41230C0.α0=258/0C0.α;α8>α70.α2870?51>8.α
H575>8078.α3138>/1JC8478<5E>αC83:8./28>α9:8α
70.αC8478<51>8.α5>38C50/0.α;αC54825C0.α?:3A78>ααααααααααααααααααααααmmα
?1>α71.α289:5.5/1.αC8α70.α.8??51>8.αργ)γα;αργ))βNααααααααααα10βlα4Y?α
α
ργ)=)1α Σ1.α 8.4:82F1.α A8235.5H78.α 8>α 87α ?1>?28/1α C8α70.α °8??51>8.α ργ)=)ρα ;α
ργ)=)βαA:8C8>α.1H28A0.02.8α?:0>C1α.8αC83:8./28α38C50>/8α8>.0;1.α1α
0>B75.5.α9:8α>1α.8αA826:C5?0α87α?13A12/0358>/1)α
α
ργ)=)<αα αφ:0>C1α 70α /20>.4828>?50α C8α 70α 4:82F0α C8α A28.4:82F1α .80α 0α /20LG.α C8α
A70>?I0.α C8α 0A1;10α 71.α 8.4:82F1.α C8α 0A70./0358>/1α .1H28α 87α ?1>?28/1α
C8H5C1α07α0>?7068α8>α?1>?28/1αA1./8>.51>0C1α?1>α284:82F1α0C8?:0C1α8>α
70.α28=51>8.α45>078.α>1α8<?8C82B>αC8Nα
α
0-α2>38C50/038>/8αC8.A:G.αC87α0>?7068αC87α/8>CE>Nα
mmmmmmmmmmmα
4Hααα\ααα]0γα4W?5α√α+ΦβKΦραJα]0β-αααα≤αααρ0β(α4W?5α
α
H-αμ8.A:G.α9:8αI0>α1?:225C1α70.αAG2C5C0.αC8αA28.4:82F1Nα

131.   ρ1ρα
mmmmmmα
4Hααα\ααα]0=α4W?α√α+ΦβKΦρ-αααα≤ααα4W?α
α
18.7    ESFUERZOS PERMISIBLES EN EL ACERO DE PRESFUER ZOα
α
α α Σ1.α 8.4:82F1.α C8α /20??5E>α 8>α 71.α /8>C1>8.α C8α A28.4:82F1α >1α C8H82B>α
8<?8C82αC8α71α.5=:58>/8Nα
α
0-αμ8H5C1α0α70α4:82F0αC87α=0/1Nα]0γα4A:αααEααα]0<α4A;α
α
87α9:8α.80α38>120αA821α>1α30;12α9:8α87αL0712α3B<531α28?138>C0C1α
A12α87α40H25?0>/8αC8α71.α/8>C1>8.αC8αA28.4:82F1α1αC8α71.α0>?7068.)α
α
H-α≥8>C1>8.α C8α A28/8>.0C10α 5>38C50/038>/8α C8.A:G.α C8α 70α
/20>.4828>?50αC87αA28.4:82F1Nα]0γβα4A;0αA821α>1α30;12α9:8α]0×<α4A:αααα
α
?-α >α 70.α F1>0.α ?1228.A1>C58>/8.α 0α 71.α 0>?7068.α ;α 0?1A70C128.α C8α 71.α
/8>C1>8.αA1./8>.0C1.0α5>38C50/038>/8αC8.A:G.αC8α70α/20>.4828>?50α
C87αA28.4:82F1Nα]0×]α4A:α
α
18.8    DEFLEXIONES 
α
ργ)γ)ραα °8α C8H82B>α ?07?:702α 70.α C8478<51>8.α 5>38C50/0.α C8α 71.α 87838>/1.α C8α
?1>?28/1α A28.412F0C1α .:68/1.α 0α 478<5E>α C5.8D0C1.α C8α 0?:82C1α ?1>α 71.α
289:5.5/1.α C8α 8./8α φ0A@/:710α A12α 38C51α C8α 71.α 3G/1C1.α 1α 4E23:70.α
:.:078.αA020αC8478<51>8.α87B./5?0.)α 7α3138>/1αC8α5>82?50αC8α70α.8??5E>α
/1/07αC8α?1>?28/1αA1C2Bα.82α:/575F0C1αA020α.8??51>8.α>1α0=258/0C0.)α
α
ργ)γ)βαα Σ0α C8478<5E>α 0C5?51>07α C54825C0α 8>α 87838>/1.α C8α ?1>?28/1α A28.412F0C1α
C8H82Bα?07?:702.8α/8>58>C1α8>α?:8>/0α71.α8.4:82F1.α8>α87α?1>?28/1α;α8>α
87α0?821αH061α?02=0α.1./8>5C0α8α5>?7:;8>C1α71.α848?/1.αC8α70α47:8>?50α;α70α
?1>/20??5E>αC87α?1>?28/10α0.@α?131α70α287060?5E>αC87α0?821)α
α
ργ)γ)1αα Σ0αC8478<5E>α?07?:70C0αC8α0?:82C1α?1>α70.α°8??51>8.αργ)γ)ρα;αργ)γ)βα>1α
C8H8α8<?8C82α71.α7@35/8.α8./5A:70C1.α8>α70α≥0H70αρ])<)<)β)α
α
18.9    RECUBRIMIENTOS  
 
ργ))ραα μ8H82BαA21A12?51>02.8α87α.5=:58>/8α28?:H25358>/1α3@>531αC8α?1>?28/1α07α
284:82F1α A28.412F0C1α ;α >1α A28.412F0C10α C:?/1.α ;α 0>?7068.α 8>α 71.α
8</2831.0α8<?8A/1α8>α71αA28L5./1α8>α70.α°8??51>8.αργ))βα;αργ))1)α
α
α
α
α
α
π8?:H25358>/1α
3@>5310α?3Nα
0-αφ1>?28/1αL0?50C1α?1>/20α87α.:871αα1α8>α
?1>/0?/1ααα?1>α0=:0αC8α302N))α ×0]α

132.    UON
N
óeNRi89s(ziN(8N9i8zg9ziN9i8N(bNfc(biNiN
()tc(fziNgbNgnó7(8z(NN
IifgfNmN8(s=gycsgfNZZZZZZZZZGN OXSN
ÓcsifNZZZZZZZZZZZZZZZ N UXLN
EzsifN(b(n(8zifNZZZZZZZZZZGGN 5XLN
N
9eNRi89s(ziN8iN()tc(fziNgbNgnó7(8z(N87N(8N
9i8zg9ziN9i8N(bNfc(biNN
IifgfNmN8(s=gycsgfNZZZZZZZZZ N OXLN
ÓcsifNZZZZZZZZZZZZZZGGN OXSN
o7HgfNmN9ibcn8gfNN
.(pc(sxiNts7897tgbNZZZZZGGGN 5XLN
0fzs7óifNmN(ft7sgb(fNZZZZZGN OXSN
Rvf9gsgfNmNbvn78gfNtb(HgygfNN
ÑgssgfNy(NSáQ^NiNn(8is(fNZZGGN  XLN
N
EzsiNz7tiNy(Ns(pc(sxiNNNNNNNNNNNNyóXNt(siN8iNn(8ifNy(NON
9nN
N
 QGJGONN Rcg8yiNbifN(fpc(sxifNy(Nzsg997–8N()9(yg8NbiN(fz7tcbgyiN(8NbgNÍ(997–8N
 QGVGOóNtgsgN(b(n(8zifNy(N9i89s(ziNts(fpisxgyiN()tc(fzifNgNbgNg997–8N
y(bN 9b7ngXN gbN fc(biN iN gN c8N n(y7iN gnó7(8z(N 9issif7=iXN (bN s(9cós7n7(8ziN
nÁ87niNy(N9i89s(ziNy(ó(svNgcn(8zgsf(N(8Nc8NSLRGN
N
 QGJGUNN 0bNs(9cós7n7(8ziNnÁ87niNtgsgN(bNs(pc(sxiN8iNts(fpisxgyiN(8N(b(n(8zifN
y(N 9i89s(ziN ts(fpisxgyiN pgós79gyifN (8N 9i8y797i8(fN y(N 9i8zsibN (8N bgN
tbg8zgXN y(ó(svN (fzgsNy(Ng9c(syiN9i8NbiN(ft(97p79gyiN(8NbgfNÍ(997i8(fN
4GOgNmN4GOóGN
N
18.10    PÉRDIDAS DE PRESFUERZO  
 
 QG LG N AgsgN y(z(sn78gsN (bN ts(fpc(sxiN (p(9z7=iN pf(Ny(ó(sv8N 9i8f7y(sgsf(N bgfN
f7Hc7(8z(fNpc(8z(fNy(Ntjsy7ygfNy(Nts(fpc(sxiNN
N
geNAjsy7ygfNtisNgf(8zgn7(8ziNy(bNg89bg/(N
N
óeNM9iszgn7(8ziN(bvfz79iNy(bN9i89s(ziN
N
9eN3bc(897gNy(bN9i89s(ziN
N
yeNRi8zsg997–8Ny(bN9i89s(ziN
N
(eN.(bg/g97–8Ny(bN(fpc(sxiN(8NbifNz(8yi8(fN
N
peN Ajsy7ygfNtisNps7997–8Ny(ó7ygfNgNbgN9cs=gzcsgN78z(897i8gbNiNg997y(8zgbNy(N
bifNz(8yi8(fNy(Ntifz(8fgyiGN
 QG LGON Ar.2D2MÍNAE.N3.DRRDd1N01NIEÍNÉ012E10ÍN20NAE ÍÉ01ÍM2EN
 
 QG LGOG N 0bN (p(9ziN y(N bgN tjsy7ygN tisN ps7997–8N (8N bifN z(8yi8(fN y(N tifz(8fgyiN

133.   ρ11α
C8H82Bα?07?:702.8αA12α38C51αC8Nα
±<α8α
+α*αl<αα]ααμαα -
α
α
φ:0>C1α+α*α7<αα]ααμααα-α>1α.80α30;12α9:8α]010α87α848?/1αC8α70αAG2C5C0αA12α
425??5E>αA1C2Bα?07?:702.8αA12α38C51αC8Nα
α
±.ααα\ααα±<αα+αρα]αα*αl<αα]ααμ α -α
α
ργ)ρ])β)βα Σ0.αAG2C5C0.αA12α425??5E>αC8H8αH0.02.8α8>α71.α?1845?58>/8.αC8α425??5E>αA12α
?:2L0/:20α ;α 070H81αμα ;α *0α C8/8235>0C1.α 8<A82538>/0738>/8α ;α C8H82B>α
L82545?02.8αC:20>/8α70.α1A820?51>8.αC8α/8>.0C1αC87α/8>CE>)α
Σ1.αL07128.αC8α*α+A12α38/21α75>807-α;αC8αμαL02@0>α0A28?50H7838>/8α?1>α87α
30/82507α;α70α25=5C8FαC87αC:?/1α;α?1>α87α3G/1C1αC8α?1>./2:??5E>)α
α
ργ)ρ])β)1α Σ1.α L07128.α C8α 71.α ?1845?58>/8.α A12α ?:2L0/:20α ;α 070H81α :.0C1.α 8>α 87α
C5.8D1α;α71.α20>=1.α0?8A/0H78.αA020α70.α4:82F0.αA21C:?5C0.αA12α87α=0/1α
8>α71.α/8>C1>8.0α07α5=:07α9:8α87α0702=0358>/1αC8α71.α/8>C1>8.0αC8H82B>α
5>C5?02.8α8>α71.αA70>1.)α
α
ργ)ρ])β)<α φ:0>C1αA:8C0α1?:2252αAG2C5C0αC8αA28.4:82F1α8>α:>α87838>/1αC8H5C1α0α70α
?1>8<5E>αC87α35.31α?1>α:>0α?1>./2:??5E>α0C;0?8>/80αC5?I0αAG2C5C0αC8α
A28.4:82F1αC8H82Bα/1302.8α8>α?1>.5C820?5E>α8>α87αC5.8D1)α
α
18.11    RESISTENCIA A LA FLEXIÓN 
 
ργ)ρρ)ρα Σ0α28.5./8>?50α0α70α478<5E>αC8αC5.8D1α.8α?07?:702Bα?1>α:>α0>B75.5.αH0.0C1α
8>α 70α ?13A0/5H575C0Cα C8α 8.4:82F1.α ;α C841230?51>8.0α:.0>C1α 70.α
?020?/82@./5?0.α C8α 8.4:82F1JC841230?5E>α C8α 71.α /8>C1>8.α ;α 70.α
.:A1.5?51>8.αC0C0.α8>α70α°8??5E>αρρ)β)α >α71.α?B7?:71.α.8α.:./5/:52Bα4A.α
A12α4;αA020α71.α/8>C1>8.αC8αA28.4:82F1)α
α
ργ)ρρ)βα  >α7:=02αC8α848?/:02α:>0αC8/8235>0?5E>α3B.αA28?5.0αC8α4A.α?1>αH0.8α8>α
70α?13A0/5H575C0CαC8αC841230?51>8.α;α.583A28α9:8α4.8α.80α30;12α1α5=:07α
0α]0(α4A:0α.8αA1C2B>α:/575F02α71.α.5=:58>/8.αL07128.α0A21<530C1.Nα
α
0-α±020α87838>/1.α?1>α/8>C1>8.αC8αA28.4:82F1α0CI825C1.Nα
α α
4A.ααα\ααα4A:αα+αραeα]0(αρρα4A:αKα4Y?α-α
α
H-α±020α 87838>/1.α ?1>α /8>C1>8.α C8α A28.4:82F1α >1α 0CI825C1.α .583A28α
9:8α70α2870?5E>α7:Fα0αA8207/8α.80α5=:07α1α38>12αC8α1(Nα
α
4A.ααα\ααα4.8αα]αα×]]αα]αα4W?αKα+ρ]]αρρ) 
α α α α α
A821α4A.α>1αC8H82Bα/1302.8α30;12α9:8α4A;α>5α9:8α+4.8α]α<β]]-)α
α
?-α±020α 3583H21.α ?1>α /8>C1>8.α C8α A28.4:82F1α >1α 0CI825C1.0α ?1>α :>0α
2870?5E>α7:Fα0αA8207/8α30;12αC8α1(Nα
α
4A.ααα\ααα4.8αα]αα×]]αα]αα4W?αKα+1]]αρρ-α

134.   ρ1<α
α
A821α4A.α>1αC8H8α/1302.8α30;12α9:8α4A;α>5α9:8α+4.8α]αβρ]]-)α
α
ργ)ρρ)1α  >α?0.1αC8α:/575F02α284:82F1α>1αA28.412F0C1α?1>α/8>C1>8.αC8αA28.4:82F10α
8./8α284:82F1αC8H82Bα?:3A752α?1>α70α°8??5E>α1)<)10α87α?:07α?1>/25H:;8α0α70α
4:82F0αC8α/20??5E>α?1>α:>α8.4:82F1α5=:07α0α70α28.5./8>?50α8.A8?545?0C0α0α70α
47:8>?50α4;)α
α
δ/21α 284:82F1α >1α A28.412F0C1α .8α A1C2Bα 5>?7:52α 8>α 71.α ?B7?:71.α C8α
28.5./8>?50α M>5?038>/8α .5α .8α 848?/M0α :>α 0>B75.5.α C8α ?13A0/5H575C0Cα C8α
C841230?51>8.α?1>α87α45>αC8αC8/8235>02α87α8.4:82F1α8>αC5?I1α284:82F1)α
 
18.12    LÍMITES DEL REFUERZO EN MIEMBROS SUJETOS A F LEXIÓN 
 
ργ)ρβ)ρα Σ0α 2870?5E>α 8>/28α 87α 284:82F1α A28.412F0C1α ;α 87α 284:82F1α >1α A28.412F0C1α
:.0C0αA020α71.α?B7?:71.αC8α28.5./8>?50α0α70α478<5E>αC8α:>α87838>/1α.82Bα
/07α9:8α71.αL07128.αC8Nαα
α
Xρ,αfαXραα]αα+XαeαXY-αCαKαCAαg)αEα
fαXρXαα]αα+XXαJαXWX-αCαKαCAαgα
α
>1α.80>α30;128.αC8α]010α8<?8A/1αA12α71αC5.A:8./1α8>α70α°8??5E>αργ)ρβ)β)α
α
ργ)ρβ)βα φ:0>C1α .8α A21A12?51>8α :>0α 2870?5E>α C8α 284:82F1α 30;12α 9:8α 70α
8.A8?545?0C0α8>α70α°8??5E>αργ)ρβ)ρ0α70α28.5./8>?50α0α70α478<5E>αC8αC5.8D1α
>1αC8H82Bα8<?8C82α70α28.5./8>?50α0α70α478<5E>αH0.0C0α8>α87α3138>/1αC8α
70α4:82F0αC8α?13A28.5E>)α
α
ργ)ρβ)1α Σ0α?0>/5C0Cα/1/07αC8α284:82F10αA28.412F0C1α;α>1αA28.412F0C10αC8H82Bα.82α
70α 0C8?:0C0α A020α 1H/8>82α :>0α ?02=0α C8α C5.8D1α C8α A12α 71α 38>1.α ρ0βα
L8?8.α70α?02=0αC8α0=258/038>/10α?07?:70C0α8>αH0.8α07α3EC:71αC8α21/:20α42α
8.A8?545?0C1α8>α70α°8??5E>αρ])<)β)10α8<?8A/1α8>α3583H21.α0α478<5E>α?1>α
28.5./8>?50α07α?12/8α;α478<5E>αC8αA12α71α38>1.α87αC1H78αC8α70α289:825C0α8>α
70α°8??5E>αρ])β)α
α
18.13    REFUERZO MÍNIMO ADHERIDO 
 
ργ)ρ1)ρα  >α/1C1.α71.α3583H21.α.:68/1.α0α478<5E>α?1>α/8>C1>8.αC8αA28.4:82F1α>1α
0CI825C1.0αC8H82BαA21A12?51>02.8α:>αB280α3@>530αC8α284:82F1α0CI825C10α
/07α?131α.8α289:5828α8>α70.α°8??51>8.αργ)ρ1)βα;αργ)ρ1)1)α
α
ργ)ρ1)βα  <?8A/1α 8>α 71α C5.A:8./1α 8>α 70α °8??5E>α ργ)ρ1)10α 87α B280α 3@>530α C87α
284:82F1α0CI825C1αC8H82Bα?07?:702.8αA12Nα
α
Φ.ααα\ααα]0]]<αΦα
α
ργ)ρ1)β)ρα  7α 284:82F1α 0CI825C1α 289:825C1α 8>α 70α °8??5E>α ργ)ρ1)βα C8H82Bα 8./02α
:>54123838>/8α C5./25H:5C1α 8>α 70α F1>0α C8α /20??5E>α A28?13A2535C00α /0>α
?82?0α?131α.80αA1.5H78αC8α70α45H20α8</2830α8>α/20??5E>)α
α

