analisis elasto-plastico marco sometido a flexion pura

JULIO 2015 ANÁLISIS ELASTO-PLÁSTICO DE ESTRUCTURA TIPO MARCO

UNIVERSIDAD AUTÓNOMA DE QUERÉTARO Página 1

UNIVERSIDAD AUTÓNOMA DE QUERÉTARO

Facultad de Ingeniería – Posgrado de Ingeniería

Maestría en Ciencias L.T. en Construcción

2do semestre

Diseño y Construcción de Estructuras de Acero

“Análisis elasto-plástico de estructura tipo marco plano sometido

a flexión pura”

Catedrático: Dr. Guadalupe Moisés Arroyo Contreras

Alumno: Ing. Guillermo Enrique Meza Tapia



I. Introducción

Un análisis elástico de una estructura es importante para estudiar su

comportamiento, especialmente en lo que se refiere a su vida útil, bajo la carga de

servicio para la cual se diseñó la estructura. Sin embargo, si se aumenta la carga

hasta que la fluencia ocurra en algunos lugares, está sufre deformaciones

elastoplásticas, y con un aumento adicional se alcanza una condición

completamente plástica, en la cual se forma un número suficiente de

articulaciones plásticas para transformar la estructura en un mecanismo. Este

mecanismo se podría colapsar bajo cualquier carga adicional. Hace falta un

estudio del mecanismo de falla así como el conocimiento de la magnitud de la

carga de colapso para poder determinar el factor de la carga para el análisis.

Alternativamente, si se especifica el factor de carga, la estructura se puede

diseñar de modo que su carga de colapso sea igual, o superior, al producto del

factor de carga por la carga de servicio.

El diseño de estructuras basado en el enfoque plástico (conocido como diseño al

límite) se está usando con mayor frecuencia y ha sido aceptado por varios

reglamentos, sobre todo para el caso de construcción de acero. Se supone que el

material se deforma de manera idealizada mostrada en la figura 1. La deformación

unitaria y el esfuerzo son proporcionalmente entre si hasta alcanzar el esfuerzo de

fluencia en el cual la deformación unitaria aumenta indefinidamente sin ninguna

aumento de adicional de la carga. Este tipo de relación carga-deformación no está

muy lejano de la que existe en el acero suave. Sin embargo, hay una reserva de

resistencia debida al endurecimiento por deformación pero no se tomará en cuenta

en el análisis considerado en este trabajo.

A continuación se considerarán los principios del análisis plástico de marcos

planos en lo que se impide la inestabilidad por pandeo y no se considera posible la

falla por fatiga o falla frágil. En la mayoría de los casos, el cálculo de la carga de

colapso involucra en tanteos que puede resultar tediosos en estructuras grandes.

Ahora para abordar el análisis plástico de vigas continuas y pórticos se definen a

continuación algunas hipótesis:

1. La estructura se conserva estable hasta que se alcanza la carga última, o

sea no se presentan fenómenos de pandeos durante el proceso de la

carga.

2. Pueden despreciarse los efectos de las fuerzas axiales y cortantes sobre el

momento plástico Mp.

3. El proceso de carga es proporcional, de tal modo que en cada instante la

relación entre las cargas se mantiene constante.



4. Las uniones son perfectamente capaces de transmitir íntegramente el

momento plástico Mp; es decir las uniones proporcionan una continuidad

completa.

Nos interesa ahora generalizar los criterios de localización de articulaciones

plásticas y así, admitiremos que las articulaciones plásticas pueden formarse en:

a) Los empotramientos, nudos rígidos y las uniones no articuladas donde

concurran dos o más elementos.

b) Los apoyos intermedios de las vigas continuas.

c) Los puntos de aplicación de las cargas concentradas.

d) Bajo carga distribuidas, a partir de los puntos donde el momento

flexionante es máximo.

II. Descripción del problema

Este trabajo tiene como finalidad entender el análisis elasto-plástico de una

estructura tipo marco plano sometido a flexión pura, razonar el comportamiento de

la estructura, así como el mecanismo de falla debido a las cargas de diseño a la

cual está sometida de manera que se convierta en una mecanismo y determinar la

carga que produce el colapso por el método por incremento de carga

monotónicamente creciente, degradación de la estructura (push over) así como

verificarlo con el método energético.

III. Descripción del método

El método se puede describir a través de los siguientes puntos:

a) Topología (forma, distribución de los elementos, interconexión, condiciones

de frontera o de apoyo).

b) Propiedades geométricas (dimensiones de los elementos como alturas,

longitud, área, momentos de inercia entre otros).

c) Propiedades mecánicas (el modulo de elasticidad, tipo de acero,

resistencias etc.).

d) Acciones (accidentales como sismo, viento, oleaje, trafico empujes o

fuerzas nodales, distribuidas etc.).

e) Leyes de comportamiento (elasto-plástico ideal o perfecto).



Topología de la estructura

Numeración de los elementos



Estructura sometida a las cargas de diseño



1er análisis elástico

Carga de diseño:

P= 1500 kg

2P= 3000 kg

4P= 6000 kg

Rango de validez: 0 kg < P < 1500 kg

Desplazamiento inicial: 3.979 cm

En este análisis se observa que el nodo i, de la barra 11 será la primera

articulación plástica que se presentara en la estructura.

