Resistência dos Materiais - Hibbeler 5ª Ed.Cap14 - Exercícios resolvidos

1. ML. À rater i subjected 10 a general

neral sate of plane
stress. Expres be sain energy deny tert of te Sa,
Us ccestan E.G, and andthe ses component 9,

sin

Er De De Hara ete ome nite

ic

ehe nee e L.
cm gant

9, pl cn og, de nom in ibe ad
bye LE ao, de rn ey o cn og

CEE
dnt ean dy

ui a
ECS Am

2. 4-2 The strain energy density aust be te same whether
{he slate of sires is repressted by oy. ch, aan or
"Be principal sus 0, and Bguite the srs caen
Srpresons (a uch of these uo cases 250 stow tal Gre
Eigen
ru Benne gua oe mason. Aig BS
aaa

one [cine]

CRC ES m

Arena 110

a

O) a

nado,
ee wt me
Eterna) eel

Hagen an

ey EB)

13. Mon and oy ar applied to an element for what
rato ot 0, 1 0, (be sr energy a mame

“Stra ee) à ot

=f file)

Sao, wt, ween,

NN

3. “14-4. Determine the torsional strain energy in the A-36
‘teal shaft. The shaft has a radius of 30 mm.

A Litas NANA
MEET
2500)

gg naa An

14-5. Determine the bending strain energy in the A36
Structural steel W 19 % 12 beam. Obtain the answer using.
‘he coordinates (a) x, and xg and (8) x and x

pues pta de

Am ta

M2 9m = 6b à me e
em hy oe
On a Sn en nib 0 ay
ger ee ae

Pee = En + 1600 de ed SI + 186000 4
TET y CL

+ hp] 2
svat o a 4e Be

ci + necia, bee

LA

4. 14-6. Determine the bending stain energy in the beam
due to the loading shown, £1 is constant.

Noe: Sein mys apt egress le sigo be momen feo.

14-7, Determie te bending slo energy in ke beam,
Eliseos

Suppen Rum sr,

ln: oc
Beating Sten Enr png

comme ¿ s
E ta . => mao.

5. 214-8. Determine the bending strain energy in the
cantilevered beam due to a uniform toad we Solve the
problem two ways (a) Apply Eq. 14-17. (6) The load w de
facing on a sepment de of the beam is displaced a distance
Y. where = the equation
Ol the clastic curve. Hence the imeral strain energy in the
üfferemial segment dx ofthe beam is equal tothe external
work, te Integrate thie equation to
‘obtain the total strain energy in the beam, EZ i constant

Bending San Brey: 8) otre Lg 17 gs

14-9, Determine the bending strain energy in the simply

supported beam due 10 a uniform load. Solve the problem

two ways (2) Apply Eq. 14-17. (6) The load w de acting on

the segment de of the beam is displaced a distance y. where

257 the equation of the

clastic core. Hence the internal strain energy in the

ema segment of the bear is equal 10 the external

ie, Integrate this equation te
‘bain the tol stain energy inthe beam. Es constant

Sapper Renton: asso RO,
Irn! Moment Fanci a en on PO).

ending Sain Eng) +9) HAE

uote

re tena] er]

“ee ma]

6. 14-10. Determine the bending stein energy In the ber.
Elis constan

Sappan Ruston: uso on ROW.
Arnal Moment Fein: shen PRO.
ending Sian Energy +A = in

“Tile a]
lerne]
zu

14-11. Determine the total axial and bending strain energy
inte A-36 sect beam. A = 2300 ma’, = 95010) mm“,

nis. ahs ts

pote we
Ha ex
un EDER aus
AR
pro
cr sra
A
SU gas
ETT

= (Uy sy «256 RARO 4963 Am

7. 14-12. The beam shown is tapered along ts width a
tov ia he Sas ad par hs er wit a af
E on be coonasrecaguar ero seca erw
eters

amet of Ina: a ean ene io,

Beading Sula Etre er ee wi ewe nn,
DTA

MR The bol bas à diameter 010 um. and he ink AB
as 2 ecamgulas eos section tat 1 me wide by Ny
{hice Determie te sala eerg ah ink due o bending
nd is the bolt due co axa (rs, The bit dpt
Ant bs a ension 01300 N Bo members ate nate 0)
36 sel Neglet the bole ste la

All Sin Eee) = oping Eg 14-160
ce
METAN

ao
cou): Am
Benin Sein Kara pie 4 ges

sus

hare

ere

Lena

©

“

Ia

san
e

8. 14-14. The tel beam i supported on wo sprigs euch
having a ses of k = 8 Min. Determine the sin te
‘ergy in eich of the spring and tbe bending stain
‘ergy inthe beam Ey = 200 GP, = Such man.

rin Sn ua nen, 0) sueo

05010") manda pit.
es,
“fo Joso?

Bending Suan Eve) > ein €

Eee]
ETS

„un
Eulen

9. 14-18. Determine the total axial and bending strain energy
inthe A-36 structural steel W 8 58 beam,

iar at
Wie hae
Las anın

an ame)
Ts

O) kp

as

= suey
Buoy
= 0346 tip» DORT

Tou rn
Weir
= 0130110") + 001597

10. “14-16. Determine the bending strain energy inthe beam
and the axial strain energy in each ofthe two post Allmem-
ders are made of aluminum and have a square cross section
50 mm by 50 mm, Assume the posts only support an axial

load By = 70 OP
pl
it
E - jrs
Met sabre
ame
se pp

(005,005) 2.4007?
1m 0101005? -osz0ex10*m

Des ml
pst 1 ,
te ea

aaa ss

ER), an
CT 000

MI Am

aida ep:

de we E E i
EMI “OMT! Ane

14-17. Determine the bending strain energy in the beast
ue to the distributed load, ET s constant

11. 14-18 The A-36 tol bar consis of two segmento, one of
eur and one of square ros section Iti mece to
the axial loading ol P determine the dimensions ofthe
squire segment otha he ala energy within be aqua

ube of Fig $20. Use
omnia for abr ses, ep THA Eg 518, ad

Ion of shat ran energy Eq 4-1, tstow
‘the twit ofthe tbe a gives by E539. Hint Bgute
Me work done bythe too T to the Anis
ser late tube, determined from integaiag the sn
ace or dieran element ig, Lover he volume
trate.

1418. Cossider the

She Soda Enr Rp 61 wi

eo

a

“Bi

12. "14-20, Determine the vertical displacement of joint C.AE
ss constant
DER 20 Kaas Fan 30 20
Fea Fea
S125 20 IO
Fea Foxe?

Cone
rn]

|
#

14-21. Determine the horizonal displacement o joint D.

AE constant.
A A > e
A Bone

er

soma Ic
open Meran

denen Mer y
sein:

Mann ro

SER=0 Peer Le
soa “la
si2K 20 re-onr-0

Canaan

Sony ane

elie

OS
CET)

13. 14-22. Determine the vertical displacement of oint D. AE

Member Force: Dy capi in, me AD en ea
‘etc Fs a (D Aug Dl 0 whe

OS

S20 Roanne m
coer)

eee rh

un mein

Atel Sr Borgo à A E 1416, weave

prom
na, RO ant

ste Work Teen ma y aa ia

Contention of Enea

j
!

