“ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.

E”

“ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO

ESTÁTICO DE LA NORMA E-030 DEL R.N.E”
MEMORIA DE CÁLCULOS

1 Datos y Calculos previos

stencia a la compresion de diseño del concreto: f'c = 280 Kg/cm2

Modulo de elasticidad del concreto: E= 250998 Kg/cm2 𝐸=𝑤_𝑐^1.5 ∗4000∗ 〖𝑓 _𝑐^′ 〗 ^0.5≅15000∗√(𝑓_𝑐^′ )
14872.26
E = 2509980 Tn/m2
Modulo de poisson: v= 0.18 entre: 0.12-0.20
Modulo de reasistencia al corte del concreto: G = 1003992 Tn/m3 𝐺=𝐸 ∗[2∗(1+𝑣)]^(−1)≅0.4∗E
0.42

2 Sistema Global de Coordenadas del Edificio GDL E IDENTIFICACION DE PORTICOS

2.1. Calculo del centroide de las plantas

15
14
13

12
11
10

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

3 Elementos: Vigas, placas, columnas y porticos

Radio Base Altura Longitu Inercia h Inercia v

Elemento Codigo Forma (si es
(espesor) (elemento) d (h piso)
Area Ix' Iy'
circular)

Columa R. C-01 Recta 0 0.30 0.30 3.5 y 3 0.09000 0.00068 0.00068

Columa C. C-02 Circular 0.17 0.00 0.00 3.5 y 4 0.09079 0.00066 0.00066
Viga V-01 Recta 0 0.25 0.50 0.12500 0.00260 0.00065
Placa V-02 Recta 0 0.25 1.20 3.5 y 3 0.30000 0.00156 0.03600

𝑃4

𝑃3

𝑃7 𝑃6 𝑃5

𝑃2

𝑃1

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 1.- METRADO DE CARGAS

CARACTERISTICAS DE LA EDIFICACIÓN
LOSA = 0.250 Tn/m²
SOBRECARGA = 0.250 Tn/m²
TABIQUERIA = 0.100 Tn/m²
ACABADOS = 0.100 Tn/m²
PISOS = 5
PESO UNITARIO DEL CONCRETO = 2.400 Tn/m³
PESO UNITARIO DEL LADRILLO = 1.800 Tn/m³
ALTURA DE LA EDIFICACIÓN = 15.500 m
ESPESOR DE LA LOSA = 0.20 m ELEGIR

PISO: 01

P concreto
N° espesor(m) Área (m2) PESO (ton.)
(ton/m3)
Losa Maciza 1 2.400 0.2 120 57.600
P concreto
N° (ton/m3) Lado (m) Lado (m) Altura (m) PESO (ton.)

4 2.4 0.3 0.3 3.50 3.024

Columnas
2 2.4 0.17 0.17 3.50 1.525
P concreto
N° (ton/m3) Base (m) Peralte (m) Luz (m) PESO (ton.)

PLACA 6 2.4 0.25 1.20 3.5 15.120

Viga En Eje Y-Y 9 2.4 0.25 0.5 4 10.800
Viga En Eje X-X 8 2.4 0.25 0.50 5.00 12.000
Peso (ton/m2) Área (m2) PESO (ton.)

Tabiqueria 0.100 120.00 12.000

Acabados 0.100 120.00 12.000
CM (ton) = 124.069
s/c (ton/m2) Área (m2)
Oficcinas 0.250 120 30.000
16.3. PESO DE LA EDIFICACIÓN CV (ton) = 30.000
b) En edificaciones de las categorías C, se tomará el 25% de la carga
25 % CV (ton) = 7.500
viva.

RESUMEN DE METRADO DE CARGAS PARA EL ANALISIS ESTÁTICO

NIVEL 01
Placa 15.120 tn
Viga En Eje Y-Y 10.800 tn
Viga En Eje X-X 12.000 tn
Columnas 4.55 tn
Aligerado 57.600 tn
Tabiquería 12.000 tn
Acabados 12.000 tn
Sobrecarga 7.500 tn
Ɯi 131.569 tn
PESO DEL PISO 1 = 131.569 tn

PISO: 02, 03, 04

 P concreto
N° (ton/m3) espesor(m) Área (m2) PESO (ton.)

Losa Maciza 1 2.400 0.2 120 57.600

P concreto
N° (ton/m3) Lado (m) Lado (m) Altura (m) PESO (ton.)

4 2.4 0.3 0.3 3.00 2.592

Columnas
2 2.4 0.17 0.17 3.00 1.307
P concreto
N° (ton/m3) Base (m) Peralte (m) Luz (m) PESO (ton.)

PLACA 6 2.4 0.25 1.20 3 12.960

Viga En Eje Y-Y 9 2.4 0.25 0.5 4 10.800
Viga En Eje X-X 8 2.4 0.25 0.50 5.00 12.000
Peso (ton/m2) Área (m2) PESO (ton.)
Tabiqueria 0.100 120.00 12.000
Acabados 0.100 120.00 12.000
CM (ton) = 121.259
s/c (ton/m2) Área (m2)
Oficcinas 0.250 120 30.000
16.3. PESO DE LA EDIFICACIÓN CV (ton) = 30.000
b) En edificaciones de las categorías C, se tomará el 25% de la carga 25 % CV (ton) = 7.500
viva.

RESUMEN DE METRADO DE CARGAS PARA EL ANALISIS ESTÁTICO

NIVEL 02, 03, 04
Placa 12.960
Viga En Eje Y-Y 10.800
Viga En Eje X-X 12.000
Columnas 3.90
Aligerado 57.600
Tabiquería 12.000
Acabados 12.000
Sobrecarga 7.500
Ɯi 128.759
PESO DEL PISO 2 = 128.759
PESO DEL PISO 3 = 128.759
PESO DEL PISO 4 = 128.759

PISO: 05

P concreto
N° (ton/m3) espesor(m) Área (m2) PESO (ton.)

Losa Maciza 1 2.400 0.2 60 28.800

P concreto
N° (ton/m3) Lado (m) Lado (m) Altura (m) PESO (ton.)

2 2.4 0.3 0.3 3.00 1.296

Columnas
2 2.4 0.17 0.17 3.00 1.307
P concreto
N° (ton/m3) Base (m) Peralte (m) Luz (m) PESO (ton.)

PLACA 4 2.4 0.25 1.20 3 8.640

Viga En Eje Y-Y 6 2.4 0.25 0.5 4 7.200
Viga En Eje X-X 4 2.4 0.25 0.50 5.00 6.000
Peso (ton/m2) Área (m2) PESO (ton.)
Tabiqueria 0.100 60.00 6.000
Acabados 0.100 60.00 6.000
CM (ton) = 65.243
 s/c (ton/m2) Área (m2)
Oficcinas 0.250 60 15.000
16.3. PESO DE LA EDIFICACIÓN CV (ton) = 15.000
b) En edificaciones de las categorías C, se tomará el 25% de la carga
25 % CV (ton) = 3.750
viva.

RESUMEN DE METRADO DE CARGAS PARA EL ANALISIS ESTÁTICO

NIVEL 05
Placa 8.640 tn
Viga En Eje Y-Y 7.200 tn
Viga En Eje X-X 6.000 tn
Columnas 2.60 tn
Aligerado 28.800 tn
Tabiquería 6.000 tn
Acabados 6.000 tn
Sobrecarga 3.750 tn
Ɯi 68.993 tn
PESO DEL PISO 5 = 68.993 tn

PESO TOTAL DEL EDIFICIO 586.84 tn

 2.- ANALISIS ESTÁTICO DE LA EDIFICACIÓN

ALTURA TOTAL DE LA EDIFICACIÓN SUMA DE LOS PESOS DE LOS ESTREPISOS

hn = 15.5 P= 586.841 TON

TABLA Nº 01 FACTORES DE ZONA TABLA Nº 03 CATEGORÍA DE LAS EDIFICACIONES

ZONA Z CATEGORÍA FACTOR U

ZONA 03 0.35 C: Edificaciones Comunes 1.0

17.2. PERIODO FUNDAMENTAL

TABLA Nº 02 PARÁMETROS DEL SUELO
CT CT
TIPO : DESCRIPCIÓN Tp(s) S
CT = 35 Para edificios cuyos elementos S2: Suelos intermedios 0.6 1.2
resistentes en la dirección considerada 35
sean únicamente pórticos

ARTÍCULO 7.- FACTOR DE AMPLIFICACIÓN SÍSMICA

T = hn/CT = 0.443 C
C = 2.5(TP/T) ; C ≤ 2.5
2.5

17.3. FUERZA CORTANTE EN LA BASE TABLA Nº 06 SISTEMAS ESTRUCTURALES

COEFICIENTE DE REDUCCIÓN,
REGULARIDAD DE LA
V = (ZUCS/R).P SISTEMA ESTRUCTURAL ESTRUCTURA
(R) PARA ESTRUCTURAS
REGULARES

V = 77.023
COEFICIENTE DE
REGULAR Concreto Armado: Pórticos REDUCCIÓN, (R) PARA 8
ESTRUCTURAS REGULARES

RESUMEN DE VALORES OBTENIDOS DE LA NORMA E-030

PARAMETROS VALORES DESCRIPCIÓN NORMA E-030
Z 0.35 ZONA TABLA Nº 01 FACTORES DE ZONA
U 1.0 CATEGORÍA TABLA Nº 03 CATEGORÍA DE LAS EDIFICACIONES
S 1.2 PARÁMETROS DEL SUELO TABLA Nº 02 PARÁMETROS DEL SUELO
R 8 COEFICIENTE DE REDUCCIÓN, (R) PARA ESTRUCTURAS REGULARES TABLA Nº 06 SISTEMAS ESTRUCTURALES
TP 0.6 PERIODO DEL SUELO TABLA Nº 02 PARÁMETROS DEL SUELO
hn 15.5 ALTURA TOTAL DE LA EDIFICACIÓN ARTÍCULO 1.- NOMENCLATURA
CT 35 COEFICIENTE SEGÚN LA RÍGIDEZ DE LA ESTRUCTURA 17.2. PERIODO FUNDAMENTAL
T 0.443 PERIODO FUNDAMENTAL DE LA ESTRUCTURA 17.2. PERIODO FUNDAMENTAL
C 2.5 FACTOR DE AMPLIFICACIÓN SÍSMICA ARTÍCULO 7.- FACTOR DE AMPLIFICACIÓN SÍSMICA
P(Tn) 586.84 SUMA DE LOS PESOS DE LOS ESTREPISOS ARTÍCULO 1.- NOMENCLATURA
V(Tn) 77.023 FUERZA CORTANTE EN LA BASE 17.3. FUERZA CORTANTE EN LA BASE
 3.- DISTRIBUCIÓN DE FUERZA EN ALTURA
PISO Pi (Tn) hi (m) Pi x hi (Tn-m) Incidencia Fuerza Sísmica Fuerza Cortante Momento
5 68.9934052 15.5 1069.39778058 0.206 15.867 15.867 22.41
4 128.7594052 12.5 1609.49256498 0.31 23.877 23.877 1.59
3 128.7594052 9.5 1223.21434939 0.235 18.100 18.100 1.46
2 128.7594052 6.5 836.936133792 0.161 12.401 12.401 1.19
1 131.5693061 3.5 460.492571228 0.089 6.855 6.855 0.68
TOTAL 586.841 5199.53339997 1.001 77.100
Momento
𝑚_𝑖=𝐹𝑧𝑎𝑆𝑖𝑠𝑚∗𝐸𝑥𝑐𝑒𝑛𝑡𝑟𝑖𝑐𝑖𝑑𝑎𝑑

F5 = 15.867 Tn m5 m5 = 0.070 Tn - s²/cm

F4 = 23.877 Tn m4 m4 = 0.131 Tn - s²/cm

F3 = 18.100 Tn m3 m3 = 0.131 Tn - s²/cm

F2 = 12.401 Tn m2 = 0.131 Tn - s²/cm

m2

F1 = 6.855 Tn m1 m1 = 0.134 Tn - s²/cm

 Centro de Centro de Excentricidad
Piso masa Rigidez Excentricidad Ei
x y x y Real
5 7.5194 6 6.1072 6 1.41 1.41
4 5.1921 6 5.1254 6 0.07 0.07
3 5.1 6 5.0195 6 0.08 0.08
2 5.1 6 5.0039 6 0.10 0.10
1 5.1 6 5.001 6 0.10 0.10
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

01.- Condensacion de la matriz de rigidez del portico P1

VISTA
ELEVACIÓN DEL
PORTICO 01.

0.25x0.50
25x1.2

30x30

3.0m
0.25x0.50 0.25x0.50
25x1.2

30x30
30x30

3.0m
0.25x0.50 0.25x0.50
25x1.2

30x30
30x30

3.0m
0.25x0.50 0.25x0.50
25x1.2

30x30
30x30

3.0m
0.25x0.50 0.25x0.50

Dato
25x1.2

30x30
30x30

E = 2509980.08 Tn/m² 3.5m

5m 5m

1.- Determinacion de Cordenadas Globales Generalizadas y GDL

30 32
GDL=33
23 5 5
ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

23 5 5

31 33
24 26 28
13 14
4 4 4
21 22

25 27 29
18 20 22
10 11 12
3 3 3
19 20
19 21 23
12 14 16
7 8 9
2 2 2
17 18
13 15 17
6 8 10
4 5 6
1 1 1
15 16
7 9 11

1 2 3
35 38 41
34 37 40

36 39 42

2.- Determinacion de Cordenadas Locales Generalizadas: {q} - {d}

1 3

Vigas
3 @6𝐸𝐼/𝐿^2 @(−12𝐸𝐼)/𝐿^3 @6𝐸𝐼/𝐿^2 ) █(6𝐸𝐼/𝐿^2 @4𝐸𝐼/𝐿@(−6𝐸𝐼)/𝐿^2 @2𝐸𝐼/𝐿) █((−12𝐸𝐼)/𝐿^3 @(−6𝐸𝐼)/𝐿^2 @12𝐸𝐼/𝐿^3 @(−6𝐸𝐼)/𝐿^2 ) █(6𝐸𝐼/𝐿^2 @2𝐸𝐼/𝐿
2
e: 7, 8, 9, 10 4
+ m.transformcion

&12𝐸𝐼/𝐿^3 &−6𝐸𝐼/𝐿^2 @0&−6𝐸𝐼/𝐿^2 &4𝐸𝐼/𝐿)&■8(−𝐸𝐴/𝐿&0&0@0&−12𝐸𝐼/𝐿^3 &−6𝐸𝐼/𝐿^2 @0&6𝐸𝐼/𝐿^2 &2𝐸𝐼/𝐿)@■8(−𝐸𝐴/𝐿&0&0@0&−12𝐸𝐼/𝐿^3 &6𝐸𝐼/𝐿^2 @0&−6𝐸𝐼/𝐿^2 &2𝐸𝐼/𝐿)&■8(𝐸𝐴/𝐿&0&
2 5

4
1
3 6
Columnas y placas
e: 1-14

Elementos
b1 16,18,20,22,23 b2

Elementos
15,17,19,21

3.- Cálculos previos - Datos de las barras 0.25x0.50

25x1.2

30x30

3.0m
0.25x0.50 0.25x0.50
ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

25x1.2

30x30
3.0m
0.25x0.50 0.25x0.50

25x1.2

30x30
30x30
3.0m
Columnas
0.25x0.50 0.25x0.50
0.30

25x1.2

30x30
30x30
3.0m
0.30 0.25x0.50
0.25x0.50

25x1.2

30x30
30x30
Placas Vigas 3.0m
0.25x0.50 0.25x0.50
0.25
0.50
1.20

25x1.2

30x30
30x30
0.25 3.5m

1.20m
5m 5m

15,17,19,21 16,18,20,22,23

(2−)𝐸𝐼/(1+ )𝐿 (12.𝐸𝐼)/((1+)

(6.𝐸𝐼)/((1+) 𝐿^2 ) 𝐿^3 )
Barra b h A E I EA EI AX AY L EA/L (4+)𝐸𝐼/(1+)𝐿 f

1 0.30 0.30 0.09 2.5E+06 6.8E-04 2.3E+05 1694 0 3.5 3.50 64542 1905.0 936.8 811.9 464.0 0.02
2 0.25 1.20 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3.5 3.50 215141 83075.4 31441.5 32719.1 18696.6 0.35
3 0.30 0.30 0.09 2.5E+06 6.8E-04 2.3E+05 1694 0 3.5 3.50 64542 1905.0 936.8 811.9 464.0 0.02
4 0.30 0.30 0.09 2.5E+06 6.8E-04 2.3E+05 1694 0 3 3.00 75299 2209.6 1080.1 1096.6 731.1 0.03
5 0.25 1.20 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3 3.00 250998 91173.3 30933.8 40702.4 27134.9 0.48
6 0.30 0.30 0.09 2.5E+06 6.8E-04 2.3E+05 1694 0 3 3.00 75299 2209.6 1080.1 1096.6 731.1 0.03
7 0.30 0.30 0.09 2.5E+06 6.8E-04 2.3E+05 1694 0 3 3.00 75299 2209.6 1080.1 1096.6 731.1 0.03
8 0.25 1.20 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3 3.00 250998 91173.3 30933.8 40702.4 27134.9 0.48
9 0.30 0.30 0.09 2.5E+06 6.8E-04 2.3E+05 1694 0 3 3.00 75299 2209.6 1080.1 1096.6 731.1 0.03
10 0.30 0.30 0.09 2.5E+06 6.8E-04 2.3E+05 1694 0 3 3.00 75299 2209.6 1080.1 1096.6 731.1 0.03
11 0.25 1.20 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3 3.00 250998 91173.3 30933.8 40702.4 27134.9 0.48
12 0.30 0.30 0.09 2.5E+06 6.8E-04 2.3E+05 1694 0 3 3.00 75299 2209.6 1080.1 1096.6 731.1 0.03
13 0.25 1.20 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3 3.00 250998 91173.3 30933.8 40702.4 27134.9 0.48
14 0.30 0.30 0.09 2.5E+06 6.8E-04 2.3E+05 1694 0 3 3.00 75299 2209.6 1080.1 1096.6 731.1 0.03
15 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 5 0 5.00 0 ∞ 5114.9 2500.3 1523.0 609.2 0.03
16 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 5 0 5.00 0 ∞ 5114.9 2500.3 1523.0 609.2 0.03
17 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 5 0 5.00 0 ∞ 5114.9 2500.3 1523.0 609.2 0.03
18 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 5 0 5.00 0 ∞ 5114.9 2500.3 1523.0 609.2 0.03
19 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 5 0 5.00 0 ∞ 5114.9 2500.3 1523.0 609.2 0.03
20 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 5 0 5.00 0 ∞ 5114.9 2500.3 1523.0 609.2 0.03
21 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 5 0 5.00 0 ∞ 5114.9 2500.3 1523.0 609.2 0.03
22 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 5 0 5.00 0 ∞ 5114.9 2500.3 1523.0 609.2 0.03
23 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 5 0 5.00 0 ∞ 5114.9 2500.3 1523.0 609.2 0.03