135.   ρ1(α
ργ)ρ1)β)βα  7α284:82F1α0CI825C1α.8α289:5828α5>C8A8>C58>/838>/8αC8α70.α?1>C5?51>8.α
C8α8.4:82F1αH061α70.α?02=0.αC8α.82L5?51)α
α
ργ)ρ1)1α  >α 71.0.α A70>0.α 0230C0.α 8>α C1.α C528??51>8.0α C845>5C0.α ?131α 71.0.α
30?5F0.α C8α A8207/8α :>5412380α 87α B280α 3@>530α ;α 70α C5./25H:?5E>α C87α
284:82F1α0CI825C1αC8H82B>αC5.A1>82.8α?1>41238α0α71α.5=:58>/8Nα
α
ργ)ρ1)1)ρα [1α .8α 289:8252Bα 284:82F1α 0CI825C1α 8>α 70.αF1>0.α C8α 3138>/1α A1.5/5L1α
C1>C8α87α284:82F1αC8α/20??5E>α?07?:70C1αA020α87α?1>?28/1αH061α?02=0.αC8α
.82L5?51α+C8.A:G.αC8α/1302α8>α?1>.5C820?5E>α70.αAG2C5C0.αC8αA28.4:82F1-α
>1α8<?8C0αC8α]0(1α√α4W?α)α
α
ργ)ρ1)1)βα  >αF1>0.αC8α3138>/1αA1.5/5L1αC1>C8α87α8.4:82F1αC8α/20??5E>α?07?:70C1α
8>α 87α ?1>?28/1α H061α ?02=0.α C8α .82L5?51α 8<?8C0α C8α ]0(1α√α 4W?α 0α 87α B280α
3@>530αC8α284:82F1α0CI825C1αC8H82Bα?07?:702.8αA12αNα
α
Φ.ααα\ααα[?αKα+]0(α4;-α
α
C1>C8α 70α 28.5./8>?50α 0α 70α 47:8>?50α C8α C5.8D1α 4Lα >1αC8H82Bα 8<?8C82α C8α
<β]]α Q=K?3β)α  7α 284:82F1α 0CI825C1α C8H82Bα C5./25H:52.8α :>54123838>/8α
.1H28α70αF1>0αC8α/20??5E>αA28?13A2535C00α/0>α?82?0α?131α.80αA1.5H78αC8α
70α45H20α8</2830α8>α/20??5E>)α
α
ργ)ρ1)1)1α  >αF1>0.αC8α3138>/1α>8=0/5L1α?82?0αC8α70.α?17:3>0.αC8α0A1;10α87αB280α
3@>530αC87α284:82F1α0CI825C1α8>α?0C0αC528??5E>αC8H82Bα?07?:702.8αA12Nα
α
Φ.ααα\ααα]0]]]×(αIαl 
α
C1>C8αlα8.α70α7:Fα75H28α8>α70αC528??5E>αA0207870α0α70αC87α284:82F1α9:8α.8α
8./BαC8/8235>0>C1)α 7α284:82F1αC8H82BαC5./25H:52.8α8>α:>0α420>60αC8α71.0α
7535/0C0αA12α71.α868.α71?075F0C1.α0αρ0(Iα4:820αC8α70.α?020.α1A:8./0.αC8α70α
?17:3>0)αμ8H82B>αA21A12?51>02.8αA12α71α38>1.α<αH0220.α1α0703H28.α8>α
?0C0α C528??5E>)α  7α 8.A0?50358>/1α C87α 284:82F1α 0CI825C1α >1α C8H82Bα
8<?8C82αC8α1]α?3)α
α
ργ)ρ1)<α Σ0α71>=5/:Cα3@>530αC87α284:82F1α0CI825C1α289:825C0αA12α70.αC5.A1.5?51>8.α
C8α70.α°8??51>8.αργ)ρ1)βα;αργ)ρ1)1αC8H82Bα.82αC8α0?:82C1α0Nα
α
ργ)ρ1)<)ρα  >αF1>0.αC8α3138>/1αA1.5/5L10α70α71>=5/:Cα3@>530αC87α284:82F1α0CI825C1α
C8H82Bα.82αρK1αC8α70α71>=5/:CαC8α70α7:Fα75H28α;α8./02α?8>/20C1α?1>α70αF1>0α
C8α3138>/1αA1.5/5L1)α
α
ργ)ρ1)<)βα  >α F1>0.α C8α 3138>/1α >8=0/5L10α 87α 284:82F1α 0CI825C1α C8H82Bα
A2171>=02.8αρK=αC8α70α7:Fα75H28α0α?0C0α70C1αC87α0A1;1)α
α
ργ)ρ1)<)1α φ:0>C1α.8α.:35>5./28α284:82F1α0CI825C1αA020α?1>/25H:52α0α70α28.5./8>?50α
C8α C5.8D1α 0α 478<5E>α C8α 0?:82C1α ?1>α 70α °8??5E>α ργ)ρρ)1α Eα A020α 70.α
?1>C5?51>8.α C8α 8.4:82F1.α C8α /20??5E>α C8α 0?:82C1α ?1>α 70α °8??5E>α
ργ)ρ1)1)β0α 70α 71>=5/:Cα 3@>530α C8H82Bα 8./02α C8α 0?:82C1α 0α 70.α
C5.A1.5?51>8.αC87αφ0A@/:71αγ)α

136.   ρ1=α
α
18.14    RESISTENCIA AL CORTANTE 
 
ργ)ρ<)ρα  7α C5.8D1α A12α 4:82F0α ?12/0>/8α C8α 87838>/1.αC8α ?1>?28/1α A28.412F0C1α
.:68/1.α0α478<5E>α.8αH0.02Bα8>α70.α8?:0?51>8.αC8α70α°8??5E>αρ1)ρ)ρα;α71α
8./0H78?5C1α8>α70α°8??5E>αρ1)ρ)β)α
α
ργ)ρ<)βα Σ0.α.8??51>8.α.5/:0C0.α0α:>0αC5./0>?50α38>12α9:8αSIKβSαC8.C8α70α?020α
C87α0A1;1αA1C2B>α.82αC5.8D0C0.αA020α70α4:82F0α?12/0>/8α:α?07?:70C0α0α
:>0αC5./0>?50αSIKβS0α.5α.8α?:3A78>α70.α.5=:58>/8.α?1>C5?51>8.Nα
α
0-αφ:0>C1α 70α 280??5E>α C87α 0A1;10α 8>α C528??5E>α C87α ?12/8α 0A75?0C10α
5>/21C:?8α ?13A28.5E>α 8>α 70.α 28=51>8.α ?82?0>0.α 07α 0A1;1α C87α
87838>/1)α
α
H-αφ:0>C1α>1α8<5./8>α?02=0.α?1>?8>/20C0.α8>/28α70α?020αC87α0A1;1α;α70α
.8??5E>α:H5?0C0α0α:>0αC5./0>?50αSIKβS)α
α
ργ)ρ<)1α φδ[≥π2+≤φ2>[αμ Σαφδ[φπ ≥δα [αΣΦαπ °2°≥ [φ2Φ αΦΣαφδπ≥ α
 
ργ)ρ<)1)ρα ±020α87838>/1.α9:8α/8>=0>α:>0α4:82F0α848?/5L0αC8αA28.4:82F1α>1α38>12α
07α<]RαC8α70α28.5./8>?50α0α70α/20??5E>αC87α284:82F1αA12α478<5E>0α0α38>1.α
9:8α .8α 848?/M8α :>α ?B7?:71α 3B.α C8/0770C1α C8α 0?:82C1α0α 70α °8??5E>α
ργ)ρ<)1)βNα
mmα α α ααα
?ααα\ααα+α]0ρ=α√α4W?αα]αα<α:αCαKα,:α-αHXαCαα
α
 7α?1?58>/8αα:αCαKα,:αα>1αC8H82Bα?1>.5C8202.8α30;12α0αρα8>α87α?B7?:71α
C8α?0αC1>C8α,:α8.α87α3138>/1α0?/:0>/8α.53:7/B>8038>/8α?1>α:α8>α70α
.8??5E>α?1>.5C820C0)α
αααααααααααααααααααααααααααααααααααααααααααααααααmmααααααααααααααααααααααααααααααααααααααααααααmmα
?α>1α.82Bα38>12α9:8Nα]0(1α√α4W?ααHXαCα>5α30;12α9:8α]0ρ1α√α4W?ααHXαC0α1α87α
L0712αC0C1α8>α70α°8??5E>ααργ)ρ<)1)<αEα8>α70α°8??5E>αργ)ρ<)1)()α
α
ργ)ρ<)1)βα Σ0α28.5./8>?50α07α?12/0>/8α.82Bα87α38>12αC8α71.αL07128.α1H/8>5C1.α8>α70.α
8<A28.51>8.α.8D070C0.α8>α0-α;α8>αH-Nα
α
0-αΣ0α28.5./8>?50α07α?12/0>/8α?5α.82BαNα
αmmα
?5ααα\ααα]0ρ=α√α4W?ααHXαCαα]ααCαα]αα5α,?2αKα,3B<α
α
C1>C8α87α3138>/1αC8α0=258/0358>/1α,?2α8./BαC0C1αA12Nα
mmα
,?2ααα\ααα+α]0ρ=α√α4W?αα]αα4A8ααJαα4Cα-ααIαKα8/α
α
;α71.αL07128.αC8α,3B<α;α5αC8H82B>α?07?:702.8αC8α70αC5./25H:?5E>αC8α70α
?02=0α9:8αA21C:F?0α87α3138>/1α3B<531α8>α70α.8??5E>0αA821α.5>α9:8α
?5α.80α38>12α9:8Nαααααααααααααααααααα
ααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααααmmα
]0<(α√α4W?ααHXαCα

137.   ρ1×α
α
H-αΣ0α28.5./8>?50α07α?12/0>/8α?Xα.82BNα
αmmα
?Xααα\ααα+α]01α√α4W?αα]αα]01α4A?α-αHXαCαα]ααAα
α α ααααα
Φ7/82>0/5L038>/80α ?Xα A1C2Bα ?1>.5C8202.8α ?131α 70α 4:82F0α ?12/0>/8α
9:8α?1228.A1>C8α0α70α?02=0α3:82/0α3B.α70α?02=0αL5L00α71α?:07αC0α?131α
28.:7/0C1α :>α 8.4:82F1α A25>?5A07α C8α /20??5E>α C8α α ρ0ρα√α 4W?α α 8>α 87α 868α
?8>/215C07α C87α 87838>/1α 1α 8>α 70α 5>/82.8??5E>α C87α 070α ?1>α 87α 07300α
?:0>C1α87α868α?8>/215C07α8./Bα8>α87α070)α >α87838>/1.α?13A:8./1.0α87α
8.4:82F1αA25>?5A07αC8α/20??5E>α.8αC8H82Bα?07?:702α:/575F0>C1α70α0??5E>α
/20>.L82.07α9:8α28.5./8α70α?02=0αL5L0)α
α
ργ)ρ<)1)1α  >α70.α8?:0?51>8.αC8α70.α°8??51>8.αργ)ρ<)1)β)0α;αργ)ρ<)1)β)H0αCα8.α70α
C5./0>?50α C8α 70α 45H20α 8</2830α 8>α ?13A28.5E>α 07α ?8>/215C8α C87α 0?821α C8α
A28.4:82F1αEαα]0γI0α87α9:8α.80α30;12)α
α
ργ)ρ<)1)<α  >α:>α87838>/1αA28.412F0C1α8>α87α?:07α70α.8??5E>α0α:>0αC5./0>?50αIKβα0α
A02/52αC8α70α?020αC87α0A1;1α8./Gα3B.α?82?0>0αC87α8</2831αC87α87838>/1α
9:8α 70α 71>=5/:Cα C8α /20>.4828>?50α C8α 71.α /8>C1>8.α C8α A28.4:82F10α 70α
28C:??5E>αC87αA28.4:82F1αC8H82Bα/8>82.8α8>α?:8>/0α?:0>C1α.8α?07?:78α
?X)α  ./8α L0712α C8α ?Xα /03H5G>α C8H82Bα ?1>.5C8202.8α?131α 87α 7@35/8α
3B<531αA020α70α8?:0?5E>αC8α70α°8??5E>αργ)ρ<)1)ρ)αμ8H8α.:A1>82.8α9:8α
70α4:82F0αC8αA28.4:82F1αL02@0α75>80738>/8αC8.C8α?821α8>α87α8</2831αC87α
/8>CE>αI0./0α:>α3B<531α0α:>0αC5./0>?50αC87α8</2831αC87α/8>CE>α5=:07α0α
70α71>=5/:CαC8α/20>.4828>?500α9:8α.8α.:A1>8α8.αC8α(]αL8?8.α87αC5B38/21α
A020α/121>8.α;αC8αρ]]αL8?8.α87αC5B38/21αA020α0703H28.α5>C5L5C:078.)α
α
ργ)ρ<)1)(α  >α:>α87838>/1αA28.412F0C1αC1>C8α70α0CI828>?50αC8α07=:>1.α/8>C1>8.α
>1α.8α8</58>C0αI0./0α87α8</2831αC87α87838>/10αC8H82Bα?1>.5C8202.8α:>α
A28.4:82F1α 28C:?5C1α 07α ?07?:702α ?α C8α 0?:82C1α ?1>α 70.α °8??51>8.α
ργ)ρ<)1)ρα Eα ργ)ρ<)1)β)α  7α L0712α C8α ?Xα 9:8α .8α ?07?:78α 07α 83A7802α 87α
A28.4:82F1α 28C:?5C10α /03H5G>α C8H82Bα /1302.8α ?131α 87α 7@35/8α 3B<531α
A020α 70α 8?:0?5E>α C8α 70α °8??5E>α ργ)ρ<)1)ρ)α Σ0α 4:82F0α C8α A28.4:82F1α
C8H5C0α0α71.α/8>C1>8.α8>α71.α9:8α70α0CI828>?50α>1α.8α8</58>C0αI0./0α87α
8</2831α C87α 87838>/10α A1C2Bα .:A1>82.8α 9:8α L02@0α 75>80738>/8α C8.C8α
?821α8>α87αA:>/1α8>α9:8α?1358>F0α70α0CI828>?50αI0./0α:>α3B<531α0α70α
C5./0>?50α C8.C8α 8./8α A:>/1α 5=:07α 0α 70α 71>=5/:Cα C8α /20>.4828>?500α
.:A1>58>C1α9:8α.80α(]αL8?8.α87αC5B38/21αA020α/121>8.α;αρ]]αL8?8.α87α
C5B38/21αA020α0703H28α5>C5L5C:07)α
α
ργ)ρ<)<α φδ[≥π2+≤φ2>[αμ Σαπ σ≤ π.δα [αΣΦαπ °2°≥ [φ2Φ αΦΣαφδπ≥ αα
α
ργ)ρ<)<)ρα Σ0α ?1>/25H:?5E>α C87α 284:82F1α 8>α 70α 28.5./8>?50α 07α ?12/8α ;α .:α C5.8D1α .8α
C8/8235>02Bα C8α 0?:82C1α 0α 70.α C5.A1.5?51>8.α 8./0H78?5C0.α 8>α 70.α
°8??51>8.αρ1)1)ρ0αρ1)1)βα;αρ1)1)1)α
α
ργ)ρ<)<)β  7α284:82F1α3@>531αA12α?12/8 
α
 7α 284:82F1α 3@>531α A12α ?12/8α ?:3A752Bα ?1>α 71α 5>C5?0C1α 8>α 70α °8??5E>α

138.   ρ1γα
ρ1)1)<)α ΦC5?51>0738>/80α .8α C8H82Bα ?:3A752α 9:8α A020α87838>/1.α 9:8α
/8>=0>α :>0α 4:82F0α C8α A28.4:82F1α 848?/5L0α >1α 38>12α C87α <]Rα C8α 70α
28.5./8>?50α0α70α/20??5E>αC87α284:82F1αA12α478<5E>0α87αB280αC87α284:82F1αA12α
?12/8α>1α.82Bα38>12α9:8α>5>=:>1αC8α71.αL07128.α1H/8>5C1.α8>α70α4E23:70α
C8α70α°8??5E>αρ1)1)<)βαα;Nαααααααααααααααααααααααααααααααααααααααααααααααααα α
αmmmmmα
ΦLααα\ααα+αΦA.α4A:α.α-αKα+αγ]α4;αCα-ααlαCαKαHXα
α
18.15    PÓRTICOS Y ELEMENTOS CONTINUOS 
 
ργ)ρ()ρα Σ1.αAE2/5?1.α;α87838>/1.α?1>/5>:1.αC8α?1>?28/1αA28.412F0C1αC8H82B>α.82α
C5.8D0C1.α A020α :>α ?13A12/0358>/1α .0/5.40?/1251α H061α ?1>C5?51>8.α C8α
?02=0.αC8α.82L5?51α;αA020α70α28.5./8>?50α0C8?:0C0)α
α
ργ)ρ()βα  7α ?13A12/0358>/1α H061α ?1>C5?51>8.α C8α ?02=0α C8α .82L5?51α C8H82Bα
C8/8235>02.8α A12α :>α 0>B75.5.α 87B./5?10α ?1>.5C820>C1α 70.α 280??51>8.0α
3138>/1.0α?12/0>/8.α;α4:82F0.α0<5078.αA21C:?5C0.αA12α87αA28.4:82F10α70α
47:8>?500α 70α ?1>/20??5E>0α 71.α ?03H51.α C8α /83A820/:200α 70α C841230?5E>α
0<5070α70.α28./25??51>8.αC8α71.α87838>/1.α8./2:?/:2078.α0C;0?8>/8.α;α71.α
0.8>/0358>/1.αC8α70α?538>/0?5E>)α
α
ργ)ρ()1α Σ1.α 3138>/1.α 0α ?1>.5C8202α A020α ?07?:702α 70α28.5./8>?50α 289:825C0α
C8H82B>α.82α70α.:30αC8α71.α3138>/1.αC8H5C1.α0α71.α848?/1.α5>C:?5C1.α
A12α87αA28.4:82F1α+?1>α:>α40?/12αC8α?02=0αC8αρ-α;α71.α3138>/1.αC8H5C1.α
0α70.α?02=0.αC8αC5.8D10α5>?7:;8>C1α70α28C5.25H:?5E>α9:8α.8αA8235/8α8>α70α
°8??5E>αργ)ρ()<)α
 