F

=
PR?
A
F
r
T
a
a

He,

TEE The nilo Beim bas a RON cm
sectional ares A, moment et ler 1, ad a modular
of else E it's load P ate a pot B 2 shows,
deiermise the displacement at B ia the econ of E
ccoo for beng, all ove, and shear

Sin Eure + Hee

tt a 11, meta

ya fine pie (eee

devo cote
vn [tage urinate rie

Commaton of Er +

ones

vemo

>=

ose

a

14. 714-24 Determine the displacement of point B 00 the A-
36 steel beam. = 80(10") mu,

4 A

LE >>
Bine,
eb

a ne
hese

t= [MEE = anno kan + as « EE

toe bp Lanny «100g

El

Gad,

PL]

15. 16-25. Demrmins the doplaconeat of pont 3 où the
OLAS Ahlen boar

Ne

ote) eras?
cs

Seppan Raso anton a PRD.

omit Pca odos o. goa Si
——— I
ver ie
le

Poma “0 te] ae

un
mm

it a um)
sone vor
ternal Wer Tos rt dy Ap fot

ao pene

Je

16. 14-26. Determine the slope at pont C ofthe A6 sel

beam f= 95000) mint.

appart Rasen: Auer on FBO.
Moment Fanon: how on RO).

ending Sian ney: Aa 1 weh
sea

fase |
Free
eau)

AN

coral Work: Tema wok dnb 12 cap on

tye Yao) es metro) ee
consten] Enr à

anna

anses Am

peed
o
se
ml CT
en

14-27. Determine the deflection ofthe beam at is center
‘caused by shear. The shear modulus is G.

Supper Reine ann 0 204.

Shan Pate A ne RDC)

Stew stay: pet hier
nn

tee Work Tec we dey Ce Ps

Conceralon of Buy:

ons

17. “14-28, The A-36stel bars are pin connected at Teach
has a square cross section, determine the vertical
displacement at 2

Sappan Kanon shown FD.

Moment Panton Abona on RD) u

ending Stata Enr à Apo 4 weave

Lente fa]
{Boson a

strat Work: etat an 0 eis

Game,

404, oem

261 Aus

14-29. Determine the slope a point A of the beam. Es

trend,
zn

Comer my
wu

nos

18. 14-30. The rod has a circular cross section with a moment
of inem LI a vertical fore P is applied at A, determine
the vertical displacement at this point. Only consider the
strain energy due 10 bending, The modulus of cast 4 2e

GMa = PER) Me Pelton
Bening se cu
CRT"

Var

19. ato each others that = "ad the decos ona

‘Tee cold plage cols andi made of matar
shear modulus Determin the ste of ering
wea tis sube to be Ind Acro thatthe a a 4
el by the torical ses a tec,

ending Sal Er» Aa 142, weve

TL, pee ice

Br De
en
wage
dns
|

ui

Cometas of Energy

june

ae

7 kg

P43 A bars 8 long and basa diameter of 03 in It
it to be used 10 ab energy lo teen om an
impact touting. determine he total amount of tule
energy that i ca abort mada of ra bra CO!

ate Sn are a ht wk «A

‘ree ty 1416 retro

ME tan qu

DRE ae

Sama wee

CSS CEE PEER

BRETTON

163% Save Prob, 18-92 i the bar made of alumioum
ames,

late Sri Er) Dig eis ner.
spiny ae

Me rte ae

ae ee

Sas veto

ROUE image ane
on ios

20. 14-34 Determine the diameter of a red brass CKMOO bar
(Gat 8 felong e I o be sed to absorb DON. of
‘nergy o teasion tom an impact losing

late Srl Bare à Te li id i= 0

14-35, “The composite aluminum bar is made from two
Segments having diameters of mm and 10 min, Determine
the maximum axial stress developed inthe bar if the Sıkg
collaris dropped from a heightofh = 100 mm. Eu = 70 GPa,
ay = 410 MPa.

zu, Sean some
AE" Too * FOOT TORI)

29813900

21. “14-36, The composite aluminum bar is made from two
segments having diameters ofS mm aad 10 mm. Determine
the maximum height from which the 5-kg collar should be
éropped so that it produces a maximun axial stes inthe
Par of Goan = 300 MPa, Ey = 70 GPa, oy = 410 MPa.

504102), somos

A ED un
SAA A A

LT finds

cos see rex

ws

NETA

TES Determine the speed v of the 50 Mg mass when t
da just over the top of the steel post, i alter Impact the
‘imum stress developed inthe posts 580 MPa Ths pon
as a Length of L = 1 m and a crossecional arca of ot
mo Ey = 200.GPa, oy = 609 MPa

AB _ coca „

200 Ne
7

Jn «sure ao = Jason y

22. 14-38, The 4-36 steel bolts required 1 boro the energy
of 2g mus at als À 230 mes the bo dr

amater of 4 mun, detemine hs required length Lo te
res in the bolt dows uot exceed 150 MP.

CET
REC FORT

Masimam Sit Au

ERS ae S631 Ma wohne

aaa

Go * He nei)
ee

14239. The AD neal bok requimd fo abserb the
energy of a 24 mus tht fal = 30 ebm I the bot has
SGiameter of mu ad elengh of L = 200mm, determine
A steel the bolt wl exnad 175 MPA.

asp à
ME OTAN 0
PRES
EE mo

Go du OSADO TE

14-40. The A-36 sel bolt is required 10 absorb the
nergy ota Zones bat fal slong od lametr bot
{Sank tat ie L = 150 mm long Determine be maximum
height A Ol release co the sten ia the Bolt does not

ceed OM
ema See yo Bh AON.
FT

noir ang ACA

(10°) ET =a BORD 7

cure, sone O]
ce) lb sem(1)]

Ars) mes Ane

23. 6-42. The 50: weight i fal a fe athe stant it
HZ above te ring and port sembly. Determine the
imum srs in tbe port tbe spring bas a ss OÙ
RE ZU Lipa, The port has a diameter of 3 lo and a
modalus of sites) of B= 620(10) ks. Assume the
rater wl ot eld

utr ing Hee

sauts, a,

Lo

Constan of Eneas: Te oi cof eos

AS

Seika, a
en Ana yy Th Em

Intention) late

a

Sa in D

soverfrearefear)obistet(Zat)

TON
MA ss amero
este nen

en

Main Ses Te ie fr epi =
emana fr poi 0,
TON ms

24. 14-42. The composite aluminum 2014-76 bars made from
two segments having diameters of 75 mm and 15 mm.
Determine the maximum axial tres developed in the bar it
the 10 collar is dropped from a height of À = 100 mm.