4.- Matriz de Transformacion de desplazamientos [A*]

NOTA: LA MATRIZ COMPLETA SE PUEDE VER EN EL ARCHIVO EXCEL ADJUNTO
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]2
ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

[A*]2
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]3
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
[A*]4
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
[A*]5
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
[A*]6
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
[A*]7
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
[A*]8
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]9
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]10
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

[A*]11
ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]11
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]12
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]13
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]14
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
[A*]15
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
[A*]16
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
[A*]17
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
[A*]18
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]19
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0

[A*]20 ANÁLISIS ESTRUCTURAL

ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]20
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]21
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]22
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]23
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

5.- Matriz de rigidez de la barra [k] i, {q}-{d}

(2−)𝐸𝐼/(1+
(4+)𝐸𝐼/(1+)𝐿 )𝐿 (12.𝐸𝐼)/((1+)
(6.𝐸𝐼)/((1+) 𝐿^2 ) 𝐿^3 )
Barra b h A E I EA EI AX AY L EA/L f

1 0.3 0.3 0.09 3E+06 0.00068 225898.2 1694.237 0 3.5 3.5 64542 1904.95 936.818 811.934 463.963 0.02
2 0.25 1.2 0.3 3E+06 0.036 752994 90359.28 0 3.5 3.5 215141 83075.4 31442 32719 18697 0.35
3 0.3 0.3 0.09 3E+06 0.00068 225898.2 1694.237 0 3.5 3.5 64542 1904.95 936.818 811.934 463.963 0.02
4 0.3 0.3 0.09 3E+06 0.00068 225898.2 1694.237 0 3 3 75299 2209.64 1080.14 1096.59 731.062 0.03
5 0.25 1.2 0.3 3E+06 0.036 752994 90359.28 0 3 3 250998 91173.3 30934 40702 27135 0.48
6 0.3 0.3 0.09 3E+06 0.00068 225898.2 1694.237 0 3 3 75299 2209.64 1080.14 1096.59 731.062 0.03
7 0.3 0.3 0.09 3E+06 0.00068 225898.2 1694.237 0 3 3 75299 2209.64 1080.14 1096.59 731.062 0.03
8 0.25 1.2 0.3 3E+06 0.036 752994 90359.28 0 3 3 250998 91173.3 30934 40702 27135 0.48
9 0.3 0.3 0.09 3E+06 0.00068 225898.2 1694.237 0 3 3 75299 2209.64 1080.14 1096.59 731.062 0.03
10 0.3 0.3 0.09 3E+06 0.00068 225898.2 1694.237 0 3 3 75299 2209.64 1080.14 1096.59 731.062 0.03
11 0.25 1.2 0.3 3E+06 0.036 752994 90359.28 0 3 3 250998 91173.3 30934 40702 27135 0.48
12 0.3 0.3 0.09 3E+06 0.00068 225898.2 1694.237 0 3 3 75299 2209.64 1080.14 1096.59 731.062 0.03
13 0.25 1.2 0.3 3E+06 0.036 752994 90359.28 0 3 3 250998 91173.3 30934 40702 27135 0.48
14 0.3 0.3 0.09 3E+06 0.00068 225898.2 1694.237 0 3 3 75299 2209.64 1080.14 1096.59 731.0622 0.03
15 0.25 0.5 0.125 3E+06 0.0026 313747.5 6536.406 5 0 5 0 5114.9 2500.33 1523 609.2185 0.03
16 0.25 0.5 0.125 3E+06 0.0026 313747.5 6536.406 5 0 5 0 5114.9 2500.33 1523 609.2185 0.03
17 0.25 0.5 0.125 3E+06 0.0026 313747.5 6536.406 5 0 5 0 5114.9 2500.33 1523 609.2185 0.03
18 0.25 0.5 0.125 3E+06 0.0026 313747.5 6536.406 5 0 5 0 5114.9 2500.33 1523 609.2185 0.03
19 0.25 0.5 0.125 3E+06 0.0026 313747.5 6536.406 5 0 5 0 5114.9 2500.33 1523 609.2185 0.03
20 0.25 0.5 0.125 3E+06 0.0026 313747.5 6536.406 5 0 5 0 5114.9 2500.33 1523 609.2185 0.03
21 0.25 0.5 0.125 3E+06 0.0026 313747.5 6536.406 5 0 5 0 5114.9 2500.33 1523 609.2185 0.03
22 0.25 0.5 0.125 3E+06 0.0026 313747.5 6536.406 5 0 5 0 5114.9 2500.33 1523 609.2185 0.03
23 0.25 0.5 0.125 3E+06 0.0026 313747.5 6536.406 5 0 5 0 5114.9 2500.33 1523 609.218 0.03

64542 0.0 0.0 -64542 0.0 0.0

0.0 464.0 -811.9 0.0 -464.0 -811.9
[k] 1,3 = 0.0 -811.9 1905.0 0.0 811.9 936.8

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

-64542 0.0 0.0 64542.3 0.0 0.0

0.0 -464.0 811.9 0.0 464.0 811.9
0.0 -811.9 936.8 0.0 811.9 1905.0

215141 0.0 0.0 -215141 0.0 0.0

0.0 18696.6 -32719.1 0.0 -18696.6 -32719.1
[k] 2 = 0.0 0.0 83075.4 0.0 0.0 31441.5
-215141 0.0 0.0 215141.1 0.0 0.0
0.0 -18696.6 0.0 0.0 18696.6 32719.1
0.0 0.0 31441.5 0.0 32719.1 83075.4

75299 0.0 0.0 -75299 0.0 0.0

0.0 731.1 -1096.6 0.0 -731.1 -1096.6
[k] 4, 6, 7, 9, 0.0 -1096.6 2209.6 0.0 1096.6 1080.1
10, 12, 14 = -75299 0.0 0.0 75299.4 0.0 0.0
0.0 -731.1 1096.6 0.0 731.1 1096.6
0.0 -1096.6 1080.1 0.0 1096.6 2209.6

250998 0.0 0.0 -250998 0.0 0.0

0.0 27134.9 -40702.4 0.0 -27134.9 -40702.4

[k] 5, 8, 11, 13 0.0 -40702.4 91173.3 0.0 40702.4 30933.8

= -250998 0.0 0.0 250998.0 0.0 0.0
0.0 -27134.9 40702.4 0.0 27134.9 40702.4

[K] =[ST] [K '] [S] 0.0 -40702.4 30933.8 0.0 40702.4 91173.3 Columas y placas
b1= 0 b2= 0.6
0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0
0.0 609.2 1523.0 0.0 -609.2 1523.0 0.0 1.0 0.0 0.0 0.0 0.0
[k]' 15, 17, 19, 0.0 1523.0 5114.9 0.0 -1523.0 2500.3 0.0 0.0 1.0 0.0 0.0 0.0
[s]15 =
21 = 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0
0.0 -609.2 -1523.0 0.0 609.2 -1523.0 0.0 0.0 0.0 0.0 1.0 -0.6
0.0 1523.0 2500.3 0.0 -1523.0 5114.9 0.0 0.0 0.0 0.0 0.0 1.0

0.0 0.0 0.0 0.0 0.0 0.0

0.0 609.2 1523.0 0.0 -609.2 1888.6
[k] 15, 17, 19, 0.0 1523.0 5114.9 0.0 -1523.0 3414.2
21 = 0.0 0.0 0.0 0.0 0.0 0.0
0.0 -609.2 -1523.0 0.0 609.2 -1888.6
[K] =[ST] [K '] [S] 0.0 1888.6 3414.2 0.0 -1888.6 7161.9
b1= 0.6 b2= 0
0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0
0.0 609.2 1523.0 0.0 -609.2 1523.0 0.0 1.0 0.6 0.0 0.0 0.0
[k]' 16, 18, 20, 0.0 1523.0 5114.9 0.0 -1523.0 2500.3 0.0 0.0 1.0 0.0 0.0 0.0
[s] 16 =
22, 23 = 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0
0.0 -609.2 -1523.0 0.0 609.2 -1523.0 0.0 0.0 0.0 0.0 1.0 0.0
0.0 1523.0 2500.3 0.0 -1523.0 5114.9 0.0 0.0 0.0 0.0 0.0 1.0

0.0 0.0 0.0 0.0 0.0 0.0

0.0 609.2 1888.6 0.0 -609.2 1523.0
[k] 16, 18, 20, 0.0 1888.6 7161.9 0.0 -1888.6 3414.2
22, 23 = 0.0 0.0 0.0 0.0 0.0 0.0

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

[k] 16, 18, 20,

22, 23 =

0.0 -609.2 -1888.6 0.0 609.2 -1523.0

0.0 1523.0 3414.2 0.0 -1523.0 5114.9 Vigas con brazo rigido

6.- Determinar la Matriz deTransformacion de desplazamientos [R]i {𝑑}=[𝑅]{𝑑^∗ }

0 1 0 0 0 0 cos a sen a 0 0 0 0
1 0 0 0 0 0 sen a -cos a 0 0 0 0
0 0 1 0 0 0 0 0 1 0 0 0
[R]1,3= [R]i=
0 0 0 0 1 0 0 0 0 cos a sen a 0
0 0 0 1 0 0 0 0 0 sen a -cos a 0
0 0 0 0 0 1 0 0 0 0 0 1

0 1 0 0 0 0
1 0 0 0 0 0
0 0 1 0 0 0
[R]2=
0 0 0 0 1 0
0 0 0 1 0 0
0 0 0 0 0 1

0 1 0 0 0 0
1 0 0 0 0 0
[R]4, 6, 7, 9, 10, 0 0 1 0 0 0
12, 14= 0 0 0 0 1 0
0 0 0 1 0 0
0 0 0 0 0 1

0 1 0 0 0 0
1 0 0 0 0 0
[R]5, 8, 11, 13 0 0 1 0 0 0
= 0 0 0 0 1 0
0 0 0 1 0 0
0 0 0 0 0 1

1 0 0 0 0 0
0 1 0 0 0 0
[R]15, 17, 19, 0 0 1 0 0 0
21= 0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1

1 0 0 0 0 0
0 1 0 0 0 0
[R]16, 18, 20, 0 0 1 0 0 0
22, 23= 0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1

7.- Matriz de rigidez de la barra [k*]i, {q*}-{d*}

[𝑘^∗ ]=[𝑅]^𝑇 [𝑘][𝑅]
464 0 -812 -464 0 -812
0 64542 0 0 -64542 0
-812 0 1905 812 0 937
[k*] 1,3 =
-464 0 812 464 0 812

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
“ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

[k*] 1,3 =

0 -64542 0 0 64542 0
-812 0 937 812 0 1905

18697 0 -32719 -18697 0 -32719

0 215141 0 0 -215141 0
0 0 83075 0 0 31442
[k*] 2 =
-18697 0 0 18697 0 32719
0 -215141 0 0 215141 0
0 0 31442 32719 0 83075

731 0 -1097 -731 0 -1097

0 75299 0 0 -75299 0
[k*] 4, 6, 7, 9, -1097 0 2210 1097 0 1080
10, 12, 14 = -731 0 1097 731 0 1097
0 -75299 0 0 75299 0
-1097 0 1080 1097 0 2210

27135 0 -40702 -27135 0 -40702

0 250998 0 0 -250998 0

[k*] 5, 8, 11, -40702 0 91173 40702 0 30934

13= -27135 0 40702 27135 0 40702
0 -250998 0 0 250998 0
-40702 0 30934 40702 0 91173

0 0 0 0 0 0
0 609 1523 0 -609 1889
[k*] 15, 17, 19, 0 1523 5115 0 -1523 3414
21 = 0 0 0 0 0 0
0 -609 -1523 0 609 -1889
0 1889 3414 0 -1889 7162 E389:J394
E396:J401
0 0 0 0 0 0 E403:J408
0 609 1889 0 -609 1523 E410:J415
[k*] 16, 18, 20, 0 1889 7162 0 -1889 3414 E417:J422
22, 23 = 0 0 0 0 0 0 E424:J429
0 -609 -1889 0 609 -1523
0 1523 3414 0 -1523 5115

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

8.- Ensamblaje de la Matriz de Rigidez Total [𝐾]= 〖 [𝑨_𝒆^∗] 〗 ^𝑻 [𝒌_𝒆^∗ ][𝑨_𝒆^∗ ]

- Ensamblaje [K]
1 2 3 4 5 6 7 8 9 10 11 12 … 33 …
464 0 0 0 0 0 812 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 4
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 5
0 0 0 0.0 0.0 64542.3 0 0 0 0 0 0 0.0 0.0 6
812 0 0 0 0 0 1905 0 0 0 0 0 0 0 7
[K]1=
0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 9
0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 0 0 0 12
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 …
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 33

1 2 3 4 5 6 7 8 9 10 11 12 … 33
464 0 0 0 0 0 0 0 812 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 4
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 5
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 6
0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
[K]2=
0 0 0 0 0 0 0 64542 0 0 0 0 0 0 8
812 0 0 0 0 0 0 0 1905 0 0 0 0 0 9
0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 0 0 0 12
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 13
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 14

1 2 3 4 5 6 7 8 9 10 11 12 … 33
464 0 0 0 0 0 0 0 0 0 812 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 4
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 5
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 6
0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
[K]3=
0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 9
0 0 0 0 0 0 0 0 0 64542 0 0 0 0 10
812 0 0 0 0 0 0 0 0 0 1905 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 0 0 0 12
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 13
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 14

1 2 3 4 5 6 7 8 9 10 11 12 … 33
731 -731 0 0 0 0 -1097 0 0 0 0 0 0 -1097 1
-731 731 0 0 0 0 1097 0 0 0 0 0 0 1097 2
ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 4
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 5
0 0 0 0.0 0.0 75299.4 0 0 0 0 0 0 -75299.4 0.0 6
-1097 1097 0 0 0 0 2210 0 0 0 0 0 0 1080 7
[K]4=
0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 9
0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 0 0 0 12
0 0 0 0.0 0.0 -75299.4 0 0 0 0 0 0 75299.4 0.0 13
-1097 1097 0 0.0 0.0 0.0 1080 0 0 0 0 0 0.0 2209.6 14

Generacion de las formulas excel para obtener el aporte de cada barra y hallar la suma directa por cuestiones de dimensiones grandes de las matrices.
Esto con el fin de hallar directamente la sumatoria de aportes sin la necesidad de hallar cada uno
Fila Fila
Matriz K * del
[K]elem Formula de multiplicacion de matrices inicial final de
elemento
de [A] [A]
[K]1 MMULT(TRANSPOSE(B115:AH120);MMULT(E389:J394;B115:AH120)) 115 120 E389:J394
[K]2 MMULT(TRANSPOSE(B121:AH126);MMULT(E396:J401;B121:AH126)) 121 126 E396:J401
[K]3 MMULT(TRANSPOSE(B127:AH132);MMULT(E389:J394;B127:AH132)) 127 132 E389:J394
[K]4 MMULT(TRANSPOSE(B133:AH138);MMULT(E403:J408;B133:AH138)) 133 138 E403:J408
[K]5 MMULT(TRANSPOSE(B139:AH144);MMULT(E410:J415;B139:AH144)) 139 144 E410:J415
[K]6 MMULT(TRANSPOSE(B145:AH150);MMULT(E403:J408;B145:AH150)) 145 150 E403:J408
[K]7 MMULT(TRANSPOSE(B151:AH156);MMULT(E403:J408;B151:AH156)) 151 156 E403:J408
[K]8 MMULT(TRANSPOSE(B157:AH162);MMULT(E410:J415;B157:AH162)) 157 162 E410:J415
[K]9 MMULT(TRANSPOSE(B163:AH168);MMULT(E403:J408;B163:AH168)) 163 168 E403:J408
[K]10 MMULT(TRANSPOSE(B169:AH174);MMULT(E403:J408;B169:AH174)) 169 174 E403:J408
[K]11 MMULT(TRANSPOSE(B175:AH180);MMULT(E410:J415;B175:AH180)) 175 180 E410:J415
[K]12 MMULT(TRANSPOSE(B181:AH186);MMULT(E403:J408;B181:AH186)) 181 186 E403:J408
[K]13 MMULT(TRANSPOSE(B187:AH192);MMULT(E410:J415;B187:AH192)) 187 192 E410:J415
[K]14 MMULT(TRANSPOSE(B193:AH198);MMULT(E403:J408;B193:AH198)) 193 198 E403:J408
[K]15 MMULT(TRANSPOSE(B199:AH204);MMULT(E417:J422;B199:AH204)) 199 204 E417:J422
[K]16 MMULT(TRANSPOSE(B205:AH210);MMULT(E424:J429;B205:AH210)) 205 210 E424:J429
[K]17 MMULT(TRANSPOSE(B211:AH216);MMULT(E417:J422;B211:AH216)) 211 216 E417:J422
[K]18 MMULT(TRANSPOSE(B217:AH222);MMULT(E424:J429;B217:AH222)) 217 222 E424:J429
[K]19 MMULT(TRANSPOSE(B223:AH228);MMULT(E417:J422;B223:AH228)) 223 228 E417:J422
[K]20 MMULT(TRANSPOSE(B229:AH234);MMULT(E424:J429;B229:AH234)) 229 234 E424:J429
[K]21 MMULT(TRANSPOSE(B235:AH240);MMULT(E417:J422;B235:AH240)) 235 240 E417:J422
[K]22 MMULT(TRANSPOSE(B241:AH246);MMULT(E424:J429;B241:AH246)) 241 246 E424:J429
[K]23 MMULT(TRANSPOSE(B247:AH252);MMULT(E424:J429;B247:AH252)) 247 252 E424:J429
NOTA: LA MATRIZ COMPLETA SE PUEDE VER EN EL ARCHIVO EXCEL ADJUNTO

