Analisis de Vigas

RELACION ENTRE CARGA DISTRIBUIDA
FUERZA CORTANTE Y MOMENTO FLEXIONANTE
෍??????
??????=&#3627409358;
??????−&#3627408536;&#3627408517;&#3627408537;−??????+&#3627408517;??????=&#3627409358;
&#3627408517;??????=−&#3627408536;.&#3627408517;&#3627408537;
න
??????&#3627408490;
??????&#3627408491;
&#3627408517;??????=−න
&#3627408537;&#3627408490;
&#3627408537;&#3627408491;
&#3627408536;&#3627408517;&#3627408537;
??????
&#3627408491;−??????
&#3627408490;=−න
&#3627408537;&#3627408516;
&#3627408537;&#3627408491;
&#3627408536;&#3627408517;&#3627408537;
Ing. Celso Sanga Quiroz

෍??????
&#3627408490;
´=&#3627409358;
−??????−??????&#3627408517;&#3627408537;+&#3627408536;&#3627408517;&#3627408537;
&#3627408517;&#3627408537;
&#3627409360;
+??????+&#3627408517;??????=&#3627409358;
&#3627408517;??????=??????.&#3627408517;&#3627408537;
න
??????&#3627408490;
??????&#3627408491;
&#3627408517;??????=න
??????&#3627408490;
??????&#3627408491;
??????.&#3627408517;&#3627408537;
??????
&#3627408491;−??????
&#3627408490;=න
&#3627408537;&#3627408490;
&#3627408537;&#3627408491;
??????.&#3627408517;&#3627408537;
Ing. Celso Sanga Quiroz

??????=න&#3627408529;&#3627408517;&#3627408537;
??????=&#3627408490;??????&#3627408531;&#3627408520;??????&#3627408533;&#3627408528;&#3627408533;??????&#3627408525;&#3627408528;&#3627408531;&#3627408518;&#3627408532;&#3627408534;&#3627408525;&#3627408533;??????&#3627408527;&#3627408533;&#3627408518;
ഥ&#3627408537;=
׬&#3627408537;.&#3627408529;.&#3627408517;&#3627408537;
??????
ഥ&#3627408537;=&#3627408516;&#3627408528;&#3627408528;&#3627408531;&#3627408517;&#3627408518;&#3627408527;??????&#3627408517;??????&#3627408517;&#3627408518;&#3627408525;&#3627408516;&#3627408518;&#3627408527;&#3627408533;&#3627408531;&#3627408528;&#3627408522;&#3627408517;&#3627408518;
Ing. Celso Sanga Quiroz

EJEMPLO DE APLICACIÓN 6.1
Calcular las reacciones en A.
Calculo de “k”: &#3627408538;=&#3627408524;.&#3627408537;
&#3627409360;
&#3627409360;=&#3627408524;&#3627409362;
&#3627409360;
→&#3627408524;=
&#3627409359;
&#3627409366;
Por teoría: ??????=׬
&#3627408537;=&#3627409358;
&#3627408525;
&#3627408536;.&#3627408517;&#3627408537;
??????=න
&#3627409358;
&#3627409362;
&#3627408537;
&#3627409360;
&#3627409366;
.&#3627408517;&#3627408537;
??????=&#3627409360;.&#3627409364;&#3627409365;??????.
Ing. Celso Sanga Quiroz

Por teoría: ??????.ഥ&#3627408537;=׬&#3627408537;&#3627408517;??????
&#3627409360;.&#3627409364;&#3627409365;ഥ&#3627408537;=න&#3627408537;.&#3627408517;??????
&#3627409360;.&#3627409364;&#3627409365;ഥ&#3627408537;=න
&#3627409358;
&#3627409362;
&#3627408537;
&#3627409360;
&#3627409366;
&#3627408517;&#3627408537;
ഥഥ&#3627408537;=&#3627409361;&#3627408526;
De la figura: σ??????
??????=&#3627409358;→??????
&#3627408488;=&#3627409360;.&#3627409364;&#3627409365;??????
σ??????
&#3627408488;=&#3627409358;→??????
&#3627408488;−&#3627409360;.&#3627409364;&#3627409365;&#3627409361;=&#3627409358;
??????
&#3627408488;=&#3627409366;??????.&#3627408526;
Ing. Celso Sanga Quiroz