aL, OIR, _wesnon
E osa oars} one)
= 70m

ee 1 asa
OS rr ais

Y, sn

sot Me RE une
oma 11612059)
= AP MPA < O MP OK Am

14-42. The composite aluminum 2014-16 baris made from
‘ovo segments having diameters of 75 ma and 15 me
Determine the maximum height / ftom which the 10g
collar should be dropped so that it produces a maximum
aa stress inthe Bar Of aan. = 300 MPa

emo» _,__Weanen
Fo aan | posan
nm

soot = (1+ [TITANIO (nas,

ha 00m = 956mm Am

25. *14-44. A finder baving the dimensions shown is made
of maguesium Am 04.61. I set by à ng
block biving a weight of 800 Ib and taveling at 2 Ai,
determine tbe maximum sess ie the eyinder Neg he
tus ofthe eine

Conse of ery: 0 gus pects yn

PERICIA

a

rest)

bea 010

A Geo

(AS. The sack of cement has weight of 90 His
rapped trom estat a eight of = à onto the center of
the W 10% 39 structural sel A.36 beam, determine te
ati bendig tes developed inte Beas due o he
Impact Alo, what he impact factor?

Impact Pair: ee ei pr.

CTA

Soe RAE

au

CE

u a OO say

DCE Am

26. 14-46. The sack of coment has a weight of 90 Ibm, ii
Determine the maximum beight À Gom wile I cn bebe PT

re ao he rot oe W 10% a =e

Impact For Fr uo in Ani

22 see
an ae

isn CCE ES

de raten)

au at „sam

DONC
sos

14-47. The 200.1 block has a downward velocity of fus
‘when its 3 from the top of the wooden bear, Determine
the maximum stress in the beam due 10 the impact and
‘compute the maximum defletionofitsend €. E, = 19(10")
ki or = 6 hs

rom pen

PR EI
7 wu u

mem oy

Pers

Lo 2 au had

isa

TH as Th
Eros

aa“ O ed aan

Wot, = 1539031960) 9.16
MOI 298122

ue 295120)

7" TE TL

“assis co OK Am

From Apex

CRT
TE RONDA

2790007 nt

dd 0318018

bene SN)
MOIN 07995, Ane

27. 14-48, The 100: block has a downward velocity of 4 (us
when itis 3 from the top ofthe wooden beam. Determine
the maximum stress in the beam due to the impact and
compete the maximum deflection of point B. Ey = 1.910)
sioy = ki.

4 a,

“ j Ces

PR OM
er Gar

murat cy
wet
Sat eue ae

EMO yas à 10000 BD = USD DK AL
DNS Ey

39814 100s = 2850

PS

19025) «TS

Le
sea 343519 #208423 SY in

OR Am

28. 14-0. Tos dvr weighs 150 nd wile hol inst
‘gi ses ae end ots wooden tio bond va à

Ed els af à Oh when À 0 Determine the

rim De sen Good inte San. Tae

DT En dan oC 15 tad wat of 15 À af
Bo 0 tare te mer doc soii,

sti Diplenen; Tess Spice een ee
Scot cer ung e sc af ny

ETES

ao)
ma]
Conservation of Energy Trennen mon

El 82) ce) }an +108. jaune
ina en nina eo

DO 207% Them eo à
erst May OSO EGO n.

Haas 246890029,

oe DE TE

29. 14-50. Te diver weight 1502 and while holding bimset
gd suites the ead of the wooden ving board.
Determine the maximum height À rom wich be can jump
ato te Board 20 tat the maximum bending see inthe
‘hood does not reed 6b. The bord has a ces of
En and width of 15. E, = 1200) ka

“State Diplaemet: Ts pean a eo of ng
tone beeen de ese le

dran ES EL.
Lente,

MOT

een]

ea serv sooo
bn. BL”
ae La

cocoa (a)

Note as Doc cr a nen
bre

30. 14-51. The T5-b block has a dowaward velocity of 2 Iva
ben 3 from be top ofthe wooden beam Determine
‘he maximum beading tessa the beam du ote inact,
And compute the maximum deflection of iu 698 D
= L910) Lomo the material wil ted

Conserva of ere) Toews csm o Bs
teen en econ wee Apt

140, ALLA]

Sr D
Le pensons

Sage stern, mete
du roza

estu Svs macia is ee a on
‘ton RS ee te Themes come
ous pn Mag = Patt E

Fa

Dpt: msn feo tebe ta Hae
MN 220 22 Pra dec
Teton ret Sen à

hall, oca >
LEE CC eC) ms

(ls el (10) 020A

EEE Nec hs verd vey da
vient 3 oc be op ft wd rim Don
Eon ening aus D in ane
{pace and coupe De main deci af a
Eu = 1X10) kai, ma»

Cane ten e nee oe se o co o
AS

ES
Tec

uae
Jrs

EE juaespan rs] toma.

Set ere pe meso
De AOD corn a

**91300(0 2467) =22095.6 = 2406. The macia nome

cusp Magy = Bag BOHOL)

31. MS Detrmie the macimam het A from which an
BE neigh canbe dropped tee
W 6218 ben Withee ec

Stale Dicen: These dame ed ea
‘ne eer ig econ my.

Pa
eae)

San)
Bomann
EE

Bat Set: he nan ot ea tg. Te
‘easement exes me po Mas = O)
Er

(10)

en
Minor.
a TR
Ben tow

onen Enron como uns

te Bag, 6 e mai dicen a o

CONTRE EE LES
vu
Wiebe faba

avi Lau (ss)

has

32. 14-84. The 80 weight is dropped from es at a beght
Oth = one the ead ofthe Ar steel W612 Beams
Deternis tbe maximum bendig stress developed inthe 4

Stu Daiana Te ide ol dr

adan)
Basen
cé

Craie fy ét ys ett a

au

WO b= a PA
un. jus

sas meo

Macia Srs ie mac ie be tn, Ad
264046) LARG Tenn nen ce
Mn ODIN à

amos)
=

Se ou, € 36%, 00 or an

33. 14-55. ‘The tugboat has a weight of 120 000 Ib and is
traveling forward a 2105 when it stikes the 12in-dianeter

made from treated white spruce and is assume
river bed, determine the maximum horizontal distance the
top ofthe post will move due to the impact. Assume the
tugboat is rigid and neglect the efec of the water

on = PRE

er

EEE se narra
(ome a

LARA sg

aay

sono tag?
ET

sone nd

das "lcd + es)

(lada LITIO ISA Aus

34. ousting at
(075m. ata ares of SM nds Bunper
{as be coasderedsnplysapprted cn wo spring supra
Conaested tothe Agi fame of the cr Forte bumper
{ake 2 30010 mt, € = 75 mm ey = 30 MER fod
ES MN

Ceara ya eam deviner enn

PER CEN 00010)
ea

DER a
se
Jj each
Janer) = ee
ape)
cna ca tt ET}

du y ne

‘eens o25(00°)

arin Se To mi ee Pn "Ke
USO?) 049.3. Te mira nen

Haze IIS,

35. 14-57. The 1504 weight haa vel of Urata eight
off om te top ofthe A 38 teal beam Determine he
maximun defection aed mucimum bendig sve in tbe
beam i the supporing springs a À and B eich ea
‘aes ot = 900 |

ra T= Tak

Ma ant E
a tn w

Contervaton of ora > Tecla eno an
‘deena wn be iat ao hd Arpa

EEC CN
a

beenden) m

And

Snag Es y

‘seep A 142050

Sat eine ee
an ran
Atina Dotan! Fat 4» sem nie.