𝐾]=∑_(𝑒=1)^𝑚▒ 〖〖 [𝐴_𝑒^∗] 〗 ^𝑇 [𝑘_𝑒^∗ ][𝐴_𝑒^∗ ] 〗

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
48222 -28597 0 0 0 0 -285 0 -7983 0 -285 0 0 -1097 -40702 0
-28597 57194 -28597 0 0 0 1097 0 40702 0 1097 0 -1097 1097 0 0
0 -28597 57194 -28597 0 0 0 0 0 0 0 0 1097 0 40702 0
0 0 -28597 56463 -27866 0 0 0 0 0 0 0 0 0 0 0
0 0 0 -27866 27866 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 140451.0 1523.0 -609.2 1888.6 0.0 0.0 0.0 -75299.4 0.0 0.0 0.0
-285 1097 0 0 0 1523.0 9229.5 -1523.0 3414.2 0.0 0.0 0.0 0.0 1080.1 0.0 0.0
[K]T=
ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

[K]T=
0 0 0 0 0 -609.2 -1523.0 467357.6 0.0 -609.2 1523.0 0.0 0.0 -250998.0 0.0 0.0
-7983 40702 0 0 0 1888.6 3414.2 0.0 188572.5 -1888.6 3414.2 0.0 0.0 0.0 30933.8 0.0
0 0 0 0 0 0.0 0.0 -609.2 -1888.6 140451.0 -1523.0 0.0 0.0 0.0 0.0 ###
-285 1097 0 0 0 0.0 0.0 1523.0 3414.2 -1523.0 9229.5 0.0 0.0 0.0 0.0 0.0
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 75908.6 1523.0 -609.2 1888.6 0.0
0 -1097 1097 0 0 -75299.4 0.0 0.0 0.0 0.0 0.0 1523.0 82623.9 -1523.0 3414.2 0.0
-1097 1097 0 0 0 0.0 1080.1 -250998.0 0.0 0.0 0.0 -609.2 -1523.0 505424.1 0.0 ###
-40702 0 40702 0 0 0.0 0.0 0.0 30933.8 0.0 0.0 1888.6 3414.2 0.0 196670.4 ###
0 0 0 0 0 0.0 0.0 0.0 0.0 -75299.4 0.0 0.0 0.0 -609.2 -1888.6 ###
-1097 0 1097 0 0 0.0 0.0 0.0 0.0 0.0 1080.1 0.0 0.0 1523.0 3414.2 ###
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 -75299.4 0.0 0.0 0.0 0.0
0 -1097 0 1097 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1080.1 0.0 0.0 0.0
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -250998.0 0.0 0.0
0 -40702 0 40702 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 30933.8 0.0
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 ###
0 -1097 0 1097 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 -1097 1097 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 -40702 0 40702 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 -1097 0 1097 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 0 -40702 40702 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 0 -1097 1097 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

* Estructura del K ordenado

- GDLE 1-5
Kuu Kur 1 2 3 4 5
[K]T= 39426.2 -26972.1 8363.5 -1146.1 209.3 1
-26972.1 39474.4 -27168.8 8455.4 -894.8 2
Kru Krr [K]L1= 8363.5 -27168.8 39616.0 -25763.8 6083.4 3
-1146.1 8455.4 -25763.8 30242.7 -11939.3 4
209.3 -894.8 6083.4 -11939.3 6565.8 5

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

02.- Condensacion de la matriz de rigidez del portico P2

VISTA ELEVACIÓN DEL PORTICO 02

1.20m

0.25x0.50 23
16 17
r=0.17

120x5

3.0m 13 14
0.25x0.50 0.25x0.50 21 22
13 14 15
120x25

r=0.17

120x25

3.0m
10 11 12
0.25x0.50 0.25x0.50 19 20
10 11 12
120x25
120x25

r=0.17

3.0m 7 9
8
0.25x0.50 0.25x0.50 17 18
7 8 9
120x25

r=0.17

120x25

3.0m 4 5 6
0.25x0.50 0.25x0.50 15 16
4 5 6
120x25

120x25
r=0.17

3.5m 1 2 3

1 2 3
5m 5m
5m 5m

Dato
E= 2509980 Tn/m²

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

1.- Determinacion de Cordenadas Globales Generalizadas y GDL

30 32
5 5

31 33 23
24 26 28
4 4 4 13 14
21 22
25 27 29
18 20 22
3 3 3 10 11 12
19 20
19 21 23
12 14 16
7 8 9
2 2 2
17 18
13 15 17
6 8 10 4 5 6
1 1 1 15 16

7 9 11
1 2 3

35 38 41
34 37 40

36 39 42
GDL: 1, 2, 3, 4, 5, 6, 7..., 8, 9, …,33
2.- Determinacion de Cordenadas Locales Generalizadas: {q} - {d}

1 3
2 5
Vigas
[𝑘𝑒]=[■8(■8(𝐸𝐴/𝐿&0&0@0&12𝐸𝐼/𝐿^3 &−6𝐸𝐼/𝐿^2 @0&−6𝐸𝐼/𝐿^2 &4𝐸𝐼/𝐿)&■8(−𝐸𝐴/𝐿&0&0@0&−12𝐸𝐼/𝐿^3 &−6𝐸𝐼/𝐿^2 @0&6𝐸𝐼/𝐿^2 &2𝐸𝐼/𝐿)@■8(−𝐸𝐴/𝐿&0&0@0&−12𝐸𝐼/𝐿^3 &6𝐸𝐼/𝐿^2 @0&−6𝐸𝐼/𝐿^2 &2
e: 15-23 4
2 4 1
+ m.transformcion 3 6
𝐿^2 ) █(6𝐸𝐼/𝐿^2 @4𝐸𝐼/𝐿@(−6𝐸𝐼)/𝐿^2 @2𝐸𝐼/𝐿) █((−12𝐸𝐼)/𝐿^3 @(−6𝐸𝐼)/𝐿^2 @12𝐸𝐼/𝐿^3 @(−6𝐸𝐼)/𝐿^2 ) █(6𝐸𝐼/𝐿^2 @2𝐸𝐼/𝐿@(−6𝐸𝐼)/𝐿^2 @4𝐸𝐼/𝐿)]
Columnas y placas
b1 16,18,20,22,23 b2 e: 1-14

15,17,19,21

3.- Cálculos previos - Datos de las barras

Columnas Vigas Placas

0.30 025
0.50 30
1.20
0.34 0.30 0.25

1.20m

15,17,19,21 16,18,20,22,23

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

(2−)𝐸𝐼/(1+
(4+)𝐸𝐼/(1+)𝐿 )𝐿 (12.𝐸𝐼)/((1+)
(6.𝐸𝐼)/((1+) 𝐿^2 ) 𝐿^3 )
Barra b h A E I EA EI AX AY L EA/L f
1 1.20 0.25 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3.5 3.50 215141 102100.2 50466.3 43590.4 24908.8 0.02
2 3.14 0.17 0.0908 2.5E+06 6.6E-04 2.3E+05 1646 0 3.5 3.50 65110 1871.8 930.9 800.8 457.6 0.01
3 1.20 0.25 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3.5 3.50 215141 102100.2 50466.3 43590.4 24908.8 0.02
4 1.20 0.30 0.36 2.5E+06 3.6E-02 9.0E+05 90359 0 3 3.00 301198 117847.2 57607.7 58485.0 38990.0 0.03
5 3.14 0.17 0.0908 2.5E+06 6.6E-04 2.3E+05 1646 0 3 3.00 75962 2179.6 1081.9 1087.2 724.8 0.01
6 1.20 0.25 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3 3.00 250998 118635.0 58395.5 59010.1 39340.1 0.02
7 1.20 0.30 0.36 2.5E+06 3.6E-02 9.0E+05 90359 0 3 3.00 301198 117847.2 57607.7 58485.0 38990.0 0.03
8 3.14 0.17 0.0908 2.5E+06 6.6E-04 2.3E+05 1646 0 3 3.00 75962 2179.6 1081.9 1087.2 724.8 0.01
9 1.20 0.25 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3 3.00 250998 118635.0 58395.5 59010.1 39340.1 0.02
10 1.20 0.25 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3 3.00 250998 118635.0 58395.5 59010.1 39340.1 0.02
11 3.14 0.17 0.0908 2.5E+06 6.6E-04 2.3E+05 1646 0 3 3.00 75962 2179.6 1081.9 1087.2 724.8 0.01
12 1.20 0.25 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3 3.00 250998 118635.0 58395.5 59010.1 39340.1 0.02
13 3.14 0.17 0.0908 2.5E+06 6.6E-04 2.3E+05 1646 0 3 3.00 75962 2179.6 1081.9 1087.2 724.8 0.01
14 1.20 0.25 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3 3.00 250998 118635.0 58395.5 59010.1 39340.1 0.02
15 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 4 0 4.00 0 ∞ 6316.9 3048.7 2341.4 1170.7 0.05
16 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 4 0 4.00 0 ∞ 6316.9 3048.7 2341.4 1170.7 0.05
17 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 4 0 4.00 0 ∞ 6316.9 3048.7 2341.4 1170.7 0.05
18 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 4 0 4.00 0 ∞ 6316.9 3048.7 2341.4 1170.7 0.05
19 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 4 0 4.00 0 ∞ 6316.9 3048.7 2341.4 1170.7 0.05
20 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 4 0 4.00 0 ∞ 6316.9 3048.7 2341.4 1170.7 0.05
21 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 4 0 4.00 0 ∞ 6316.9 3048.7 2341.4 1170.7 0.05
22 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 4 0 4.00 0 ∞ 6316.9 3048.7 2341.4 1170.7 0.05
23 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 4 0 4.00 0 ∞ 6316.9 3048.7 2341.4 1170.7 0.05

Momento de inercia de los Elementos

Grafico barras Ix Iy

2,5,8,11,13 6.6E-04 6.6E-04

R=0.17

0.30
…
0.30
0.50
15,16,17,18,19,20,21,22 2.6E-03 6.5E-04
0.25
0.25

1,3,4,6,7,9,10,12,14 3.6E-02 1.6E-03

1.20

4.- Matriz de Transformacion de desplazamientos [A*]

NOTA: LA MATRIZ COMPLETA SE PUEDE VER EN EL ARCHIVO EXCEL ADJUNTO
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]2
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]3
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
[A*]4
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
[A*]5
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
[A*]6
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
[A*]7
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
[A*]8
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]9
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]10
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]11
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]12
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]13
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”
[A*]13

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]14
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
[A*]15
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
[A*]16
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
[A*]17
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
[A*]18
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]19
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]20
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]21
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]22
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]23
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

[A*]23

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

5.- Matriz de rigidez de la barra [k]i, {q}-{d}

(2−)𝐸𝐼/(1+
(4+)𝐸𝐼/(1+)𝐿 )𝐿 (12.𝐸𝐼)/((1+)
(6.𝐸𝐼)/((1+) 𝐿^2 ) 𝐿^3 )
Barra b h A E I EA EI AX AY L EA/L f

1 1.2 0.25 0.3 2509980 0.036 752994.02388 90359.283 0 3.5 3.5 215141 102100 50466.28 43590.41 24908.8 0.02
2 3.1416 0.17 0.090792 2509980 0.00066 227886.18089 1646.4777 0 3.5 3.5 65110.34 1871.771 930.9263 800.7705 457.5832 0.01
3 1.2 0.25 0.3 2509980 0.036 752994.02388 90359.283 0 3.5 3.5 215141 102100 50466.28 43590.41 24908.8 0.02
4 1.2 0.3 0.36 2509980 0.036 903592.82866 90359.283 0 3 3 301198 117847 57607.7 58485 38990 0.03
5 3.1416 0.17 0.090792 2509980 0.00066 227886.18089 1646.4777 0 3 3 75962.06 2179.594 1081.942 1087.179 724.7857 0.01
6 1.2 0.25 0.3 2509980 0.036 752994.02388 90359.283 0 3 3 250998 118635 58395.45 59010.14 39340.1 0.02
7 1.2 0.3 0.36 2509980 0.036 903592.82866 90359.283 0 3 3 301198 117847 57607.7 58485 38990 0.03
8 3.1416 0.17 0.090792 2509980 0.00066 227886.18089 1646.4777 0 3 3 75962.06 2179.594 1081.942 1087.179 724.7857 0.01
9 1.2 0.25 0.3 2509980 0.036 752994.02388 90359.283 0 3 3 250998 118635 58395.45 59010.14 39340.1 0.02
10 1.2 0.25 0.3 2509980 0.036 752994.02388 90359.283 0 3 3 250998 118635 58395.45 59010.14 39340.1 0.02
11 3.1416 0.17 0.090792 2509980 0.00066 227886.18089 1646.4777 0 3 3 75962.06 2179.594 1081.942 1087.179 724.7857 0.01
12 1.2 0.25 0.3 2509980 0.036 752994.02388 90359.283 0 3 3 250998 118635 58395.45 59010.14 39340.1 0.02
13 3.1416 0.17 0.090792 2509980 0.00066 227886.18089 1646.4777 0 3 3 75962.06 2179.594 1081.942 1087.179 724.7857 0.01
14 1.2 0.25 0.3 2509980 0.036 752994.02388 90359.283 0 3 3 250998 118635 58395.45 59010.14 39340.1 0.02
15 0.25 0.5 0.125 2509980 0.0026 313747.50995 6536.4065 4 0 4 0 6316.9 3048.697 2341.399 1170.7 0.05
16 0.25 0.5 0.125 2509980 0.0026 313747.50995 6536.4065 4 0 4 0 6316.9 3048.697 2341.399 1170.7 0.05
17 0.25 0.5 0.125 2509980 0.0026 313747.50995 6536.4065 4 0 4 0 6316.9 3048.697 2341.399 1170.7 0.05
18 0.25 0.5 0.125 2509980 0.0026 313747.50995 6536.4065 4 0 4 0 6316.9 3048.697 2341.399 1170.7 0.05
19 0.25 0.5 0.125 2509980 0.0026 313747.50995 6536.4065 4 0 4 0 6316.9 3048.697 2341.399 1170.7 0.05
20 0.25 0.5 0.125 2509980 0.0026 313747.50995 6536.4065 4 0 4 0 6316.9 3048.697 2341.399 1170.7 0.05
21 0.25 0.5 0.125 2509980 0.0026 313747.50995 6536.4065 4 0 4 0 6316.9 3048.697 2341.399 1170.7 0.05
22 0.25 0.5 0.125 2509980 0.0026 313747.50995 6536.4065 4 0 4 0 6316.9 3048.697 2341.399 1170.7 0.05
23 0.25 0.5 0.125 2509980 0.0026 313747.50995 6536.4065 4 0 4 0 6316.9 3048.697 2341.399 1170.7 0.05

215141 0.0 0.0 -215141 0.0 0.0

0.0 24908.8 -43590.4 0.0 -24908.8 -43590.4
0.0 -43590.4 102100.2 0.0 43590.4 50466.3
[k] 1,3 =
-215141 0.0 0.0 215141.1 0.0 0.0
0.0 -24908.8 43590.4 0.0 24908.8 43590.4
0.0 -43590.4 50466.3 0.0 43590.4 102100.2

65110 0.0 0.0 -65110 0.0 0.0

0.0 457.6 -800.8 0.0 -457.6 -800.8
0.0 0.0 1871.8 0.0 0.0 930.9
[k] 2 =
-65110 0.0 0.0 65110.3 0.0 0.0
0.0 -457.6 0.0 0.0 457.6 800.8
0.0 0.0 930.9 0.0 800.8 1871.8

301198 0.0 0.0 -301198 0.0 0.0

0.0 38990.0 -58485.0 0.0 -38990.0 -58485.0
[k] 4, 6, 7, 0.0 -58485.0 117847.2 0.0 58485.0 57607.7
9, 10, 12, 14
= -301198 0.0 0.0 301197.6 0.0 0.0
0.0 -38990.0 58485.0 0.0 38990.0 58485.0
0.0 -58485.0 57607.7 0.0 58485.0 117847.2