ργ)ρ()<α π μ2°≥π2+≤φ2>[α μ α ,δ, [≥δ°α [ √Φ≥2δ°α μ +2μδ °α Φα
φΦπ√Φ°α μ α √πΦ μΦμα  [α  Σ , [≥δ°α ±π °σδπ.Φμδ°α
φδ[≥2[≤δ°α°≤5 ≥δ°αΦασΣ 2>[α
 
ργ)ρ()<)ρα φ:0>C1α.8αA21A12?51>8α284:82F1α0CI825C1α8>α71.α0A1;1.αC8α0?:82C1α?1>α
70α°8??5E>αργ)ρ1)β0α71.α3138>/1.α>8=0/5L1.α?07?:70C1.αA12α38C51αC8α70α
/812@0α 87B./5?0α A020α :>0α C5./25H:?5E>α C8α ?02=0α .:A:8./00α A1C2B>α
0:38>/02.8α1αC5.35>:52.8α8>α>1α3B.αC8Nα
α
β]ααiαραeαfαXρ  ]αα+XeXY-αCαKαCραgαKα+])1=αβρ-αjαRα
α
ργ)ρ()<)βα Σ1.α 3138>/1.α >8=0/5L1.α 31C545?0C1.α C8H8>α:/575F02.8α A020α ?1228=52.8α
71.α 3138>/1.α 8>α 70.α C83B.α .8??51>8.α C8>/21α C8α 70α 7:Fα 75H28α A020α 70α
35.30αC5./25H:?5E>αC8α?02=0.)α
α
ργ)ρ()<)1α Σ0α28C5./25H:?5E>αC8α3138>/1.α>8=0/5L1.α.8αI02BαM>5?038>/8α?:0>C1α70α
.8??5E>α8>α70α9:8α.8α28C:F?0α87α3138>/1α.8αC5.8D8αC8α/07α30>820α9:8Nα
α
XA0αααααfαXρ  ]αα+XeXY-αCαKαCραgαααααEαααααfαXρXαα]αα+XXeXXY-αCαKαCραgα
α
70α9:8α.80α0A75?0H780α.80α38>12α9:8α]0β<αβρ)α
α
18.16    ELEMENTOS  EN  COMPRESIÓN:  CARGA  AXIAL  Y  FLEXI ÓN 

139.   ρ1α
COMBINADAS 
 
Σ1.α 87838>/1.α C8α ?1>?28/1α A28.412F0C1α .:68/1.α 0α?02=0α0<507α;α478<5E>α
?13H5>0C0.0α ?1>α 1α .5>α 284:82F1α >1α A28.412F0C10α C8H82B>α .82α
C538>.51>0C1.αC8α0?:82C1α?1>α71.α3G/1C1.αC8αC5.8D1αC8α28.5./8>?50αC8α
8./0α[1230αA020α87838>/1.α.5>αA28.4:82F1)αμ8H82B>α5>?7:52.8α71.α848?/1.α
C87αA28.4:82F10α70α?1>/20??5E>0α70α47:8>?50α;α87α?03H51αC8α/83A820/:20)α
 
18.17    SISTEMAS DE LOSAS 
 
ργ)ρ×)ρα Σ1.α.5./830.αC8α71.0.αA28.412F0C0.α28412F0C0.αA020α478<5E>α8>α3B.αC8α
:>0α C528??5E>α A1C2B>α C5.8D02.8α A12α ?:079:582α A21?8C5358>/1α 9:8α
.0/5.40=0α 70.α ?1>C5?51>8.α C8α 89:575H251α ;α C8α ?13A0/5H575C0Cα=813G/25?0)α
Σ0.α25=5C8?8.αC8α70.α?17:3>0.α;αC8α70.α?1>8<51>8.α71.0J?17:3>00α07α5=:07α
9:8α 71.α 848?/1.α C87α A28.4:82F1α C8α 0?:82C1α ?1>α 70α °8??5E>α ργ)ρ(0α
C8H82B>α/1302.8α8>α?1>.5C820?5E>α8>α87α3G/1C1αC8α0>B75.5.)α
α
ργ)ρ×)βα Σ1.α?1845?58>/8.αC8α?12/0>/8α;αC8α3138>/1α:/575F0C1.αA020α87αC5.8D1αC8α
71.α.5./830.αC8α71.0α28412F0C0α?1>α0?821α>1αA28.412F0C1α>1αC8H82B>α.82α
0A75?0C1.α0α71.α.5./830.αC8α71.0.αA28.412F0C0.)α
α
18.18    ZONAS DE ANCLAJE DE LOS TENDONES 
 
ργ)ργ)ρα  >α 70.α F1>0.α C8α 0>?7068α C8α 71.α /8>C1>8.0α C8H82Bα A21A12?51>02.8α 87α
284:82F1α 9:8α .8α 289:5820α A020α 28.5./52α 71.α 848?/1.αC8α 21/:20α L5178>/00α
.8A020?5E>α ;α C8.?0.?020358>/1α 5>C:?5C1.α A12α 87α 0>?7068α C8α 71.α
/8>C1>8.)αΣ0.αF1>0.αC8α?03H51αH2:.?1αC8α.8??5E>αC8H82B>α28412F02.8α
0C8?:0C038>/8)α
α
ργ)ργ)βα ±020α28.5./52α87α0A70./0358>/1α1αA020αC5./25H:52α70.α4:82F0.α?1>?8>/20C0.α
C8αA28.4:82F10αC8H82B>α?171?02.8αH719:8.αC8α8</2831α?:0>C1αG./1.α.8α
289:5820>)α
α
ργ)ργ)1α Σ1.α0>?7068.αA020αA1./8>.0C1α;α87α?1>?28/1α9:8α71.α.1A12/8αC8H82B>α.82α
C5.8D0C1.α A020α 28.5./52α 70α 4:82F0α 3B<530α C87α =0/1α C8α 0?:82C1α ?1>α 70α
28.5./8>?50αC87α?1>?28/1α8>α87α3138>/1αC8α70α0A75?0?5E>αC87αA28.4:82F1)α
α
ργ)ργ)<α Σ0.α F1>0.α C8α 0>?7068.α A020α A1./8>.0C1.α C8H82B>α .82α C5.8D0C0.α A020α
C8.02217702α70α28.5./8>?50αM7/530α0α70α/8>.5E>α=020>/5F0C0αC87α/8>CE>αC8α
A28.4:82F10α:/575F0>C1α:>α40?/12αC8α28C:??5E>αφαC8α]0αA020α87α?1>?28/1)α
α
18.19    PROTECCIÓN  CONTRA  LA  CORROSIÓN  DE  TENDONES  D E 
PRESFUERZO NO ADHERIDOS 
α
ργ)ρ)ρα Σ1.α/8>C1>8.α>1α0CI825C1.αC8H82B>α28?:H252.8α?13A78/038>/8α?1>α:>α
30/82507α0C8?:0C1α9:8α0.8=:28α70αA21/8??5E>α?1>/20α70α?1221.5E>)α
α
ργ)ρ)βα  7α28?:H25358>/1αC8α71.α/8>C1>8.αC8H82Bα.82α?1>/5>:1α8>α/1C0α70α71>=5/:Cα
9:8α>1αL0;0α0α0CI8252.80α;αC8H8αA28L8>52.8α70α?1>/035>0?5E>αC8αA0./0α
C8α ?838>/1α ;α 70α AG2C5C0α C87α 30/82507α C8α 28?:H25358>/1α C:20>/8α 70α

140.    5LN
9ibi9g97–8Ny(bN9i89s(ziGN
N
18.20    PROTECCIÓN DE LOS TENDONES DE PRESFUERZO 
 
 QGOLG N 0bN g9(siN y(N ts(z(8fgsN (fzgsvN b7nt7iN mN b7ós(N y(N –)7yiN ()9(f7=iXN
789scfzg97i8(fNmNt79gycsgfGNÍ(Nt(sn7z7svNc8gNi)7yg97–8Nb7H(sgGN0bNg9(siN
8iNgyh(s7yiN(fzgsvNtsiz(H7yiNt(sng8(8z(n(8z(Ny(NbgN9issif7–8GN
N
 QGOLGON IgfN it(sg97i8(fN y(N 9iszgsN 9i8N fitb(z(N (8N bgN =(978ygyN y(bN g9(siN
ts(z(8fisXN f(N hgsv8N 9c7ygyifgn(8z(N tgsgN Kc(N (bN g9(siN ts(z(8fisN 8iN
(fzjN fc/(ziN gN z(nt(sgzcsgfN ()9(f7=gfXN 9h7ftgxifN y(NfibygycsgN iN
9iss7(8z(N(bj9zs79gNgNz7(ssgGN
N
18.21    DUCTOS PARA POSTENSADO 
 
 QGO G N IifN yc9zifN tgsgN bifN z(8yi8(fN Kc(N f(N =gmg8N gN s(9cós7sN 9i8N b(9hgygN iN
tgsgN bifN z(8yi8(fN Kc(N 8iN =gmg8N gN Kc(ygsN gyh(s7yifXNy(ó(sv8N f(sN
h(snjz79ifNgbNnisz(siNmN8iNs(g997i8gsN9i8N(bN9i89s(ziXNbifNz(8yi8(fNiN(bN
ngz(s7gbNy(Ns(bb(8iGN
N
 QGO GON IifN yc9zifN tgsgN z(8yi8(fN y(N c8N fibiN gbgnós(XN zis–8N iN ógssgN Kc(N f(N
=gmg8NgNs(9cós7sN9i8Nb(9hgygXNy(ó(sv8Nz(8(sNc8Ny7vn(zsiN78z(s7isNtisNbiN
n(8ifNVnnNngmisNKc(N(bNy7vn(zsiNy(bNz(8y–8GN
N
 QGO GUN IifN yc9zifN tgsgN z(8yi8(fN y(N gbgnós(fXN zisi8(fN iN ógssgfN nMbz7tb(fXN
y(ó(sv8N z(8(sN c8N vs(gN zsg8f=(sfgbN 78z(s7isN ngmisN iN7HcgbN gN ON =(9(fN (bN
vs(gN8(zgNy(NbifNz(8yi8(fGN
N
 QGO G5N IifNyc9zifNy(ó(8Nng8z(8(sf(Nb7ós(fNy(NgHcgN9cg8yiNbifN(b(n(8zifNKc(N
f(N =gmg8N gN 78m(9zgsN 9i8N b(9hgygN (fzgN ()tc(fzifN gN z(nt(sgzcsgfN
78p(s7is(fNgbNtc8ziNy(N9i8H(bg97–8Ng8z(fNy(NbgN78m(997–8Ny(NbgNb(9hgygGN
N
18.22    LECHADA PARA TENDONES DE PRESFUERZO ADHERIDO S 
 
 QGOOG N IgNb(9hgygNy(ó(svN9i8f7fz7sNy(N9(n(8ziNtiszbg8yNmNgHcgNiNy(N9(n(8ziN
tiszbg8yXNgs(8gNmNgHcgGN
NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN
 QGOOGON IifNngz(s7gb(fNtgsgNbgNb(9hgygNy(ó(sv8Nf(sN9i8pisn(fNgNbiNf7Hc7(8z(NN
N
N N geN 0bN9(n(8ziNtiszbg8yNy(ó(svN9cntb7sN9i8NbgNÍ(99 7–8NUG GN
N
N N óeN 0bNgHcgNy(ó(svN9cntb7sN9i8NbgNÍ(997–8NUGUGN
N
N N 9eN Í7N f(N cfgN gs(8gXN jfzgN y(ó(svN 9cntb7sN 9i8N biN 78y79gyiN (8N bgN
Í(997–8NUGOG GN
N
N N yeN Í(Ntiysv8Ncz7b7xgsNgy7z7=ifNKc(N9cntbg8N9i8Nbg NÍ(997–8NUGSXNy(NbifN
9cgb(fNf(Nf(tgNKc(N8iNtsiyc9(8N(p(9zifNt(s/cy797gb(fN(8N(bNg9(siXN
(8N(bN9i89s(ziNiN(8NbgNb(9hgygGN1iNy(ó(svN(ntb(gsf(N9biscsiNy(N
9gb97iGN

141.   ρ<ρα
α
ργ)ββ)1α ° Σ φφ2>[αμ αΣΦαμδ°2σ2φΦφ2>[α±ΦπΦαΣΦαΣ φTΦμ Φα
 
ργ)ββ)1)ρα Σ0.αC1.545?0?51>8.αC8α71.α30/825078.αA020α70α78?I0C0αC8H8αH0.02.8α8>α
:>0αC8α70.αC1.α?1>C5?51>8.α.5=:58>/8.Nα
α α α
0-αα Σ1.α 28.:7/0C1.α C8α A2:8H0.α C8α 78?I0C0.α 428.?0.α 1α 8>C:28?5C0.α
0>/8.αC8α5>5?502α70.α1A820?51>8.αC8α5>;8??5E>αC8α70α78?I0C00α1αα
H-α μ1?:38>/0?5E>α 8<A82538>/07α A28L50α ?1>α 30/825078.α ;α 89:5A1.α
.83860>/8.α;αH061α?1>C5?51>8.αC8α?03A1α?13A020H78.)α
α
ργ)ββ)1)βα  7α?838>/1α:/575F0C1α8>α70α1H20αC8H82Bα?1228.A1>C82α0α09:G7α8>α87α?:07α
.8αH0.Eα70α.878??5E>αC8α70αC1.545?0?5E>)α
α
ργ)ββ)1)1α  7α?1>/8>5C1αC8α0=:0αC8H82Bα.82α87α3@>531α>8?8.0251αA020α87αH13H81α
0C8?:0C1α C8α 70α 78?I0C0)α [1α 1H./0>/80α 70α 2870?5E>α 0=:0K?838>/1α >1α
C8H82Bα8<?8C82αC8α]0<(αA12αA8.1α+ρα75/21.αA12α.0?1-)α
α
ργ)ββ)1)<α [1α.8αC8H82Bα0D0C52α0=:0α?1>α87α45>αC8α0:38>/02α70α47:5C8FαC8α70α78?I0C0α
9:8αI0;0αC5.35>:5C1αA12α87α:.1α28/20.0C1αC8αG./0)α
α
ργ)ββ)<α , .φΣΦμδα8α+δ,+ δαμ αΣΦαΣ φTΦμΦ  
 
ργ)ββ)<)ρα Σ0α 78?I0C0α C8H82Bα .82α A28A020C0α 8>α :>α 89:5A1α ?0A0Fα C8α 848?/:02α :>α
38F?70C1α ;α :>0α 0=5/0?5E>α 38?B>5?0α ?1>/5>:1.0α 9:8α A21C:F?0>α :>0α
C5./25H:?5E>α:>541238αC8α71.α30/825078.)αμ8H8α?25H02.8α;αH13H802.8αC8α
30>820α/07α9:8α.8α778>8>αA12α?13A78/1α71.αC:?/1.αC8α71.α/8>C1>8.)α
α
ργ)ββ)<)βα Φ>/8.α C8α 70α 5>;8??5E>0α 71.α C:?/1.α 8./02B>α 75H28.α C8α 0=:00α .:?58C0Cα ;α
1/20.α .:./0>?50.α 8</20D0.)α  7α 3G/1C1α C8α 5>;8?/0C1α .82Bα /07α 9:8α .8α
0.8=:28α 87α 778>0C1α ?13A78/1α C8α /1C1.α 71.α L0?@1.α 8>/28α 87α 0?821α
A28/8>.120α87αC:?/1α;α71.α0C5/038>/1.αC8α0>?7068)α
α
ργ)ββ)<)1α Σ0α /83A820/:20α C8α 71.α 87838>/1.α 07α 3138>/1α C8α 70α 5>;8??5E>α C8α 70α
78?I0C0αC8H82Bα.82α30;12αC8αβ°φα;αC8H8α30>/8>82.8αA12α0225H0αC8α8./0α
/83A820/:20αI0./0α9:8α71.α?:H1.α40H25?0C1.α?1>α70α35.30α78?I0C00αC8α(α
?3α <α (α ?30α ?:20C1.α 8>α 70α 1H20α 71=28>α :>0α 28.5./8>?50α 3@>530α 0α 70α
?13A28.5E>αC8α(=αQ=K?3β)α
α
ργ)ββ)<)<α Σ0α/83A820/:20αC8α70α78?I0C0α>1αC8H82Bα.82α.:A82512α0α1β°φαC:20>/8α87α
38F?70C1α;α87αH13H81)α
α
18.23    APLICACIÓN Y MEDIDA DE LA FUERZA DE PRESFUER ZO 
 
ργ)β1)ρα Σ0α4:82F0αC8αA28.4:82F1αC8H82Bα.82αC8/8235>0C0αA12α38C51αC8α71.αC1.α
3G/1C1.α.5=:58>/8.Nα
α
0-α Σ0α 38C5C0α C87α 0702=0358>/1α C87α /8>CE>)α Σ1.α 289:5.5/1.α C8α
0702=0358>/1α C8H82B>α C8/8235>02.8α 0α A02/52α C8α 70.α ?:2L0.α
A2138C51α ?02=0J0702=0358>/1α C8α 71.α /8>C1>8.α C8α A28.4:82F1α

142.    5ON
cz7b7xgyifGN
N
óeN IgNióf(s=g97–8Ny(NbgNpc(sxgNy(bNHgziN(8Nc8Nng8–n(zsiN9gb7ósgyiNiN
9i8Nc8gN9(bygNy(N9gsHgNiNcz7b7xg8yiNc8Ny78gn–n(zsiN9gb7ósgyiGN
N
2(ó(N 78=(fz7Hgsf(N mN 9iss(H7sf(N bgN 9gcfgN y(N 9cgbKc7(sN y7p(s(897gN (8N bgN
y(z(sn78g97–8Ny(NbgNpc(sxgN(8zs(NugeNmNuóeNKc(N()9(ygN(bNSRGN
N
 QGOUGON Rcg8yiN bgN zsg8fp(s(897gN y(N bgN pc(sxgN y(N bifN ()zs(nifN y(N bgN 9gngN y(N
ts(z(8fgyiNgbN9i89s(ziNf(N(p(9zM(N9iszg8yiNbifNz(8yi8(fNy(Nts(fpc(sxiN
9i8N fitb(z(XN bifN tc8zifN y(N 9isz(N mN bgN f(9c(897gN y(N9isz(N y(ó(sv8N
ts(y(z(sn78gsf(NtgsgN(=7zgsN(fpc(sxifNz(ntisgb(fN78y(f(gób(fGN
N
 QGOUGUN IifN zsgnifN bgsHifN ()tc(fzifN y(N bifN zisi8(fNts(z(8fgyifN y(ó(sv8N
9iszgsf(NbiNnvfN9(s9gNtif7ób(Ny(bN(b(n(8ziNtgsgNs(yc97sNbifN7ntg9zifNgbN
9i89s(ziGN
N
 QGOUG5N IgN tjsy7ygN zizgbN y(bN ts(fpc(sxiN y(ó7ygN gN z(8yi8(fN sizifN 8iN
s((ntbgxgyifN8iNy(ó(svN()9(y(sNy(bNORNy(bNts(fpc(sxiNzizgbGN
N
18.24    ANCLAJES Y ACOPLADORES PARA POSTENSADO 
 