Ban hy ine ERS A

Marina Ses To hu =

Set 00 JS e rei na

36. 14-58. The 15. weight haa veloc 64s ata high
LA (om the top ofthe AS steal Dex Determine the
Fond factor nif the supporting springs at A and Beach kare
Anime of = 20 ia.

tren Pi, er

o

Comentan of Entry erp esto tn
cute ue efec a in Arda

Leet ot a

Sang EG

m

sum

taste 27672000

ed Putre mi oo A on * Be

Bad capa

Ent au #936 rest

37. 14-59. | Determine the vertical displacement of joint B of
the truss Each A-36 steel member has a cross Sectional area
Of 300 mm.

Pr re
a” aim de fain
tes ns mn
O

zoom

TER Determin he horizontal displacement of joint 3
tte tus Each À 36 sel member as y mas 2
area oF 300 mme

Dia de
2 ai Be
Emi

za

38. 14-61, Determine the horizontal displacement of point B.
Each A-36 steel member bas a ctoa-ectionl area of

Member Real Forces N: ui on es.
Mander Viral Foret: be nce).

Viral Work Equation: Ain 14-9, cede

ir
hassen
cocina

nina
ran ee

14-62 Determine the vercal displacement of pola.
Esch AS eel member bat a crossecional wen of

3

embar Ral Perce N: usb una

Member Yan Free: has i).
Viral Werk Equation: pine BM

vant

vm ae einen
sconce
vay an

SS

an.

39. 14-63. Determine the vertical displacement of cit. For

‘ach À 36 steel member A= LS it al po ad
ay rE E

ae RE ae,

a = CIAO HENO

IN + AMAIA
O + cesse ra

contin Am

MET

14-64 Determine the vertical displacement of joint. For
each À 36 steel member A = 15 in

ASA (Lars)

+ COIN + ONCE
AO + A

a e

40. 14-45. Determine the Brot! planen of pont
Esch À 6 mehr barre eset See

su sms,

be NE alg] Ne le
a] KE
2. 0 aw) 2
Be m ns) 15 une) | N
FE ww) à 0 m
Pe 8
Zune wa A
Er LN
ca] a
“BAG aros am
tea, Deiter dienes tpt à
Nitti acer ncaa oo
antral oe MA sue aime
in Val oc Mont i"
Vina Wo Ei eg =v AXE
ae 10 mol) 2 mo) A e
Fe om ir) 18 0)
G 18 ur) 2 sf)
mo rr ar
es 80) 25 ss)
Eoin) en
ropa
cap, «ANION

aE
ss)
ET

En

41. 14-67, Determine the vertical displacement of poat À
Each À 36 tel member has a rostsectonal ara of 3

Member Rel Forces Aso Cea,

Member Vitel Force escu

Vinal Work Ernten Api E =. mete
CRE
Era

E
E
o

2-4. Determine the vesical displacement ot pia
Esch À 6 el member brs casera ent Sit

Member Ral Forces Washoe es
Member Viral Forces Ausb un)

Viral Wark Equation: Ago 4-99, vere

se ES
so em
Losey
tajo
ne aa
[DEE oo dam

w

42. 14-6. Determine the vertical displacement of pat A. Each
(A6 sesl member has cros-seconal are of 400 man?

AB 0750 (IP) 1s 253125(10')
ac -07s0 2310) 15 rast)

RTE am
GO saat) à von)
Fre Er
oe tant) 18 mm)
Eau) He
vase
Inc, str
Fi

a RO

2710") mern Am

14-70. Determne the vertical displacement of pont 2. Each
(A6 steel member bas a rosssectonal are of 400 mm

Viral Work Equation: orig E 14-39, weave

e
AA

0 as) as ° A
3€ 0-20) as o ji
4 0 ms) as o

ce 2 er Pe Feen)

Em) 10)

DE wu) 15 ke

Zraszs(10) wm

aE
asso)

Hal
32107)

rn Am

43. , pet,
ps
Be, Deco wl mm

Viral Work Equation: Ap E 2% we hae

Me
> am as wae)
co am u) a conte)
Pe to mente)
Ge a) a
ne + un) ae
Eau) on
rer
cn, I

RARA
0%) matin + Am

an]

114-7. Determine he horizontal déplacemet ol point E
Each A tel member asa crossectionl area (200 mn

Viral Work Equacions ping 1

De
A 5
» ne) 5 o

9 nasa) as

ue) a (19)
Π0 ami)

132010)
a) ae ae)
Zoo) wm

DS:
Iran, DIEU re
a Bao
O]

SO”) mon Am

44. 14-72 Determine the vertical placement of poat Bach
‘36, seal member Das a ersssectonl area of
SE

Viral Work Egeo AE 16-39, vetar

Mate ea 7
2 : Sel
se Pe
5 a 7 Eee
ES zos ee gu
ra a o se
a moon tw
se nm
Limit hee >
A free

oO Ane +

M74, Determine deveria dsplacementl point
A el member bs roc ar SL

Viral Work Equation Ape E 1-3 edo

ay ow 33 |
5e omer ae
Deo. oo o.
Ae o er
ce “ons Tun im ae
E Zu Se Lee
En o lo.
AsH Re, e

Tamm" men} Am e

45. 14-76. Determine the vertical displacement of joint C Each
A6 cel member has a ros sectional area of 4 5 in?

Sana]

tote, = BME
am Fe
en

14-76. Determine the vertical displacement of joint H.
Each À 36 steel member has actos sectional are of 45 in?

zart

Er

RS once Am
Han 7 2

se

46. 14-77. Determine the displacement at point C. El is

ant meer

14-72 Determine the diplacement of polat CET is

ton Pro me ts os

Virtual Moment Punctions m(x) : As shown on figure). ur di

eto etn ttn JE
ua:

van fa ‘

47. 14-79. Determine the slope at point C. El is constant.