75962 0.0 0.0 -75962 0.0 0.0

0.0 724.8 -1087.2 0.0 -724.8 -1087.2
[k] 5, 8, 11, 0.0 -1087.2 2179.6 0.0 1087.2 1081.9
13 = -75962 0.0 0.0 75962.1 0.0 0.0
0.0 -724.8 1087.2 0.0 724.8 1087.2

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 [k]PSEUDO-TRIDIMENCIONAL
“ANÁLISIS 5, 8, 11, DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”
13 =

0.0 -1087.2 1081.9 0.0 1087.2 2179.6 Columas y placas

b1= 0 b2= 0
[K] =[ST] [K '] [S] 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0
0.0 1170.7 2341.4 0.0 -1170.7 2341.4 0.0 1.0 0.0 0.0 0.0 0.0
[k]' 15, 17, 0.0 2341.4 6316.9 0.0 -2341.4 3048.7 0.0 0.0 1.0 0.0 0.0 0.0
[s] 15 =
19, 21 = 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0
0.0 -1170.7 -2341.4 0.0 1170.7 -2341.4 0.0 0.0 0.0 0.0 1.0 0.0
0.0 2341.4 3048.7 0.0 -2341.4 6316.9 0.0 0.0 0.0 0.0 0.0 1.0

0.0 0.0 0.0 0.0 0.0 0.0

0.0 1170.7 2341.4 0.0 -1170.7 2341.4
[k] 15, 17, 0.0 2341.4 6316.9 0.0 -2341.4 3048.7
19, 21 = 0.0 0.0 0.0 0.0 0.0 0.0
0.0 -1170.7 -2341.4 0.0 1170.7 -2341.4
0.0 2341.4 3048.7 0.0 -2341.4 6316.9
b1= 0 b2= 0
[K] =[ST] [K '] [S] 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0
0.0 1170.7 2341.4 0.0 -1170.7 2341.4 0.0 1.0 0.0 0.0 0.0 0.0
[k]' 16, 18, 0.0 2341.4 6316.9 0.0 -2341.4 3048.7 0.0 0.0 1.0 0.0 0.0 0.0
[s] 16 =
20, 22, 23 = 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0
0.0 -1170.7 -2341.4 0.0 1170.7 -2341.4 0.0 0.0 0.0 0.0 1.0 0.0
0.0 2341.4 3048.7 0.0 -2341.4 6316.9 0.0 0.0 0.0 0.0 0.0 1.0

0.0 0.0 0.0 0.0 0.0 0.0

0.0 1170.7 2341.4 0.0 -1170.7 2341.4
[k] 16, 18, 0.0 2341.4 6316.9 0.0 -2341.4 3048.7
=
20, 22, 23 0.0 0.0 0.0 0.0 0.0 0.0
0.0 -1170.7 -2341.4 0.0 1170.7 -2341.4
0.0 2341.4 3048.7 0.0 -2341.4 6316.9 Vigas con brazo rigido

6.- Determinar la Matriz deTransformacion de desplazamientos [R]i {𝑑}=[𝑅]{𝑑^∗ }

cos a sen a 0 0 0 0
sen a -cos a 0 0 0 0
0 0 1 0 0 0
[R]i=
0 0 0 cos a sen a 0
0 0 0 sen a -cos a 0
0 0 0 0 0 1

0 1 0 0 0 0
1 0 0 0 0 0
0 0 1 0 0 0
[R]1,3=
0 0 0 0 1 0
0 0 0 1 0 0
0 0 0 0 0 1

0 1 0 0 0 0
1 0 0 0 0 0
0 0 1 0 0 0
[R]2=
0 0 0 0 1 0
0 0 0 1 0 0
0 0 0 0 0 1

0 1 0 0 0 0
1 0 0 0 0 0
[R]4, 6, 0 0 1 0 0 0
7, 9, 10, 12,
0 0 0 0 1 0
14 =

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”
[R]4, 6,
7, 9, 10, 12,
14 =
0 0 0 1 0 0
0 0 0 0 0 1

0 1 0 0 0 0
1 0 0 0 0 0
[R]5, 8, 0 0 1 0 0 0
11, 13 = 0 0 0 0 1 0
0 0 0 1 0 0
0 0 0 0 0 1

1 0 0 0 0 0
0 1 0 0 0 0
[R]15, 0 0 1 0 0 0
=
17, 19, 21 0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1

1 0 0 0 0 0
0 1 0 0 0 0
[R]16, 0 0 1 0 0 0
18, 20, 22,
0 0 0 1 0 0
23 =
0 0 0 0 1 0
0 0 0 0 0 1

7.- Matriz de rigidez de la barra [k*]i, {q*}-{d*} [𝑘^∗ ]=[𝑅]^𝑇 [𝑘][𝑅]

24908.8 0.0 -43590.4 -24908.8 0.0 -43590.4

0.0 215141.1 0.0 0.0 -215141.1 0.0
-43590.4 0.0 102100.2 43590.4 0.0 50466.3
[k*] 1,3 =
-24908.8 0.0 43590.4 24908.8 0.0 43590.4
0.0 ### 0.0 0.0 215141.1 0.0
-43590.4 0.0 50466.3 43590.4 0.0 102100.2

457.6 0.0 -800.8 -457.6 0.0 -800.8

0.0 65110.3 0.0 0.0 -65110.3 0.0
0.0 0.0 1871.8 0.0 0.0 930.9
[k*] 2 =
-457.6 0.0 0.0 457.6 0.0 800.8
0.0 -65110.3 0.0 0.0 65110.3 0.0
0.0 0.0 930.9 800.8 0.0 1871.8

38990.0 0.0 -58485.0 -38990.0 0.0 -58485.0

0.0 301197.6 0.0 0.0 -301197.6 0.0
[k*] 4, 6, -58485.0 0.0 117847.2 58485.0 0.0 57607.7
7, 9, 10, 12, 14
-38990.0 0.0 58485.0 38990.0 0.0 58485.0
=
0.0 ### 0.0 0.0 301197.6 0.0
-58485.0 0.0 57607.7 58485.0 0.0 117847.2

724.8 0.0 -1087.2 -724.8 0.0 -1087.2

0.0 75962.1 0.0 0.0 -75962.1 0.0

[k*] 5, 8, -1087.2 0.0 2179.6 1087.2 0.0 1081.9

11, 13= -724.8 0.0 1087.2 724.8 0.0 1087.2
0.0 -75962.1 0.0 0.0 75962.1 0.0
-1087.2 0.0 1081.9 1087.2 0.0 2179.6

0.0 0.0 0.0 0.0 0.0 0.0

[k*] 15, ANÁLISIS ESTRUCTURAL

= ING. HUGO OLAZA HENOSTROZA
17, 19, 21
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

0.0 1170.7 2341.4 0.0 -1170.7 2341.4

[k*] 15, 0.0 2341.4 6316.9 0.0 -2341.4 3048.7

17, 19, 21 = 0.0 0.0 0.0 0.0 0.0 0.0
0.0 -1170.7 -2341.4 0.0 1170.7 -2341.4
0.0 2341.4 3048.7 0.0 -2341.4 6316.9

0.0 0.0 0.0 0.0 0.0 0.0

0.0 1170.7 2341.4 0.0 -1170.7 2341.4
[k*] 16, 0.0 6316.9 0.0 -2341.4 3048.7
2341.4
18, 20, 22, 23
0.0 0.0 0.0 0.0 0.0 0.0
=
0.0 -1170.7 -2341.4 0.0 1170.7 -2341.4
0.0 2341.4 3048.7 0.0 -2341.4 6316.9

8.- Ensamblaje de la Matriz de Rigidez Total [𝐾]= 〖 [𝑨_𝒆^∗] 〗 ^𝑻 [𝒌_𝒆^∗ ][𝑨_𝒆^∗ ]

- Ensamblaje [K]
1 2 3 4 5 6 7 8 9 10 11 12 … 33 …
24909 0 0 0 0 0 43590 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 4
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 5
0 0 0 0.0 0.0 215141.1 0 0 0 0 0 0 0.0 0.0 6
43590 0 0 0 0 0 102100 0 0 0 0 0 0 0 7
[K]1=
0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 9
0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 0 0 0 12
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 …
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 33

1 2 3 4 5 6 7 8 9 10 11 12 … 33
458 0 0 0 0 0 0 0 801 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 4
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 5
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 6
0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
[K]2=
0 0 0 0 0 0 0 65110 0 0 0 0 0 0 8
801 0 0 0 0 0 0 0 1872 0 0 0 0 0 9
0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 0 0 0 12
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 13
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 14

1 2 3 4 5 6 7 8 9 10 11 12 … 33
24909 0 0 0 0 0 0 0 0 0 43590 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 3

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA

[K]3=
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 4

0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 5
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 6
0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
[K]3=
0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 9
0 0 0 0 0 0 0 0 0 215141 0 0 0 0 10
43590 0 0 0 0 0 0 0 0 0 102100 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 0 0 0 12
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 13
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 14

1 2 3 4 5 6 7 8 9 10 11 12 … 33
38990 -38990 0 0 0 0 -58485 0 0 0 0 0 0 -58485 1
-38990 38990 0 0 0 0 58485 0 0 0 0 0 0 58485 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 4
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 5
0 0 0 0.0 0.0 301197.6 0 0 0 0 0 0 -301197.6 0.0 6
-58485 58485 0 0 0 0 117847 0 0 0 0 0 0 57608 7
[K]4=
0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 9
0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 0 0 0 12
0 0 0 0.0 0.0 -301197.6 0 0 0 0 0 0 301197.6 0.0 13
-58485 58485 0 0.0 0.0 0.0 57608 0 0 0 0 0 0.0 117847.2 14

Generacion de las formulas excel para obtener el aporte de cada barra y hallar la suma directa por cuestiones de dimensiones grandes de las
matrices. Esto con el fin de hallar directamente la sumatoria de aportes sin la necesidad de hallar cada uno
Fila Fila
Matriz K * del
[K]elem Formula de multiplicacion de matrices inicial final de
elemento
de [A] [A]
[K]1 MMULT(TRANSPOSE(B117:AH122);MMULT(E394:J399;B117:AH122)) 117 122 E394:J399
[K]2 MMULT(TRANSPOSE(B123:AH128);MMULT(E401:J406;B123:AH128)) 123 128 E401:J406
[K]3 MMULT(TRANSPOSE(B129:AH134);MMULT(E394:J399;B129:AH134)) 129 134 E394:J399
[K]4 MMULT(TRANSPOSE(B135:AH140);MMULT(E408:J413;B135:AH140)) 135 140 E408:J413
[K]5 MMULT(TRANSPOSE(B141:AH146);MMULT(E415:J420;B141:AH146)) 141 146 E415:J420
[K]6 MMULT(TRANSPOSE(B147:AH152);MMULT(E408:J413;B147:AH152)) 147 152 E408:J413
[K]7 MMULT(TRANSPOSE(B153:AH158);MMULT(E408:J413;B153:AH158)) 153 158 E408:J413
[K]8 MMULT(TRANSPOSE(B159:AH164);MMULT(E415:J420;B159:AH164)) 159 164 E415:J420
[K]9 MMULT(TRANSPOSE(B165:AH170);MMULT(E408:J413;B165:AH170)) 165 170 E408:J413
[K]10 MMULT(TRANSPOSE(B171:AH176);MMULT(E408:J413;B171:AH176)) 171 176 E408:J413
[K]11 MMULT(TRANSPOSE(B177:AH182);MMULT(E415:J420;B177:AH182)) 177 182 E415:J420
[K]12 MMULT(TRANSPOSE(B183:AH188);MMULT(E408:J413;B183:AH188)) 183 188 E408:J413
[K]13 MMULT(TRANSPOSE(B189:AH194);MMULT(E415:J420;B189:AH194)) 189 194 E415:J420
[K]14 MMULT(TRANSPOSE(B195:AH200);MMULT(E408:J413;B195:AH200)) 195 200 E408:J413
[K]15 MMULT(TRANSPOSE(B201:AH206);MMULT(E422:J427;B201:AH206)) 201 206 E422:J427
[K]16 MMULT(TRANSPOSE(B207:AH212);MMULT(E429:J434;B207:AH212)) 207 212 E429:J434
[K]17 MMULT(TRANSPOSE(B213:AH218);MMULT(E422:J427;B213:AH218)) 213 218 E422:J427
[K]18 MMULT(TRANSPOSE(B219:AH224);MMULT(E429:J434;B219:AH224)) 219 224 E429:J434
[K]19 MMULT(TRANSPOSE(B225:AH230);MMULT(E422:J427;B225:AH230)) 225 230 E422:J427
[K]20 MMULT(TRANSPOSE(B231:AH236);MMULT(E429:J434;B231:AH236)) 231 236 E429:J434
[K]21 MMULT(TRANSPOSE(B237:AH242);MMULT(E422:J427;B237:AH242)) 237 242 E422:J427
[K]22 MMULT(TRANSPOSE(B243:AH248);MMULT(E429:J434;B243:AH248)) 243 248 E429:J434

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

[K]23 MMULT(TRANSPOSE(B249:AH254);MMULT(E429:J434;B249:AH254)) 249 254 E429:J434

[𝐾]=∑_(𝑒=1)^𝑚▒ 〖〖 [𝐴_𝑒^∗] 〗 ^𝑇 [𝑘_𝑒^∗ ][𝐴_𝑒^∗ ] 〗

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

[𝐾]=∑_(𝑒=1)^𝑚▒ 〖〖 [𝐴_𝑒^∗] 〗 ^𝑇 [𝑘_𝑒^∗ ][𝐴_𝑒^∗ ] 〗

NOTA: LA MATRIZ COMPLETA SE PUEDE VER EN EL ARCHIVO EXCEL ADJUNTO

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
128980 -78705 0 0 0 0 -14895 0 -286 0 -14895 0 0 -58485 -1087 0
-78705 157409 -78705 0 0 0 58485 0 1087 0 58485 0 -58485 58485 0 0
0 -78705 157409 -78705 0 0 0 0 0 0 0 0 58485 0 1087 0
0 0 -78705 118420 -39715 0 0 0 0 0 0 0 0 0 0 0
0 0 0 -39715 39715 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 517509.5 2341.4 -1170.7 2341.4 0.0 0.0 0.0 -301197.6 0.0 0.0 0.0
-14895 58485 0 0 0 2341.4 226264.3 -2341.4 3048.7 0.0 0.0 0.0 0.0 57607.7 0.0 0.0
[K]T=
0 0 0 0 0 -1170.7 -2341.4 143413.8 0.0 -1170.7 2341.4 0.0 0.0 -75962.1 0.0 0.0
-286 1087 0 0 0 2341.4 3048.7 0.0 16685.2 -2341.4 3048.7 0.0 0.0 0.0 1081.9 0.0
0 0 0 0 0 0.0 0.0 -1170.7 -2341.4 517509.5 -2341.4 0.0 0.0 0.0 0.0 ###
-14895 58485 0 0 0 0.0 0.0 2341.4 3048.7 -2341.4 226264.3 0.0 0.0 0.0 0.0 0.0
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 302368.3 2341.4 -1170.7 2341.4 0.0
0 -58485 58485 0 0 -301197.6 0.0 0.0 0.0 0.0 0.0 2341.4 425361.7 -2341.4 3048.7 0.0
-58485 58485 0 0 0 0.0 57607.7 -75962.1 0.0 0.0 0.0 -1170.7 -2341.4 272112.7 0.0 ###
-1087 0 1087 0 0 0.0 0.0 0.0 1081.9 0.0 0.0 2341.4 3048.7 0.0 16993.0 ###
0 0 0 0 0 0.0 0.0 0.0 0.0 -301197.6 0.0 0.0 0.0 -1170.7 -2341.4 ###
-58485 0 58485 0 0 0.0 0.0 0.0 0.0 0.0 57607.7 0.0 0.0 2341.4 3048.7 ###
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 -301197.6 0.0 0.0 0.0 0.0
0 -58485 0 58485 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 57607.7 0.0 0.0 0.0
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -75962.1 0.0 0.0
0 -1087 0 1087 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1081.9 0.0
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 ###
0 -58485 0 58485 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 -58485 58485 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 -1087 0 1087 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 -58485 0 58485 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 0 -1087 1087 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 0 -58485 58485 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

* Estructura del K ordenado

Kuu Kur
[K]T=

Kru Krr

- GDLE 1-5
1 2 3 4 5
92253.9 -54184.6 14023.9 -3246.1 96.1 1
[K]L2=
-54184.6 74354.1 -57936.7 20330.4 -1725.5 2
14023.9 -57936.7 84111.0 -45783.3 8499.6 3
-3246.1 20330.4 -45783.3 42025.1 -14010.5 4
96.1 -1725.5 8499.6 -14010.5 7155.7 5

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
03.- Condensacion de la matriz de rigidez del portico P3

VISTA ELEVACIÓN DEL PORTICO 03

1.20m

0.25x0.50 23
16 17
r=0.17

120x5

3.0m 13 14
0.25x0.50 0.25x0.50 21 22
13 14 15
120x25

r=0.17

120x25

3.0m 12
10 11
0.25x0.50 0.25x0.50 19 20
10 11 12
120x25
120x25

r=0.17

3.0m 7 8 9
0.25x0.50 0.25x0.50 17 18
7 8 9
120x25

r=0.17

120x25

3.0m 4 5 6
0.25x0.50 0.25x0.50 15 16
4 5 6
120x25

120x25
r=0.17

3.5m 1 2 3

1 2 3
5m 5m
5m 5m

Dato
E= 3E+06 Tn/m²
1.- Determinacion de Cordenadas Globales Generalizadas y GDL
30 32
5 5