Primer incremento de carga λ= 2.9285

Primer incremento de carga λP = 2.9285*1500 = 4392.75 kg

Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 7221.177 3.9085

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 2940.834 9.5974

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 8072.931 3.4962

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 4953.453 5.6979

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 7954.051 3.5484

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 4873.969 5.7908

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 8107.719 3.4812

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 5375.870 5.2502

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 4376.050 6.4497

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 4660.022 6.0567

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 7424.677 3.8014

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 7603.671 3.7119

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 6540.818 4.3151

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 5394.764 5.2318

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 2160.639 13.0629

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 3797.560 7.4322

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 4792.884 5.8888

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 6311.333 4.4720

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 1738.762 16.2324

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 3698.825 7.6306

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -7316.885 2.9285

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -6544.658 3.2740

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -5833.473 3.6732

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -5807.266 3.6898

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -5607.521 3.8212

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -5375.870 3.9858

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -6820.661 3.1415

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -6118.266 3.5022

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -6278.288 3.4129

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -7133.526 3.0038

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -3797.560 5.6424

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -3173.976 6.7510

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -3137.357 6.8298

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -3698.825 5.7930

Sx (cm3) Zx (cm3) Fy (kg/cm2) Es (kg/cm2) λ

1ER ANALISIS LINEAL, DETERMINACIÓN DE LA PRIMERA ROTULA PROXIMA A PLASTIFICARSE

Elemento Nodo Sección Longitud (cm) Área (cm2) Inercia (cm4) rx (cm)

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10

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2do análisis con incremento de carga (análisis elástico)

Carga de diseño:

P= 4392.75 kg

2P= 8785.50 kg

4P= 17570 kg

Rango de validez: 1500 kg < P < 4392.75 kg

Desplazamiento: 11.653 cm

En este análisis se observa que el nodo i, de la barra 11 ya se formó la articulación

plástica. Y que la siguiente articulación plástica será en el nodo j, de la barra 15.

Segundo incremento de carga λ=2.9990

Incremento de carga λP= 2.9990*1500= 4485.00 kg

Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 21147.216 1.3347

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 8612.233 3.2772

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 23641.546 1.1938

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 14506.187 1.9457

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 23293.439 1.2117

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 14273.419 1.9774

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 23473.453 1.2024

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 15743.234 1.7928

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 12815.264 2.2024

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 13646.873 2.0682

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 21743.167 1.2981

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 22267.350 1.2675

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 19154.785 1.4735

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 15798.567 1.7865

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 6327.431 4.4606

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 11121.155 2.5379

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 14035.959 2.0109

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 18482.738 1.5271

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 5091.965 5.5429

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 10832.010 2.6056

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -19166.030 1.1180

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -17083.326 1.2543

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -17006.579 1.2599

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -16421.626 1.3048

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -15743.234 1.3611

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -19974.304 1.0727

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -17917.342 1.1959

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -18385.968 1.1654

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -20890.532 1.0257

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -11121.155 1.9267

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -9294.988 2.3053

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -9187.750 2.3322

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -10832.010 1.9782

Fy (kg/cm2) Es (kg/cm2) λ

2DO ANALISIS ELASTICO LINEAL DEL SISTEMA ESTRUCTURAL INCREMENTADO POR EL 1ER INCREMENTO DE CARGA MULTIPLICANDO λP

Elemento Nodo Sección Longitud (cm) Área (cm2) Inercia (cm4) rx (cm)

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Sx (cm3) Zx (cm3)

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3er análisis elástico (estructura equivalente)

Carga de diseño:

P= 4392.75 kg

2P= 8785.50 kg

4P= 17570 kg

Rango de validez: 1500 kg < P < 4392.75 kg

En este análisis se libera el nodo i de la barra 11 donde se formó la articulación

plástica y se haciendo la estructura equivalente se comprueba que la estructura

sigue teniendo los momentos momentos flexionantes demandados en el 2do

análisis.

Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -21147.216 1.3347

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 8612.233 3.2772

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -23641.546 1.1938

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 14506.187 1.9457

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -23293.439 1.2117

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 14273.419 1.9774

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -23473.453 1.2024

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 15743.234 1.7928

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -12815.264 2.2024

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 13646.873 2.0682

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -21743.167 1.2981

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 22267.350 1.2675

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -19154.785 1.4735

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 15798.567 1.7865

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -6327.431 4.4606

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 11121.155 2.5379

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -14035.959 2.0109

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 18482.738 1.5271

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -5091.965 5.5429

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 10832.010 2.6056

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -8819.794 2.4295

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 17083.326 1.2543

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -17006.579 1.2599

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 16421.626 1.3048

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -15743.234 1.3611

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 19974.304 1.0727

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -17917.342 1.1959

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 18385.968 1.1654

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -20890.532 1.0257

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 11121.155 1.9267

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -9294.988 2.3053

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 9187.750 2.3322

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -10832.010 1.9782

V

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a

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11

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3ER ANALISIS ELASTICO DE VERIFICACIÓN, 1ER INCREMENTO DE CARGA MULTIPLICANDO λP

Elemento Nodo Sección Longitud (cm) Área (cm2) Inercia (cm4) rx (cm) Sx (cm3) Zx (cm3) Fy (kg/cm2) Es (kg/cm2) λ

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4to análisis elasto-plástico (2do incremento de carga)

Cargas sometidas a la estructura:

P= 4485.00 kg

2P= 8970 kg

4P=17940 kg

Rango de validez: 4392.75 Kg < P < 4485.00 kg

Deformación= 11.954 cm

En este análisis se observa que el nodo j, de la barra 15 ya se formó una

articulación plástica. Y el nodo i, de la barra 14 es la siguiente articulación plástica.