 QGO5G N IifNg89bg/(fNmNg9itbgyis(fNtgsgNz(8yi8(fNy(Nts(fpc(sxiNgyh(s7yifNmN8iN
gyh(s7yifNy(ó(sv8Ny(fgssibbgsNgbNn(8ifNJSRNy(NbgNs(f7fz(897gNgNbgNsizcsgN
(ft(97p79gygN (8N bifN z(8yi8(fN gbN f(sN tsiógyifN óg/iN 9i8y797–8N y(N 8iN
gyh(s(897gXN f78N ()9(y(sN bifN 9iss7n7(8zifN ts(=7fzifGN AgsgN z(8yi8(fN
gyh(s7yifXNbifNg89bg/(fNmNg9itbgyis(fNy(ó(sv8N(fzgsNbi9gb7xgyifNy(NzgbN
ng8(sgN Kc(N (bN  LLRN y(N bgN s(f7fz(897gN gN bgN sizcsgN (ft(97p79gygN y(N bifN
z(8yi8(fNf(Ny(fgssibb(N(8Nf(997i8(fN9sÁz79gfNy(ftcjfNKc(NbifNz(8yi8(fN
(fzj8Ngyh(s7yifN(8N(bN(b(n(8ziGN
N
 QGO5GON IifN g9itbgyis(fN y(ó(sv8N 9ibi9gsf(N (8N xi8gfNgtsiógygfN tisN (bN
D8ft(9zisN mN (8N yc9zifN fcp797(8z(n(8z(N Hsg8y(fN tgsgNt(sn7z7sN bifN
ni=7n7(8zifN8(9(fgs7ifGN
N
 QGO5GUN AgsgN (b(n(8zifN 8iN gyh(s7yifN fc/(zifN gN 9gsHgfN s(t(z7z7=gfXN y(ó(svN
ts(fzgsf(N(ft(97gbNgz(897–8NgNbgNtif7ó7b7ygyNy(NKc(Nf(Nts(f(8z(Npgz7HgN(8N
bifNg89bg/(fNmNg9itbgyis(fGN
N
 QGO5G5N IifN g89bg/(fXN bifN g9itbgyis(fN mN bifN y7ftif7z7=ifN gc)7b7gs(fN y(ó(sv8N
tsiz(H(sf(Nt(sng8(8z(n(8z(N9i8zsgN9issif7–8GN
N
18.25    DESARROLLO PARA TORONES DE PRESFUERZO 
 
 QGOSG N IifNzisi8(fNy(Nts(z(8fgyiNy(Nzs(fNiNf7(z(Ngbgnós(fNy(ó(sv8Ngyh(s7sf(N
nvfNgbbvNy(NbgNf(997–8N9sÁz79gN9i8Nc8gNbi8H7zcyNy(Ny(fgssibbiN8iNn(8isN
Kc(NN
N
LXL 5NuNptfNNeNNONpf(NáNUNeNyóN
N

143.    5UN
yi8y(NyóN(fN(bNy7vn(zsiNy(bNzis–8N(8N9(8zÁn(zsifXNptfNmNpf(Nf(N()ts(fg8N
(8NQHá9nONGN
N
 QGOSGON IgN78=(fz7Hg97–8Nf(NtiysvNb7n7zgsNgNgKc(bbgfNf(997i8(fNzsg8f=(sfgb(fNnvfN
9(s9g8gfN gN 9gygN ()zs(niN y(bN (b(n(8ziN 9cg8yiN f(N s(Kc7(sgN Kc(N
y(fgssibb(8NfcNs(f7fz(897gNzizgbNóg/iNbgfN9gsHgfNgntb7p79gygfGN
N
 QGOSGUN Rcg8yiNbgNgyh(s(897gNy(Nc8Nzis–8N8iNf(N()z7(8ygNhgfzgN(bN()zs(niNy(N
c8N(b(n(8ziXNy(ó(svNyctb79gsf(NbgNbi8H7zcyNy(Ny(fgssibbiNy(Ngyh(s(897gN
(ft(97p79gygN(8NbgNÍ(997–8N QGOSG GN
N
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
CAPÍTULO 19 – CÁSCARAS Y LÁMINAS PLEGADAS 
 
19.1    ALCANCE Y DEFINICIONES.- 
 
 JG G NN IgfNy7ftif797i8(fNy(N(fz(N9gtÁzcbiNfi8Ngtb79gób(fNgN9vf9gsgfNy(bHgygfNmN
bvn78gfNtb(HgygfNy(N9i89s(ziXN789bcm(8yiN8(s=7ifNmN(b(n(8zifNy(Nóisy(GN
N

144.    55N
 JG GONN ÉiygfNbgfNy7ftif797i8(fNy(N(fzgN1isngNKc(N8iN(fzj8N(ft(9Áp79gn(8z(N
()9bc7ygfN mN Kc(N 8iN (fzj8N (8N 9i8pb79ziN 9i8N bgfN y7ftif797i8(fN y(N (fz(N
RgtÁzcbiXNf(Ngtb79gsv8NgNbgfN9vf9gsgfGN
N
 JG GU   Cáscaras.-   Íi8N(fzsc9zcsgfN(ftg97gb(fXNpisngygfNtisNc8gNiNnvfNbifgfN
9cs=gfNiNbvn78gfNtb(HgygfXN9cmifN(ft(fis(fNfi8Nt(Kc(:ifN9intgsgyifN
9i8NfcfNizsgfNy7n(8f7i8(fGNIgfN9vf9gsgfNf(N9gsg9z(s7xg8NtisNfcNng8(sgN
(ftg97gbN y(N fitiszgsN 9gsHgfXN Kc(N (fN y(z(sn78gygN tisN fcN pisngN
H(injzs79gXNbgNng8(sgN(8NKc(N(fzvNgtimgygNmN(bNz7tiNy(N9gsHgNgtb79gygGN
N
 JG G5N  Láminas plegadas.- Íi8Nc8Nz7tiN(ft(97gbNy(N(fzsc9zcsgNbgn78gsNpisngygN
tisN bgN c87–8XN gN biN bgsHiN y(N fcfN óisy(fXN y(N bifgfN y(bHgygfN tbg8gfXN y(N
ng8(sgNy(N9s(gsNc8gN(fzsc9zcsgN(ftg97gbGN
N
 JG GSN  Cáscaras  nervadas.-  Íi8N (fzsc9zcsgfN (ftg97gb(fN 9i8N (bN ngz(s7gbN
9ibi9gyiN ts7897tgbn(8z(N gN biN bgsHiN y(N 97(szgfN bÁ8(gfN 8(s=gygfXN 9i8N (bN
vs(gN(8zs(NbifN8(s=7ifNgó7(szgNiN9có7(szgN9i8Nc8gNbifgNy(bHgygGN
N
 JG GVN  Elementos  auxiliares.- N Íi8N bifN 8(s=7ifN iN =7HgfN y(N óisy(N Kc(N f7s=(8N
tgsgN s7H7y7xgsXN hg9(sN nvfN s(f7fz(8z(N máiN f(s=7sN y(NgtimiN gN bgN 9vf9gsgGN
Cfcgbn(8z(NbifN(b(n(8zifNgc)7b7gs(fNg9zMg8N(8N9i8/c8ziN9i8NbgN9vf9gsgGN
N
 JG G4   Análisis elástico.-N0fNc8Ng8vb7f7fNy(Npc(sxgfN78z(s8gfNmNy(pisng97i8(fN
ógfgyiN (8N fgz7fpg9(sN bgfN 9i8y797i8(fN y(N (Kc7b7ós7iNmN 9intgz7ó7b7ygyN y(N
y(pisng97i8(fNgfcn7(8yiNc8N9intiszgn7(8ziN(bvfz79iNmNs(ts(f(8zg8yiN
9i8Nc8gNgtsi)7ng97–8Ngy(9cgygN(bN9intiszgn7(8ziNzs7y7n(8f7i8gbNy(NbgN
9vf9gsgN/c8ziN9i8NfcfN(b(n(8zifNgc)7b7gs(fGN
N
 JG GQ   Análisis inelástico.- 0fNc8Ng8vb7f7fNy(Npc(sxgfN78z(s8gfNmNy(pisng97i8(fN
ógfgyiN (8N fgz7fpg9(sN bgfN 9i8y797i8(fN y(N (Kc7b7ós7iXN bgfN s(bg97i8(fN 8iN
b78(gb(fN y(N (fpc(sxiky(pisng97–8N tgsgN (bN 9i89s(ziN mN (bN g9(siN
9i8f7y(sg8yiNbgNp7fcsg97–8NmNbgfNg997i8(fNy(t(8y7(8z(fNy(bNz7(ntiNmNbgN
9intgz7ó7b7ygyN y(N y(pisng97i8(fGN 0bN g8vb7f7fN s(ts(f(8zgsvN 9i8N c8gN
gtsi)7ng97–8Ngy(9cgygN(bN9intiszgn7(8ziNzs7y7n(8f7i8gbNy(NbgN9vf9gsgN
/c8ziN9i8NfcfN(b(n(8zifNgc)7b7gs(fGN
N
 JG GJ   Análisis experimental.-N0fNc8Ntsi9(y7n7(8ziNy(Ng8vb7f7fNógfgyiN(8NbgN
n(y7ygNy(Ny(ftbgxgn7(8ziNmáiNy(pisng97i8(fNc87zgs7gfNy(NbgN(fzsc9zcsgN
iN fcN niy(biGN 0bN g8vb7f7fN ()t(s7n(8zgbN tc(y(N ógfgsf(N (8N c8N
9intiszgn7(8ziN(bvfz79iNiN78(bvfz79iGN
 
 
 
19.2    ANÁLISIS Y DISEÑO 
 
 JGOG NN 0bN 9intiszgn7(8ziN (bvfz79iN f(svN c8N pc8ygn(8ziN g9(tzgyiN tgsgN
y(z(sn78gsN pc(sxgfN 78z(s8gfN mN y(ftbgxgn7(8zifN y(N bgfN 9vf9gsgfGN 0fz(N
z7tiNy(N9intiszgn7(8ziNtc(y(N(fzgób(9(sf(NtisN9vb9cbifNógfgyifN(8Nc8N
g8vb7f7fN y(N bgN(fzsc9zcsgNy(N9i89s(ziN8iNp7fcsgygXN(8NbgNKc(Nf(Ngfcn(N
Kc(N (bN ngz(s7gbN (fN b78(gbn(8z(N (bvfz79iXN hiniHj8(iN(N 7fizs–t79iGN 0bN

145.    5SN
n–ycbiNy(NAi7ffi8Ny(bN9i89s(ziNtc(y(Ngfcn7sf(N7HcgbNgN9(siGN
N
 JGOGONN 08Ng8vb7f7fN78(bvfz79iNtiysvNcfgsf(N9cg8yiNf(Nnc(fzs(NKc(NzgbNnjziyiN
ygNc8gNógf(Nf(HcsgNtgsgN(bNy7f(:iGNN
N
 JGOGUNN Í(N hgsv8N =(s7p79g97i8(fN y(N (Kc7b7ós7iN (8zs(N bgfN pc(sxgfN 78z(s8gfN mN bgfN
9gsHgfN()z(s8gfNtgsgNgf(HcsgsNc8gN9i8f7fz(897gNy(NbifNs(fcbzgyifGN
N
 JGOG5NN IifNtsi9(y7n7(8zifNy(Ng8vb7f7fN8cnjs79iNiN()t(s7n(8zgbNtiysv8Ncfgsf(N
9cg8yiNf(Nnc(fzs(NKc(N(fzifNyg8Nc8gNógf(Nf(HcsgNtgsgN(bNy7f(:iGN
N
 JGOGSNN IifN njziyifN gtsi)7ngyifN y(N g8vb7f7fN Kc(N 8iN fgz7fpgHg8N bgN
9intgz7ó7b7ygyNy(Ny(pisng97i8(fNy(8zsiNy(NbgN9vf9gsgNiN(8zs(NbgN9vf9gsgN
mNfcfN(b(n(8zifNgc)7b7gs(fNtiysv8Ncfgsf(N9cg8yiNf(Nnc(fzs(NKc(Nzgb(fN
njziyifNyg8Nc8gNógf(Nf(HcsgNtgsgN(bNy7f(:iGN
N
 JGOGVNN 08N 9vf9gsgfN ts(fpisxgygfXN (bN g8vb7f7fN y(ó(svN 9i8f7y(sgsN (bN
9intiszgn7(8ziNóg/iNbgfN9gsHgfN78yc97ygfNtisN(bNts(fpc(sxiXNgbN87=(bNy(N
9gsHgfN y(N p7fcsg97–8N mN y(N 9gsHgfN gntb7p79gygfGN Rcg8yiN bifN 9gób(fN y(N
ts(fpc(sxiNf(N9cs=(8Ny(8zsiNy(Nc8gN9vf9gsgXN(bNy7f(:iNz(8ysvN(8N9c(8zgN
bgfN9inti8(8z(fNy(NbgNpc(sxgNfiós(NbgN9vf9gsgNKc(Ns(fcbzg8Ny(bNh(9hiN
Kc(N(bN9gób(Ns(fcbzg8z(N8iN(fzvN(8Nc8Ntbg8iGN
N
 JGOG4NN 0bN(ft(fisNhNy(Nc8gN9vf9gsgNy(bHgygNmNfcNs(pc(sxiNf(sv8Ny(z(sn78gyifN
tgsgNfgz7fpg9(sNbgNs(f7fz(897gNmN9i8y797i8(fNy(Nf(s=797iNs(Kc(s7ygfGN
N
 JGOGQNN 0bN y7f(:iN y(N bgfN 9vf9gsgfN y(ó(svN 9i8f7y(sgsN mN (=7zgsN bgN tif7ó7b7ygyN y(N
c8gNpgbbgNtisN78(fzgó7b7ygyNH(8(sgbNiNbi9gbGN
N
 JGOGJNN IifN (b(n(8zifN gc)7b7gs(fN f(N y7f(:gsv8N gtb79g8yiN bgfN y7ftif797i8(fN
t(sz78(8z(fNy(N(fzgN1isngGNC8gNtgsz(Ny(NbgN9vf9gsgN7HcgbNgbNg89hiNy(N
gbgN (ft(97p79gyiN (8N bgN Í(997–8N JGQN tc(y(N gfcn7sf(N Kc(N g9zMgN 9i8N (bN
(b(n(8ziN gc)7b7gsGN 08N (fgfN tgsz(fN y(N bgN 9vf9gsgXN (bN s(pc(sxiN
t(st(8y79cbgsNgbN(b(n(8ziNgc)7b7gsNf(svNtisNbiNn(8ifN7HcgbNgbN()7H7yiN(8N
bgNÍ(997–8NJGQGSNtgsgN(bNgbgNy(Nc8gN=7HgNÉGN
N
19.3    RESISTENCIA DE DISEÑO DE LOS MATERIALES 
 
 JGUG NN IgNs(f7fz(897gN(8N9ints(f7–8N(ft(97p79gygNy(bN9i89s(ziNpW9NgNOQNyÁgfN8iN
f(svNn(8isNKc(NO LNQHá9nOGN
N
 JGUGONN 0bNs(pc(sxiNy(Npbc(897gN(ft(97p79gyiNy(bNg9(siNpmN8iNf(svNngmisNy(N5OLLN
QHá9nOGN
19.4    REFUERZO DE LA CÁSCARA 
 
 JG5G NN 0bN s(pc(sxiN y(N bgN 9vf9gsgN f(N 9ibi9gsvN tgsgNs(f7fz7sN bifN (fpc(sxifN y(N
zsg997–8N tsiyc97yifN tisN bgN pc(sxgfN n(nósg8gb(fN 78z(s8gfXN tgsgN s(f7fz7sN
bifN nin(8zifN y(N pb()7–8N mN y(N zisf7–8XN tgsgN 9i8zsibgsN bgN p7fcsg97–8N
tsiyc97ygN tisN bgN 9i8zsg997–8N y(N psgHcgN mN 9gnó7ifN y(N z(nt(sgzcsgN mN
9iniN s(pc(sxiN (ft(97gbN (8N bifN óisy(fXN gó(szcsgfN mN tc8zifN yi8y(N f(N