PRÉ ob mayb

Farb fa]
* &

Viral Moment Puntos): A enn ent),

=
wat Pis
= + * o À
Ta pases op dE Samoa
a
sets unten rome ten
ime atin: tet
pan
An Rte
AL
neos

Jun parties

‘ase Tis

48. 14-82. Determine th
am diameter As

isplacemest at C of the
pes

ea lement Pucon Me) A on on gua)

Viral Moment Fasten mie) shows aq)

Vineet Werk Equation: Fra cena np ee Je

AP
Per 7m
tanta
Scars
CRETE
osm?
= a
esco
A] Js]
el") anión da EL.
tot
MAR. Deals ed a te ply at CU e A
ta a 8 co dancer
at Maman Pann Mi) hoon + a,
Vina! Moment Pcs mA ce)
Vinal ar geen Fr pape ernten &
Pr Fam
“a re
23801000. ÉTAT 0)

cost Am

om]

49. “14-44 Determine the diplacemeat of collr B. The
(AG reel hf as à diameter of 0 mm.

a Moment Fenton MG) A nn on gs
Viral Moment Fucins m2) one),

Viral Werk Eglo Foe pement ar

rafia

raya Ef opa

2 bff cono pan
Ef omnes

20841000,
“fo

EAS Determine the slope at C The A 6 steel has
2 diameter of 60 mm.

‘eat Moment Panton Mix): show cigs

au 1
Virtual Moment Functions m, (2) : hs shown ca fuí). Massen, |e y Haze,
ae um EREG:
cfa ate.
Ly .
tie ee mapa,

+ em sonne,

eus
Dane mas,
rn

Unna,

ua] 7
= AMES
ao.

coa y Sarat
“ay o Am

50. 14-86. Determine the slope at A, The A-36 steel shaft bas
A diameter of 60 mm.

ea Moment Panton bie) a sown fs
Viral Moment Faces mya) bornes Fat)

Viral Work Eaton Far pep, py En 140

[i039 s0m]020-n Ndr oem

AA “f sooo,
FEINE ba I
ES Etat En en

200000 os oe

a omen on

TORT, The A6 reel beam tas a moment of arta of
12 1250109 mn‘. Determine the displacement,

isin Cena

a Moment Fenton Mi) ah at, aro

mo te), pas

nat Work Equation Fr eon DEA

sous

Bacon
Bi
(107) mean TA

14-88. Tue AG steel beam has a moment fiera of
1125019) men‘. Determine the slope E

ea Moment Fanon Mi) a no ge Maroma
Yin Maman Pc ms bora, bal Gens
Vinal Work Equation: o bee poo, py By un Pa

Bang Marianne

= at tn
ocio mo ge
nn

51. 10-09 The A6 structural tel beam has a moment of
nera of f= 125(0" mint, Determie the slope of the
team at B

ea Moment Faction Mix): own où Burt

tm en. mes
don no
[—- 3
Eh
im dm
TR Damian the digimon
moment of me sc parie D ae
tees the
Der Toe moda olay fre mal
‘ut Monet anon ME): sown cs er
en
Vina Moments ms) bonne el)
CR: me]
oat Wot Egon Fr pent
ae Seam
. FRA,
cts
wok

1491. Determine the diplacemen of poa € of we
W 14 x 26 beam made from A-36 steel. Y à

Lace fe RM
“ur mer mo
Ho pes
La ea Ft

“Banas an

52. “14-92, Determine the slope at À of the W 14 x 26 bear
made from A-36 steel, us

me 1m nee
vel

damos fn,

zum a
Ban Am

143% Determine the disent Co he A6 steel
beam, 2 7000) me

pet Monet Fonction MG) Aon Get.
uncon mb): sown oe

AS
ee — |
oe - le
a. rar
o

muero, noch

53. A Deter
7000" ma

js the lope a A ofthe A36 sel beam,

neat Moment Penton Mi) ho a gt)

Vial Work Equation: Fortean poets, ty Eg

Eo

ue Lain es mayo

CO o As

mio ai

HS. ‘Determine the slope a B ofthe A Heal DAR
TE a.

ea Moment Pucon MS Aeon cn Ge.

ine! Moment Fenton ms): shown cna

inet Work Equation Face pe pl, 9844-8,

ar
0
meio a me
Der me be
en os am er
ce pes
14-96, Th eus ce ol Dogs fr Determine te
Su
at Moen Peal wi): one qu
nt Moment Pasco ct, mare mage] a
onal Wok Ein ae pc pth ty =
a et
ss ze Ta
va fi 2
ray coed ost 130140)
AS
se ae ro,

7 ns, mages
fer

ma

ni) meisten Am Fu a

54. 14-97. ‘The beam is made of Douglas fr. Deter
slope ac. WB fe Determine the

Vinal Work Equation: E e dopo pl, ES.

H
H

magnon,

|
5

APS
wm
pom,

=e N gun
7

one ous
o

14-98, The beam is rade of oak for wich E, = 11 GP.
Deteriae the slope and displacement at À

Work Equation: Fr spice pb
e. or

EL (2m rn 600) 4,

me

votant sc +60)

ese

sumo
Hueco]

2520107) ma Am

ange Mrs

Eau

oo ee

AN

o

=
»

ine meso m0 tome

55. 14-99,

joa)" |

Determine the displacement at point €. El is

*14-100.. ‘Determine the slope at 8. EI is constant,

; R y

Y

56. 14-101, Beam AB bas a square cos secon of 10 am
‘by 100 mn Bar CD has a diameter of 10 man. If both
member are made of À steak, determine the vera
‘Goplcement of pot D duet the loading of 10KN.

ea Maman Facto M(x): ao i)

inal omen Pancionsm(z): Asbo ca fe)

use foutre

ficar

ALTA

caco? sun

EP ss

“NO FA

n0n0stmsosen Am

agregar
ne sa

x [a

opus Huy Im
[oran
i

rote

AU. Beam AP as à qu rs secs of 10 zum
110 ma Bu CD a ion an.
eben re mado A eras here

due to the loading of 10 kN. ma

Viral Moment Fens g(t): ash nee)

Viral Work Equation Forte pnp, on 4-6
Etre

Efron,
«¿focos
amet
Foo A11(1000)

[TC NON) Fm

Gare gern ra
[me sx

57. eam, Bar ABC bas à rectangular cross secon of
300 men by 100 mm Attached rod DB bas a diameter of
25 am If bot members ao made of A6 seek, determine
the vericl deplnrment of plat C due o the loudng.
Consider oly the elec of bending in ABC and axl force,

oa.
Mont Puedo np
ne Monn Pecos maw cen
Yea Wak Eu Fc nc ne
PRES
La: a
near onen]
a

ono) so

RARA an

Cama ame Au

aout Mets À
„set

a

tors 208.380 su

18-106. Bar ABC has a recanglar cross section of
300 mam by 100 mu Attached rod DB as à diameter of 20
‘am If both members ae made of A:36stec determine the
Slope a À due tote leading, Considr only the elect of
‘ending in ABC und ail ore in DB.

‘eat Moment Fenton Mis): shown on pi)
inal Moment Pancon my) Ae sun
Vial Work quan Fre peep comb 1403

mule

NE
em ne fama
comentan

peat mon

man” rin toh, | Ben]

ROO] a ac)
E u L ose

=-2991(10") mel Au

58. 14-108. The L-shaped frame is made from two segments,
ach of length L and flexural stiffness Itt subjected
to the uniform distributed load, determine the horieontal
displacement of the end €.