Tercer incremento de carga λ= 3.1155

Tercer incremento de carga λP= 3.1155*1500= 4673.25 kg

Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -21572.531 1.3083

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 8542.088 3.3041

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -24295.959 1.1617

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 14950.302 1.8879

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -23908.535 1.1805

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 14645.795 1.9271

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -24373.494 1.1580

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 16161.811 1.7464

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -12885.314 2.1904

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 13943.763 2.0241

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -22370.843 1.2617

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 22877.981 1.2337

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -19657.000 1.4358

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 16228.694 1.7392

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -6507.728 4.3370

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 11937.137 2.3644

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -14353.078 1.9664

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 18928.078 1.4911

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -5198.355 5.4295

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 11092.681 2.5444

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -9120.668 2.3493

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 17497.377 1.2246

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -17442.218 1.2285

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 16860.991 1.2708

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -16161.811 1.3258

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 20451.492 1.0477

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -18367.050 1.1666

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 18864.009 1.1359

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 11397.137 1.8801

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -9521.550 2.2504

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 9406.979 2.2778

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -11092.681 1.9317

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4TO ANALISIS ELASTO-PLÁSTICO, 2DO INCREMENTO DE CARGA MULTIPLICANDO λP

Fy (kg/cm2) Es (kg/cm2) λElemento Nodo



5to análisis elasto-plástico (estructura equivalente)


P= 4485.00 kg

2P= 8970 kg

4P=17940 kg


En este análisis se libera el nodo j de la barra 15 donde se formó la articulación

plástica y haciendo la estructura equivalente se comprueba que la estructura

sigue teniendo los momentos momentos flexionantes demandados en el 4to

análisis.

Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -21572.531 1.3083

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 8542.088 3.3041

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -24295.959 1.1617

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 14950.302 1.8879

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -23908.535 1.1805

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 14645.795 1.9271

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -24373.494 1.1580

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 16161.811 1.7464

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -12885.314 2.1904

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 13943.763 2.0241

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -22370.843 1.2617

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 22877.981 1.2337

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -19657.000 1.4358

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 16228.694 1.7392

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -6507.728 4.3370

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 11937.137 2.3644

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -14353.078 1.9664

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 18928.078 1.4911

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -5198.355 5.4295

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 11092.681 2.5444

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -9120.668 2.3493

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 17497.377 1.2246

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -17442.218 1.2285

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 16860.991 1.2708

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -16161.811 1.3258

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 20451.492 1.0477

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -18367.050 1.1666

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 8508.133 2.5185

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 11397.137 1.8801

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -9521.550 2.2504

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 9406.979 2.2778

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -11092.681 1.9317

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5TO ANALISIS DE VERIFICACIÓN, 2DO INCREMENTO DE CARGA MULTIPLICANDO λP


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6to análisis elasto-plástico (3er incremento de carga)


P= 4673.25 kg

2P= 9346.50 kg

4P=18693.00 kg


Desplazamiento= 12.546 cm

En este análisis se observa que el nodo i de la barra 14 ya se formó una

articulación plástica dado λ=1.00 es decir alcanzó la fluencia. Y la próxima

articulación plástica en presentarse será el nodo i de la barra 4.

4to incremento de carga λ= 3.3822

4to incremento de carga λP= 3.3822*1500= 5073.30 kg

Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -22304.184 1.2654

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 8323.179 3.3910

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -25334.283 1.1141

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 15429.099 1.8293

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -25043.529 1.1270

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 15373.593 1.8359

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -25504.270 1.1066

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 16905.126 1.6696

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -13104.223 2.1538

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 14556.625 1.9389

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -23399.347 1.2062

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 24013.814 1.1753

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -20544.002 1.3738

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 16539.997 1.7064

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -6871.110 4.1077

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 11966.394 2.3586

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -15019.315 1.8792

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 19228.886 1.4678

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -4887.404 5.7749

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 11525.653 2.4488

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -9668.696 2.2162

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 18456.649 1.1610

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -18300.158 1.1709

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 17617.437 1.2163

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -16905.126 1.2675

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -19273.735 1.1117

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 9056.190 2.3661

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 11966.394 1.7906

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -10002.560 2.1422

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 9826.325 2.1806

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -11525.653 1.8591

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6TO ANALISIS ELASTO-PLASTICO , 3ER INCREMENTO DE CARGA MULTIPLICANDO λP




7mo análisis elasto-plástico (estructura equivalente)


P= 4673.25 kg

2P= 9346.50 kg

4P=18693.00 kg





análisis.

Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -22304.184 1.2654

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 8323.179 3.3910

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -25334.283 1.1141

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 15429.099 1.8293

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -25043.529 1.1270

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 15373.593 1.8359

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -25504.270 1.1066

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 16905.126 1.6696

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -13104.223 2.1538

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 14556.625 1.9389

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -23399.347 1.2062

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 24013.814 1.1753

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -20544.002 1.3738

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 16539.997 1.7064

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -6871.110 4.1077

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 11966.394 2.3586

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -15019.315 1.8792

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 19228.886 1.4678

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -4887.404 5.7749

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 11525.653 2.4488

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -9668.696 2.2162

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 18456.649 1.1610

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -18300.158 1.1709

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 17617.437 1.2163

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -16905.126 1.2675

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -8890.745 2.4101

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 9056.190 2.3661

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 11966.394 1.7906

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -10002.560 2.1422

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 9826.325 2.1806

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -11525.653 1.8591

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8vo análisis elasto-plástico (4to incremento de carga)


P= 5073.30 kg

2P= 10146.6 kg

4P=20923.20 kg




articulación plástica dado que λ=1.00 es decir el momento flexionante alcanzó la

resistencia (fluencia). Y la próxima articulación plástica se presentará en el nodo i

de la barra 2.



Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -24007.441 1.1756

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 7730.070 3.6512

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -27734.874 1.0176

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 16404.672 1.7205

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -27672.172 1.0200

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 16925.806 1.6675

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 18719.389 1.5078

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -13697.333 2.0606

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 14812.285 1.9055

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -26286.593 1.0737

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 26530.661 1.0638

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -23151.434 1.2191

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 17280.902 1.6333

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -6615.116 4.2666

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 13464.103 2.0963

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -16493.014 1.7113

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 22457.068 1.2568

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -4146.499 6.8068

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 12923.709 2.1839

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -11067.642 1.9360

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 20920.520 1.0242

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -20532.141 1.0436

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 19545.100 1.0963

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -18719.389 1.1447

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -10782.260 1.9873

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 10814.012 1.9814

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 13464.103 1.5914

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -11341.159 1.8893

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 11115.908 1.9276

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -12923.709 1.6580

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8VO ANALISIS , 4TO INCREMENTO DE CARGA MULTIPLICANDO λP




9no análisis elasto-plástico (estructura equivalente)


P= 5073.30 kg

2P= 10146.6 kg

4P=20923.20 kg





análisis.