146.   F
?1719:8>5>.82/1.A0200A75?02?02=0.070?B.?020F
F
# 7284:82F1383H20>07.8?171?02B8>C1.13B.FC528??51>8.F8>F/1C1.F
71.A:>/1.C870?B.?020
F
# 7B280C8284:82F1C870?B.?0208>?:079:582.8??5E>38C5C08>C1.
C528??51>8.A82A8>C5?:7028.>1.82B38>129:887284:82F1F8<5=5C1FA020F
70. 71.0. 5>C5?0C1 8> 70 8??5E> A12 848?/1. C8F F ?1>/20??5E>F C8F
420=:01/83A820/:20
F
# 7 284:82F1 >8?8.0251 A020 28.5./52 70. 4:82F0.F 383H20>078.F C8F 70F
?B.?020F.82BF?171?0C1FC8F30>820F9:8F70F28.5./8>?50FC8FC5.8D1F8>F?0C0F
C528??5E>F .80F A12F 71F 38>1.F 5=:07F 0F 70F ?13A1>8>/8F C8F 70.F 4:82F0.F
A25>?5A078.F C8F 383H20>0F 8>F 70F 35.30F C528??5E>F C8H5C0.F 0F 70.F ?02=0.F
03A7545?0C0.
F
# 7B280C8284:82F1C8/20??5E>C870?B.?020F.82BF7535/0C0FC8F30>820F
9:8F 87F 284:82F1F 07?0>?8F 70F 47:8>?50F 0>/8.F C8F 9:8F A:8C0F A21C:?52.8F 87F
0A70./0358>/1C87?1>?28/18>?13A28.5E>
F
# >70.F1>0.C88.4:82F1.878L0C1.C8/20??5E>87284:82F1383H20>07
.82B ?171?0C1 C8 .82 A1.5H78 8> 70. C528??51>8. C8F 70.F 4:82F0.F
A25>?5A078. C8 /20??5E> :0>C1 8./1 >1 28.:7/8 A2B?/5?1 87 284:82F1
383H20>07FA1C2BF?171?02.8F8>FC528??51>8.F12/1=1>078.
F
# 570C528??5E>8>9:8.8?171?087284:82F1F/:L5820F:>0FL0250?5E>F30;12F
C8O28.A8?/1070C528??5E>C870.4:82F0.383H20>078.FA25>?5A078.F
C8 /20??5E> A1C2B .82 >8?8.0251 5>?2838>/02 70 ?0>/5C0CF C8F 0?821F C8F
284:82F1F A020F 7535/02F 87F 0>?I1F C8F A1.5H78.F 45.:20.F8>F ?1>C5?51>8.F C8F
.82L5?51
F
# :0>C1 70 30=>5/:C C8 71. 8.4:82F1. 383H20>078.F A25>?5A078.F C8F
/20??5E>F L02@8F .5=>545?0/5L038>/8F .1H28F 87F B280F C8F70F .:A8245?58F C8F 70F
?B.?020 87 B280 C8 284:82F1 9:8 28.5./8 70 /20??5E>F /1/07F A1C2BF
?1>?8>/202.8F8>F70.FF1>0.FC8F3B<531F8.4:82F1FC8F/20??5E>?:0>C1.8
C83:8./28F9:8F8./1FC0F:>0FH0.8F.8=:20FA020F87FC5.8D15>83H02=170
?:0>/@0F C8F 284:82F1F 8>F ?:079:582F A02/8F C8F 70F F1>0F C8F /20??5E>F C8F 70F
?B.?020 >1 .82B 38>12 C8 8> H0.8 07 8.A8.12F /1/07F C8F 70F
?B.?020
F
## 7284:82F1>8?8.0251A02028.5./5271.3138>/1.FC8F478<5E>FC8F70F?B.?020F
.82BF?07?:70C1F?1>.5C820>C1F70F0??5E>F.53:7/B>80FC8F70.F4:82F0.F0<5078.F
383H20>078. 9:8 0?/M0> 8> 70 35.30 F1>0 :0>C1 870?821F C8F
284:82F1F .8F >8?8.5/8F .E71F 8>F :>0F ?020F C8F 70F ?B.?020F A020F 28.5./52F 71.F
3138>/1.C8478<5E>:>0?0>/5C0C5=:07C8284:82F1F.82BF?171?0C0F8>F70F
1/20F?020FC8F70F?B.?020F0:>9:8F71.F0>B75.5.F>1F5>C59:8>F:>0F5>L82.5E>FC8F
3138>/1.C8478<5E>
F
# 7284:82F18>?:079:582C528??5E>>18./02B8.A0?50C13B.C8?3>5
?5>?1 L8?8. 87 8.A8.12 C8 70 ?B.?020 :0>C1 71. 8.4:82F1.F

147.   ρ<×α
383H20>078.α A25>?5A078.α C8α /20??5E>0α 8>α 87α B280α /1/07α C8α ?1>?28/10α
C8H5C1α 0α 70.α ?02=0.α 03A7545?0C0.0α 8<?8C0>α C8α ]01βφ√4W?α 0α 87α 0?821α C8α
284:82F1α >1α 8./02Bα 8.A0?50C1α 3B.α C8α /28.α L8?8.α 87α 8.A8.12α C8α 70α
?B.?020)α 7αL0712αC8αφα.82Bαα]0)α
α
ρ)<)ρρα  7α 284:82F1α 8>α 70α :>5E>α C8α 70α ?B.?020α ;α 71.α 87838>/1.α C8α 0A1;1α 1α C8α
H12C8α.8α0>?702Bα1α.8α8</8>C82Bα0α/20LG.αC8α/078.α87838>/1.αC8α0?:82C1α
?1>α 71.α 289:5.5/1.α C87α φ0A@/:71α γ0α 8<?8A/1α 9:8α 70α 71>=5/:Cα 3@>530α C8α
C8.0221771α.82Bααρ0βαlC0αA821α>1α38>1.αC8α<(α?3)α
α
ρ)<)ρβα Σ0.α71>=5/:C8.αC8α/20.70A8αC8α284:82F1αC8α70α?B.?020α.82B>α70.α5>C5?0C0.α
8>α87αφ0A@/:71αγ0α8<?8A/1α9:8α70α71>=5/:Cα3@>530αC8α/20.70A8αC8αH0220.α
8>α /20??5E>α .82Bα ρ0βα L8?8.α 87α L0712α 5>C5?0C1α A12α /07α ?0A@/:710α A821α >1α
38>1.α C8α <(α ?3)α  7α >M3821α C8α 83A0738.α 8>α 87α 0?821α A25>?5A07α C8α
/20??5E>α .82Bα 87α 3@>531α >8?8.0251)α μ1>C8α 71.α 83A0738.α .80>α
>8?8.0251.α.8αC8.A70F02B>α07/82>0C038>/8αA12α71α38>1.α:>0αC5./0>?50α
lC)α[1α.8α/20.70A02Bα3B.αC8α:>α/82?51αC87α284:82F1α8>α?:079:582α.8??5E>)α
α
19.5    CONSTRUCCIÓN 
 
ρ)()ραα φ:0>C1α70α2831?5E>αC87α8>?1420C1α8./GαH0.0C1α8>α70α1H/8>?5E>αC8α:>α
3EC:71αC8α870./5?5C0Cα8.A8?@45?1αC87α?1>?28/1αC8H5C1α0α?1>.5C820?51>8.α
C8α 8./0H575C0Cα 1α C8478<51>8.0α 87α L0712α C87α 3EC:71α C8α 870./5?5C0Cα  ?α .8α
C8/8235>02Bα0αA02/52αC8α8>.0;1.αC8α478<5E>α8>αA21H8/0.αC8αL5=0.α?:20C0.α
8>α ?1>C5?51>8.α C8α 1H20)α  7α >M3821α C8α A21H8/0.α 8>.0;0C0.0α 70.α
C538>.51>8.α C8α 70.α A21H8/0.α ;α 87α A21?8C5358>/1α C8α 8>.0;1α .82B>α
8.A8?545?0C1.αA12α87α2>=8>5821α±21;8?/5./0)α
α
ρ)()βαα  7α2>=8>5821α±21;8?/5./0α8.A8?545?02Bα70.α/17820>?50.αA020α70α41230αC8α70α
?B.?020)α°5α70α?1>./2:??5E>α28.:7/020α?1>αC54828>?50.0α28.A8?/1α0α70α41230α
C8α70α?B.?0200α30;128.α9:8α70.α/17820>?50.α8.A8?545?0C0.0α.8α848?/:02Bα
:>α 0>B75.5.α C87α 848?/1α C8α 70.α C54828>?50.α ;α .8α /1302B>α 70.α 38C5C0.α
>8?8.0250.αA020α0.8=:202α:>α?13A12/0358>/1α.8=:21αC8α70α?B.?020)α
 
 
 
 
 
 
 
 
 
CAPÍTULO 20 - CONCRETO SIMPLE 
 
20.1    GENERALIDADES α
α
β])ρ)ραα  ./0α .8??5E>α A21L88α 71.α 289:825358>/1.α 3@>531.α A020α 87α C5.8D1α C8α
87838>/1.α C8α ?1>?28/1α >1α 28412F0C1α 1α ?1>α 284:82F1.α38>128.α 0α 71.α
3@>531.α 8.A8?545?0C1.α A020α ?1>?28/1α 28412F0C10α ;0α .80>α L0?50C1.α 8>α
.5/51α1αA2840H25?0C1.)α

148.    5QN
N
OLG GONN 08NbgfN(fzsc9zcsgfN(ft(97gb(fXNzgb(fN9iniNgs9ifXN(fzsc9zcsgfN(8z(ssgygfN
mN ncsifN y(N Hsg=(ygyXN f(N 9cntb7sv8N bifN s(Kc7f7zifN y(N (fzgN f(997–8N
9cg8yiNf(g8Ngtb79gób(fGN
N
20.2    LIMITACIONES 
 
OLGOG NN 0bN cfiN y(bN 9i89s(ziN f7ntb(N y(ó(svN b7n7zgsf(N gN (b(n(8zifN zizgbn(8z(N
gtimgyifNfiós(N(bNfc(biNiNfitiszgyifNtisNizsifN(b(n(8zifN(fzsc9zcsgb(fN
9gtg9(fN y(N tsi=((sN c8N gtimiN =(sz79gbN 9i8z78ciN iN 9cg8yiN (bN (p(9ziN y(N
gs9iNgf(Hcs(N(fpc(sxifNy(N9ints(f7–8NtgsgNziyifNbifN(fzgyifNy(N9gsHgGN
N
OLGOGONN 1iNf(Nt(sn7z7svN(bN(ntb(iNy(N9i89s(ziNf7ntb(N(8N(b(n(8zifN(fzsc9zcsgb(fN
fin(z7yifN gN fib797zg97i8(fN fÁfn79gfN Kc(N hgmg8N f7yiNy(z(sn78gygfN (8N
ógf(NgNbgN9gtg97ygyNy(NbgN(fzsc9zcsgNy(Ny7f7tgsN(8(sHÁgNtisNyc9z7b7ygyGN
N
OLGOGUNN 0bNcfiNy(N9i89s(ziNf7ntb(NtgsgN(b(n(8zifN(8N9ints(f7–8NKc(N8iNf(g8N
gs9ifNiNncsifXNf(Nt(sn7z7svNf–biN(8Nt(y(fzgb(fN9i8N(fó(bz(9(fNn(8is(fN
Kc(NUGN
N
OLGOG5NN 0bNt(sgbz(NnÁ87niNtgsgNxgtgzgfNy(N9i89s(ziNf7ntb(Nf(svNy(NULN9nGN1iNf(N
t(sn7z7svN(bNcfiNy(NxgtgzgfNy(N9i89s(ziNf7ntb(NgtimgygfNfiós(Nt7biz(fGN
N
OLGOGSNN ÉiyifN bifN ngz(s7gb(fN Kc(Nf(N(ntb((8NtgsgNbgNpgós79g97–8Ny(bN9i89s(ziN
f7ntb(N u9(n(8ziXN gHs(HgyifXN gHcgXN gy7z7=ifXN (z9GeN y(ó(sv8N 9cntb7sN bifN
n7fnifNs(Kc7f7zifNKc(NtgsgN9i89s(ziNgsngyiGN
N N 0fzgN ()7H(897gN zgnó7j8N f(svN gtb79gób(N gN bgN yif7p79g97–8XN (8fgmiN y(N
tsió(zgfN 97bÁ8ys79gfXN (89ipsgyifXN 9ibi9g97–8XN 9csgyiXN (=gbcg97–8N mN
g9(tzg97–8Ny(bN9i89s(ziGN
N
OLGOGVNN IgN s(f7fz(897gN nÁ87ngN y(bN 9i89s(ziN f7ntb(N tgsgN p78(fN (fzsc9zcsgb(fN
n(y7ygN (8N z(fz7HifN 97bÁ8ys79ifN gN bifN OQN yÁgfN y(N (ygyN f(svN y(N  5LN
aHá9nOGN
N
OLGOG4NN IgfN /c8zgfN y(ó(sv8N y7=7y7sN (bN (b(n(8ziN (fzsc9zcsgbN (8N (b(n(8zifN
y7f9i8z78cifN(8Npb()7–8GN0bNzgng:iNmNbgNcó79g97–8Ny(NbgfN/c8zgfNy(ó(sv8N
gf(HcsgsNKc(N8iNf(Nts(f(8z(8N(fpc(sxifN78z(s8ifN()9(f7=ifNy(ó7yiNgNbgN
s(zsg997–8Ny(NpsgHcgyiXN9gnó7ifNy(Nz(nt(sgzcsgNmNpbc/iNtbvfz79iGN
N
IgfN78z(ssct97i8(fN(8N(bNbb(8gyiNy(bN9i89s(ziNf(Nt(sn7z7sv8Nf–biN(8NbgfN
/c8zgfNts(y(p787ygfGN
N
N
20.3    DISEÑO 
 
OLGUG NN IifN (fpc(sxifN f(N 9gb9cbgsv8N fcti87(8yiN c8N 9intiszgn7(8ziN b78(gbN
(bvfz79iNóg/iNbgfN9gsHgfNy(Ny7f(:iNuncbz7tb79gygfNtisN(bNpg9zisNy(N9gsHgN
9iss(fti8y7(8z(eNmN8iNy(ó(sv8N()9(y(sNbifNf7Hc7(8z(fN=gbis(fNN
N
geNRints(f7–8NtisNpb()7–8NN p9NN\NNLXVSNpW9N

149.   ρ<α
αmmα
H-α≥20??5E>αA12α478<5E>Nα 4/ααα\αα]0γ(α √α4W?α
α α
?-α .4:82F1α?12/0>/80α?131α38C5C0αC8α70α/20??5E>αC50=1>07α8>α87838>/1.α
9:8α/20H060>α8>α:>0αC528??5E>Nααααααααααααααααααααααααααααααααααααααααααmmα
L?αα\αα]01(α√α4W?α
α
C-α .4:82F1α ?12/0>/80α ?131α 38C5C0α C8α 70α /20??5E>α C50=1>07α ?:0>C1α 87α
87838>/1α/20H068α8>αC1.αC528??51>8.α;α70α40770α.80α?E>5?0α1αA52035C07α
0728C8C12αC8α70αα?02=0α+A:>F1>0358>/1-Nααααααααααααααααααααααααααmmα
L?αα\ααα]0×α√α4W?α
α
8-αφ13A28.5E>α0<507Nα
40ααα\ααα]0<α4W?ααiαραeαfα+*αl?-αKα+1βαI-αgαnαjα
α
4-α  .4:82F1αC8α0A70./0358>/1Nα 4Aαα\αα]0((α4W?α
α
 >α 8./1.α 8.4:82F1.α ;0α .8α I0α 5>?7:5C1α 87α 40?/12α C8α 28C:??5E>α C8α
28.5./8>?50αφ)αα
α
°5α .8α 8<?8C5820>α 8./1.α 8.4:82F1.0α C8H82Bα ?171?02.8α284:82F1α ;α 87α
87838>/1α.8αC5.8D02Bα?131α:>1αC8α?1>?28/1α0230C1)α
α
β])1)βαα  >α87α?B7?:71αC8α8.4:82F1.αC8H5C1.α0α478<5E>0α478<5E>α?13A:8./0α;α?12/80α
C8H82Bα ?1>.5C8202.8α 70α .8??5E>α /20>.L82.07α ?13A78/0α C87α 87838>/10α
8<?8A/1αA020α87α?0.1αC8α?1>?28/1αL0?50C1α?1>/20α87α/8228>1αA020α87α?:07α
70α07/:20α1αA8207/8αC87α87838>/1α.8α?1>.5C8202Bα28C:?5C0α8>α(α?3)α
α
β])1)1αα Σ1.α 87838>/1.α C8α ?1>?28/1α .53A78α .138/5C1.α0α 478<5E>α ?13A:8./0α
C8H82B>α.82αC5.8D0C1.αC8α0?:82C1α0Nα
α
σ0αKα40ααα]ααασ?αKα4?ααα`αααρα
C1>C8Nα
σ0Nα .4:82F1αC8α?13A28.5E>α0<507αC8αC5.8D1)α+±:KΦ280-)α
40Nα  .4:82F1α0C35.5H78αC8α?13A28.5E>αA12α0<507)α
σ?Nα .4:82F1αC8α?13A28.5E>αA12α478<5E>αC8αC5.8D1)α+,:8/K2=-)α
4?Nα  .4:82F1α0C35.5H78αC8α?13A28.5E>αA12α478<5E>)α
α
Σ1.α 8.4:82F1.α C8α /20??5E>α .:A82A:8./1.α >1α 8<?8C82B>α C8α 71.α
8.A8?545?0C1.α8>α70α°8??5E>αβ])1)ρH-)α
α
β])1)<αα  7α8.4:82F1α?12/0>/8α8>α.8??51>8.α28?/0>=:7028.α.8α?07?:702Bα?1>Nα
α
L:ααα\αααρ0(α:αKα+βαHαI-α
α
β])1)(αα ±020α1/21.α/5A1.αC8α.8??51>8.0α87α8.4:82F1α?12/0>/8α.8α?07?:702Bα?1>Nα
αααααααααααααααααααααααααααααααααααα α α α
L:ααα\ααα+:α∆-αKα+I=αH-α
α
 7α3B<531α8.4:82F1α?12/0>/8α:α.8α?07?:702Bα0α:>0αC5./0>?50αIαC8α70α?020α

150.    SLN
y(bNgtimiGN6N(fN(bNnin(8ziN(fzvz79iNy(bNvs(gNtisN(897ngNy(NbgNtis97–8N
yi8y(N f(N 9gb9cbgN (bN (fpc(sxiN 9iszg8z(N 9i8N s(ft(9ziNy(N bgN f(997–8N
zsg8f=(sfgbNgbN9(8zsiNy(NHsg=(ygyGN
N
20.4    CONCRETO CICLOPEO 
 
OLG5G    Definición 
 
Í(Ny(8in78gN9i89s(ziN979b–t(iNgNgKc(bN9i89s(ziNf7ntb(NKc(N(fN9ibi9gyiN
9i8/c8zgn(8z(N 9i8N t7(ysgN y(ftbgxgyisgN mN Kc(N z7(8(N bgfN f7Hc7(8z(fN
9gsg9z(sÁfz79gfNN
N
geNIgNs(f7fz(897gNnÁ87ngNy(bN9i89s(ziNy(NbgNngzs7xNf(svNpY9N\N LLNQHá9nOGN
N
óeNIgN t7(ysgN y(ftbgxgyisgN 8iN ()9(y(svN y(bN ULRN y(bN =ibcn(8N zizgbN y(N
9i89s(ziN979b–t(iNmNf(svN9ibi9gygNy(Nng8(sgNhiniHj8(gXNy(ó7(8yiN
Kc(ygsNziyifNfcfNóisy(fN(nó(ó7yifN(8N(bN9i89s(ziGN
N
9eNIgN ngmisN y7n(8f7–8N y(N bgN t7(ysgN y(ftbgxgyisgN 8iN()9(y(svN y(N bgN
n7zgyNy(NbgNn(8isNy7n(8f7–8Ny(bN(b(n(8ziN87Nf(svNngmisNy(NOSLNnnGN
N
OLG5GO   Limitaciones 
 
OLG5GOG N 0bN cfiN y(N (fz(N 9i89s(ziN (fzgsvN b7n7zgyiN gN97n7(8zifN 9iss7yifXN
fiós(97n7(8zifXNncsifNy(N9i8z(897–8Ny(NHsg=(ygyNmNpgbfgfNxgtgzgfGN
N
OLG5GOGON 08N (b(n(8zifN (8N =ibgy7xifN 9i8N c8gN bi8H7zcyN ngmisN gN bgN n7zgyN y(N fcN
t(sgbz(XNf(svN8(9(fgs7iN=(s7p79gsNbifN(fpc(sxifNy(Npb()7–8NmN9isz(GN
 