El
BL,

TE-106, The L-shaped frame is made from two segments,

each of length L and flexural sifness EI It its subjected

the uniform distributed load, determine the ven
displacement of point 8.

59. 14-107. Determine the horizontal and

displacement of point C. There is a fixed support a

A A agg

d'a [Monnet u

18:10. Detemnise be horizontal placement of pot
A on the ange back due tothe concentrate fore P The
acte à ted eonsecid to lu support. Elle coman
{Consider al he ete of beading.

o
a
res

>

60. 14-109, The rame ls made from two segments, cach of
leogth£ and flexural stes BL Wit brad tothe
valor distributed load,” determine te vendait
“placement ofpoiat € Conte" aly the ft ot end.

Ra amant Fanlo Mig): a tons ee.
Viral Moment Fanaon mie) A own

Viral Work Eqn Fre eel pcm
renin

AAA The tame i made om sv segment ech ot
PR ne" a a eae
Septet pt 8. Cone aye eect oe
eat Ment Frio Mi) en ae

na Moment Prem mi) teen ca).

inal Work Equation: oder dicen ap,

tatoo,

61. 14-111. The semicircular rod has a moment of inertia 7
and modulus of elasticity E. Determine the horizontal
‘defection at the roller due to bending

LE

That Nina 0e0

EM: MoPsinor eo
apres

ir]

ELEC

zut tune 0
em muro o

62. “14-112. Solve Prob. 14-60 using Casigliano’s theatem

” aver MP0) L oa,
N 0 5 -2007
00957 05 ms 0m
wor ORS ws un
Ee-90.00

Mente N AMP PaO) LON
Ms a
Ac os. 05 os 12000.
ve ns a

2061556
NL, 055610)

00m lid Ans

NT ECT

63. EAM Solve Pro. 14-61 using Cai

Member Foren Mendo tn de na oe Psd ee a
(tom oro ef

Cage's Secon Peron pin neh

De
An con 005 9 10
Ce OH OM) WE as

PR an) m+ Am

14-115. Soie Prob, 16-62 using Casinos theorem.

Member Fores N Menos eel o nd xr pis
dor a ben on e Aga

Catlins Second Thtorem Aspa E 14-48, web
Monte ” Em

Fo men.
An ~(08250 sion

Us user in
BE (Om Im as 10 100
A6 ame ons m

TE Am

64. jé. Sole Prob. 14-64 using Castglinos theorem

LAEHL-OSSIIN + (LENS)
ANO + ANNO

+ SEND) + ONLINE VE

ss

rin A
TO

14-137. Solve Prob. 14-63 using Castilano theorem.

ox
DATE
MOP AE

353-0468) + (1.306678)
HOSE) + LEEN)

+ wasn» encase

E 00
TGS tn Am

65. 18-118. Save Prob 14-65 wing Catgliano's theorem
Member Force NM oes ee oa and ene
pa

Crean Second Theorem: epg 144, weave

CN

pr E ms à A :
a mE E
ata Bob | k
de H 5 A
Enea E
€
nu”
D EL)
' LE) cei = am
EA Teg Caio or
ener
EE rs
ei strate .
De er er hen
tae tae A « k
o A al Ne, (E
= o o 15 o El
pá clas as 25 ms
A =
À
ann
saat OT
MIO?) we 16m 4 ie

EE Sale Prob 1 wing Casino orm

amber Pres Md ud ne oc ad el pi
pa

Cargas" Second Thor Ag 6-8 mr

me o e le

Fe ie un te à 2

Mareo <->
+2)

Pe

66. 14-121. Solve Prob 14-67 using Casta theorem.

tambor Forces 5 Mento det cra oe and eat
on be

ailes Second Theorem Arba E 14-48, vete

PP à M
O wa
M + % à +
ile ie A

MAD. Soie Prob, 16-69 ing Catigiaso’ theorem

Member Fores N ben exe fe ner pe
(Gon wenn one

Canton Second Trorm Apo E 146 weve

FE ven af
o
Ur CS sas
a D à von
Sos Sa ee
ae ee Zu os
Pe
tel
tap, ES

“amo
m0) má Am

67. 11. Solve Prob 14-70 wing Canos theorem.

tm À E
>
se las o
MS 0 m
Euren ms as
Er im EE
Dessus

OT) aa da

124 Solve Prob 16-72 win Casino» theorem.

bar Fores mb os ea ut
fen we bow on ge

Cat Second Tram Apps B44, webne

monte E enn a 3
B i 3 im D
ans ala m de age
eae im Fe}
fe vu u

Eee

Bano,
RA
ou) mean Am

68. MOUS, Sole Prob. 14-71 wing Casighan theorem.

Member Fret ane i neo an eng
pa

Coreano" econ There: pro Eg 144 weve

wate A
we ie aw
sm os
8 e tS, ss
Rate TB GSB

acm Ee as

ES
a un)
en) mete + Am

M-I2S, Solve Prob. 14-73 wing Casigiano! theorem,

Member Forces Mende os en fa ee pet

pen
ets nt Fern A ot
x

Me a à E

Mo ou stan

Pre

o 8 3 208

Fe ë de

# AS Fe B
Esso

69. MIET. Solve Prob 14-74 wing Castigan’ theorem,

Member Force Metso ue ea Pade it

nte

Cases Second Thre

Mate

An ours
ae Sansa

co Ne
bee
oo

Ae amour
ri

“RA

x

wo

sexes

ELLE]

corn à

De 144 votre

pa

ADR. Solve Prob. 14-76 ing Casino» theorem

amber Frcs eme ld ral a exe pls

a naetge

Essen y Second There

Be eo
> neo

FS

M ora
Cu camer 1339)
at omar een
25 lomera
ho Ssterci00
Du comerse
A]
AS

El

Ds

etek 144, vor

momo e dE
un man
ne

ow

error

Eh
un en

en
an m

70. 14-129 Solve Prob, 14-75 wing Casigiano! theorem.

amber Fo Memes le do rare nen i

car sen nes ett tee
as

nao E e +

run oan aye

ana de D Ee

pee D ON ine

a E

Te cn ao on ane

Me 23 a Da

en I ee

EEE we

Er 2 8 ie

a “ns 2S te

= de en
o e m Me AE
“ or dal ón do Am
pene “HT
PER
re

, Ei

ser=0

men Meare
bie een
Cepo ane

Ane

71. MAM, Solve Prob. 14-78 using Cangas theorem

Aura Moment Panton (x) a at tn
La ey pl lr o d

[det
cajas

AS 00070)

Er: Am

"MIDA. Solve Prob. 14-84 ung Casino theorem,

neral Moment Faction MG): en wren aon
is fe a Pa enn pil dr or be

Catalano Secon Pharm e pme ne

MAP 5 200

7
| fosse

Bi
97

ER

72. 14-128. Solve Prob. 14-8) wing Carigiano» theorem

mera Moment anclas Mi) Tem min
Rp mone nd ee pln
on ee

Caines Second Theron Tsien Com oran
even, MEM as a
ren

ame

EE

A]

areas,

¢

PS

pa

PRES

Pr

14-154. Save Prob. 1-8 wing Casino theorem

trat Moment Pasen Me) Peine cn
las of de ap momen nen pale

shown epee

Casan y Second Thearem Pepe Eh dre
ing. wig ME
snr. win ME
Er

fs

Socio
PO

73. (gas à Second Theron ee a ede
eet 10m
pere

moot. ME som
“ar

of
fat

(101) a

aa)
u “OOH Ane

+14-136. Solve Prob. 14-97 using Castiliano’s theorem.

eto oir
ma 0 MBA the CNET
bi = een
Pert, TR Teer FRR RER

28000.
FU

40507) nd Ans

74. 1A=137. Soie Prob 14-102 wog Catane theorem.