Resistencia Demanda

Mpx Skx

Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -24007.441 1.1756

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 7730.070 3.6512

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 16602.051 1.7000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -27672.172 1.0200

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 16925.806 1.6675

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 5114.161 5.5188

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -13697.333 2.0606

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 14812.285 1.9055

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -26286.593 1.0737

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 26530.661 1.0638

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -23151.434 1.2191

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 17280.902 1.6333

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -6615.116 4.2666

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 13464.103 2.0963

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -16493.014 1.7113

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 22457.068 1.2568

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -4146.499 6.8068

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 12923.709 2.1839

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -11067.642 1.9360

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 20920.520 1.0242

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -20532.141 1.0436

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 19545.100 1.0963

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -18719.389 1.1447

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -10782.260 1.9873

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 10814.012 1.9814

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 13464.103 1.5914

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -11341.159 1.8893

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 11115.908 1.9276

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -12923.709 1.6580

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Area (cm2) Inercia (cm4) rx (cm) Sx (cm3) Zx (cm3) Fy (kg/cm2) Es (kg/cm2) λ

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Nodo Sección Longitud (cm)

9NO ANALISIS EQUIVALENTE , 4TO INCREMENTO DE CARGA MULTIPLICANDO λP




10mo análisis elasto-plástico (5to incremento de carga)


P= 5154.90 kg

2P= 10309.80 kg

4P=20619.69 kg




articulación plástica dado que λ=1.00 es decir el momento flexionante alcanzó

la resistencia (fluencia). Tambien se observa que el nodo i de la barra 3 se

formó una articulación plástica simultaneo con el nodo i de la barra 2. Y la

próxima articulación plástica se presentará en el nodo i de la barra 6.

6to incremento de carga λ=3.5432


Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -24355.661 1.1588

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 7610.362 3.7087

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 16602.051 1.7000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 17314.860 1.6301

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 5427.293 5.2004

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -13817.040 2.0427

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 14857.595 1.8997

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -26857.398 1.0509

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 27006.111 1.0451

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -23741.388 1.1888

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 17438.078 1.6185

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -6559.807 4.3026

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 13776.297 2.0488

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -16776.781 1.6823

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 22997.781 1.2273

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -3989.323 7.0749

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 13213.416 2.1360

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -11354.208 1.8872

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21402.137 1.0012

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -20940.298 1.0233

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 20115.172 1.0652

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -19539.392 1.0966

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -11161.942 1.9197

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 11193.593 1.9143

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 13776.297 1.5554

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -11616.986 1.8445

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 11380.899 1.8828

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -13213.416 1.6216

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10MO ANALISIS ELASTO-PLÁSTICO, 5TO INCREMENTO DE CARGA MULTIPLICANDO λP





P= 5154.90 kg

2P= 10309.80 kg

4P=20619.69 kg


En este análisis se libera el nodo i de la barra 2 y 3 donde se formó la articulación


sigue teniendo los momentos momentos flexionantes demandados en el 10mo

análisis. Así también con este 5to incremento se formó una rotula plástica en el

nodo i de la barra 12.

Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -24355.661 1.1588

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 7610.362 3.7087

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 3002.411 9.4005

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 3860.195 7.3116

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 5270.019 5.3556

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -13817.040 2.0427

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 14857.595 1.8997

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -26857.398 1.0509

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 27006.111 1.0451

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -23741.388 1.1888

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 17438.078 1.6185

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -6559.807 4.3026

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 13776.297 2.0488

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -16776.781 1.6823

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 22997.781 1.2273

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -3989.323 7.0749

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 13213.416 2.1360

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -11354.208 1.8872

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -10792.013 1.9855

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -19539.392 1.0966

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -11161.942 1.9197

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 11193.593 1.9143

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 13776.297 1.5554

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -11616.986 1.8445

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 11380.899 1.8828

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -13213.416 1.6216

11VO ANALISIS ELASTO-PLÁSTICO (ESTRUCTURA EQUIVALENTE), 5TO INCREMENTO DE CARGA MULTIPLICANDO λP


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12do análisis elasto-plástico (6to incremento de carga)


P= 5314.80 kg

2P= 10629.60 kg

4P= 21259.20 kg





resistencia (fluencia). Y también se observa que simultáneamente con el 6to

incremento de carga se forma una articulación plástica en el nodo i de la barra 13.

La próxima articulación plástica en presentarse será en el nodo i de la barra 1.

7mo incremento de carga λ= 3.62

7mo incremento de carga λP= 3.62*1500= 5430.00 kg

Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -26090.042 1.0818

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 7656.604 3.6863

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 3295.186 8.5653

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 4814.675 5.8621

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 6522.992 4.3269

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -13770.779 2.0496

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 15124.626 1.8661

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -27531.606 1.0252

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -24921.741 1.1325

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 17981.405 1.5696

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -6302.777 4.4781

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 14475.886 1.9497

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -17393.806 1.6227

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 24242.415 1.1643

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -3445.998 8.1904

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 13861.129 2.0362

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -12808.389 1.6729

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -11603.958 1.8466

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -20635.092 1.0384

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -12078.884 1.7740

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 12112.552 1.7690

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 14475.886 1.4802

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -12250.555 1.7491

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 11991.859 1.7868

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -12861.129 1.6661

12VO ANALISIS ELASTO-PLÁSTICO, 6TO INCREMENTO DE CARGA MULTIPLICANDO λP

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Elemento Nodo Sección Longitud (cm) Área (cm2) Inercia (cm4) rx (cm) Sx (cm3) Zx (cm3)



13ro análisis elasto-plástico (estructura equivalente) Cargas sometidas a la estructura:

P= 5314.80 kg

2P= 10629.60 kg

4P= 21259.20 kg


En este análisis se libera el nodo j de la barra 6 y el nodo i de la barra 13 donde

se formó la articulación plástica y haciendo la estructura equivalente se

comprueba que la estructura sigue teniendo los momentos momentos flexionantes

demandados en el 12do análisis.

Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -26090.042 1.0818

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 7656.604 3.6863

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 3295.186 8.5653

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 4814.675 5.8621

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 6522.992 4.3269

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -13770.779 2.0496

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 15124.626 1.8661

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -14027.285 2.0121

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -24921.741 1.1325

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 17981.405 1.5696

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -6302.777 4.4781

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 14475.886 1.9497

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -17393.806 1.6227

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 24242.415 1.1643

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -3445.998 8.1904

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 13861.129 2.0362

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -12808.389 1.6729

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -11603.958 1.8466

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -10142.378 2.1127

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -12078.884 1.7740

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 12112.552 1.7690

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 14475.886 1.4802

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -12250.555 1.7491

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 11991.859 1.7868

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -12861.129 1.6661

13VO ANALISIS ELASTO-PLÁSTOCO DE VERIFICACIÓN, 6TO INCREMENTO DE CARGA MULTIPLICANDO λP

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14to análisis elasto-plástico (7mo incremento de carga)


P= 5430.00 kg

2P= 10860.00 kg

4P= 21720.00 kg





resistencia (fluencia). La próxima articulación plástica en presentarse será en el


8vo incremento de carga λ=3.8548

8vo incremento de carga λP= 5782.20 kg

Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 7971.687 3.5406

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 3286.954 8.5868

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 5130.631 5.5011

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 7567.476 3.7297

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -13445.714 2.0991

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 15514.787 1.8192

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -14785.348 1.9089

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -25633.379 1.1011

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 18594.481 1.5179

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -5912.615 4.7736

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 14953.615 1.8875

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -18229.252 1.5483

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 25224.519 1.1189

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -2832.921 9.9630

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 14297.089 1.9741

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -14166.101 1.5126

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -12745.609 1.6812

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -10976.475 1.9521

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -12495.599 1.7148

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 12530.555 1.7100

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 14953.615 1.4329

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -12750.896 1.6805

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 12473.625 1.7178

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -14297.089 1.4987

14VO ANALISIS ELASTO-PLASTICO, 7MO INCREMENTO DE CARGA MULTIPLICANDO λP

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P= 5430.00 kg

2P= 10860.00 kg

4P= 21720.00 kg





análisis.

Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -5697.336 4.9539

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 3286.954 8.5868

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 5130.631 5.5011

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 7567.476 3.7297

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -13445.714 2.0991

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 15514.787 1.8192

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -14785.348 1.9089

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -25633.379 1.1011

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 18594.481 1.5179

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -5912.615 4.7736

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 14953.615 1.8875

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -18229.252 1.5483

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 25224.519 1.1189

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -2832.921 9.9630

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 14297.089 1.9741

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -14166.101 1.5126

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -12745.609 1.6812

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -10976.475 1.9521

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -12495.599 1.7148

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 12530.555 1.7100

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 14953.615 1.4329

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -12750.896 1.6805

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 12473.625 1.7178

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -14297.089 1.4987

15VO ANALISIS ELASTO-PLASTICO DE VERFICACIÓN, 7MO INCREMENTO DE CARGA MULTIPLICANDO λP

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16to análisis elasto-plástico (8vo incremento de carga)


P= 5782.20 kg

2P= 11564.40 kg

4P= 23128.80 kg



En este análisis se observa que el nodo j de la barra 9 ya se formó una



nodo j de la barra 11.

9no incremento de carga λ= 3.9359

9no incremento de carga λP= 3.9359*1500= 5903.85 kg

Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -5189.002 5.4392

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 6654.720 4.2412

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 8013.364 3.5221

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 11988.323 2.3543

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -12504.303 2.2572

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 17626.124 1.6013

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -16564.983 1.7039

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 21516.854 1.3117

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -3801.277 7.4249

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 16695.080 1.6906

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -21454.800 1.3155

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -89.453 315.5205

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 15885.841 1.7767

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -19313.502 1.1095

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -18219.209 1.1761

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -15397.323 1.3916

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -14106.799 1.5189

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 14144.903 1.5148

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 16695.080 1.2835

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -14666.102 1.4610

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 14319.365 1.4964

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -15885.841 1.3488

16VO ANALISIS ELASTO-PLÁSTICO , 8VO INCREMENTO DE CARGA MULTIPLICANDO λP

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P= 5782.20 kg

2P= 11564.40 kg

4P= 23128.80 kg





análisis.

Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -5189.002 5.4392

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 6654.720 4.2412

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 8013.364 3.5221

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 11988.323 2.3543

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -12504.303 2.2572

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 17626.124 1.6013

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -16564.983 1.7039

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 21516.854 1.3117

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -3801.277 7.4249

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 16695.080 1.6906

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -21454.800 1.3155

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -89.453 315.5205

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 15885.841 1.7767

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -19313.502 1.1095

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -18219.209 1.1761

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -15397.323 1.3916

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -14106.799 1.5189

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 14144.903 1.5148

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 16695.080 1.2835

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -14666.102 1.4610

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 14319.365 1.4964

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -15885.841 1.3488

17VO ANALISIS DE VERIFICACIÓN, 8VO INCREMENTO DE CARGA MULTIPLICANDO λP

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18vo análisis elasto-plástico (9no incremento de carga)


P= 5903.85 kg

2P= 11807.70 kg

4P= 23615.40 kg


Deformación= 23.509 cm En este análisis se observa que el nodo j de la barra 11 ya se formó una