 
 
 
 
 
 
 
 
 
 
 
 
CAPÍTULO 21 - CONCRETO PREFABRICADO 
 
21.1    OBJETIVO N
N
O G G NN IgfN y7ftif797i8(fN y(N (fz(N 9gtÁzcbiN f(N gtb79gsv8N (8N (bN y7f(:iN y(N
(b(n(8zifN y(N 9i89s(ziN ts(pgós79gyiXN zgbN 9iniN f(N b(fN y(p78(N (8N (bN
RgtÁzcbiNOGN
N
O G GONN ÉiygN bgfN y7ftif797i8(fN y(N (fzgN 1isngN Kc(N 8iN (fzj8N (ft(9Áp79gn(8z(N
()9bc7ygfN mN Kc(N 8iN 9i8zsgy7Hg8N bgfN y7ftif797i8(fN y(N (fz(N RgtÁzcbiXN

151.    S N
y(ó(sv8Ngtb79gsf(NgbN9i89s(ziNts(pgós79gyiGN
N
21.2    DISEÑO 
 
O GOG NN 0bN y7f(:iN y(N (b(n(8zifN ts(pgós79gyifN y(ó(svN 9i8f7y(sgsN ziygfN bgfN
9i8y797i8(fNy(N9gsHgfNmNs(fzs7997i8(fNy(fy(NbgNpgós79g97–8N78797gbNhgfzgN
9intb(zgsN bgN (fzsc9zcsgXN 789bcm(8yiN (bN y(f(89ipsgyiXN gbng9(8gn7(8ziXN
zsg8ftisz(NmNni8zg/(GN
N
O GOGONN 08N 9i8fzsc997i8(fN ts(pgós79gygfN Kc(N 8iN z(8Hg8N c8N 9intiszgn7(8ziN
ni8ibÁz79iXNy(ó(sv8N9i8f7y(sgsf(NbifN(p(9zifN(8NziygfNbgfN9i8()7i8(fNmN
c87i8(fN tgsgN gf(HcsgsN c8N 9intiszgn7(8ziN gy(9cgyiN y(bN f7fz(ngN
(fzsc9zcsgbGN
N
O GOGUNN 2(ó(sv8N9i8f7y(sgsf(NbifN(p(9zifNy(NbgfNy(pb()7i8(fN78797gb(fNmNy7p(s7ygfXN
789bcm(8yiNbifN(p(9zifNfiós(NbifN(b(n(8zifN78z(s9i8(9zgyifGN
N
O GOG5NN 0bNy7f(:iNy(NbgfNc87i8(fNmNbifNgtimifNy(ó(svN789bc7sNbifN(p(9zifNy(NziygfN
bgfNpc(sxgfNKc(Nf(sv8Nzsg8fn7z7ygfXN789bcm(8yiNbgN9i8zsg997–8XNbgNpbc(897gXN
bgNz(nt(sgzcsgXNbgNy(pisng97–8N(bvfz79gXN(bN=7(8ziNmN(bNf7fniGN
N
O GOGSNN ÉiyifNbifNy(zgbb(fNy(ó(sv8Ny7f(:gsf(Nzing8yiN(8N9c(8zgNbgfNzib(sg897gfN
y(Npgós79g97–8NmNni8zg/(NmNbifN(fpc(sxifNz(ntisgb(fNy(bNni8zg/(GN
N
21.3    PANELES PREFABRICADAS PARA MUROS 
 
O GUG NN IifN ncsifN ts(pgós79gyifXN y(N 9gsHgN mN y7=7fis7ifXN y(ó(sv8N y7f(:gsf(N y(N
g9c(syiN9i8NbgfNy7ftif797i8(fNy(bNRgtÁzcbiN SGN
N
O GUGONN Rcg8yiN bifN zgób(sifN ts(pgós79gyifN f(N y7f(:(8N tgsgN 9cós7sN bc9(fN
his7xi8zgb(fN(8zs(N9ibcn8gfNiNxgtgzgfNg7fbgygfXNbgNs(bg97–8Ny(NgbzcsgNgN
(ft(fisN8iNy(ó(svNb7n7zgsf(XNf7(nts(NKc(N(bN(p(9ziNy(NbgNg997–8Ny(N=7HgN
y(NHsg8Nt(sgbz(XN(bNtg8y(iNbgz(sgbNmNbgfNy(pb()7i8(fNf(Nhgmg8NzingyiN(8N
9c(8zgN(8N(bNy7f(:iGNo(sNRgtÁzcbiN 5GN
N
21.4    DETALLES 
 
O G5G NN ÉiyifNbifNy(zgbb(fNy(bNs(pc(sxiXNc87i8(fXN(b(n(8zifNy(NgtimiXN78f(szifXN
g89bg/(fXN s(9cós7n7(8ziN y(bN 9i89s(ziXN gó(szcsgfXN y7ftif7z7=ifN y(N 7xg/(XN
pgós79g97–8NmNbgNzib(sg897gN(8N(bNni8zg/(Ny(ó(sv8N(fzgsN78y79gyifN(8NbifN
tbg8ifGN
O G5GONN Rcg8yiNbiNgtsc(ó(N(bNAsim(9z7fzgXNbifNy7ftif7z7=ifNy(Ng89bg/(Nuzgb(fN9iniN
(ft7HgfN iN 78f(s97i8(feN Kc(N fiós(fgbHg8N y(bN 9i89s(ziN iN t(sng8(x9g8N
()tc(fzifNtgsgN78ft(997–8Ntiysv8Nf(sN(nó(ó7yifNn7(8zsgfN(bN9i89s(ziN
(fzjN(8N(fzgyiNtbvfz79iNf7(nts(NmN9cg8yiNN
N
O G5GOG N IifN y7ftif7z7=ifN y(N g89bg/(N 8iN (fzj8N fc/(zifN gbN s(pc(sxiN tisN n(y7iN y(N
(b(n(8zifNy(Nfc/(97–8NiNHg89hifNy(8zsiNy(bN9i89s(ziNtbvfz79iGN
N
O G5GOGON IifN y7ftif7z7=ifN y(N g89bg/(N f(N ng8z(8Hg8N (8N bgN tif797–8N 9iss(9zgN (8N

152.    SON
zg8ziN(bN9i89s(ziNt(sng8(x9gN(8N(fzgyiNtbvfz79iGN
N
O G5GOGUN IifN y7ftif7z7=ifN y(N g89bg/(N (fzj8N y(ó7ygn(8z(N g89bgyifN gN p78N y(N
y(fgssibbgsNbgfN9gsHgfNgntb7p79gygfNs(Kc(s7ygfGN
N
21.5    IDENTIFICACION Y MARCADO 
 
O GSG NN RgygN(b(n(8ziNts(pgós79gyiNy(ó(svNngs9gsf(NtgsgN78y79gsNfcNcó79g97–8N
(8N bgN (fzsc9zcsgXN bgN tif797–8N (8N Kc(N f(N y(ógN 9ibi9gsN mN bgN p(9hgN y(N
pgós79g97–8GN
N
O GSGONN IgfNngs9gfNy(N7y(8z7p79g97–8Ny(ó(sv8N9iss(fti8y(sNgNbgfNy(NbifNtbg8ifN
y(Nni8zg/(GN
 
21.6    TRANSPORTE, ALMACENAMIENTO Y MONTAJE 
 
O GVG NN 2csg8z(N (bN 9csgyiXN y(f(89ipsgyiXN gbng9(8gn7(8ziXN zsg8ftisz(N mN
ni8zg/(XN bifN (b(n(8zifN ts(pgós79gyifN 8iN y(ó(sv8N fiós((fpisxgsf(XN
gbgó(gsf(XN yg:gsf(N iXN (8N (bN gbHc8gN izsgN pisngXNz(8(sNc8gN9i8zsgpb(9hgN
Kc(NbifNtc(ygNgp(9zgsNgy=(sfgn(8z(GN
N
O GVGONN IifN(b(n(8zifNts(pgós79gyifNy(ó(sv8N(fzgsNgss7ifzsgyifNmNfitiszgyifN(8N
pisngN gy(9cgygN ycsg8z(N (bN ni8zg/(N tgsgN Hgsg8z7xgsN c8N gb78(gn7(8ziN
gtsit7gyiNmNbgN78z(Hs7ygyN(fzsc9zcsgbNhgfzgNKc(NbgfNc87i8(fNt(sng8(8z(fN
(fzj8Nz(sn78gygfGN
N
21.7    DEFLEXIONES 
 
o(sN(bNRgtÁzcbiNOONÍ(997–8NOOG4GN
N
N
N
N
N
N
N
N
N
N
N
N
CAPÍTULO 22 -   ELEMENTOS DE CONCRETO COMPUESTOS SUJ ETOS A 
FLEXIÓN 
N
22.1    OBJETIVO 
 
OOG G NN IgfN y7ftif797i8(fN y(N (fz(N 9gtÁzcbiN y(ó(sv8Ngtb79gsf(N gbN y7f(:iN y(N bifN
(b(n(8zifN9intc(fzifNfc/(zifNgNpb()7–8XNy(p787yifN9iniN(b(n(8zifNy(N
9i89s(ziXN ts(pgós79gyifN iN =g97gyifN (8N iósgXN pgós79gyifN (8N bcHgs(fN

153.    SUN
y7p(s(8z(fN t(siN 78z(s9i8(9zgyifN y(N ng8(sgN zgbN Kc(N s(fti8yg8N gN bgfN
9gsHgfN9iniNc8gNfibgNc87ygyGN
N
OOG GONN ÉiygfN bgfN y7ftif797i8(fN y(N (fzgN 1isngN f(N gtb79g8N gN bifN (b(n(8zifN
9intc(fzifNfc/(zifNgNpb()7–8XN()9(tziN(8NbiN(ft(9Áp79gn(8z(N78y79gyiN(8N
(fz(N9gtÁzcbiGN
N
22.2    GENERALIDADES 
 
OOGOG NN C8N(b(n(8ziN9intc(fziXN(8NfcNzizgb7ygyNiN(8Ntgsz(fNy(bNn7fniXNtiysvN
f(sN(ntb(gyiNtgsgNs(f7fz7sN9iszg8z(NmNnin(8ziGN
N
OOGOGONN RgygN(b(n(8ziN78y7=7ycgbNy(ó(svNf(sN78=(fz7HgyiNtgsgNziygfNbgfN(zgtgfN
9sÁz79gfNy(N9gsHgGN
N
OOGOGUNN Í7NbgNs(f7fz(897gN(ft(97p79gygXN(bNt(fiN=ibcnjzs79iNcNizsgfNtsit7(ygy(fN
y(NbifNy7=(sfifN(b(n(8zifNfi8Ny7p(s(8z(fXNy(ó(sv8Ncz7b7xgsf(N(8N(bNy7f(:iN
bgfNtsit7(ygy(fNy(NbifN(b(n(8zifN78y7=7ycgb(fNiNbifN=gbis(fNnvfN9sÁz79ifGN
N
OOGOG5NN 08N bifN 9vb9cbifN y(N s(f7fz(897gN y(N (b(n(8zifN 9intc(fzifN 8iN y(ó(svN
hg9(sf(N y7fz7897–8N (8zs(N bifN (b(n(8zifN gtc8zgbgyifNmN bifN 8iN
gtc8zgbgyifGN
N
OOGOGSNN ÉiyifNbifN(b(n(8zifNy(ó(sv8Ny7f(:gsf(NtgsgNs(f7fz7sNziygfNbgfN9gsHgfNgN
bgfNKc(Nf(sv8Nfin(z7ygfNg8z(fNy(bNy(fgssibbiNzizgbNy(NbgNs(f7fz(897gNy(N
y7f(:iNy(bN(b(n(8ziN9intc(fziGN
N
OOGOGVNN Í(N y(ó(svN tsitis97i8gsN (bN s(pc(sxiN s(Kc(s7yiN tgsgN 9i8zsibgsN (bN
gHs7(zgn7(8ziNmNts(=(87sNbgNf(tgsg97–8Ny(NbifN(b(n(8zifN78y7=7ycgb(fNy(N
bifN(b(n(8zifN9intc(fzifGN
N
OOGOG4NN IifN(b(n(8zifN9intc(fzifNy(ó(sv8N9cntb7sN9i8NbifNs(Kc7f7zifNy(N9i8zsibN
y(Ny(pb()7i8(fNygyifN(8NbgNÍ(997–8NOOG4GN
N
22.3    APUNTALAMIENTO 
N N N
Rcg8yiN f(N (ntb((N gtc8zgbgn7(8ziXN (fz(N 8iN y(ó(svN f(sN s(z7sgyiN hgfzgN
Kc(N bifN (b(n(8zifN fitiszgyifN hgmg8N y(fgssibbgyiN bgfN tsit7(ygy(fN y(N
y7f(:iN s(Kc(s7ygfN tgsgN s(f7fz7sN bgfN 9gsHgfN mN b7n7zgsN bgfN y(pb()7i8(fN mN (bN
gHs7(zgn7(8ziN(8N(bNnin(8ziNy(Ns(z7sgsNbifNtc8zgb(fGN
22.4    RESISTENCIA AL CORTANTE VERTICAL 
 
OOG5G NN Rcg8yiNf(N9i8f7y(s(NKc(N(bN9iszg8z(N=(sz79gbN=gNgNf(sNs(f7fz7yiNtisNziyiN
(bN(b(n(8ziN9intc(fziXNf(Ny(ó(svNy7f(:gsNy(Ng9c(syiN9i8NbifNs(Kc7f7zifN
y(bN RgtÁzcbiN  UXN 9iniN f7N f(N zsgzgsgN y(N c8N (b(n(8ziN=g97gyiN
ni8ibÁz79gn(8z(N9i8NbgNn7fngNpisngNy(Nf(997–8Nzsg8f=(sfgbGN
N
OOG5GONN 0bNs(pc(sxiNtisN9iszg8z(Ny(ó(svN(fzgsNzizgbn(8z(Ng89bgyiNy(8zsiNy(NbifN
(b(n(8zifN78z(s9i8(9zgyifXNy(Ng9c(syiN9i8NbiNy7ftc(fziN(8NbgNÍ(997–8N
4G  GOGN

154.   ρ(<α
α
ββ)<)1αα  7α 284:82F1α A12α ?12/0>/80α 0>?70C1α 1α A2171>=0C10α A1C2Bα ?1>.5C8202.8α
?131α284:82F1α/20>.L82.07αA020α/1302α87α?12/0>/8αI125F1>/07)α
α
22.5    RESISTENCIA AL CORTANTE HORIZONTAL 
 
ββ)()ραα  >α:>α87838>/1α?13A:8./10αC8H82Bα0.8=:202.8α70α/20>.35.5E>α?13A78/0α
C8α70.α4:82F0.α?12/0>/8.αI125F1>/078.α8>α70.α.:A8245?58.αC8α?1>/0?/1αC8α
71.α87838>/1.α5>/82?1>8?/0C1.)α
α
ββ)()βαα Φα38>1.α9:8α.8α?07?:78αC8α0?:82C1α?1>α70α°8??5E>αββ)()10α87αC5.8D1αC8α
70.α.8??51>8.α/20>.L82.078.α.:68/0.α0α?12/0>/8αI125F1>/07αC8H82BαH0.02.8α
8>Nα
:ααα≤αααφα>Iα
α
C1>C8α:α8.α70α4:82F0α?12/0>/8α03A7545?0C0α8>α70α.8??5E>α?1>.5C820C0α;α
>Iα 8.α70α28.5./8>?50α>135>07α07α?12/0>/8αI125F1>/07αC8α0?:82C1α?1>α71α
.5=:58>/8Nα
α
ββ)()β)ρα φ:0>C1α70.α.:A8245?58.αC8α?1>/0?/1α8./G>α753A50.α;α75H28.αC8α78?I0C0α;α
.8αI0;0>αI8?I1α5>/8>?51>0738>/8α2:=1.0.0α70α28.5./8>?50α07α?12/0>/8α>I0α
>1αC8H82Bα.82α30;12αC8α(0=αHLαC0α8>α*=)α
α
C1>C8α HLα 8.α 87α 0>?I1α C8α 70α .8??5E>α /20>.L82.07α 8>α 70α .:A8245?58α C8α
?1>/0?/1α9:8α.8α0>075F0αA020α87α?12/8αI125F1>/07)α
α
ββ)()β)βα φ:0>C1α.8αA21A12?51>8α284:82F1α/20>.L82.07α3@>531αC8α0?:82C1α?1>α70α
°8??5E>α ββ)=α ;α 70.α .:A8245?58.α C8α ?1>/0?/1α 8./G>α 753A50.α ;α 75H28.α C8α
78?I0C0α A821α >1α .8α I0;0>α I8?I1α 5>/8>?51>0738>/8α 2:=1.0.0α 70α
28.5./8>?50α07α?12/0>/8α>I0α>1αC8H82Bα/1302.8α30;12αC8α(0=αHLαC0α8>α
*=)α
α
ββ)()β)1α φ:0>C1α.8αA21A12?51>8α284:82F1α/20>.L82.07α3@>531αC8α0?:82C1α?1>α70α
°8??5E>α ββ)=α ;α 70.α .:A8245?58.α C8α ?1>/0?/1α 8./G>α 753A50.α ;α 75H28.α C8α
78?I0C0α;α.8αI0;0>αI8?I1α5>/8>?51>0738>/8α2:=1.0.α0α:>0α03A75/:Cα/1/07α
C8α=α330α70α28.5./8>?50α07α?12/0>/8α>I0α>1αC8H82Bα/1302.8α30;12αC8αβ(α
HLαC0α8>α*=α
α
ββ)()β)<α φ:0>C1α 70α 4:82F0α ?12/0>/8α 03A7545?0C0α :α 8>α 70α .8??5E>α .:68/0α 0α
?1>.5C820?5E>α8<?8C8αC8ααφα+β<0=αHLαC-0αα87αC5.8D1αA12α?12/0>/8αI125F1>/07α
C8H82BαI0?82.8αC8α0?:82C1α?1>α70α°8??5E>αρ1)()α
ββ)()1αα  7α?12/0>/8αI125F1>/07αA1C2Bα5>L8./5=02.8α?07?:70>C1α87α?03H51α2807αC8α70α
4:82F0α C8α ?13A28.5E>α 1α C8α /20??5E>α 8>α ?:079:582α .8=38>/1α ;αC8H82B>α
/1302.8α38C5C0.αA020α/20>.48252α8.0α4:82F0α?131α?12/0>/8αI125F1>/07α07α
87838>/1α C8α 0A1;1)α Σ0α 4:82F0α 03A7545?0C0α C8α ?12/0>/8α I125F1>/07α >1α
C8H82Bα 8<?8C82α 70α 28.5./8>?50α 07α ?12/0>/8α I125F1>/07α αφα >Iα α ?131α .8α
5>C5?0α 8>α 70.α °8??51>8.α ββ)()β)ρα 0α ββ)()β)<0α C1>C8α87α B280α C8α 70α
.:A8245?58αC8α?1>/0?/1αΦ?α.:./5/:;8α0ααHLαC)α
α
ββ)()<αα φ:0>C1α8<5./0α/20??5E>α0α/20LG.αC8α?:079:582α.:A8245?58αC8α?1>/0?/1α8>/28α