Arnal Asa Frc MT en a fee CO la

neral Moment Penco M(x): Te ier ine ton
Lu lp mom Moder il
o

14-138. Solve Prob, 14-98 using Castigianos theorem,

DEC

Pride
monte ne

SE line

@

ade show og) mc) expe.

stant Second Theorem edson A cb

Ma
ee one pet wea En 14-30 vi AD a,
reinigen MED, MEP wy 0d ‘ae

La

dns P=. and ang 0:

fans
al, Gao
GA (CRE 0)

son
nee]
=325(10°) ná am

75. 14-139. Solve Proh 14-06 nine Castillas theorem,

“14-140, Sole Prob. 14-96 wing Caio! theorem.

trat ame Fanon Ma): Tae mon cn
A AS
Des

(sens Sted Thor e apne one

mal mile Em]

0e e Pod,

Peso,
EN

GS) mnttóna TA

76. 14-141, Solve Prob. 16-10 wing Casino theorem,

tra All For N Toca of ai
ected td wena nb

ra Maman Pectin ie): end nm ce
nn enger
=

tn Sod Theorem: ec one
ET
een y ot 10088164 win 2

sina, os rn

[mio
erfor

Joue ‚ann

F yoy, son
NO AAA

Zea 1e
rt
rete À Ji
ver,
pe

14-142, Solve Prob 14-106 using Castigliano's theorem.

77. 14-163. Solve Prob 14-107 using Castglano' theorem.

EN
er

Sang P=0
Mean Men

Brno
Pre

i) Me A, 120092

MAA Solve Prob.

{mara Mama Fasten Ms) Te mm cn

‘rare o era apt de owe

pa

Case Second Thorn Tebo dicen

hein 140 wig MD
LA

EI trs PP.

os

nenne,

108 wig Casinos ihrem.

om
ré,

%

78. HAUS Salve Prob 14-109 wing Csiglaos bear

rel amen Func MG) Tor onan cio

er A ud ee epee own on

Aa
jean

“ai

703
iy Erne

14-146, Solve Prob. 14-111 using Castipiano’s theorem.

79. 14-147. The cantilevered beam is subjected to a couple
moment Mo applied a its end. Determine the displacement
ofthe beam at 3, E is constant. Use the method ol virtual
work

——-

alg. jean

ten lez (Re
PET
El

“14-148. Solve Prob 14-347 using Castiglianos theorem.

de)

DEN
ar
me

TET

TEO, Die the method of visual work to determine the
lsplacemast a point AE's casan

‘ea Moment Pein Mi) Aush Pigs
Vine omen Fancon mie) Ae ons ee)

ined Werk queen Fr e een pt ty
Etre

vate
nr

fl),

80. 14-150, Solve Prob. 14-149 using Casiglanos theorem.

tra Moment Pnttn Mi) Turn men ion
etic an na pd nd ae or on de

Cui’ Sco Thorn Ta ipa cto
ca og ME, MG 7

5 motte
ars ase
ne ee
[Hs SEIT |
“ Ber Be

Las

TEASE, Dearne the slope of pol Co he A36 eel
beam 1 SOCIO mnt Ure the method of viral work

augen Mae ann

Raul Moment Function M(x): As shown fier) > )
Viral Momen Panton male) As own au roa
Lon” son!
aa Work Equation Fa eg arnt py BO. &
Srta moi A
Aforo, ages
OS Cp eed

CORRE
Hoe nt e

100,
PA

“TEASE. Save Prob. 14-151 wing Cala theorem.

tra Mamet Funcion MG) Ti nen tion
‘Sem fesse mone Meena ot

Calme à Second Taaram Toe eras

ag aso Men

yu

te
en on

81. 14-153. Determine the vertical displacement of joint £.For
each member A = 400 mm’, E = 200 GPa, Use the method
of virtual work

Mente nN kL
a o tots o
M om ss ns
M ome) Mo 200
er o o 20 o
E al
ED ous) D 2 am
se 9 0 20 o
MD om MS m
Ds as 15 m
gens

me
DEIN) no )e2 mm Am

on

82. 14-184, Solve Prob. 14153 using Casiglianos theorem,

Montes ”
de os
as ey
se 225-03"
A
ne o
o osa)
DE ae

anu mars

ie sale a

23625009,

“co

ave

asser
as
om

as

DCR
0 1s
Een
wo 20

as is

ms 25

o 20

as is
>00 20

295007029500 Ans

mar
mans
am
aes
nn
1605

o

rena

MASS, Determine the stain energy in the hoiconal
une ar ue foi. Tee avr fore Ping

Pr
Tonto Sian Energy Ha e 8 re E 1

sfr
ENT
fotoo ye

Ant-wun-r=o

Tepe)

83. {1-186 Determine the total sio energy in the A
eee Cone ei sin aint
ia-dametr ros andthe teng ss rc le à
han or Pee UE Een

Suppen Recon to FED). +
Inara ames Fac Askoen tO)

aa Sate Etre» nine EL ad 1

inf ere} (20)

MEAN

a do un
AS TR

HIST, The W 10% 12 beam made ol A wel and
cantilevered from the wall The spring mounted en

eam as asno of ~ 100 Ihe. a weight ot
Is dropped onto the spring trom a height of = 3, CI
determino the maximum Bonding res developed i he T
bem i

pion Fy =P Ti

DES w

onsen of Energy Tous cant be
azar vd econ sb Ads.

RS

a

WO ann)

seg ip

fe
aan] PR

ea ea ane

ares pet ene

Mina Se Te sine eco a nn
ONE) = 406 end namen men ne

Maus „ERS rn

Sei dag £0,236 Bear mp

84. ‘Act Detemine the dan Y to the cold C of be
ams cosaeciootl aca, The beam is symmetric wih
rape hey as
noo
ANA OH

AS Am
ÓN

ALL. Determine Land orbe beams rotation area

Momento

sof Qo) 309023)]
Loc +4509

O a

[AS Determine the ditanceF tothe cetrid € of the
Sram crosesectona are, thea ad

Arien 926048
ANDAS

aio Am

amet nd
ame

Ars

amas

85. A4. Detrmise forthe beam’ rosca! aes,

Moment of tet:

ETC

coco) hone)

A-S. Determine Y which locates tbe centró and then
fad the moments of inertial, ae, forte Töcam.