31 33 23
24 26 28
4 4 4
13 14
25 27 29 21 22
18 20 22
3 3 3
10 11 12
19 21 23 19 20
12 14 16
2 2 2 7 8 9
17 18
13 15 17
6 8 10
1 1 1 4 5 6
15 16
7 9 11

35 38 41 1 2 3
34 37 40

36 39 42

GDL: 33
 2.- Determinacion de Cordenadas Locales Generalizadas: {q} - {d}

1 3
2 5
Vigas
[𝑘𝑒]=[■8(■8(𝐸𝐴/𝐿&0&0@0&12𝐸𝐼/𝐿^3 &−6𝐸𝐼/𝐿^2 @0&−6𝐸𝐼/𝐿^2 &4𝐸𝐼/𝐿)&■8(−𝐸𝐴/𝐿&0&0@0&−12𝐸𝐼/𝐿^3 &−6𝐸𝐼/𝐿^2 @0&6𝐸𝐼/𝐿^2 &2𝐸𝐼/𝐿)@■8(−𝐸𝐴/𝐿&0&0@0&−12𝐸𝐼/𝐿^3 &6𝐸𝐼/𝐿^2 @0&−6𝐸𝐼/𝐿^2 &2𝐸𝐼/𝐿)&■8(𝐸𝐴/𝐿&0&0@
e: 15-23 4
2 4 1
+ m.transformcion 3 6
)/𝐿^3 @6𝐸𝐼/𝐿^2 ) █(6𝐸𝐼/𝐿^2 @4𝐸𝐼/𝐿@(−6𝐸𝐼)/𝐿^2 @2𝐸𝐼/𝐿) █((−12𝐸𝐼)/𝐿^3 @(−6𝐸𝐼)/𝐿^2 @12𝐸𝐼/𝐿^3 @(−6𝐸𝐼)/𝐿^2 ) █(6𝐸𝐼/𝐿^2 @2𝐸𝐼/𝐿@(−6𝐸𝐼)/𝐿^2 @4𝐸𝐼/𝐿)]
Columnas y placas
b1 16,18,20,22,23 b2 e: 1-14

15,17,19,21

3.- Cálculos previos - Datos de las barras

Columnas Vigas Placas

0.30 0.50 025

1.20 30
0.34 0.30 0.25

1.20m

15,17,19,21 16,18,20,22,23

(2−)𝐸𝐼/(1+)𝐿 (12.𝐸𝐼)/((1+)
Barra b h A E I EA EI AX AY L EA/L (4+)𝐸𝐼/(1+)𝐿(6.𝐸𝐼)/((1+) 𝐿^2 ) 𝐿^3 )
f

1 1.20 0.25 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3.5 3.50 215141 102100.2 50466.3 43590.4 24908.8 0.02
2 3.14 0.17 0.090792 2.5E+06 6.6E-04 2.3E+05 1646 0 3.5 3.50 65110 1871.8 930.9 800.8 457.6 0.01
3 1.20 0.25 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3.5 3.50 215141 102100.2 50466.3 43590.4 24908.8 0.02
4 1.20 0.30 0.36 2.5E+06 3.6E-02 9.0E+05 90359 0 3 3.00 301198 117847.2 57607.7 58485.0 38990.0 0.03
5 3.14 0.17 0.090792 2.5E+06 6.6E-04 2.3E+05 1646 0 3 3.00 75962 2179.6 1081.9 1087.2 724.8 0.01
6 1.20 0.25 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3 3.00 250998 118635.0 58395.5 59010.1 39340.1 0.02
7 1.20 0.30 0.36 2.5E+06 3.6E-02 9.0E+05 90359 0 3 3.00 301198 117847.2 57607.7 58485.0 38990.0 0.03
8 3.14 0.17 0.090792 2.5E+06 6.6E-04 2.3E+05 1646 0 3 3.00 75962 2179.6 1081.9 1087.2 724.8 0.01
9 1.20 0.25 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3 3.00 250998 118635.0 58395.5 59010.1 39340.1 0.02
10 1.20 0.25 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3 3.00 250998 118635.0 58395.5 59010.1 39340.1 0.02
11 3.14 0.17 0.090792 2.5E+06 6.6E-04 2.3E+05 1646 0 3 3.00 75962 2179.6 1081.9 1087.2 724.8 0.01
12 1.20 0.25 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3 3.00 250998 118635.0 58395.5 59010.1 39340.1 0.02
13 3.14 0.17 0.090792 2.5E+06 6.6E-04 2.3E+05 1646 0 3 3.00 75962 2179.6 1081.9 1087.2 724.8 0.01
14 1.20 0.25 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3 3.00 250998 118635.0 58395.5 59010.1 39340.1 0.02
15 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 4 0 4.00 0 ∞ 6316.9 3048.7 2341.4 1170.7 0.05
16 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 4 0 4.00 0 ∞ 6316.9 3048.7 2341.4 1170.7 0.05
17 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 4 0 4.00 0 ∞ 6316.9 3048.7 2341.4 1170.7 0.05
18 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 4 0 4.00 0 ∞ 6316.9 3048.7 2341.4 1170.7 0.05
19 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 4 0 4.00 0 ∞ 6316.9 3048.7 2341.4 1170.7 0.05
20 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 4 0 4.00 0 ∞ 6316.9 3048.7 2341.4 1170.7 0.05
21 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 4 0 4.00 0 ∞ 6316.9 3048.7 2341.4 1170.7 0.05
22 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 4 0 4.00 0 ∞ 6316.9 3048.7 2341.4 1170.7 0.05
23 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 4 0 4.00 0 ∞ 6316.9 3048.7 2341.4 1170.7 0.05

Momento de inercia de los Elementos

Grafico barras Ix Iy

2,5,8,11,13 6.6E-04 6.6E-04

R=0.17
0.30
…
0.30
0.50 15,16,17,18,19,20,21, 2.6E-03 6.5E-04
0.25 22
0.25

1,3,4,6,7,9,10,12,14 3.6E-02 1.6E-03

1.20

NOTA: LA MATRIZ COMPLETA SE PUEDE VER EN EL ARCHIVO EXCEL ADJUNTO

4.- Matriz de Transformacion de desplazamientos [A*]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]1
[A*]1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]2
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]3
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
[A*]4
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
[A*]5
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
[A*]6
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
[A*]7
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
[A*]8
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]9
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]10
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]11
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]12
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]13
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

[A*]14
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]14
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
[A*]15
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
[A*]16
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
[A*]17
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
[A*]18
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]19
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]20
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]21
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]22
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
[A*]22

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]23
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

5.- Matriz de rigidez de la barra [k]i, {q}-{d}

(2−)𝐸𝐼/(1+ )𝐿 (12.𝐸𝐼)/((1+)

Barra b h A E I EA EI AX AY L EA/L (4+)𝐸𝐼/(1+)𝐿 (6.𝐸𝐼)/((1+) 𝐿^2 ) 𝐿^3 )
f

1 1.2 0.25 0.3 3E+06 0.036 752994.024 90359.283 0 3.5 3.5 215141 102100 50466.28 43590.4 24908.8 0.02
2 3.1415927 0.17 0.090792 3E+06 0.00066 227886.181 1646.4777 0 3.5 3.5 65110 1871.771 930.9263 800.771 457.5832 0.01
3 1.2 0.25 0.3 3E+06 0.036 752994.024 90359.283 0 3.5 3.5 215141 102100 50466.28 43590.4 24908.8 0.02
4 1.2 0.3 0.36 3E+06 0.036 903592.829 90359.283 0 3 3 301198 117847 57607.7 58485 38990 0.03
5 3.1415927 0.17 0.090792 3E+06 0.00066 227886.181 1646.4777 0 3 3 75962 2179.594 1081.942 1087.18 724.7857 0.01
6 1.2 0.25 0.3 3E+06 0.036 752994.024 90359.283 0 3 3 250998 118635 58395.45 59010.1 39340.1 0.02
7 1.2 0.3 0.36 3E+06 0.036 903592.829 90359.283 0 3 3 301198 117847 57607.7 58485 38990 0.03
8 3.1415927 0.17 0.090792 3E+06 0.00066 227886.181 1646.4777 0 3 3 75962 2179.594 1081.942 1087.18 724.7857 0.01
9 1.2 0.25 0.3 3E+06 0.036 752994.024 90359.283 0 3 3 250998 118635 58395.45 59010.1 39340.1 0.02
10 1.2 0.25 0.3 3E+06 0.036 752994.024 90359.283 0 3 3 250998 118635 58395.45 59010.1 39340.1 0.02
11 3.1415927 0.17 0.090792 3E+06 0.00066 227886.181 1646.4777 0 3 3 75962 2179.594 1081.942 1087.18 724.7857 0.01
12 1.2 0.25 0.3 3E+06 0.036 752994.024 90359.283 0 3 3 250998 118635 58395.45 59010.1 39340.1 0.02
13 3.1415927 0.17 0.090792 3E+06 0.00066 227886.181 1646.4777 0 3 3 75962 2179.594 1081.942 1087.18 724.7857 0.01
14 1.2 0.25 0.3 3E+06 0.036 752994.024 90359.283 0 3 3 250998 118635 58395.45 59010.1 39340.1 0.02
15 0.25 0.5 0.125 3E+06 0.0026 313747.51 6536.4065 4 0 4 0 6316.9 3048.697 2341.4 1170.7 0.05
16 0.25 0.5 0.125 3E+06 0.0026 313747.51 6536.4065 4 0 4 0 6316.9 3048.697 2341.4 1170.7 0.05
17 0.25 0.5 0.125 3E+06 0.0026 313747.51 6536.4065 4 0 4 0 6316.9 3048.697 2341.4 1170.7 0.05
18 0.25 0.5 0.125 3E+06 0.0026 313747.51 6536.4065 4 0 4 0 6316.9 3048.697 2341.4 1170.7 0.05
19 0.25 0.5 0.125 3E+06 0.0026 313747.51 6536.4065 4 0 4 0 6316.9 3048.697 2341.4 1170.7 0.05
20 0.25 0.5 0.125 3E+06 0.0026 313747.51 6536.4065 4 0 4 0 6316.9 3048.697 2341.4 1170.7 0.05
21 0.25 0.5 0.125 3E+06 0.0026 313747.51 6536.4065 4 0 4 0 6316.9 3048.697 2341.4 1170.7 0.05
22 0.25 0.5 0.125 3E+06 0.0026 313747.51 6536.4065 4 0 4 0 6316.9 3048.697 2341.4 1170.7 0.05
23 0.25 0.5 0.125 3E+06 0.0026 313747.51 6536.4065 4 0 4 0 6316.9 3048.697 2341.4 1170.7 0.05

215141 0.0 0.0 -215141 0.0 0.0

0.0 24908.8 -43590.4 0.0 -24908.8 -43590.4
0.0 -43590.4 102100.2 0.0 43590.4 50466.3
[k] 1,3 =
-215141 0.0 0.0 215141.1 0.0 0.0
0.0 -24908.8 43590.4 0.0 24908.8 43590.4
0.0 -43590.4 50466.3 0.0 43590.4 102100.2

65110 0.0 0.0 -65110 0.0 0.0

0.0 457.6 -800.8 0.0 -457.6 -800.8
0.0 0.0 1871.8 0.0 0.0 930.9
[k] 2 =
-65110 0.0 0.0 65110.3 0.0 0.0
0.0 -457.6 0.0 0.0 457.6 800.8
0.0 0.0 930.9 0.0 800.8 1871.8

301198 0.0 0.0 -301198 0.0 0.0

0.0 38990.0 -58485.0 0.0 -38990.0 -58485.0

[k] 4, 6, 7, 9, 0.0 -58485.0 117847.2 0.0 58485.0 57607.7

10, 12, 14 = -301198 0.0 0.0 301197.6 0.0 0.0
0.0 -38990.0 58485.0 0.0 38990.0 58485.0
0.0 -58485.0 57607.7 0.0 58485.0 117847.2

75962 0.0 0.0 -75962 0.0 0.0

0.0 724.8 -1087.2 0.0 -724.8 -1087.2
[k] 5, 8, 11, 0.0 -1087.2 2179.6 0.0 1087.2 1081.9
13 = -75962 0.0 0.0 75962.1 0.0 0.0
0.0 -724.8 1087.2 0.0 724.8 1087.2
0.0 -1087.2 1081.9 0.0 1087.2 2179.6 Columas y placas
b1= 0 b2= 0
[K] =[ST] [K '] [S] 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0
0.0 1170.7 2341.4 0.0 -1170.7 2341.4 0.0 1.0 0.0 0.0 0.0 0.0
[k]' 15, 17, 0.0 2341.4 6316.9 0.0 -2341.4 3048.7 0.0 0.0 1.0 0.0 0.0 0.0
[s] 15 =
19, 21 = 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0
0.0 -1170.7 -2341.4 0.0 1170.7 -2341.4 0.0 0.0 0.0 0.0 1.0 0.0
0.0 2341.4 3048.7 0.0 -2341.4 6316.9 0.0 0.0 0.0 0.0 0.0 1.0
 0.0 0.0 0.0 0.0 0.0 0.0
0.0 1170.7 2341.4 0.0 -1170.7 2341.4
[k] 15, 17, 19, 0.0 2341.4 6316.9 0.0 -2341.4 3048.7
21 = 0.0 0.0 0.0 0.0 0.0 0.0
0.0 -1170.7 -2341.4 0.0 1170.7 -2341.4
0.0 2341.4 3048.7 0.0 -2341.4 6316.9

b1= 0 b2= 0
[K] =[ST] [K '] [S] 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0
0.0 1170.7 2341.4 0.0 -1170.7 2341.4 0.0 1.0 0.0 0.0 0.0 0.0
[k]' 16, 18, 0.0 2341.4 6316.9 0.0 -2341.4 3048.7 0.0 0.0 1.0 0.0 0.0 0.0
[s] 16 =
20, 22, 23 = 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0
0.0 -1170.7 -2341.4 0.0 1170.7 -2341.4 0.0 0.0 0.0 0.0 1.0 0.0
0.0 2341.4 3048.7 0.0 -2341.4 6316.9 0.0 0.0 0.0 0.0 0.0 1.0

0.0 0.0 0.0 0.0 0.0 0.0

0.0 1170.7 2341.4 0.0 -1170.7 2341.4
[k] 16, 18, 20, 0.0 2341.4 6316.9 0.0 -2341.4 3048.7
22, 23 = 0.0 0.0 0.0 0.0 0.0 0.0
0.0 -1170.7 -2341.4 0.0 1170.7 -2341.4
0.0 2341.4 3048.7 0.0 -2341.4 6316.9 Vigas con brazo rigido

6.- Determinar la Matriz deTransformacion de desplazamientos [R] i {𝑑}=[𝑅]{𝑑^∗ }

cos a sen a 0 0 0 0
sen a -cos a 0 0 0 0
0 0 1 0 0 0
[R]i=
0 0 0 cos a sen a 0
0 0 0 sen a -cos a 0
0 0 0 0 0 1

0 1 0 0 0 0
1 0 0 0 0 0
0 0 1 0 0 0
[R]1,3=
0 0 0 0 1 0
0 0 0 1 0 0
0 0 0 0 0 1

0 1 0 0 0 0
1 0 0 0 0 0
0 0 1 0 0 0
[R]2=
0 0 0 0 1 0
0 0 0 1 0 0
0 0 0 0 0 1

0 1 0 0 0 0
1 0 0 0 0 0
[R]4, 6, 7, 9, 0 0 1 0 0 0
10, 12, 14= 0 0 0 0 1 0
0 0 0 1 0 0
0 0 0 0 0 1

0 1 0 0 0 0
1 0 0 0 0 0
[R]5, 8, 11, 13 0 0 1 0 0 0
= 0 0 0 0 1 0
0 0 0 1 0 0
0 0 0 0 0 1

1 0 0 0 0 0
0 1 0 0 0 0
[R]15, 17, 19, 0 0 1 0 0 0
21= 0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1

1 0 0 0 0 0
0 1 0 0 0 0
[R]16, 18, 20, 0 0 1 0 0 0
22, 23= 0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1
7.- Matriz de rigidez de la barra [k*]i, {q*}-{d*} [𝑘^∗ ]=[𝑅]^𝑇 [𝑘][𝑅]

24908.8 0.0 -43590.4 -24908.8 0.0 -43590.4 E394:J399

0.0 215141.1 0.0 0.0 -215141.1 0.0 E401:J406
-43590.4 0.0 102100.2 43590.4 0.0 50466.3 E408:J413
[k*] 1,3 =
-24908.8 0.0 43590.4 24908.8 0.0 43590.4 E415:J420
0.0 ### 0.0 0.0 215141.1 0.0 E422:J427
-43590.4 0.0 50466.3 43590.4 0.0 102100.2 E429:J434

457.6 0.0 -800.8 -457.6 0.0 -800.8

0.0 65110.3 0.0 0.0 -65110.3 0.0
0.0 0.0 1871.8 0.0 0.0 930.9
[k*] 2 =
-457.6 0.0 0.0 457.6 0.0 800.8
0.0 -65110.3 0.0 0.0 65110.3 0.0
0.0 0.0 930.9 800.8 0.0 1871.8