155.    SSN
(b(n(8zifN 78z(s9i8(9zgyifXN y(ó(svN fcti8(sf(N zsg8fn7f7–8N y(N 9iszg8z(N
tisN9i8zg9ziNf–biN9cg8yiNf(Ntsitis97i8(N(bNnÁ87niNs(pc(sxiNzsg8f=(sfgbN
y(Ng9c(syiN9i8NbgNÍ(997–8NOOGVGN
N
22.6  REFUERZO TRANSVERSAL PARA CORTANTE HORIZONTAL 
 
OOGVG NN Rcg8yiN f(N tsitis97i8(N s(pc(sxiN zsg8f=(sfgbNtgsgN zsg8fn7z7sN 9iszg8z(N
his7xi8zgbXN (bN vs(gN y(N (fz(N s(pc(sxiN 8iN y(ó(svN f(sNn(8isN Kc(N bgN
s(Kc(s7ygN (8N bgN Í(997–8N  UG5G5GUN mN fcN (ftg97gn7(8ziN 8iN ()9(y(svN y(N
9cgzsiN=(9(fNbgNn(8isNy7n(8f7–8Ny(bN(b(n(8ziNfitiszgyiN87Ny(NVLN9nGN
N
OOGVGONN 0bNs(pc(sxiNzsg8f=(sfgbNtgsgN9iszg8z(Nhis7xi8zgbNtiysvN9i8f7fz7sN(8NógssgfN
78y7=7ycgb(fNiNgbgnós(XN(fzs7óifNy(NsgngfNnMbz7tb(fNiNsgngfN=(sz79gb(fN
y(NngbbgNy(Ngbgnós(NfibygyiNub7fiNiN9isscHgyieGN
N
OOGVGUNN ÉiyiN (bN s(pc(sxiN zsg8f=(sfgbN y(ó(svN g89bgsf(N zizgbn(8z(N y(8zsiN y(N bifN
(b(n(8zifN78z(s9i8(9zgyifNy(Ng9c(syiN9i8NbgNÍ(997–8NQGUGN
N
22.7    DEFLEXIONES 
 
OOG4G    0I0Ó01ÉEÍNMAC1ÉMIM2EÍ  
 
Í7N bifN (b(n(8zifN 9intc(fzifN fc/(zifN gN pb()7–8N f(N gtimg8N ycsg8z(N fcN
9i8fzsc997–8Ny(NzgbNpisngNKc(Ny(ftcjfNy(Ns(z7sgsNbifNgtimifNz(ntisgb(fN
bgN 9gsHgN nc(szgN f(gN fitiszgygN tisN bgN f(997–8N 9intc(fzgN zizgbXN (bN
(b(n(8ziN 9intc(fziN f(N tiysvN 9i8f7y(sgsN (Kc7=gb(8z(NgN c8N (b(n(8ziN
=g97gyiNni8ibÁz79gn(8z(NtgsgN(bN9vb9cbiNy(Ny(pb()7i8(fGN
N
08N (b(n(8zifN 8iN ts(fpisxgyifXN bgN tgsz(N y(bN (b(n(8ziN (8N 9ints(f7–8N
y(z(sn78gsvNf7Nf(Ngtb79g8NbifN=gbis(fNygyifN(8NbgNÍ(997–8N LG5G NtgsgN(bN
9i89s(ziNy(Nt(fiN8isngbGNÍ7Nf(N9gb9cbgNbgNy(pb()7–8XNy(ó(sv8Nzingsf(N(8N
9c(8zgN bgfN 9cs=gzcsgfN Kc(N s(fcbzg8N y(N bgN 9i8zsg997–8Ny7p(s(897gbNy(NbifN
9inti8(8z(fN ts(pgós79gyifN mN =g97gyifN (8N f7z7iN mN bifN (p(9zifN y(N bgN
pbc(897gNg)7gbNy(Nc8N(b(n(8ziNy(N9i89s(ziNts(fpisxgyiGN
N
OOG4GO   0I0Ó01ÉEÍNÍD1NMAC1ÉMIM.  
 
Í7N(bNt(sgbz(Ny(Nc8N(b(n(8ziNts(pgós79gyiN8iNts(fpisxgyiNfc/(ziNgNpb()7–8N
9cntb(N9i8NbifNs(Kc7f7zifNy(NbgNÍ(997–8N LG5G XN8iN8(9(f7zgN9gb9cbgsf(NbgN
y(pb()7–8NKc(Ni9css(Ny(ftcjfNKc(N(bN(b(n(8ziNf(N9i8=7(sz(N(8N(b(n(8ziN
9intc(fziGNÍ78N(nógsHiXNbgNy(pb()7–8Ny7p(s7ygNy(bN(b(n(8ziNts(pgós79gyiN
y(ó(svN 78=(fz7Hgsf(N tgsgN bgN ngH87zcyN mN ycsg97–8N y(N9gsHgfN g8z(fN y(bN
78797iNy(NNc8gNg997–8N9intc(fzgN(p(9z7=gGN
N
OOG4GUNN IgN y(pb()7–8N 9gb9cbgygN y(N g9c(syiN 9i8N bifN s(Kc7f7zifN y(N bgN Í(997i8(fN
OOG4G N mN OOG4GON 8iN y(ó(svN ()9(y(sN y(N bifN bÁn7z(fN ygyifN (8N bgN zgóbgN
 LG5G5GOGN
N
N
N

156.    SVN
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
PARTE 6  EVALUACIÓN DE ESTRUCTURAS 
N
CAPÍTULO 23 - EVALUACIÓN DE ESTRUCTURAS 
 
23.1    GENERALIDADES 
N
Í7N()7fz(8NycygfNsgxi8gób(fNs(ft(9ziNy(NbgNf(Hcs7ygyNy(Nc8gN(fzsc9zcsgN
iNy(NgbHc8iNy(NfcfN(b(n(8zifNiNf7Nf(N8(9(f7zgN78pisng97–8Ng9(s9gNy(NbgN
9gtg97ygyNy(N9gsHgNy(Nc8gN(fzsc9zcsgN(8Nf(s=797iNtgsgNp7/gsNfcfNbÁn7z(fNy(N

157.    S4N
9gsHgXNf(NtiysvNisy(8gsNKc(Nf(N(p(9zM(Nc8gN(=gbcg97–8Ny(NbgNs(f7fz(897gN
(fzsc9zcsgbNmgNf(gNtisNg8vb7f7fXN(ntb(g8yiNtsc(ógfNy(N9gsHgNiNtisNc8gN
9inó78g97–8Ny(NgnóifNtsi9(y7n7(8zifGNIgN(=gbcg97–8Nf(svNs(gb7xgygNtisN
c8N78H(87(siN97=7bN9gb7p79gyiGN
N
23.2    EVALUACIÓN POR MEDIO DEL CÁLCULO 
 
OUGOG NN Í7NbgN(=gbcg97–8Ny(NbgNs(f7fz(897gNf(N=gNgNhg9(sNtisNn(y7iNy(bNg8vb7f7fXNf(N
y(ó(svNs(gb7xgsNc8gNn78c97ifgN(=gbcg97–8N(8NiósgNy(NbgfNy7n(8f7i8(fNmN
y(zgbb(fN y(N bifN (b(n(8zifN (fzsc9zcsgb(fXN bgfN N tsit7(ygy(fN y(N bifN
ngz(s7gb(fNmNy(nvfN9i8y797i8(fNtsit7gfNy(NbgN(fzsc9zcsgNzgbN9iniN(fzvN
9i8fzsc7ygGN
N
OUGOGONN IifN 9vb9cbifN ógfgyifN (8N biN 78y79gyiN (8N bgN Í(997–8N OUGOG N y(ó(sv8N
Hgsg8z7xgsN Kc(N bifN pg9zis(fN y(N 9gsHgN 9cntb(8N 9i8N bifN s(Kc7f7zifN mN
tsit–f7zifNy(N(fzgN1isngGN
 
23.3    PRUEBAS DE CARGA 
 
OUGUG    P010.MID2M20ÍN
 
OUGUG G N Í7N bgN (=gbcg97–8N y(N bgN s(f7fz(897gN f(N hg9(N tisN n(y7iN y(N tsc(ógfN y(N
9gsHgXN(fzgfNy(ó(sv8Nf(sNs(gb7xgygfNtisNc8N78H(87(siN97=7bN9gb7p79gyiGN
N
OUGUG GON M8z(fN y(N (p(9zcgsN bgfN tsc(ógfN y(N 9gsHgXN f(N y(ó(sv8N 7y(8z7p79gsN bifN
9inti8(8z(fN 9sÁz79ifN tisN n(y7iN y(bN g8vb7f7fGN 2(ó(svN 78=(fz7Hgsf(N
(ft(97gbn(8z(N bgN s(f7fz(897gN gbN 9isz(N y(N bifN (b(n(8zifN (fzsc9zcsgb(fN
9c(fz7i8gyifGN
N
OUGUG GUN IgNtsc(ógNy(N9gsHgNy(ó(svNhg9(sf(N9cg8yiNbgNtgsz(Ny(NbgN(fzsc9zcsgNKc(N
f(N =gN gN fin(z(sN gN tsc(ógN z(8HgN 9iniN nÁ87niN SVN yÁgfNy(N (ygyGN Í78N
(nógsHiXN f7N (bN D8ft(9zisXN (bN Asim(9z7fzgN mN (bN Ri8fzsc9zisN (fzv8N y(N
g9c(syiXNf(NtiysvNhg9(sN(bN(8fgmiNgNc8gN(ygyNn(8isGN
N
OUGUG G5N Rcg8yiN f(N =gmgN gN tsiógsN óg/iN 9gsHgN M879gn(8z(N c8gN tgsz(N y(N bgN
(fzsc9zcsgXN jfzgN y(ó(svN 9gsHgsf(N y(N ng8(sgN Kc(N f(N tc(ygN tsiógsN
gy(9cgygn(8z(NbgNxi8gNKc(Nf(Nfift(9h(Nf(gNyjó7bGN
N
OUGUG GSN Rcgs(8zgNmNi9hiNhisgfNg8z(fNy(Ngtb79gsNbgN9gsHgNy(Ntsc(ógXNf(Ny(ó(svN
gtb79gsNc8gN9gsHgNKc(Nf7ncb(N(bN(p(9ziNy(NgKc(bbgNtis97–8Ny(NbgfN9gsHgfN
nc(szgfN Kc(N gM8N 8iN (fzv8N g9zcg8yiXN y(ó7(8yiN t(sng8(9(sN gtb79gygfN
hgfzgNKc(NbgNtsc(ógNhgmgN9i89bc7yiGN
OUGUGON A.C0ÑMÍN20NRM.PMN20N0I0Ó01ÉEÍN01N3I0lDd1  
 
OUGUGOG N Rcg8yiNf(Nfin(zg8NgNtsc(ógfNy(N9gsHgNbifN(b(n(8zifNgNpb()7–8Ny(Nc8gN
9i8fzsc997–8XN 789bcm(8yiN =7HgfN mN bifgfXN f(N gtb79gsv8N bgfN y7ftif797i8(fN
gy797i8gb(fNy(NNbgNÍ(997–8NOUGUGOGN
N
OUGUGOGON D8n(y7gzgn(8z(Ng8z(fNy(Ngtb79gsNbgN9gsHgNy(Ntsc(ógNf(Nzingsv8Nb(9zcsgfN
78797gb(fGN

158.   F
F
0 A02/8 C8 70 8./2:?/:20 .878??51>0C0 A020F 0A75?02F 70F ?02=0F C8H82BF
28?5H52 :>0 ?02=0 /1/07 9:8 5>?7:;0 70. ?02=0. 3:82/0.F 9:8F ;0F 8./B>F
0?/:0>C189:5L078>/80+]'-0C8/8235>0?5E>FC8F70F
?02=0F L5L0F +a'-F C8H82BF 5>?7:52F 70F 28C:??5E>F A8235/5C0 A12 70 1230
02=0.
F
0?02=0C8A2:8H0C8H82B0A75?02.8=20C:0738>/8?1>:>3@>531C8
?:0/215>?2838>/1.0A21<530C038>/85=:078..5>1?0.51>02F53A0?/1F0F70F
8./2:?/:20F;FC8F30>820FF/07F9:8F>1F.8FA21C:F?0F87F848?/1FC8F02?1F8>F71.F
30/825078.
F
8.A:G.C8/20>.?:2252I120.C8700A75?0?5E>C870?02=0C8A2:8H0
.8/1302B>78?/:20.C870C8478<5E>5>5?507
F
0 ?02=0 C8 A2:8H0 C8H82B 28/5202.8 5>38C50/038>/8F C8.A:G.F C8F
/130C0.70.78?/:20.C870C8478<5E>5>5?5070.78?/:20.FC8F70FC8478<5E>F
45>07 .8 /1302B> I120. C8.A:G. C8 I0H82.8 28/520C1F 70F ?02=0F C8F
A2:8H0
F
5 70 A02/8 C8 70 8./2:?/:20 .138/5C0 0 70F ?02=0F C8F A2:8H0F A28.8>/0F
8L5C8>?50L5.5H78C840770+45.:20?5E>C8.A28>C5358>/1FC87F28?:H25358>/1F1F
C8478<51>8.F C8F /07F 30=>5/:CF 9:8F .80>F 5>?13A0/5H78.F?1>F 71.F
289:825358>/1. C8 .8=:25C0C C8 70 8./2:?/:20- .8 ?1>.5C8202BF 9:8F 70F
8./2:?/:20F >1F I0F A0.0C1F .0/5.40?/125038>/8F 70F A2:8H0 >1 C8H58>C1
0:/125F02.8F >:8L0.F A2:8H0.F 8>F 70F A02/8F C8F 70F 8./2:?/:20F A28L5038>/8F
8>.0;0C0
F
5 70 A02/8 C8 70 8./2:?/:20 .138/5C0 0 A2:8H0F C8F ?02=0F >1F A28.8>/0F
8L5C8>?50 L5.5H78 C8 40770 .8 ?1>.5C8202B ?131 :>0F 5>C5?0?5E>F C8F :>F
?13A12/0358>/1F.0/5.40?/1251F?:079:5820FC8F71.FC1.F?25/8251.F.5=:58>/8.NF
F
0- 570C8478<5E>3B<53038C5C0C8:>0L5=0A5.11F/8?I1F8.F38>12F
C8NF
F
nK+I-
F
C1>C8 I 8. 87 A8207/8 C87 87838>/1 ; 70 C5./0>?50F 0F 868.F C8F 71.F
0A1;1.F 1F 70F 7:FF 75H28F 8>/28F 0A1;1.F 3B.F87FA8207/8FC8787838>/170
9:8.8038>1202071.0.0230C0.8>C1.C528??51>8..82B70
7:F30.?12/0
F
H- 5 .8 8<?8C8 70 ?1>C5?5E> 0>/82512 C8H82B ?:3A752.8F 9:8F 70F
28?:A820?5E> C8 70 C8478<5E> C8>/21 C8 70. I120.F .5=:58>/8.F 07F
28/521C870?02=0C8A2:8H08.A127138>1.87RFC8F70FC8478<5E>F
3B<530 A020 ?1>?28/1. >1 A28.412F0C1. ; C8 R A020F?1>?28/1.F
A28.412F0C1.
F
# > 87 8>.0;1 C8 L170C5F1. 87 L0712 C8 .8F ?1>.5C8202BF 5=:07F 0F C1.F
L8?8.F70FC5./0>?50FC8.C8F87F0A1;1F07F8</2831FC87FL170C5F1F;F70FC8478<5E>F

159.    SJN
y(ó(svNg/cfzgsf(N(8N(bN9gfiNy(NKc(N(bNgtimiN()t(s7n(8z(Nni=7n7(8zifN
y(N9cgbKc7(sNz7tiGN
N
OUGUGOG LN IgfN9i8fzsc997i8(fNy(N9i89s(ziNgsngyiNKc(N8iNs(9ct(s(8N(bN4SRNy(NbgN
y(pb()7–8N nv)7ngXN tiysv8N =ib=(sf(N gN tsiógsN 8iN g8z(fN y(N 4ON hisgfN y(N
s(z7sgygNbgNts7n(sgN9gsHgNy(Ntsc(ógGNIgNtgsz(Ny(NbgN(fzsc9zcsgN(8fgmgygN
f(N9i8f7y(sgsvNfgz7fpg9zis7gN9cg8yiNbgNtgsz(NtsiógygNy(NbgN(fzsc9zcsgN8iN
nc(fzs(N(=7y(897gfN=7f7ób(fNy(NpgbbgNgbNfin(z(sbgNgNtsc(ógN8c(=gn(8z(NmN
bgN s(9ct(sg97–8N y(N bgN y(pb()7–8N 9gcfgygN tisN (fzgN f(Hc8ygN 9gsHgN y(N
tsc(ógN(fNtisNbiNn(8ifN(bNQLRNy(NbgNy(pb()7–8Nnv)7ngNi9css7ygN(8N(bN
f(Hc8yiN(8fgmiGN
N
OUGUGOG  N 08N bifN f7fz(ngfN y(N 9i89s(ziN ts(fpisxgyiN 8iN f(N y(ó(sv8N s(t(z7sN bgfN
tsc(ógfGN
N
OUGUGUNN EÉ.EÍN0I0Ó01ÉEÍN0ÍÉ.CRÉC.MI0ÍN
 
IifN (b(n(8zifN (fzsc9zcsgb(fN 8iN fc/(zifN gN pb()7–8N y(ó(sv8N
ts(p(s(8z(n(8z(Nf(sN78=(fz7HgyifNtisNn(y7iNy(bNg8vb7f7fGN
N
OUG5N N MR0AÉMRDd1N20NÓ01E.0ÍNRMAMRD2M20ÍN20NRM.PMN
 