Auen on
es

mr
yo) aa
Lo rea
Jo jo am

Ach. Determina , whic acts tb eeu, and then
gue the moment of feria 7, and J, forthe cr.

‘008,009 -006(008 = 4019) a
54 00(008(008)-095(005(000 =0190(10%) =

Moment of tei

Le tan (ous) «0000 (004-0000 4
{ie00 (au os ats]

(19% 2 =231(10) mat am

(000 (00 =j(000(008)

29109) wf =309(10) nt Am

86. (ALT. Detemise the locaton (9) ofthe eratrid Cote
‘ges oser are, thea fd the moments of sera
Lust.

o :
ANO seu
PARTNERS

mn mm
PAR CET As
mm =

Lo) oo

momo
pomor
Lor

LA. Determine the loetion (7) le cesto Cote
LA cocinas. Ben id the product ones,
pen then andy ans.

Pd

NANO 6008

NADO 2908
q oo An
PES Am

Proc of Ie:

LISAS

87. AL). Determine the locas (2,7) ofthe centred € af he
anges coseeconal wen md then Computo the
‘momen of teria 2307,

coal:

A 7000 3000 D nt
aC 47500 05) = 500 ma?
{22514520 270 130900 = 1a

Foo (19) +0050 75-2649
29300) mat pa

som) «sono
ECO TE
TES Am

AID. Deterine the Iction (7) of he centrid C ofthe
{apes cromsecona aes, andthe compute be produc of
Inert, with espect he xn ye

ASTON +3018 = 1240
ASNO = 550 a?

A S00 270) SO) = LG
itn
re RES

tase na: bl phone

LN
AAA
ill) Am

88. ‘Act, Determine te Icon (,) lth haa ro
A peered thea gerne the moment of nts
El

Aminen»
NAO ION 4550

EEE mein Am

Moment of lea:

cn) emo
Lan) som

120010) me Am

Le hoc) ete)
AG) at Am

TAI Determine the location.) othe chansels ces:
LAS as anses determine be producto ira ay
‘ht espect tthe 2 andy" ax

man 43009 «3300
LO NINO

mens

Een

a ey wi

sia: Dose oy ss

Pet Am

18, Dee e nome teas ot
Der

89. ATA Determine the produc of ner , ofthe cou

‘ional aren afte Zion Te org fordere
at the centroid €. “

pS
dun A
1, on naine a
Las su
AE Desa te lee (7 ls seri ci
‘Re corcel aca dear te mena
dell, sah td eps o ayer atte
{heir origin located atthe ceatoid €
A
PATTES
Em eo
pue am
Mont of tte:
ro msn"
Lot) umo
Le hate) our"
MORTE
Te Ducs be oan 7) afte are Cot
se ac der lemon pods of
o te andy un
aan aso?
atea ae!
Bassinet ot Seen
Luo Am el
ES TE [sens
Eu 2 =
oe am his
den RA

LAI ARANA

90. AcIT. Determine the prodict of ints fy of the cos

Sectional are with respect tothe à ad y ance
Proc of men los
1, = 05 (0,025+351051029,225 E
jure au

AIR. Compute ie moments ol nera La and J andthe
producto ours Lay ofthe ereccion ares Ue the
Eguatios of See Ad.

Moment of ea und Prue o nena bon an yes:

129 (2) Laien) «cone
HOTTE

¿opa ani) ma) at

De tty aly =D.

Moment of Inn nd Proc of le abot end" Aue
Kennen 00 pes

be en
on. to, so. Droit

LI) at Am

poh tna o

„ln mm, o
IE) ma Am

‘oe =

mr)
(6) eat a

91. Ari. Dewi te momen aad
caga we Toe las
Fiabe dees e ula ne

Moment of Ita nd Prod of Inn abot und y a à

ZO) ne

Late) une

ze
Dame une
om tt an Pratt ant e nt ht:
Potier
he nn
pole Etat ne
Lab mn
“4-22, Deemine he laos GP e rod Col .
ia csrsctoal re. et fd he rod of 5
Ir nn Ute equ al See Aa q 33
; et
Armen nen ey
nO «eos -
PAS per
ar 2e +] u es
PRE am ae
fer und Prd of fea en xan a an

oras ¿oc ns
¿Lomas to sé

mE da a nera o yA SERA I0

om clio

ao cg

92. ACM. Determine the location (27) of the centroid C of

‘tinea with respect be wand y se.

oo
PETT

Er

nn
o Am
mn Mm

Moment of Ie nd Proc of nera va aná y

o nos
ME) as

ms
Loa

CS

niet Moment of Inertia: AREA vs

93. ALL Deiermise te moments of nei and fy ad the
rod of neta La forte semicicodar aes

tnt of nea nd Prod ten en
ung [Eco Jasa) ma >

tony ey a y 20

et an Prac of nea ban dy As

tea ths the

eee

msi) ant nd
yeichhcheusnenmie

cl ne te

= 161(104) mnt saad

94. ALZA. Determine the pricpal moments of inertia andthe
catas of de pricipal ares of ie for the
‘pes ers seco are with respecto à st of papa
‘estat ave thi orga located atthe ceatoidC Use he
ion developed in See Ad.

Moment of tei and Proc of Ine ant nd yu

baja han ie) ro
Ea) stato!
ee) mt

AS
nl) wat

nam

Principat Moat of Inara: Ai BNE ee

)

pee

Lo}

per

uni) mt

PORC

remain of the Principal At of nera An Aol es

wann ee EL Ne
iy" ROBO
o wt 0

0 eg A 1, weave

A
génies
10) ane

mu use eue 4e

95. "AZ2A. Solve Prob. A-23 wing Mob ce

omen’ of Iara nd Proc of nea sont end y un:

ate o) venas"

O) se
2196960) mt

OCN

(9) at

ot Congracion Cra ec eth ue eb
fe thee (PI 16010) ee,

au 11019) cool)

es oi

= (ON) (1) me

mar) mn Am
nem) #853010) mt A

(remain of he Principal As of Inn rm bei,

100 eue (Countach) A

Lecaros

sb

Ca

u ma

96. Io of the propa ares of
Rie toi vii Located a the ceatrolé

Moat of nie nd Product of Inara hon and ya

O)!

4

ponte) Last) um

y SOCIA #17029 001-179)

Barons
amp pao fi: pet i et

His E

rm of te Principal Ane of tea: opio, A es

nos
mas

97. (AL Solve Prob. A-2 using Mohs ce

ra nd rode of Ia abo and y ant à

TE)

yola) «tom unse

ANA AA

inte Connie Core frac vd Cee
DE (EOS à ru a ee,

caso

a (SS eat

cipal Moment of nera e cs of is Bw D ra
Tea lg mc

LISIS An

nain of the Principal Ar of nera Po ie

De (Comme Am

ER