38990.0 0.0 -58485.0 -38990.0 0.0 -58485.0

0.0 301197.6 0.0 0.0 -301197.6 0.0

[k*] 4, 6, 7, -58485.0 0.0 117847.2 58485.0 0.0 57607.7

9, 10, 12, 14 = -38990.0 0.0 58485.0 38990.0 0.0 58485.0
0.0 ### 0.0 0.0 301197.6 0.0
-58485.0 0.0 57607.7 58485.0 0.0 117847.2

724.8 0.0 -1087.2 -724.8 0.0 -1087.2

0.0 75962.1 0.0 0.0 -75962.1 0.0

[k*] 5, 8, 11, -1087.2 0.0 2179.6 1087.2 0.0 1081.9

13= -724.8 0.0 1087.2 724.8 0.0 1087.2
0.0 -75962.1 0.0 0.0 75962.1 0.0
-1087.2 0.0 1081.9 1087.2 0.0 2179.6

0.0 0.0 0.0 0.0 0.0 0.0

0.0 1170.7 2341.4 0.0 -1170.7 2341.4
[k*] 15, 17, 0.0 2341.4 6316.9 0.0 -2341.4 3048.7
19, 21 = 0.0 0.0 0.0 0.0 0.0 0.0
0.0 -1170.7 -2341.4 0.0 1170.7 -2341.4
0.0 2341.4 3048.7 0.0 -2341.4 6316.9

0.0 0.0 0.0 0.0 0.0 0.0

0.0 1170.7 2341.4 0.0 -1170.7 2341.4
[k*] 16, 18, 0.0 2341.4 6316.9 0.0 -2341.4 3048.7
20, 22, 23 = 0.0 0.0 0.0 0.0 0.0 0.0
0.0 -1170.7 -2341.4 0.0 1170.7 -2341.4
0.0 2341.4 3048.7 0.0 -2341.4 6316.9

8.- Ensamblaje de la Matriz de Rigidez Total [𝐾]= 〖 [𝑨_𝒆^∗] 〗 ^𝑻 [𝒌_𝒆^∗ ][𝑨_𝒆^∗ ]

- Ensamblaje [K]
1 2 3 4 5 6 7 8 9 10 11 12 … 33 …
24909 0 0 0 0 0 43590 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 4
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 5
0 0 0 0.0 0.0 215141.1 0 0 0 0 0 0 0.0 0.0 6
43590 0 0 0 0 0 102100 0 0 0 0 0 0 0 7
[K]1=
0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 9
0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 0 0 0 12
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 …
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 33
 1 2 3 4 5 6 7 8 9 10 11 12 … 33
458 0 0 0 0 0 0 0 801 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 4
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 5
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 6
0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
[K]2=
0 0 0 0 0 0 0 65110 0 0 0 0 0 0 8
801 0 0 0 0 0 0 0 1872 0 0 0 0 0 9
0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 0 0 0 12
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 13
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 14

1 2 3 4 5 6 7 8 9 10 11 12 … 33
24909 0 0 0 0 0 0 0 0 0 43590 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 4
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 5
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 6
0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
[K]3=
0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 9
0 0 0 0 0 0 0 0 0 215141 0 0 0 0 10
43590 0 0 0 0 0 0 0 0 0 102100 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 0 0 0 12
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 13
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 14

1 2 3 4 5 6 7 8 9 10 11 12 … 33
38990 -38990 0 0 0 0 -58485 0 0 0 0 0 0 -58485 1
-38990 38990 0 0 0 0 58485 0 0 0 0 0 0 58485 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 4
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 5
0 0 0 0.0 0.0 301197.6 0 0 0 0 0 0 -301197.6 0.0 6
-58485 58485 0 0 0 0 117847 0 0 0 0 0 0 57608 7
[K]4=
0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 9
0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 0 0 0 12
0 0 0 0.0 0.0 -301197.6 0 0 0 0 0 0 301197.6 0.0 13
-58485 58485 0 0.0 0.0 0.0 57608 0 0 0 0 0 0.0 117847.2 14

Generacion de las formulas excel para obtener el aporte de cada barra y hallar la suma directa por cuestiones de dimensiones grandes de las
matrices. Esto con el fin de hallar directamente la sumatoria de aportes sin la necesidad de hallar cada uno
Fila Fila
Matriz K * del
[K]elem Formula de multiplicacion de matrices inicial final de
elemento
de [A] [A]
[K]1 MMULT(TRANSPOSE(B117:AH122);MMULT(E394:J399;B117:AH122)) 117 122 E394:J399
[K]2 MMULT(TRANSPOSE(B123:AH128);MMULT(E401:J406;B123:AH128)) 123 128 E401:J406
[K]3 MMULT(TRANSPOSE(B129:AH134);MMULT(E394:J399;B129:AH134)) 129 134 E394:J399
[K]4 MMULT(TRANSPOSE(B135:AH140);MMULT(E408:J413;B135:AH140)) 135 140 E408:J413
[K]5 MMULT(TRANSPOSE(B141:AH146);MMULT(E415:J420;B141:AH146)) 141 146 E415:J420
[K]6 MMULT(TRANSPOSE(B147:AH152);MMULT(E408:J413;B147:AH152)) 147 152 E408:J413
[K]7 MMULT(TRANSPOSE(B153:AH158);MMULT(E408:J413;B153:AH158)) 153 158 E408:J413
[K]8 MMULT(TRANSPOSE(B159:AH164);MMULT(E415:J420;B159:AH164)) 159 164 E415:J420
[K]9 MMULT(TRANSPOSE(B165:AH170);MMULT(E408:J413;B165:AH170)) 165 170 E408:J413
[K]10 MMULT(TRANSPOSE(B171:AH176);MMULT(E408:J413;B171:AH176)) 171 176 E408:J413
[K]11 MMULT(TRANSPOSE(B177:AH182);MMULT(E415:J420;B177:AH182)) 177 182 E415:J420
[K]12 MMULT(TRANSPOSE(B183:AH188);MMULT(E408:J413;B183:AH188)) 183 188 E408:J413
[K]13 MMULT(TRANSPOSE(B189:AH194);MMULT(E415:J420;B189:AH194)) 189 194 E415:J420
[K]14 MMULT(TRANSPOSE(B195:AH200);MMULT(E408:J413;B195:AH200)) 195 200 E408:J413
[K]15 MMULT(TRANSPOSE(B201:AH206);MMULT(E422:J427;B201:AH206)) 201 206 E422:J427
[K]16 MMULT(TRANSPOSE(B207:AH212);MMULT(E429:J434;B207:AH212)) 207 212 E429:J434
[K]17 MMULT(TRANSPOSE(B213:AH218);MMULT(E422:J427;B213:AH218)) 213 218 E422:J427
[K]18 MMULT(TRANSPOSE(B219:AH224);MMULT(E429:J434;B219:AH224)) 219 224 E429:J434
[K]19 MMULT(TRANSPOSE(B225:AH230);MMULT(E422:J427;B225:AH230)) 225 230 E422:J427
[K]20 MMULT(TRANSPOSE(B231:AH236);MMULT(E429:J434;B231:AH236)) 231 236 E429:J434
[K]21 MMULT(TRANSPOSE(B237:AH242);MMULT(E422:J427;B237:AH242)) 237 242 E422:J427
[K]22 MMULT(TRANSPOSE(B243:AH248);MMULT(E429:J434;B243:AH248)) 243 248 E429:J434
 [K]23 MMULT(TRANSPOSE(B249:AH254);MMULT(E429:J434;B249:AH254)) 249 254 E429:J434

[𝐾]=∑_(𝑒=1)^𝑚▒ 〖〖 [𝐴_𝑒^∗] 〗 ^𝑇 [𝑘_𝑒^∗ ][𝐴_𝑒^∗ ] 〗

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
128980 -78705 0 0 0 0 -14895 0 -286 0 -14895 0 0 -58485 -1087 0
-78705 157409 -78705 0 0 0 58485 0 1087 0 58485 0 -58485 58485 0 0
0 -78705 157409 -78705 0 0 0 0 0 0 0 0 58485 0 1087 0
0 0 -78705 118420 -39715 0 0 0 0 0 0 0 0 0 0 0
0 0 0 -39715 39715 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 517509.5 2341.4 -1170.7 2341.4 0.0 0.0 0.0 -301197.6 0.0 0.0 0.0
-14895 58485 0 0 0 2341.4 226264.3 -2341.4 3048.7 0.0 0.0 0.0 0.0 57607.7 0.0 0.0
[K]T=
0 0 0 0 0 -1170.7 -2341.4 143413.8 0.0 -1170.7 2341.4 0.0 0.0 -75962.1 0.0 0.0
-286 1087 0 0 0 2341.4 3048.7 0.0 16685.2 -2341.4 3048.7 0.0 0.0 0.0 1081.9 0.0
0 0 0 0 0 0.0 0.0 -1170.7 -2341.4 517509.5 -2341.4 0.0 0.0 0.0 0.0 ###
-14895 58485 0 0 0 0.0 0.0 2341.4 3048.7 -2341.4 226264.3 0.0 0.0 0.0 0.0 0.0
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 302368.3 2341.4 -1170.7 2341.4 0.0
0 -58485 58485 0 0 -301197.6 0.0 0.0 0.0 0.0 0.0 2341.4 425361.7 -2341.4 3048.7 0.0
-58485 58485 0 0 0 0.0 57607.7 -75962.1 0.0 0.0 0.0 -1170.7 -2341.4 272112.7 0.0 ###
-1087 0 1087 0 0 0.0 0.0 0.0 1081.9 0.0 0.0 2341.4 3048.7 0.0 16993.0 ###
0 0 0 0 0 0.0 0.0 0.0 0.0 -301197.6 0.0 0.0 0.0 -1170.7 -2341.4 ###
-58485 0 58485 0 0 0.0 0.0 0.0 0.0 0.0 57607.7 0.0 0.0 2341.4 3048.7 ###
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 -301197.6 0.0 0.0 0.0 0.0
0 -58485 0 58485 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 57607.7 0.0 0.0 0.0
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -75962.1 0.0 0.0
0 -1087 0 1087 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1081.9 0.0
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 ###
0 -58485 0 58485 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 -58485 58485 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 -1087 0 1087 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 -58485 0 58485 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 0 -1087 1087 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 0 -58485 58485 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

* Estructura del K ordenado

Kuu Kur
[K]T=

Kru Krr

- GDLE 1-5
1 2 3 4 5
92253.9 -54184.6 14023.9 -3246.1 96.1 1
[K]L3=
-54184.6 74354.1 -57936.7 20330.4 -1725.5 2
14023.9 -57936.7 84111.0 -45783.3 8499.6 3
-3246.1 20330.4 -45783.3 42025.1 -14010.5 4
96.1 -1725.5 8499.6 -14010.5 7155.7 5
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

04.- Condensacion de la matriz de rigidez del portico P4

VISTA ELEVACIÓN DEL PORTICO 04

1.20m

23
0.25x0.50
16 17
25x1.2

30x30

13 14
3.0m
0.25x0.50 0.25x0.50 21 22
13 14 15
25x1.2

30x30
30x30

3.0m 10 11 12
19 20
0.25x0.50 0.25x0.50
10 11 12
Dato
25x1.2

9
30x30
30x30

3.0m 7 8
17 18 E= 2509980 Tn/m²
0.25x0.50 0.25x0.50
7 8 9
25x1.2

30x30
30x30

4 5 6
3.0m
15 16
0.25x0.50 0.25x0.50
4 5 6
30x30

3
30x30

1 2
25x1.2

3.5m
1 2 3
5m 5m
5m 5m

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

1.- Determinacion de Cordenadas Globales Generalizadas y GDL

30 32
5 5

31 33 23
24 26 28
4 4 4 13 14
21 22
25 27 29
18 20 22
3 3 3 10 11 12
19 20
19 21 23
12 14 16
7 8 9
2 2 2
17 18
13 15 17
6 8 10 4 5 6
1 1 1 15 16

7 9 11
1 2 3

35 38 41
34 37 40

36 39 42
GDL: 1, 2, 3, 4, 5, 6, 7..., 8, 9, …,33
2.- Determinacion de Cordenadas Locales Generalizadas: {q} - {d}

1 3
2 5
Vigas
[𝑘𝑒]=[■8(■8(𝐸𝐴/𝐿&0&0@0&12𝐸𝐼/𝐿^3 &−6𝐸𝐼/𝐿^2 @0&−6𝐸𝐼/𝐿^2 &4𝐸𝐼/𝐿)&■8(−𝐸𝐴/𝐿&0&0@0&−12𝐸𝐼/𝐿^3 &−6𝐸𝐼/𝐿^2 @0&6𝐸𝐼/𝐿^2 &2𝐸𝐼/𝐿)@■8(−𝐸𝐴/𝐿&0&0@0&−12𝐸𝐼/𝐿^3 &6𝐸
e: 7, 8, 9, 10 4
2 4 1
+ m.transformcion 3 6
𝐸𝐼/𝐿^2 ) █(6𝐸𝐼/𝐿^2 @4𝐸𝐼/𝐿@(−6𝐸𝐼)/𝐿^2 @2𝐸𝐼/𝐿) █((−12𝐸𝐼)/𝐿^3 @(−6𝐸𝐼)/𝐿^2 @12𝐸𝐼/𝐿^3 @(−6𝐸𝐼)/𝐿^2 ) █(6𝐸𝐼/𝐿^2 @2𝐸𝐼/𝐿@(−6𝐸𝐼)/𝐿^2 @4𝐸𝐼/𝐿)]
Columnas y placas
b1 16,18,20,22,23 b2 e: 1-14

15,17,19,21

3.- Cálculos previos - Datos de las barras

Columnas Vigas Placas

0.30 0.25
0.50
1.20
0.30 0.25

1.20m

15,17,19,21 16,18,20,22,23

(2−)𝐸𝐼/(1+
(4+)𝐸𝐼/(1+)𝐿 )𝐿 (12.𝐸𝐼)/((1+)
(6.𝐸𝐼)/((1+) 𝐿^2 ) 𝐿^3 )
Barra b h A E I EA EI AX AY L EA/L
1 0.30 0.30 0.09 2.5E+06 6.8E-04 2.3E+05 1694 0 3.5 3.50 64542 1905.0 936.8 811.9 464.0
2 0.25 1.20 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3.5 3.50 215141 83075.4 31441.5 32719.1 18696.6
3 0.30 0.30 0.09 2.5E+06 6.8E-04 2.3E+05 1694 0 3.5 3.50 64542 1905.0 936.8 811.9 464.0

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

4 0.30 0.30 0.09 2.5E+06 6.8E-04 2.3E+05 1694 0 3 3.00 75299 2209.6 1080.1 1096.6 731.1
5 0.25 1.20 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3 3.00 250998 91173.3 30933.8 40702.4 27134.9
6 0.30 0.30 0.09 2.5E+06 6.8E-04 2.3E+05 1694 0 3 3.00 75299 2209.6 1080.1 1096.6 731.1
7 0.30 0.30 0.09 2.5E+06 6.8E-04 2.3E+05 1694 0 3 3.00 75299 2209.6 1080.1 1096.6 731.1
8 0.25 1.20 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3 3.00 250998 91173.3 30933.8 40702.4 27134.9
9 0.30 0.30 0.09 2.5E+06 6.8E-04 2.3E+05 1694 0 3 3.00 75299 2209.6 1080.1 1096.6 731.1
10 0.30 0.30 0.09 2.5E+06 6.8E-04 2.3E+05 1694 0 3 3.00 75299 2209.6 1080.1 1096.6 731.1
11 0.25 1.20 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3 3.00 250998 91173.3 30933.8 40702.4 27134.9
12 0.30 0.30 0.09 2.5E+06 6.8E-04 2.3E+05 1694 0 3 3.00 75299 2209.6 1080.1 1096.6 731.1
13 0.25 1.20 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3 3.00 250998 91173.3 30933.8 40702.4 27134.9
14 0.30 0.30 0.09 2.5E+06 6.8E-04 2.3E+05 1694 0 3 3.00 75299 2209.6 1080.1 1096.6 731.1
15 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 4 0 4.00 0 ∞ 6316.9 3048.7 2341.4 1170.7
16 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 4 0 4.00 0 ∞ 6316.9 3048.7 2341.4 1170.7
17 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 4 0 4.00 0 ∞ 6316.9 3048.7 2341.4 1170.7
18 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 4 0 4.00 0 ∞ 6316.9 3048.7 2341.4 1170.7
19 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 4 0 4.00 0 ∞ 6316.9 3048.7 2341.4 1170.7
20 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 4 0 4.00 0 ∞ 6316.9 3048.7 2341.4 1170.7
21 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 4 0 4.00 0 ∞ 6316.9 3048.7 2341.4 1170.7
22 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 4 0 4.00 0 ∞ 6316.9 3048.7 2341.4 1170.7
23 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 4 0 4.00 0 ∞ 6316.9 3048.7 2341.4 1170.7

4.- Matriz de Transformacion de desplazamientos [A*]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]2
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]3
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
[A*]4
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
[A*]5
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
[A*]6
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
[A*]7
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
[A*]8
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]9
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]10
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]11
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]12
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]13
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]14
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
[A*]15
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
[A*]16
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
[A*]17
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
[A*]18
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]19
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]20
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]21
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]22
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]23
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