EJEMPLO DE APLICACIÓN 6.2
Dibujar los diagramas de V y MDe la figura: &#3627408530;
&#3627408537;=??????.&#3627408537;
&#3627409360;
&#3627409364;=??????.&#3627409360;
&#3627409360;
→ &#3627408530;
&#3627408537;=
&#3627409361;
&#3627409360;
&#3627408537;
&#3627409360;
Por teoría: ??????=׬
&#3627408537;=&#3627409358;
&#3627408525;
&#3627408536;&#3627408517;&#3627408537;
??????=න
&#3627409358;
&#3627409360;
&#3627408530;
&#3627408537;&#3627408517;&#3627408537;
??????=׬
&#3627409358;
&#3627409360;&#3627409361;
&#3627409360;
&#3627408537;
&#3627409360;
&#3627408517;&#3627408537;→ ??????=&#3627409362;&#3627408524;&#3627408520;
Ing. Celso Sanga Quiroz

Por teoría: ??????.ഥ&#3627408537;=׬&#3627408537;.&#3627408517;??????
&#3627409362;ഥ&#3627408537;=׬&#3627408537;.&#3627408530;
&#3627408537;&#3627408517;&#3627408537;
&#3627409362;ഥ&#3627408537;=׬
&#3627409358;
&#3627409360;
&#3627408537;.
&#3627409361;
&#3627409360;
&#3627408537;
&#3627409360;
&#3627408517;&#3627408537;
ഥ&#3627408537;=
&#3627409361;
&#3627409360;
&#3627408526;
Ing. Celso Sanga Quiroz

Calculo de las reacciones:
෍??????
&#3627408488;=&#3627409358;
−??????
&#3627409361;
&#3627409360;
&#3627408526;+&#3627408489;&#3627409360;&#3627408526;=&#3627409358;
−&#3627409362;&#3627408524;&#3627408520;
&#3627409361;
&#3627409360;
&#3627408526;+&#3627408489;&#3627409360;=&#3627409358;
&#3627408489;=&#3627409361;&#3627408524;&#3627408520;
&#3627408488;=&#3627409359;&#3627408524;&#3627408520;
↑ ↑
&#3627408488; &#3627408489;
Ing. Celso Sanga Quiroz

න
??????&#3627408488;
??????
&#3627408517;??????=න
&#3627409358;
&#3627408537;
&#3627408530;
&#3627408537;&#3627408517;&#3627408537;
??????−??????
&#3627408488;=−න
&#3627409358;
&#3627408537;
&#3627409361;
&#3627409360;
&#3627408537;
&#3627409360;
&#3627408517;&#3627408537;
??????=??????
&#3627408488;−
&#3627408537;
&#3627409361;
&#3627409360;
??????=&#3627409359;−
&#3627408537;
&#3627409361;
&#3627409360;
Por teoría: ׬
??????&#3627409359;
??????&#3627409360;
&#3627408517;??????=׬
&#3627408537;&#3627409359;
&#3627408537;&#3627409360;
&#3627408536;&#3627408517;&#3627408537;
??????
Ing. Celso Sanga Quiroz

Por teoría:
න
&#3627409358;
??????
&#3627408517;??????=න
&#3627409358;
??????
(&#3627409359;−
&#3627408537;
&#3627409361;
&#3627409360;
).&#3627408517;&#3627408537;
??????=&#3627408537;−
&#3627408537;
&#3627409362;
&#3627409366;
Por teoría:
න
??????&#3627408490;
??????&#3627408491;
&#3627408517;??????=න
??????&#3627408490;
??????&#3627408491;
??????.&#3627408517;&#3627408537;
Ing. Celso Sanga Quiroz