10mo incremento de carga λ= 3.9910

10mo incremento de carga λP= 3.9910*1500= 5986.50 kg

Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -5395.366 5.2312

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 7601.669 3.7129

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 9652.240 2.9241

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 13623.313 2.0718

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -12710.667 2.2205

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 18096.176 1.5597

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -17732.335 1.5917

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 8480.629 3.3281

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -3331.226 8.4726

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 17708.513 1.5938

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -9569.223 2.9495

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 1165.328 24.2200

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 16777.825 1.6822

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -19858.139 1.0790

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -17032.312 1.2580

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -15218.700 1.4080

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 15259.523 1.4042

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 17708.513 1.2100

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -14313.036 1.4971

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 13911.266 1.5403

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -16777.825 1.2771

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18VO ANALISIS ELASTO-PLÁSTICO, 9NO INCREMENTO DE CARGA MULTIPLICANDO λP





P= 5903.85 kg

2P= 11807.70 kg

4P= 23615.40 kg





análisis.

Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -5395.366 5.2312

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 7601.669 3.7129

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 9652.240 2.9241

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 13623.313 2.0718

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -12710.667 2.2205

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 18096.176 1.5597

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -17732.335 1.5917

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 8480.629 3.3281

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -3331.226 8.4726

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 17708.513 1.5938

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -9569.223 2.9495

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 1165.328 24.2200

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 16777.825 1.6822

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -19858.139 1.0790

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -17032.312 1.2580

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -15218.700 1.4080

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 15259.523 1.4042

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 17708.513 1.2100

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -14313.036 1.4971

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 13911.266 1.5403

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -16777.825 1.2771

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19NO ANALISIS ELASTO-PLÁSTICO DE VERIFICACIÓN, 9NO INCREMENTO DE CARGA MULTIPLICANDO λP


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20mo análisis elasto-plástico (10 incremento de carga)


P= 5986.50 kg

2P= 11973.00 kg

4P= 23946.00 kg


Deformación= 25.498 cm En este análisis se observa que el nodo j de la barra 12 ya se formó una




11ro incremento de carga λ= 4.0547

11ro incremento de carga λP= 4.0547*1500= 6082.05 kg

Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -5680.109 4.9690

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 7484.103 3.7712

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 11220.858 2.5153

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 15184.451 1.8588

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -12995.410 2.1719

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 18911.679 1.4924

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -17849.499 1.5812

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 9246.818 3.0523

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -2515.723 11.2191

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 18460.385 1.5289

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -10861.051 2.5987

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 1931.516 14.6125

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 17555.567 1.6077

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -18593.451 1.1524

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -15855.162 1.3514

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 15914.891 1.3464

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 18460.385 1.1607

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -14297.451 1.4987

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 13926.850 1.5386

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -17555.567 1.2205

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20MO ANALISIS ELASTO-PLÁSTICO, 10MO INCREMENTO DE CARGA MULTIPLICANDO λP

Es (kg/cm2) λ

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21ro análisis elasto-plástico (estructura equivalente)


P= 5986.50 kg

2P= 11973.00 kg

4P= 23946.00 kg





análisis

Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -5701.282 4.9505

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 7460.569 3.7831

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 11221.563 2.5152

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 15184.355 1.8588

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -13016.583 2.1683

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 18905.547 1.4929

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -17873.033 1.5792

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 9237.045 3.0556

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -2521.855 11.1919

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 18486.083 1.5268

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -10895.481 2.5905

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 1921.744 14.6868

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 17581.233 1.6054

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -18593.356 1.1524

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -15872.377 1.3500

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 15932.104 1.3449

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 18486.083 1.1591

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -14297.462 1.4987

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 13926.841 1.5386

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -17581.233 1.2188

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21RO ANALISIS ELASTO-PLÁSTICO DE VERIFICACIÓN, 10MO INCREMENTO DE CARGA MULTIPLICANDO λP


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22do análisis elasto-plástico (11 incremento de carga)


P= 6082.05 kg

2P= 12164.10 kg

4P= 24328.20 kg







12do incremento de carga λ=4.1187

12do incremento de carga λP= 4.1187*1500= 6178.05 kg

Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -5658.229 4.9882

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 7780.602 3.6275

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 11221.502 2.5152

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 18018.575 1.5664

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -12973.531 2.1755

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 20198.537 1.3973

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -17553.001 1.6079

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 10571.533 2.6698

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -1228.864 22.9678

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 19590.265 1.4407

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -12738.609 2.2156

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 3256.232 8.6678

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 18592.950 1.5180

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -16834.985 1.2728

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 16812.624 1.2745

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 19590.265 1.0938

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -14360.405 1.4921

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 13863.897 1.5456

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -18592.950 1.1524

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22DO ANALISIS ELASTO-PLASTICO, 11MO INCREMENTO DE CARGA MULTIPLICANDO λP


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P= 6082.05 kg

2P= 12164.10 kg

4P= 24328.20 kg




sigue teniendo los momentos momentos flexionantes demandados en el 22Do

análisis.

Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -5658.229 4.9882

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 7780.602 3.6275

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 11221.502 2.5152

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 18018.575 1.5664

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -12973.531 2.1755

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 20198.537 1.3973

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -17553.001 1.6079

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 10571.533 2.6698

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -1228.864 22.9678

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 19590.265 1.4407

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -12738.609 2.2156

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 3256.232 8.6678

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 18592.950 1.5180

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -16834.985 1.2728

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 16812.624 1.2745

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 19590.265 1.0938

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -14360.405 1.4921

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 13863.897 1.5456

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -18592.950 1.1524

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23RO ANALISIS ELASTO-PLÁSTICO DE VERIFICACIÓN, 11MO INCREMENTO DE CARGA MULTIPLICANDO λP


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24to análisis elasto-plástico (12do incremento de carga)


P= 6178.05 kg

2P= 12356.10 kg

4P= 24712.20 kg







13ro incremento de carga λ= 4.1446

13ro incremento de carga λP= 4.1446*1500= 6216.90 kg

Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -4364.591 6.4666

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 9655.128 2.9232

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 11221.502 2.5152

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 18018.402 1.5664

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -11679.893 2.4165

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 22795.400 1.2382

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -15678.474 1.8002

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 13446.831 2.0990

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 1367.998 20.6318

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 21427.181 1.3172

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -16022.201 1.7616

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 6131.529 4.6031

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 20384.595 1.3846

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -18473.129 1.1599

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 18458.072 1.1609

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -14367.522 1.4914

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 13856.779 1.5463

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -20384.595 1.0512

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P= 6178.05 kg

2P= 12356.10 kg

4P= 24712.20 kg





análisis.

Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -4364.591 6.4666

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 9655.128 2.9232

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 11221.502 2.5152

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 18018.402 1.5664

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -11679.893 2.4165

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 22795.400 1.2382

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -15678.474 1.8002

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 13446.831 2.0990

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 1367.998 20.6318

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 21427.181 1.3172

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -16022.201 1.7616

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 6131.529 4.6031

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 20384.595 1.3846

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -18473.129 1.1599

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 18458.072 1.1609

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -3898.394 5.4965

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 13856.779 1.5463

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -20384.595 1.0512

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Fy (kg/cm2)

25TO ANALISIS ELASTO-PLÁSTICO DE VERIFICACIÓN, 12VO INCREMENTO DE CARGA MULTIPLICANDO λP

Es (kg/cm2) λ

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26to análisis elasto-plástico (13ro incremento de carga)


P= 6216.90 kg

2P= 12433.80 kg

4P= 24867.60 kg









Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -3851.334 7.3284

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 10423.934 2.7076

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 11221.502 2.5152

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 18018.402 1.5664

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -11166.635 2.5276

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 23958.951 1.1780

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -14909.668 1.8930

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 14497.753 1.9468

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 2531.548 11.1490

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 21427.402 1.3172

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -17775.218 1.5878

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 7182.451 3.9296

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 21428.589 1.3171

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -19351.763 1.1073

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 19332.454 1.1084

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -3644.055 5.8801

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 13877.145 1.5441

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

26TO ANALISIS ELASTO-PLÁSTICO, 13VO INCREMENTO DE CARGA MULTIPLICANDO λP


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P= 6216.90 kg

2P= 12433.80 kg

4P= 24867.60 kg





análisis.

Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -3851.334 7.3284

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 10423.934 2.7076

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 11221.502 2.5152

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 18018.402 1.5664

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -11166.635 2.5276

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 23958.951 1.1780

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -14909.668 1.8930

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 14497.753 1.9468

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 2531.548 11.1490

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 21427.402 1.3172

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -17775.218 1.5878

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 7182.451 3.9296

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 21428.589 1.3171

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -19351.763 1.1073

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 19332.454 1.1084

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -3644.055 5.8801

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 3387.910 6.3247

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000


27TO ANALISIS ELASTO-PLÁSTICO DE VERIFICACIÓN, 13VO INCREMENTO DE CARGA MULTIPLICANDO λP

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Elemento Nodo



28vo análisis elasto-plástico (14to incremento de carga)


P= 6274.50 kg

2P= 12549.00 kg

4P= 25098.00 kg







15to incremento de carga λ=4.1832

15to incremento de carga λP= 4.1832* 6274.80 kg

Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -3073.176 9.1841

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 11546.579 2.4444

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 11221.502 2.5152

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 18018.402 1.5664

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -10338.477 2.7300

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 25519.548 1.1060

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -13787.023 2.0472

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 16220.360 1.7401

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 4092.147 6.8972

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 21427.402 1.3172

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -21923.612 1.2874

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 8905.059 3.1695

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 21427.402 1.3172

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21405.744 1.0010

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -3408.990 6.2856

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 3387.910 6.3247

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000


28VO ANALISIS ELASTO-PLASTICO, 14TO INCREMENTO DE CARGA MULTIPLICANDO λP

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Elemento Nodo





P= 6274.50 kg

2P= 12549.00 kg

4P= 25098.00 kg





análisis.

Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -3073.176 9.1841

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 11546.579 2.4444

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 11221.502 2.5152

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 18018.402 1.5664

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -10338.477 2.7300

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 25519.548 1.1060

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -13787.023 2.0472

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 16220.360 1.7401

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 4092.147 6.8972

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 21427.402 1.3172

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -21923.612 1.2874

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 8905.059 3.1695

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 21427.402 1.3172

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21405.744 1.0010

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -3408.990 6.2856

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 3387.910 6.3247

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000


29NO ANALISIS ELASTO-PLÁSTICO DE VERFICACION, 14TO INCREMENTO DE CARGA MULTIPLICANDO λP

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Elemento Nodo



30mo análisis elasto-plástico (15to incremento de carga)


P= 6274.8 kg

2P= 12549.60 kg

4P= 25099.20 kg





resistencia (fluencia).

Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -3069.126 9.1962

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 11552.422 2.4431

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 11221.502 2.5152

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 18018.402 1.5664

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -10384.428 2.7179

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 25527.672 1.1056

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -13781.179 2.0480

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 16229.324 1.7391

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 4100.269 6.8835

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 21427.402 1.3172

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -21945.197 1.2861

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 8914.024 3.1663

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 21427.402 1.3172

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -3408.990 6.2856

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 3387.910 6.3247

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000


30RO ANALISIS ELASTO-PLÁSTICO, 15TO INCREMENTO DE CARGA MULTIPLICANDO λP

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Elemento Nodo





P= 6274.8 kg

2P= 12549.60 kg

4P= 25099.20 kg





análisis.