5.- Matriz de rigidez de la barra [k]i, {q}-{d}

(2−)𝐸𝐼/(1+
(4+)𝐸𝐼/(1+)𝐿 )𝐿 (12.𝐸𝐼)/((1+)
(6.𝐸𝐼)/((1+) 𝐿^2 ) 𝐿^3 )
Barra b h A E I EA EI AX AY L EA/L

1 0.3 0.3 0.09 2509980 0.00068 225898.207164 1694.2366 0 3.5 3.5 64542.34 1904.953 936.8177 811.9345 463.9625
2 0.25 1.2 0.3 2509980 0.036 752994.023881 90359.283 0 3.5 3.5 215141 83075.39 31441.51 32719.11 18696.64
3 0.3 0.3 0.09 2509980 0.00068 225898.207164 1694.2366 0 3.5 3.5 64542.34 1904.953 936.8177 811.9345 463.9625
4 0.3 0.3 0.09 2509980 0.00068 225898.207164 1694.2366 0 3 3 75299.4 2209.635 1080.144 1096.593 731.0622
5 0.25 1.2 0.3 2509980 0.036 752994.023881 90359.283 0 3 3 250998 91173.33 30933.81 40702.38 27134.92
6 0.3 0.3 0.09 2509980 0.00068 225898.207164 1694.2366 0 3 3 75299.4 2209.635 1080.144 1096.593 731.0622
7 0.3 0.3 0.09 2509980 0.00068 225898.207164 1694.2366 0 3 3 75299.4 2209.635 1080.144 1096.593 731.0622
8 0.25 1.2 0.3 2509980 0.036 752994.023881 90359.283 0 3 3 250998 91173.33 30933.81 40702.38 27134.92
9 0.3 0.3 0.09 2509980 0.00068 225898.207164 1694.2366 0 3 3 75299.4 2209.635 1080.144 1096.593 731.0622
10 0.3 0.3 0.09 2509980 0.00068 225898.207164 1694.2366 0 3 3 75299.4 2209.635 1080.144 1096.593 731.0622
11 0.25 1.2 0.3 2509980 0.036 752994.023881 90359.283 0 3 3 250998 91173.33 30933.81 40702.38 27134.92
12 0.3 0.3 0.09 2509980 0.00068 225898.207164 1694.2366 0 3 3 75299.4 2209.635 1080.144 1096.593 731.0622
13 0.25 1.2 0.3 2509980 0.036 752994.023881 90359.283 0 3 3 250998 91173.33 30933.81 40702.38 27134.92
14 0.3 0.3 0.09 2509980 0.00068 225898.207164 1694.2366 0 3 3 75299.4 2209.635 1080.144 1096.593 731.0622
15 0.25 0.5 0.125 2509980 0.0026 313747.50995 6536.4065 4 0 4 0 6316.9 3048.697 2341.399 1170.7
16 0.25 0.5 0.125 2509980 0.0026 313747.50995 6536.4065 4 0 4 0 6316.9 3048.697 2341.399 1170.7
17 0.25 0.5 0.125 2509980 0.0026 313747.50995 6536.4065 4 0 4 0 6316.9 3048.697 2341.399 1170.7
18 0.25 0.5 0.125 2509980 0.0026 313747.50995 6536.4065 4 0 4 0 6316.9 3048.697 2341.399 1170.7
19 0.25 0.5 0.125 2509980 0.0026 313747.50995 6536.4065 4 0 4 0 6316.9 3048.697 2341.399 1170.7
20 0.25 0.5 0.125 2509980 0.0026 313747.50995 6536.4065 4 0 4 0 6316.9 3048.697 2341.399 1170.7
21 0.25 0.5 0.125 2509980 0.0026 313747.50995 6536.4065 4 0 4 0 6316.9 3048.697 2341.399 1170.7
22 0.25 0.5 0.125 2509980 0.0026 313747.50995 6536.4065 4 0 4 0 6316.9 3048.697 2341.399 1170.7
23 0.25 0.5 0.125 2509980 0.0026 313747.50995 6536.4065 4 0 4 0 6316.9 3048.697 2341.399 1170.7

64542 0.0 0.0 -64542 0.0 0.0

0.0 464.0 -811.9 0.0 -464.0 -811.9
0.0 -811.9 1905.0 0.0 811.9 936.8
[k] 1,3 =
-64542 0.0 0.0 64542.3 0.0 0.0
0.0 -464.0 811.9 0.0 464.0 811.9
0.0 -811.9 936.8 0.0 811.9 1905.0

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

215141 0.0 0.0 -215141 0.0 0.0

0.0 18696.6 -32719.1 0.0 -18696.6 -32719.1
0.0 0.0 83075.4 0.0 0.0 31441.5
[k] 2 =
-215141 0.0 0.0 215141.1 0.0 0.0
0.0 -18696.6 0.0 0.0 18696.6 32719.1
0.0 0.0 31441.5 0.0 32719.1 83075.4

75299 0.0 0.0 -75299 0.0 0.0

0.0 731.1 -1096.6 0.0 -731.1 -1096.6
[k] 4, 6, 7, 9, 0.0 -1096.6 2209.6 0.0 1096.6 1080.1
10, 12, 14 = -75299 0.0 0.0 75299.4 0.0 0.0
0.0 -731.1 1096.6 0.0 731.1 1096.6
0.0 -1096.6 1080.1 0.0 1096.6 2209.6

250998 0.0 0.0 -250998 0.0 0.0

0.0 27134.9 -40702.4 0.0 -27134.9 -40702.4

[k] 5, 8, 11, 13 0.0 -40702.4 91173.3 0.0 40702.4 30933.8

= -250998 0.0 0.0 250998.0 0.0 0.0
0.0 -27134.9 40702.4 0.0 27134.9 40702.4
0.0 -40702.4 30933.8 0.0 40702.4 91173.3 Columas y placas
b1= 0 b2= 0.6
[K] =[ST] [K '] [S] 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0
0.0 1170.7 2341.4 0.0 -1170.7 2341.4 0.0 1.0 0.0 0.0 0.0
[k]' 15, 17, 19, 0.0 2341.4 6316.9 0.0 -2341.4 3048.7 0.0 0.0 1.0 0.0 0.0
[s] 15 =
21 = 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0
0.0 -1170.7 -2341.4 0.0 1170.7 -2341.4 0.0 0.0 0.0 0.0 1.0
0.0 2341.4 3048.7 0.0 -2341.4 6316.9 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0

0.0 1170.7 2341.4 0.0 -1170.7 3043.8
[k] 15, 17, 19, 0.0 2341.4 6316.9 0.0 -2341.4 4453.5
21 = 0.0 0.0 0.0 0.0 0.0 0.0
0.0 -1170.7 -2341.4 0.0 1170.7 -3043.8
0.0 3043.8 4453.5 0.0 -3043.8 9548.0
b1= 0.6 b2= 0
[K] =[ST] [K '] [S] 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0
0.0 1170.7 2341.4 0.0 -1170.7 2341.4 0.0 1.0 0.6 0.0 0.0
[k]' 16, 18, 20, 0.0 2341.4 6316.9 0.0 -2341.4 3048.7 0.0 0.0 1.0 0.0 0.0
[s] 16 =
22, 23 = 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0
0.0 -1170.7 -2341.4 0.0 1170.7 -2341.4 0.0 0.0 0.0 0.0 1.0
0.0 2341.4 3048.7 0.0 -2341.4 6316.9 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0

0.0 1170.7 3043.8 0.0 -1170.7 2341.4
[k] 16, 18, 20, 0.0 3043.8 9548.0 0.0 -3043.8 4453.5
22, 23 = 0.0 0.0 0.0 0.0 0.0 0.0
0.0 -1170.7 -3043.8 0.0 1170.7 -2341.4
0.0 2341.4 4453.5 0.0 -2341.4 6316.9 Vigas con brazo rigido

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

6.- Determinar la Matriz deTransformacion de desplazamientos [R]i {𝑑}=[𝑅]{𝑑^∗ }

cos a sen a 0 0 0 0
sen a -cos a 0 0 0 0
0 0 1 0 0 0
[R]i=
0 0 0 cos a sen a 0
0 0 0 sen a -cos a 0
0 0 0 0 0 1

0 1 0 0 0 0
1 0 0 0 0 0
0 0 1 0 0 0
[R]1,3=
0 0 0 0 1 0
0 0 0 1 0 0
0 0 0 0 0 1

0 1 0 0 0 0
1 0 0 0 0 0
0 0 1 0 0 0
[R]2=
0 0 0 0 1 0
0 0 0 1 0 0
0 0 0 0 0 1

0 1 0 0 0 0
1 0 0 0 0 0
[R]4, 6, 7, 9, 0 0 1 0 0 0
10, 12, 14= 0 0 0 0 1 0
0 0 0 1 0 0
0 0 0 0 0 1

0 1 0 0 0 0
1 0 0 0 0 0
[R]5, 8, 11, 0 0 1 0 0 0
13 = 0 0 0 0 1 0
0 0 0 1 0 0
0 0 0 0 0 1

1 0 0 0 0 0
0 1 0 0 0 0
[R]15, 17, 0 0 1 0 0 0
19, 21= 0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1

1 0 0 0 0 0
0 1 0 0 0 0
[R]16, 18, 0 0 1 0 0 0
20, 22, 23= 0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

7.- Matriz de rigidez de la barra [k*]i, {q*}-{d*} [𝑘^∗ ]=[𝑅]^𝑇 [𝑘][𝑅]

464.0 0.0 -811.9 -464.0 0.0 -811.9 E382:J387

0.0 64542.3 0.0 0.0 -64542.3 0.0 E389:J394
-811.9 0.0 1905.0 811.9 0.0 936.8 E396:J401
[k*] 1,3 =
-464.0 0.0 811.9 464.0 0.0 811.9 E403:J408
0.0 -64542.3 0.0 0.0 64542.3 0.0 E410:J415
-811.9 0.0 936.8 811.9 0.0 1905.0 E417:J422

18696.6 0.0 -32719.1 -18696.6 0.0 -32719.1

0.0 215141.1 0.0 0.0 -215141.1 0.0
0.0 0.0 83075.4 0.0 0.0 31441.5
[k*] 2 =
-18696.6 0.0 0.0 18696.6 0.0 32719.1
0.0 ### 0.0 0.0 215141.1 0.0
0.0 0.0 31441.5 32719.1 0.0 83075.4

731.1 0.0 -1096.6 -731.1 0.0 -1096.6

0.0 75299.4 0.0 0.0 -75299.4 0.0

[k*] 4, 6, 7, 9, -1096.6 0.0 2209.6 1096.6 0.0 1080.1

10, 12, 14 = -731.1 0.0 1096.6 731.1 0.0 1096.6
0.0 -75299.4 0.0 0.0 75299.4 0.0
-1096.6 0.0 1080.1 1096.6 0.0 2209.6

27134.9 0.0 -40702.4 -27134.9 0.0 -40702.4

0.0 250998.0 0.0 0.0 -250998.0 0.0

[k*] 5, 8, 11, -40702.4 0.0 91173.3 40702.4 0.0 30933.8

13= -27134.9 0.0 40702.4 27134.9 0.0 40702.4
0.0 ### 0.0 0.0 250998.0 0.0
-40702.4 0.0 30933.8 40702.4 0.0 91173.3

0.0 0.0 0.0 0.0 0.0 0.0

0.0 1170.7 2341.4 0.0 -1170.7 3043.8

[k*] 15, 17, 0.0 2341.4 6316.9 0.0 -2341.4 4453.5

19, 21 = 0.0 0.0 0.0 0.0 0.0 0.0
0.0 -1170.7 -2341.4 0.0 1170.7 -3043.8
0.0 3043.8 4453.5 0.0 -3043.8 9548.0

0.0 0.0 0.0 0.0 0.0 0.0

0.0 1170.7 3043.8 0.0 -1170.7 2341.4

[k*] 16, 18, 0.0 3043.8 9548.0 0.0 -3043.8 4453.5

20, 22, 23 = 0.0 0.0 0.0 0.0 0.0 0.0
0.0 -1170.7 -3043.8 0.0 1170.7 -2341.4
0.0 2341.4 4453.5 0.0 -2341.4 6316.9

8.- Ensamblaje de la Matriz de Rigidez Total [𝐾]= 〖 [𝑨_𝒆^∗] 〗 ^𝑻 [𝒌_𝒆^∗ ][𝑨_𝒆^∗ ]

- Ensamblaje [K]
1 2 3 4 5 6 7 8 9 10 11 12 … 33 …
464 0 0 0 0 0 812 0 0 0 0 0 0 0 1

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 4
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 5
0 0 0 0.0 0.0 64542.3 0 0 0 0 0 0 0.0 0.0 6
812 0 0 0 0 0 1905 0 0 0 0 0 0 0 7
[K]1=
0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 9
0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 0 0 0 12
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 …
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 33

1 2 3 4 5 6 7 8 9 10 11 12 … 33
464 0 0 0 0 0 0 0 812 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 4
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 5
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 6
0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
[K]2=
0 0 0 0 0 0 0 64542 0 0 0 0 0 0 8
812 0 0 0 0 0 0 0 1905 0 0 0 0 0 9
0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 0 0 0 12
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 13
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 14

1 2 3 4 5 6 7 8 9 10 11 12 … 33
464 0 0 0 0 0 0 0 0 0 812 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 4
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 5
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 6
0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
[K]3=
0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 9
0 0 0 0 0 0 0 0 0 64542 0 0 0 0 10
812 0 0 0 0 0 0 0 0 0 1905 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 0 0 0 12
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 13
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 14

1 2 3 4 5 6 7 8 9 10 11 12 … 33
731 -731 0 0 0 0 -1097 0 0 0 0 0 0 -1097 1
-731 731 0 0 0 0 1097 0 0 0 0 0 0 1097 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 4

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
[K]4=
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 5

0 0 0 0.0 0.0 75299.4 0 0 0 0 0 0 -75299.4 0.0 6
-1097 1097 0 0 0 0 2210 0 0 0 0 0 0 1080 7
[K]4=
0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 9
0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 0 0 0 12
0 0 0 0.0 0.0 -75299.4 0 0 0 0 0 0 75299.4 0.0 13
-1097 1097 0 0.0 0.0 0.0 1080 0 0 0 0 0 0.0 2209.6 14

Generacion de las formulas excel para obtener el aporte de cada barra y hallar la suma directa por cuestiones de dimensiones
grandes de las matrices. Esto con el fin de hallar directamente la sumatoria de aportes sin la necesidad de hallar cada uno
Fila
Fila final Matriz K * del
[K]elem Formula de multiplicacion de matrices inicial de
de [A] elemento
[A]
[K]1 MMULT(TRANSPOSE(B105:AH110);MMULT(E382:J387;B105:AH110)) 105 110 E382:J387
[K]2 MMULT(TRANSPOSE(B111:AH116);MMULT(E389:J394;B111:AH116)) 111 116 E389:J394
[K]3 MMULT(TRANSPOSE(B117:AH122);MMULT(E382:J387;B117:AH122)) 117 122 E382:J387
[K]4 MMULT(TRANSPOSE(B123:AH128);MMULT(E396:J401;B123:AH128)) 123 128 E396:J401
[K]5 MMULT(TRANSPOSE(B129:AH134);MMULT(E403:J408;B129:AH134)) 129 134 E403:J408
[K]6 MMULT(TRANSPOSE(B135:AH140);MMULT(E396:J401;B135:AH140)) 135 140 E396:J401
[K]7 MMULT(TRANSPOSE(B141:AH146);MMULT(E396:J401;B141:AH146)) 141 146 E396:J401
[K]8 MMULT(TRANSPOSE(B147:AH152);MMULT(E403:J408;B147:AH152)) 147 152 E403:J408
[K]9 MMULT(TRANSPOSE(B153:AH158);MMULT(E396:J401;B153:AH158)) 153 158 E396:J401
[K]10 MMULT(TRANSPOSE(B159:AH164);MMULT(E396:J401;B159:AH164)) 159 164 E396:J401
[K]11 MMULT(TRANSPOSE(B165:AH170);MMULT(E403:J408;B165:AH170)) 165 170 E403:J408
[K]12 MMULT(TRANSPOSE(B171:AH176);MMULT(E396:J401;B171:AH176)) 171 176 E396:J401
[K]13 MMULT(TRANSPOSE(B177:AH182);MMULT(E403:J408;B177:AH182)) 177 182 E403:J408
[K]14 MMULT(TRANSPOSE(B183:AH188);MMULT(E396:J401;B183:AH188)) 183 188 E396:J401
[K]15 MMULT(TRANSPOSE(B189:AH194);MMULT(E410:J415;B189:AH194)) 189 194 E410:J415
[K]16 MMULT(TRANSPOSE(B195:AH200);MMULT(E417:J422;B195:AH200)) 195 200 E417:J422
[K]17 MMULT(TRANSPOSE(B201:AH206);MMULT(E410:J415;B201:AH206)) 201 206 E410:J415
[K]18 MMULT(TRANSPOSE(B207:AH212);MMULT(E417:J422;B207:AH212)) 207 212 E417:J422
[K]19 MMULT(TRANSPOSE(B213:AH218);MMULT(E410:J415;B213:AH218)) 213 218 E410:J415
[K]20 MMULT(TRANSPOSE(B219:AH224);MMULT(E417:J422;B219:AH224)) 219 224 E417:J422
[K]21 MMULT(TRANSPOSE(B225:AH230);MMULT(E410:J415;B225:AH230)) 225 230 E410:J415
[K]22 MMULT(TRANSPOSE(B231:AH236);MMULT(E417:J422;B231:AH236)) 231 236 E417:J422
[K]23 MMULT(TRANSPOSE(B237:AH242);MMULT(E417:J422;B237:AH242)) 237 242 E417:J422