??????=&#3627409359;−
&#3627408537;
&#3627409361;
&#3627409360;
&#3627408537;=&#3627409358;→??????=&#3627409359;
&#3627408537;=&#3627409360;→??????=−&#3627409361;
&#3627408537;=&#3627409359;.&#3627409360;&#3627409364;→??????=&#3627409358;
&#3627408537;=&#3627409358;.&#3627409364;&#3627409361;→??????=&#3627409358;.&#3627409366;&#3627409365;
??????=&#3627408537;−
&#3627408537;
&#3627409362;
&#3627409366;
&#3627408537;=&#3627409358;→??????=&#3627409358;
&#3627408537;=&#3627409360;→??????=&#3627409358;
&#3627408537;=&#3627409359;.&#3627409360;&#3627409364;→??????=&#3627409358;.&#3627409367;&#3627409362;
Ing. Celso Sanga Quiroz

EJEMPLO DE APLICACIÓN 6.3
Lavigaenvoladizosoportalacarga
repartida(fuerzaporunidadde
longitud)&#3627408529;=&#3627408529;
&#3627408528;&#3627408532;&#3627408518;&#3627408527;(Τ
??????.&#3627408537;
&#3627408525;
).
DeterminarlafuerzacortanteVyel
momentoflectorMcomofunciones
delcocienteΤ
&#3627408537;
&#3627408525;
.
Calculodelareacciónenellado
empotrado.
෍??????
&#3627408538;=&#3627409358;
??????
&#3627408528;−න
&#3627409358;
&#3627408525;
&#3627408529;&#3627408517;&#3627408537;=&#3627409358;
??????
&#3627409358;=න
&#3627409358;
&#3627408525;
&#3627408529;
&#3627409358;&#3627408532;&#3627408518;&#3627408527;
??????&#3627408537;
&#3627408525;
&#3627408517;&#3627408537;=
&#3627409360;&#3627408529;
&#3627409358;&#3627408525;
??????
??????
&#3627409358;=
&#3627409360;&#3627408529;
&#3627409358;&#3627408525;
??????
??????
&#3627409358;=??????&#3627408534;&#3627408518;&#3627408531;&#3627408539;??????&#3627408517;&#3627408518;&#3627408531;&#3627408518;??????&#3627408516;&#3627408516;&#3627408522;&#3627408528;&#3627408527;&#3627408518;&#3627408527;&#3627408518;&#3627408525;&#3627408525;??????&#3627408517;&#3627408528;
empotrado
Ing. Celso Sanga Quiroz

Calculodelmomentoenellado
empotrado.
෍??????=&#3627409358;
−??????
&#3627409358;−න
&#3627409358;
&#3627408525;
&#3627408537;.&#3627408529;&#3627408517;&#3627408537;=&#3627409358;
??????
&#3627409358;=−න
&#3627409358;
&#3627408525;
&#3627408529;
&#3627409358;.&#3627408537;.&#3627408532;&#3627408518;&#3627408527;
??????&#3627408537;
&#3627408525;
&#3627408517;&#3627408537;
??????
&#3627409358;=−
&#3627408529;
&#3627409358;
??????
.&#3627408525;
&#3627409360;
&#3627408488;&#3627408527;??????&#3627408525;&#3627408522;&#3627408532;??????&#3627408527;&#3627408517;&#3627408528;&#3627408525;??????&#3627408535;&#3627408522;&#3627408520;????????????&#3627408534;&#3627408527;??????&#3627408517;&#3627408522;&#3627408532;&#3627408533;??????&#3627408527;&#3627408516;&#3627408522;??????&#3627408537;
Ing. Celso Sanga Quiroz