NOTA: En este 31ro análisis equivalente si se incrementa un poco más la carga

0.025 kg (25 gramos) y la estructura se convierte en mecanismo, el cual se

verificara con el método energético.

Resistencia Demanda

Mpx Skx

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -3069.126 9.1962

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 11552.422 2.4431

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 11221.502 2.5152

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 18018.402 1.5664

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -10384.428 2.7179

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 25527.672 1.1056

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -13781.179 2.0480

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -28224.255 1.0000

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 16229.324 1.7391

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 4100.269 6.8835

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 21427.402 1.3172

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 -21945.197 1.2861

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 28224.255 1.0000

i W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 8914.024 3.1663

j W8X48 300.00 90.968 7658.658 9.18 707.921 802.966 3515.00 2000000.00 28224.255 21427.402 1.3172

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 21427.405 1.0000

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -3408.990 6.2856

i W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 3387.910 6.3247

j W12X26 500.00 49.355 8491.121 13.12 547.330 609.599 3515.00 2000000.00 21427.405 -21427.405 1.0000


31RO ANALISIS ELASTO-PLÁSTICO DE VERIFICACIÓN, 15TO INCREMENTO DE CARGA MULTIPLICANDO λP

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Elemento Nodo



Desplazamiento con carga de P= 6274.80 kg= 44.429 cm

Desplazamiento con carga de P= 6274.825 kg= 10125.794 cm

Por lo tanto como conclusión del método paso a paso (sistematizado) se obtuvo

una carga que produce el mecanismo de falla de P= 4.1832*1500= 6274.80 kg +

0.025 kg= 6274.825 kg.

Deformada del marco antes de convertirse en mecanismo (P=6274.80 kg)

Deformada del marco al convertirse en mecanismo (P=6274.825 kg)



Aparición de articulaciones plásticas

A continuación se muestran en orden las 19 rotulas que se presentaron para que

la estructura se convirtiera en mecanismo de falla.

1. Barra 11, nodo i.

2. Barra 15, nodo j.


4. Barra 4, nodo i.

5. Barra 2, nodo i.

6. Barra 3, nodo i.


8. Barra 6, nodo j.







15. Barra 13, nodo j,







Método energético (Mecanismo de falla)

Trabajo externo

We= 12 Θ Mp(viga) + 7 ΘMp(columna)

We= 12 Θ (21, 427.405) + 7 Θ (28, 224. 255) = 454, 698.645 Θ

Trabajo interno

Wi= 2P(3 Θ) + 2P(6 Θ) + 4P(9 Θ) + P(3 Θ) + P(6 Θ) + P(9 Θ)= 72P Θ

Trabajo interno- Trabajo externo= 0

Wi – We= 0

72P Θ= 454, 698. 645 Θ

72P= 454, 698. 645

P=

P= 6315.25896 kg



Historial Carga-Deformación

Carga P (kg) Deformación (cm) Incremento

0.000 0.000 0.00000

1500.000 3.979 1.00000

4392.750 11.653 2.92850 1er incremento

4498.500 11.954 2.99900 2do increment

4673.250 12.546 3.11550 3er incremento

5073.300 14.224 3.38220 4to increment

5154.900 14.568 3.43660 5to incremento

5314.800 15.615 3.54320 6to incremento

5430.000 16.611 3.62000 7mo incremento

5782.200 21.313 3.85480 8vo incremento

5903.850 23.509 3.93590 9no incremento

5986.500 25.498 3.99100 10mo incremento

6082.050 28.773 4.05470 11mo incremento

6178.050 35.344 4.11870 12vo incremento

6216.900 38.417 4.14460 13vo incremento

6274.500 44.401 4.18300 14vo incremento

6274.800 44.429 4.18320 15vo increment

Pequeño

incremento para

mecanismo

6274.830 10125.000 4.18322

0.000

500.000

1000.000

1500.000

2000.000

2500.000

3000.000

3500.000

4000.000

4500.000

5000.000

5500.000

6000.000

6500.000

7000.000

0.000 2500.000 5000.000 7500.000 10000.000

Car

ga P

en

Kg

Desplazamiento en cm

Series1



Para poder apreciar mejor la curva del historial Carga-Deformación se

reduce la escala.

0.000

500.000

1000.000

1500.000

2000.000

2500.000

3000.000

3500.000

4000.000

4500.000

5000.000

5500.000

6000.000

6500.000

7000.000

0.000 10.000 20.000 30.000 40.000 50.000 60.000 70.000 80.000 90.000 100.000

Historial Carga- Deformación

Historial Carga- Deformación



Conclusiones

Como se apreció en la determinación de la carga P que produce el colapso hubo

una diferencia de 40.46 kg entre el método paso a paso (sistematizado) y el

método energético, sin embargo se debe que a que el método energético es

aproximado aceptable que se utiliza en este tipo de análisis para determinar la

carga última que hace colapsar la estructura, sin embargo el método

(sistematizado) es más exacto ya que se realiza un análisis no lineal (push over)

en el cual se van incrementando las cargas y , en la cual se forma un número

suficiente de articulaciones plásticas para transformar la estructura en un

mecanismo. Este mecanismo se podría colapsar bajo cualquier carga adicional, en

el cual en nuestro trabajo se formaron 19 articulaciones plásticas que al

incrementar la carga P en 0.025 kg se convirtió en un mecanismo.

Se determina así que la carga que produce el mecanismo es P= 6274.80 kg

Rango de la etapa elástica

0 kg < P < 4392.75 kg

Rango de la etapa elasto-plástica

4392.75 kg < P < 6274.80 kg

La solución obtenida para la etapa elástica y elasto-plástica es la solución exacta

al problema para cuando P varía entre el rango:

O kg < P < 6274.80 kg

Por otro lado la carga P=6274.80 kg no puede ser excedida.

analisis elasto-plastico marco sometido a flexion pura

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