Í7NbgN(fzsc9zcsgNKc(N(fzvNf7(8yiN78=(fz7HgygN8iNfgz7fpg9(NbifNs(Kc7f7zifNiN
9s7z(s7ifN 78y79gyifN (8N bgfN f(997i8(fN g8z(s7is(fXN f(HM8N 9iss(fti8ygXN f(N
tiysvN gtsiógsN (bN (ntb(iN y(N 9gsHgfN zizgb(fN n(8is(fN (8N bgN (fzsc9zcsgN
ógfv8yif(N(8NbifNs(fcbzgyifNy(NbgNtsc(ógNy(N9gsHgNiN(8N(bNg8vb7f7fGN
N
OUGSN N Í0PC.D2M2N
 
IgfN tsc(ógfN y(N 9gsHgN y(ó(sv8N (p(9zcgsf(N y(N ng8(sgN y(N Hgsg8z7xgsN bgN
f(Hcs7ygyNy(NbgfNt(sfi8gfNmNy(NbgN(fzsc9zcsgNycsg8z(NbgfNn7fngfGN
N
IgfNn(y7ygfNy(Nf(Hcs7ygyN8iNy(ó(sv8N78z(sp(s7sN9i8N(bNtsi9(y7n7(8ziNy(N
(8fgmiNiNgp(9zgsNfcfNs(fcbzgyifGN
N
N
N
N
N
N
N
N
N

160.   F
F
F
F
F

161.   F
 
 
 

162.   F
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

163.   F
 

164.   F
 
 
 

165.   F
 

166.   F
 

167.   F
 

168.   F
 

169.   #F
 

170.   F
 

171.   F
 

172.   ρ×βα
ESPECIFICACIONES NORMATIVAS PARA DISEÑO EN CONCRETO  
ARMADO EN EL CASO DE EDIFICACIONES CON MUROS DE 
DUCTILIDAD LIMITADA  (EMDL) 
α
α
ρα ,Φ≥ π2ΦΣ °α
α
ρ)ρα Σ0α28.5./8>?50α0α70α?13A28.5E>αC87α?1>?28/1α8>α71.α ,μΣ0αC8H8α.82α?131α
3@>531α α 4_?\α ρ×(α Q=K?3n0α .07L1α 8>α 71.α .5./830.α C8α /20>.4828>?50α C1>C8α
C8H82Bα:.02.8α4_?\αβγ]αQ=K?3n)α
α
ρ)βα  7α C5.8D1α C8α 38F?70.α A020α 71.α 3:21.α C8α 8.A8.128.α 28C:?5C1.0α C8H82Bα
/1302α8>α?:8>/0α70.α?1>.5C820?51>8.αC8α/20H060H575C0C)α
α
ρ)1α  7α 0?821α C8α 70.α H0220.α C8α 284:82F1α 8>α 71.α 3:21.0α C8H82Bα .82α CM?/570α C8α
=20C1α=]α.5=:58>C1α70.α8.A8?545?0?51>8.αΦ°≥,αΦ=ρ(α;ααΦ°≥,αΦ×]=)αα
α
ρ)<α °8αA1C2Bα:.02α30770α878?/21.17C0C0α?122:=0C0α?1>α8.A8?545?0?51>8.αΦ°≥,α
Φ<=α;αΦ<×α?1>α70.α7535/0?51>8.αα5>C5?0C0.α8>αβ)β)α
αα
α
βα μ2° δαμ α,≤πδ°α
α
β)ρα  7α8.A8.12α3@>531αC8α71.α3:21.αC8αC:?/575C0Cα7535/0C0αC8H82Bα.82αC8α]0ρ]α
3)α
α
β)βα °8αA1C2Bα:.02α30770α878?/21.17C0C0α?131α284:82F1α28A02/5C1αC8α71.α3:21.αα
C8α8C545?51.αC8αI0./0α1αA5.1.α;0α8>α87α?0.1αC8α30;12α>M3821αC8αA5.1.0α.8α
A1C2Bα:.02α30770.α.E71α8>α71.αA5.1.α.:A825128.0αC8H5G>C1.8α:.02α0?821α9:8α
?:3A70α?1>αρ)1α8>α87α/82?51α5>482512αC8α70α07/:20)α
α
β)1α  >α/1C1.α71.α?0.1.α87α284:82F1α?1>?8>/20C1α8>α71.α8</2831.αC8α71.α3:21.α
C8H82Bα06:./02.8α0α71α5>C5?0C1α8>αρ)1)αα
α
β)<α °5α .8α :.0α 30770α 878?/21.17C0C00α A020α 87α C5.8D1αC8H82Bα 83A7802.8α ?131α
8.4:82F1ααC8α47:8>?500α87αL0712α3B<531αC8α4;\α<β]]αQ=K?3n)α
α
β)(α  >α8C545?51.αC8α3B.αC8α/28.αA5.1.0αC8H82BαA21L882.8αC87α284:82F1α>8?8.0251α
A020α=020>/5F02α:>0α28.5./8>?50α>135>07α0α478<1α?13A28.5E>αC87α3:21αA12α71α
38>1.α 5=:07α 0α ρ0βα L8?8.α 87α 3138>/1α C8α 0=258/0358>/1α C8α .:α .8??5E>)ααα
 ./0αC5.A1.5?5E>αA1C2Bα7535/02.8α07α/82?51α5>482512αC87α8C545?51α;α0α>1α38>1.α
C8α71.αC1.αA253821.αA5.1.)α
β)=α Σ0α A214:>C5C0Cα C87α 868α >8:/210α c?^α 0C8α 71.α 3:21.α C8α C:?/575C0Cα 7535/0C0α
C8H82Bα.0/5.40?82α70α.5=:58>/8α2870?5E>Nααα
α
)(600
m
m
m
h
l
c
∆
×
<

173.   ρ×1α
μ1>C8Nα
 
l
mα8.α70α71>=5/:CαC87α3:21α8>α87αA70>1αI125F1>/070αα
hmα70α07/:20α/1/07αC87α3:21α;αα
∆∆∆∆mα8.α87αC8.A70F0358>/1αC87α>5L87α3B.α07/1αC87α3:210α?1228.A1>C58>/8α0α
h
m)αα;α9:8αC8H8α.82αα?07?:70C1αC8α0?:82C1α07α02/@?:71αρ=)<αC8α70α[≥ α )]1]α
μ5.8D1α°5.31228.5./8>/8)α
α
±020α 87α ?B7?:71α C8α c?^α .8α C8H82Bα ?1>.5C8202α 87α 0A12/8α C8α 71.α 3:21.α
A82A8>C5?:7028.α+078/0.-α:.0>C1α?131α71>=5/:CαC8α70α078/0α?1>/25H:;8>/8α0α
?0C0α70C1αC87α0730α87α38>12αL0712α8>/28α87αρ]αRαC8α70α07/:20α/1/07αC87α3:21α
;α70α35/0CαC8α70αC5./0>?50α07α3:21α0C;0?8>/8αA0207871)ααμ8H82Bα:.02.8α87α
30;12αL0712αC8αc?^α9:8α.8α1H/8>=0αC8α?1>.5C8202α?13A28.5E>α0α?0C0α70C1α
C87α3:21)α
α
β)×α φ:0>C1α87αL0712αC8αc?^α>1α?:3A70α?1>α71α5>C5?0C1α8>α87α02/@?:71αβ)=0α71.α
8</2831.αC87α3:21αC8H82B>α?1>45>02.8α?1>α8./25H1.α?8220C1.0αA020α71α?:07α
C8H82Bα5>?2838>/02.8α87α8.A8.12αC87α3:21α0α:>α3@>531αC8α]0ρ(α3)αΣ1.α
8./25H1.αC8α?1>45>0358>/1αC8H82B>α/8>82α:>αC5B38/21α3@>531αC8αγα33α;α
:>α 8.A0?50358>/1α 3B<531α C8α ρβα L8?8.α 87α C5B38/21α C8α70α H0220α L82/5?070α
A821α>1α30;12α0α]0β]α3)α
α
β)γα φ:0>C1αC8α0?:82C1α0αβ)=α>1α.80α>8?8.0251α?1>45>02α71.α8</2831.αC8α:>α
3:210α 87α 284:82F1α C8H82Bα 8.A0?502.8α C8α 30>820α /07α 9:8α .:α ?:0>/@0α8./Gα
A12αC8H061αC8αραRαC87αB280α8>α70α?:07α.8αC5./25H:;8)αα
α
β)α Σ0α4:82F0α?12/0>/8αM7/530αC8ααC5.8D1α+V
u-αC8H8α.82α30;12α1α5=:07α9:8α87α
?12/0>/8αM7/531αA21L8>58>/8αC87α0>B75.5.α+V
ua-α03A7545?0C1αA12α87α?1?58>/8α
8>/28α87α3138>/1α>135>07α0.1?50C1α07α0?821α?171?0C1α+M
n-α;α87α3138>/1α
A21L8>58>/8αC87α0>B75.5.α+M
ua-0αα8.αC8?52Nα
α
α
±020α 87α ?B7?:71α C8αM
nα.8α C8H8α ?1>.5C8202α ?131α 8.4:82F1α C8α 47:8>?50α
848?/5L1αρ0β(α4;α
α
 >α70α35/0Cα.:A82512αC87α8C545?51αA1C2Bα:.02.8αρ0(α?131αL0712α3B<531αC87α
?1?58>/8α+αM
n / Mua -α
α
β)ρ]α Σ0α 28.5./8>?50α 07α ?12/8α C8α 71.α 3:21.0α .8α A1C2Bα C8/8235>02α ?1>α 70α
8<A28.5E>Nα
α
)(
au
n
auu
M
M
VV≥
( )( )fyAcfA
s
V
c
VVn
hccρφαφφφφ+=+= '

174.   ρ×<α
C1>C8αφφφφ = 0,85α 0α α cΦ ?cα α 28A28.8>/0α 87α B280α C8α ?12/8α 8>α 70α C528??5E>α
0>075F0C00α α c
ρρρρhcα 70α ?:0>/@0α I125F1>/07α C87α 3:21α ;α cααααS  8.α :>α L0712α 9:8α
C8A8>C8αC87α?1?58>/8α8>/28α70α07/:20α/1/07αC87α3:21αch
m^α+C87α.:871α07α>5L87α
3B.α07/1-α;α70α71>=5/:CαC87α3:21α8>αA70>/0αα
lmα
α
α
 7αL0712α3B<531αC8α>α.82Bαα
CAcfVn ´7,2<α
α
β)ρρα  7α284:82F1αL82/5?07αC5./25H:5C1αC8H8α=020>/5F02α:>0α0C8?:0C0α28.5./8>?50α
07α?12/8α425??5E>α+φφφφα>-α8>α70αH0.8αC8α/1C1.α71.α3:21.)αα
α
Σ0α28.5./8>?50α0α?12/8α425??5E>αC8H82Bα?07?:702.8α?131Nα
α
μ1>C8α 70α 4:82F0α >12307α M7/530α +[
:-α .8α ?07?:70α 8>α 4:>?5E>α C8α 70α ?02=0α
3:82/0α +[
,-α ?131α [:\]0α [,0α α 87α ?1845?58>/8α C8α 425??5E>α C8H8α /1302.8α
?131αμμμμ\α ]0=α ;αφφφφ = 0,85.α α  <?8A?51>0738>/8α ?:0>C1α .8α A28A028α
0C8?:0C038>/8α70α6:>/0α.8α/1302Bαμμμμ\αρ0]α;α87αC8/0778α?1228.A1>C58>/8α.8α
C8H82Bα5>?7:52α8>α71.αA70>1.)α
α
β)ρβα  7α 284:82F1α L82/5?07α C8α 71.α3:21.αC8H82Bα8./02α0C8?:0C038>/8α0>?70C10α
8>α 70α A70/80α C8α ?538>/0?5E>α +1α 8>α 71.0α C8α /20>.4828>?50-0α A020α A1C82α
C8.02217702α.:α3B<530α28.5./8>?50α0α/20??5E>0α38C50>/8α0>?7068.α28?/1.α1α
?1>α=0>?I1α8./B>C02αC8α]OPα70.α71>=5/:C8.αα?1228.A1>C58>/8.α0α03H1.α
?0.1.αC8H82B>α8./02αC8α0?:82C1α0α71α.8D070C1α8>α70α[≥ α )]=]αφ1>?28/1α
Φ230C1)α
α
β)ρ1α φ:0>C1α8<?8A?51>0738>/8α.8αC8?5C0α83A07302αA12α/20.70A8α/1C1α87α0?821α
L82/5?07αC8α71.α3:21.αC8α:>αA5.10αα70α71>=5/:CαC8α83A0738α+le-αC8H82Bα.82α
?131α3@>531αC1.αL8?8.α70α71>=5/:CαC8αC8.0221771α+ld-0α8.αC8?52αle = 2 ld)α
 >α71.α?0.1.αC8α30770.α878?/21.17C0C0.α.8αC8H82Bα:.02αle = 3 ld)α
α
β)ρ<α  7α 28?:H25358>/1α C87α 0?821α C8α 284:82F1α 8>α 71.α8</2831.α C8α 71.α 3:21.α
C8H82Bα .82α ?131α 3@>531α C8α β0(α ?3)α  >α 71.α ?0.1.α C8α 87838>/1.α 8>α
?1>/0?/1α?1>α87α/8228>1α.8αC8H82Bα5>?2838>/02α87α8.A8.12αC87α3:21αI0./0α
1H/8>82α:>α28?:H25358>/1α3@>531αC8α<α?3)α
α
β)ρ(α Σ0α?:0>/@0α3@>530αC8α284:82F1αL82/5?07α;αI125F1>/07αC8α71.α3:21.αC8H82Bα
?:3A752α?1>α70.α.5=:58>/8.α7535/0?51>8.Nαα
53,08,0     2,5        1,5 si
53,05,2si
8,05,1si
  y  e ando  entre  inerpolse  obtien
l
h
l
h
l
h
m
m
m
m
m
m
α
α
α<








<
=≥








=≤








)( fyANVn
vu
+=μφφ

175.   ρ×(α
α
 ./0.α?:0>/@0.α.1>α0A75?0H78.α5>C5./5>/038>/8α0α70α28.5./8>?50αC87α0?821)α
α
1α μ2° δαμ αΣδ°Φ°αμ α [≥π ±2°δα8α≥ φTδα
α
1)ρα °8α A1C2Bα 83A7802α 30770α 878?/21.17C0C0α A020α 87α C5.8D1α C8α 70.α 71.0.0α
C8H5G>C1.8α?:3A752α71.α8.A0?50358>/1.α3B<531.α5>C5?0C1.α8>α87α°8??5E>α
ρρ)()<αC8α70α[≥ α )]=]αC8αφ1>?28/1αΦ230C1)αα
α
1)βα °8α A1C2Bα 83A7802α 28C5./25H:?5E>α C8α 3138>/1.α I0./0α 8>α :>α β]α R0α .E71α
?:0>C1α87α0?821αC8α284:82F1α?:3A70α?1>αρ)1α
α
<α μ2° δαμ Σα°2°≥ ,Φαμ α≥πΦ[°σ π [φ2Φαα
α
<)ρα  >α 8C545?51.α ?1>α 3:21.α C5.?1>/5>:1.α A821α 9:8α .0 /5.40?8>α 71.α
289:825358>/1.αC87α0?BA5/8α<)ρ)HαC8α70.α8.A8?545?0?51>8.α?13A7838>/0250.α
C8α C5.8D1α .5.31228.5./8>/80α 87α .5./830α C8α /20>.4828>?50α +A02257700α 71.0α ;α
87838>/1.αL82/5?078.αC8α.1A12/8-α.8αC8H82BαC5.8D02α83A780>C1α:>α40?/12α
C8α28C:??5E>αC8α4:82F0.α[email protected]?0.α+π°≥-α5=:07α07α83A780C1α8>α87α8C545?51αα
παC5L5C5C1α8>/28αρ0(0αα8.αC8?52αααπ°≥α\απαKαρ0()α
α
<)βα  >α71.α8C545?51.α?1>α3:21.αC5.?1>/5>:1.αC8.?25/1.α8>α87α0?BA5/8α<)ρ)8αC8α
70.α 8.A8?545?0?51>8.α ?13A7838>/0250.α C8α C5.8D1α .5.31228.5./8>/80α α A020α
/1C1.α71.α3:21.α9:8αC8.?0>.0>α8>α87α>5L87αC8α/20>.4828>?500α.8α?07?:702B>α
70.α 28.5./8>?50.α >135>078.α 0α 478<5E>α +,>-α 0.1?50C0.α 0α ?0C0α L0712α C8α 70α
?02=0α 0<5070α ±:0α α Σ1.α L07128.α C8α ,>α ;α ±:α .8α 03A7545?02B>α A12α ρ0βα ;α α .8α
:.02B>α 8>α 70.α ?13H5>0?51>8.α C8α C5.8D1α:.:078.α8>α70.α9:8α.8α5>?7:52B>α
0C83B.α70.α?02=0.αC528?/038>/8α0A75?0C0.α8>α87α>5L87αC8α/20>.4828>?50)α
α
(α μ2° δαμ αΣΦαφ2, [≥Φφ2>[α
α
()ρα φ:0>C1α .8α C8?5C0α 83A7802α A70/80.α .:A8245?5078.αC8α ?538>/0?5E>α .1H28α
28778>1.α?1>/2170C1.0αα.8αC8H82Bα8.A8?545?02α8>α71.αA70>1.αC87αA21;8?/1α70α
?0A0?5C0CαA12/0>/8αC87α28778>1α8>α70α.:A8245?58αC8α?1>/0?/1α?1>α70αA70/800α
0.@α ?131α .:.α ?020?/82@./5?0.α +C8>.5C0Cα 3@>5300α α A214:>C5C0C0α 8.A8.120α
8/?)-)αα
α
()βα Σ0.αA70/80.αC8H82B>α/8>82α:D0.α?1>α:>0αA214:>C5C0Cα3@>530αA12αC8H061α
C8α70α71.0α1αC87α>5L87α8</825120αα87α9:8α.80α3B.αH0610αC8α]0=]α3α8>α70αF1>0α
C8α 71.α 7@35/8.α C8α A21A58C0Cα α ;α βα L8?8.α 87α 8.A8.12α C8α 70α 71.0α 8>α F1>0.α
5>/825128.)α
)I125F1>/07α?:0>/@0α70α9:8ααααααααααααααααααααααααααα
α38>12α.82ααC8H82Bα>1α284:82F1αC8αL82/5?07α?:0>/@0α70ααααααα
7
I
αα
ααα;αααααααααααα
α;ααααα8>/1>?8.ααααααα
3 2
0015,00020,05,0
0025,00025,05,0
≤
≥≥<
≥≥>
m
Si 
vhentoncesVcVuSi
vhVcVuSi
ρρφ
ρρφ