&#3627408517;??????=−&#3627408529;.&#3627408517;&#3627408537;
න
??????&#3627408528;
??????
&#3627408517;??????=−න
&#3627409358;
&#3627408537;
&#3627408529;
&#3627409358;&#3627408532;&#3627408518;&#3627408527;
??????&#3627408537;
&#3627408525;
&#3627408517;&#3627408537;
??????−??????
&#3627409358;=
&#3627408529;
&#3627408528;
??????
&#3627408525;.&#3627408516;&#3627408528;&#3627408532;(
??????&#3627408537;
&#3627408525;
)
&#3627408528;
&#3627408537;
??????
&#3627408529;
&#3627408528;&#3627408525;
=
&#3627409359;
??????
.(&#3627409359;+&#3627408516;&#3627408528;&#3627408532;
??????&#3627408537;
&#3627408525;
)
&#3627408488;&#3627408527;??????&#3627408525;&#3627408522;&#3627408539;??????&#3627408527;&#3627408517;&#3627408528;&#3627408525;??????&#3627408535;&#3627408522;&#3627408520;????????????&#3627408534;&#3627408527;??????&#3627408517;&#3627408522;&#3627408532;&#3627408533;??????&#3627408527;&#3627408516;&#3627408522;??????&#3627408537;,&#3627408529;??????&#3627408531;??????
&#3627408521;??????&#3627408525;&#3627408525;??????&#3627408531;&#3627408525;??????&#3627408519;&#3627408534;&#3627408518;&#3627408531;&#3627408539;??????&#3627408516;&#3627408528;&#3627408531;&#3627408533;??????&#3627408527;&#3627408533;&#3627408518;&#3627408522;&#3627408527;&#3627408533;&#3627408518;&#3627408531;&#3627408527;??????&#3627408517;&#3627408518;&#3627408525;??????&#3627408535;&#3627408522;&#3627408520;??????
Ing. Celso Sanga Quiroz

&#3627408517;??????=??????.&#3627408517;&#3627408537;
න
??????&#3627408528;
??????
&#3627408517;??????=න
&#3627408528;
&#3627408537;
&#3627408525;.&#3627408529;
&#3627408528;
??????
&#3627409359;+&#3627408516;&#3627408528;&#3627408532;
??????&#3627408537;
&#3627408525;
&#3627408517;&#3627408537;
??????−??????
&#3627408528;=
&#3627408525;.&#3627408529;
&#3627408528;
??????
&#3627408537;+
&#3627408525;
??????
&#3627408532;&#3627408518;&#3627408527;
??????&#3627408537;
&#3627408525;
&#3627409358;
&#3627408537;
??????
&#3627408525;
&#3627409360;
.&#3627408529;
&#3627408528;
=
&#3627409359;
??????
(
&#3627408537;
&#3627408525;
−&#3627409359;+
&#3627409359;
??????
&#3627408532;&#3627408518;&#3627408527;
??????&#3627408537;
&#3627408525;
)
&#3627408488;&#3627408527;??????&#3627408525;&#3627408522;&#3627408539;??????&#3627408527;&#3627408517;&#3627408528;&#3627408525;??????&#3627408535;&#3627408522;&#3627408520;????????????&#3627408534;&#3627408527;??????&#3627408517;&#3627408522;&#3627408532;&#3627408533;??????&#3627408527;&#3627408516;&#3627408522;??????&#3627408537;,&#3627408529;??????&#3627408531;??????
&#3627408521;??????&#3627408525;&#3627408525;??????&#3627408531;&#3627408518;&#3627408525;&#3627408526;&#3627408528;&#3627408526;&#3627408518;&#3627408527;&#3627408533;&#3627408528;&#3627408519;&#3627408525;&#3627408518;&#3627408537;&#3627408522;&#3627408528;&#3627408527;??????&#3627408527;&#3627408533;&#3627408518;&#3627408522;&#3627408527;&#3627408533;&#3627408518;&#3627408531;&#3627408527;&#3627408528;&#3627408517;&#3627408518;&#3627408525;??????&#3627408535;&#3627408522;&#3627408520;??????
Ing. Celso Sanga Quiroz

??????
&#3627408529;
&#3627408528;&#3627408525;
=
&#3627409359;
??????
.(&#3627409359;+&#3627408516;&#3627408528;&#3627408532;
??????&#3627408537;
&#3627408525;
)
??????
&#3627408525;
&#3627409360;
.&#3627408529;
&#3627408528;
=
&#3627409359;
??????
(
&#3627408537;
&#3627408525;
−&#3627409359;+
&#3627409359;
??????
&#3627408532;&#3627408518;&#3627408527;
??????&#3627408537;
&#3627408525;
)
Ing. Celso Sanga Quiroz
&#3627408491;??????&#3627408490;
&#3627408491;????????????

Analisis de Vigas

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Analisis de Vigas

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