NOTA: LA MATRIZ COMPLETA SE PUEDE VER EN EL ARCHIVO EXCEL ADJUNTO

[𝐾]=∑_(𝑒=1)^𝑚▒ 〖〖 [𝐴_𝑒^∗] 〗 ^𝑇 [𝑘_𝑒^∗ ][𝐴_𝑒^∗ ] 〗

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
48222 -28597 0 0 0 0 -285 0 -7983 0 -285 0 0 -1097 -40702
-28597 57194 -28597 0 0 0 1097 0 40702 0 1097 0 -1097 1097 0
0 -28597 57194 -28597 0 0 0 0 0 0 0 0 1097 0 40702
0 0 -28597 56463 -27866 0 0 0 0 0 0 0 0 0 0
0 0 0 -27866 27866 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 141012.4 2341.4 -1170.7 3043.8 0.0 0.0 0.0 -75299.4 0.0 0.0

[K]T=
ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

-285 1097 0 0 0 2341.4 10431.5 -2341.4 4453.5 0.0 0.0 0.0 0.0 1080.1 0.0
[K]T=
0 0 0 0 0 -1170.7 -2341.4 468480.6 0.0 -1170.7 2341.4 0.0 0.0 -250998.0 0.0
-7983 40702 0 0 0 3043.8 4453.5 0.0 193344.8 -3043.8 4453.5 0.0 0.0 0.0 30933.8
0 0 0 0 0 0.0 0.0 -1170.7 -3043.8 141012.4 -2341.4 0.0 0.0 0.0 0.0
-285 1097 0 0 0 0.0 0.0 2341.4 4453.5 -2341.4 10431.5 0.0 0.0 0.0 0.0
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 76470.1 2341.4 -1170.7 3043.8
0 -1097 1097 0 0 -75299.4 0.0 0.0 0.0 0.0 0.0 2341.4 83825.9 -2341.4 4453.5
-1097 1097 0 0 0 0.0 1080.1 ### 0.0 0.0 0.0 -1170.7 -2341.4 506547.1 0.0
-40702 0 40702 0 0 0.0 0.0 0.0 30933.8 0.0 0.0 3043.8 4453.5 0.0 201442.7
0 0 0 0 0 0.0 0.0 0.0 0.0 -75299.4 0.0 0.0 0.0 -1170.7 -3043.8
-1097 0 1097 0 0 0.0 0.0 0.0 0.0 0.0 1080.1 0.0 0.0 2341.4 4453.5
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 -75299.4 0.0 0.0 0.0
0 -1097 0 1097 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1080.1 0.0 0.0
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -250998.0 0.0
0 -40702 0 40702 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 30933.8
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 -1097 0 1097 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 -1097 1097 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 -40702 0 40702 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 -1097 0 1097 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 0 -40702 40702 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0 0 -1097 1097 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

* Estructura del K ordenado

Kuu Kur
[K]T=

Kru Krr

- GDLE 1-5
1 2 3 4 5
39608.2 -27047.6 8163.2 -1059.5 226.4 1
[K]L4=
-27047.6 39898.2 -27228.9 8280.9 -829.2 2
8163.2 -27228.9 40088.7 -25921.6 5979.4 3
-1059.5 8280.9 -25921.6 30804.8 -12237.5 4
226.4 -829.2 5979.4 -12237.5 6882.4 5

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
“ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

/𝐿&0&0@0&−12𝐸𝐼/𝐿^3 &6𝐸𝐼/𝐿^2 @0&−6𝐸𝐼/𝐿^2 &2𝐸𝐼/𝐿)&■8(𝐸𝐴/𝐿&0&0@0&12𝐸𝐼/𝐿^3 &6𝐸𝐼/𝐿^2 @0&6𝐸𝐼/𝐿^2 &4𝐸𝐼/𝐿))]

^2 @4𝐸𝐼/𝐿)]

0.25

.𝐸𝐼)/((1+) 𝐿^3 )
f
0.02
0.35
0.02

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

0.03
0.48
0.03
0.03
0.48
0.03
0.03
0.48
0.03
0.48
0.03
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05

16
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

.𝐸𝐼)/((1+) 𝐿^3 )
f

0.02
0.35
0.02
0.03
0.48
0.03
0.03
0.48
0.03
0.03
0.48
0.03
0.48
0.03
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

0.0
0.0
0.0
0.0
-0.6
1.0

0.0
0.0
0.0
0.0
0.0
1.0

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

15,17,19,21

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
“ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

ones
o

16
0
0
0
0
0
0.0

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

0.0
0.0
0.0
###
0.0
0.0
0.0
###
###
###
###
0.0
0.0
0.0
0.0
###
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

06.- Condensacion de la matriz de rigidez del portico 5

VISTA EN ELEVACION DEL

PORTICO 05

0.25x0.50 0.25x0.50 0.25x0.50

30x30

25x1.2
25x1.2

30x30
3.0m

0.25x0.50 0.25x0.50 0.25x0.50

30x30

25x1.2
25x1.2

30x30

3.0m

0.25x0.50 0.25x0.50 0.25x0.50

30x30

25x1.2
25x1.2

30x30

3.0m

0.25x0.50 0.25x0.50 0.25x0.50

30x30

25x1.2

25x1.2

30x30

3.0m

0.25x0.50 0.25x0.50 0.25x0.50

30x30

25x1.2

25x1.2

30x30

3.5m

4m 4m 4m

Dato
E= 2173706.5119 Tn/m²

1.- Determinacion de Cordenadas Globales Generalizadas y GDL

38 40 42 44
5 5 5 5
39 41 43 45
30 34 36
ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

30 32 34 36
4 4 4 4

31 33 35 37
22 24 26 28
3 3 3 3
23 25 27 29
14 16 18 20
2 2 2 2

15 17 19 21
6 8 10 12
1 1 1 1

7 9 11 13

47 50 53 56
46 49 52 55

48 51 54 57

33 34 35
GDL: 45

17 18 19 20
30 31 32

13 14 15 16
27 28 29

9 10 11 12
24 25 26

5 6 7 8
21 22 23

1 2 3 4

2.- Determinacion de Cordenadas Locales Generalizadas: {q} - {d}

1 3

Vigas
(12𝐸𝐼/𝐿^3 @6𝐸𝐼/𝐿^2 @(−12𝐸𝐼)/𝐿^3 e:
@6𝐸𝐼/𝐿^2
7, 8, 9, 10) █(6𝐸𝐼/𝐿^2 @4𝐸𝐼/𝐿@(−6𝐸𝐼)/𝐿^2 @2𝐸𝐼/𝐿) █((−12𝐸𝐼)/𝐿^3 @(−6𝐸𝐼)/𝐿^2 @12𝐸𝐼/𝐿^3 @(−6𝐸𝐼)/𝐿^2 ) █(6𝐸𝐼/𝐿^2 @2𝐸𝐼/𝐿@(−6𝐸𝐼)/𝐿^2 @4𝐸𝐼/𝐿)]
2 4
+ m.transformcion

&0&0@0&12𝐸𝐼/𝐿^3 &−6𝐸𝐼/𝐿^2 @0&−6𝐸𝐼/𝐿^2 &4𝐸𝐼/𝐿)&■8(−𝐸𝐴/𝐿&0&0@0&−12𝐸𝐼/𝐿^3 &−6𝐸𝐼/𝐿^2 @0&6𝐸𝐼/𝐿^2 &2𝐸𝐼/𝐿)@■8(−𝐸𝐴/𝐿&0&0@0&−12𝐸𝐼/𝐿^3 &6𝐸𝐼/𝐿^2 @0&−6𝐸𝐼/𝐿^2 &2𝐸𝐼/𝐿)&■8(𝐸𝐴/𝐿&0&0@0&12𝐸𝐼/𝐿^3 &6𝐸𝐼/𝐿^2 @0&6𝐸𝐼/𝐿^2 &4𝐸𝐼/𝐿))]

2 5

4
1
3 6
Columnas y placas
e: 1-14

b1 b2
23,26,29,32,35

21,24,27,30,33

22,25,28,31,34

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

3.- Cálculos previos - Datos de las barras

Columnas
Vigas 1.20m 1.20m
0.30
Placas
0.30 0.50 21,24,27,30,33 22,25, 23,26,29,32,35
0.25
1.20 0.25 28,31,34

0.25x0.50 0.25x0.50 0.25x0.50

30x30

25x1.2
25x1.2

30x30
3.0m
33 34 35
0.25x0.50 0.25x0.50 0.25x0.50

18 19
30x30

17 20
25x1.2
25x1.2

30x30
3.0m 30 31 32

0.25x0.50 0.25x0.50 0.25x0.50

13 14 15 16
30x30

27 28 29
25x1.2
25x1.2

30x30 3.0m

0.25x0.50 0.25x0.50 0.25x0.50 9 10 11 12

24 25 26
30x30

25x1.2

25x1.2

30x30

3.0m 5 6 7 8
0.25x0.50 0.25x0.50 0.25x0.50 21 22 23
30x30

1 2 3 4
25x1.2

25x1.2

30x30

3.5m

4m 4m 4m

(2−)𝐸𝐼/(1+
(4+)𝐸𝐼/(1+)𝐿 )𝐿 (12.𝐸𝐼)/((1+)
(6.𝐸𝐼)/((1+) 𝐿^2 ) 𝐿^3 )
Barra b h A E I EA EI AX AY L EA/L f

1 0.30 0.30 0.09 2.2E+06 6.8E-04 2.0E+05 1467 0 3.5 3.50 55895 1649.7 811.3 703.2 401.8 0.02
2 0.25 1.20 0.3 2.2E+06 3.6E-02 6.5E+05 78253 0 3.5 3.50 186318 71945.4 27229.1 28335.6 16191.8 0.35
3 0.25 1.20 0.3 2.2E+06 3.6E-02 6.5E+05 78253 0 3.5 3.50 186318 71945.4 27229.1 28335.6 16191.8 0.35
4 0.30 0.30 0.09 2.2E+06 6.8E-04 2.0E+05 1467 0 3.5 3.50 55895 1649.7 811.3 703.2 401.8 0.02
5 0.30 0.30 0.09 2.2E+06 6.8E-04 2.0E+05 1467 0 3 3.00 65211 1913.6 935.4 949.7 633.1 0.03
6 0.25 1.20 0.3 2.2E+06 3.6E-02 6.5E+05 78253 0 3 3.00 217371 78958.4 26789.5 35249.3 23499.5 0.48
7 0.25 1.20 0.3 2.2E+06 3.6E-02 6.5E+05 78253 0 3 3.00 217371 78958.4 26789.5 35249.3 23499.5 0.48
8 0.30 0.30 0.09 2.2E+06 6.8E-04 2.0E+05 1467 0 3 3.00 65211 1913.6 935.4 949.7 633.1 0.03
9 0.30 0.30 0.09 2.2E+06 6.8E-04 2.0E+05 1467[𝑘𝑒]=[■8(■8(𝐸𝐴/𝐿&0&0@0&12𝐸𝐼/𝐿^3
0 3 3.00 &−6𝐸𝐼/𝐿^2
65211 @0&−6𝐸𝐼/𝐿^2
1913.6 935.4 &4𝐸𝐼/𝐿)&■8(−𝐸𝐴/𝐿&0&0@0&−12𝐸𝐼/𝐿^3
949.7 633.1 0.03 &−6𝐸𝐼/𝐿^2 @0&6𝐸𝐼/𝐿^2 &2𝐸

10 0.25 1.20 0.3 2.2E+06 3.6E-02 6.5E+05 78253 0 3 3.00 217371 78958.4 26789.5 35249.3 23499.5 0.48
11 0.25 1.20 0.3 2.2E+06 3.6E-02 6.5E+05 78253 0 3 3.00 217371 78958.4 26789.5 35249.3 23499.5 0.48
12 0.30 0.30 0.09 2.2E+06 6.8E-04 2.0E+05 1467 0 3 3.00 65211 1913.6 935.4 949.7 633.1 0.03
13 0.30 0.30 0.09 2.2E+06 6.8E-04 2.0E+05 1467 0 3 3.00 65211 1913.6 935.4 949.7 633.1 0.03
14 0.25 1.20 0.3 2.2E+06 3.6E-02 6.5E+05 78253 0 3 3.00 217371 78958.4 26789.5 35249.3 23499.5 0.48
15 0.25 1.20 0.3 2.2E+06 3.6E-02 6.5E+05 78253 0 3 3.00 217371 78958.4 26789.5 35249.3 23499.5 0.48
16 0.30 0.30 0.09 2.2E+06 6.8E-04 2.0E+05 1467 0 3 3.00 65211 1913.6 935.4 949.7 633.1 0.03
17 0.30 0.30 0.09 2.2E+06 6.8E-04 2.0E+05 1467 0 3 3.00 65211 1913.6 935.4 949.7 633.1 0.03
18 0.25 1.20 0.3 2.2E+06 3.6E-02 6.5E+05 78253 0 3 3.00 217371 78958.4 26789.5 35249.3 23499.5 0.48
19 0.25 1.20 0.3 2.2E+06 3.6E-02 6.5E+05 78253 0 3 3.00 217371 78958.4 26789.5 35249.3 23499.5 0.48
20 0.30 0.30 0.09 2.2E+06 6.8E-04 2.0E+05 1467 0 3 3.00 65211 1913.6 935.4 949.7 633.1 0.03
21 0.25 0.50 0.125 2.2E+06 2.6E-03 2.7E+05 5661 4 0 4.00 0 ∞ 5470.6 2640.2 2027.7 1013.9 0.05
22 0.25 0.50 0.125 2.2E+06 2.6E-03 2.7E+05 5661 4 0 4.00 0 ∞ 5470.6 2640.2 2027.7 1013.9 0.05
23 0.25 0.50 0.125 2.2E+06 2.6E-03 2.7E+05 5661 4 0 4.00 0 ∞ 5470.6 2640.2 2027.7 1013.9 0.05
24 0.25 0.50 0.125 2.2E+06 2.6E-03 2.7E+05 5661 4 0 4.00 0 ∞ 5470.6 2640.2 2027.7 1013.9 0.05
25 0.25 0.50 0.125 2.2E+06 2.6E-03 2.7E+05 5661 4 0 4.00 0 ∞ 5470.6 2640.2 2027.7 1013.9 0.05
26 0.25 0.50 0.125 2.2E+06 2.6E-03 2.7E+05 5661 4 0 4.00 0 ∞ 5470.6 2640.2 2027.7 1013.9 0.05
27 0.25 0.50 0.125 2.2E+06 2.6E-03 2.7E+05 5661 4 0 4.00 0 ∞ 5470.6 2640.2 2027.7 1013.9 0.05
28 0.25 0.50 0.125 2.2E+06 2.6E-03 2.7E+05 5661 4 0 4.00 0 ∞ 5470.6 2640.2 2027.7 1013.9 0.05
29 0.25 0.50 0.125 2.2E+06 2.6E-03 2.7E+05 5661 4 0 4.00 0 ∞ 5470.6 2640.2 2027.7 1013.9 0.05
30 0.25 0.50 0.125 2.2E+06 2.6E-03 2.7E+05 5661 4 0 4.00 0 ∞ 5470.6 2640.2 2027.7 1013.9 0.05
31 0.25 0.50 0.125 2.2E+06 2.6E-03 2.7E+05 5661 4 0 4.00 0 ∞ 5470.6 2640.2 2027.7 1013.9 0.05
32 0.25 0.50 0.125 2.2E+06 2.6E-03 2.7E+05 5661 4 0 4.00 0 ∞ 5470.6 2640.2 2027.7 1013.9 0.05
33 0.25 0.50 0.125 2.2E+06 2.6E-03 2.7E+05 5661 4 0 4.00 0 ∞ 5470.6 2640.2 2027.7 1013.9 0.05
34 0.25 0.50 0.125 2.2E+06 2.6E-03 2.7E+05 5661 4 0 4.00 0 ∞ 5470.6 2640.2 2027.7 1013.9 0.05
35 0.25 0.50 0.125 2.2E+06 2.6E-03 2.7E+05 5661 4 0 4.00 0 ∞ 5470.6 2640.2 2027.7 1013.9 0.05

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

4.- Matriz de Transformacion de desplazamientos [A*]

NOTA: LA MATRIZ COMPLETA SE PUEDE VER EN EL ARCHIVO EXCEL ADJUNTO
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]2
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]3
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]4
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
[A*]5
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
[A*]6
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
[A*]7
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
[A*]8
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
[A*]9
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]10
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]11
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]12
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

[A*]12

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]13
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]14
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]15
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]16
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]17
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]18
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]19
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]20
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
[A*]21
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
[A*]22
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
[A*]23
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
[A*]24
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”
[A*]24

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]25
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]26
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]27
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]28
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]29
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]30
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]31
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]32
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]33
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]34
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]35
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

5.- Matriz de rigidez de la barra [k]i, {q}-{d}

[𝑘𝑒]=[■8(■8(𝐸𝐴/𝐿&0&0@0&12𝐸𝐼/𝐿^3
55895 &−6𝐸𝐼/𝐿^2
0.0 @0&−6𝐸𝐼/𝐿^2
0.0 &4𝐸𝐼/𝐿)&■8(−𝐸𝐴/𝐿&0&0@0&−12𝐸𝐼/𝐿^3
-55895 0.0 0.0 &−6𝐸𝐼/𝐿^2 @0&6𝐸𝐼/𝐿^2 &2𝐸𝐼/𝐿)@■8(−𝐸𝐴/𝐿&0&0@0&−12𝐸𝐼/𝐿^3 &6𝐸𝐼/𝐿^2 @0&−6𝐸𝐼/𝐿^2 &2𝐸𝐼/𝐿)&

0.0 401.8 -703.2 0.0 -401.8 -703.2

[k] 1, 4 = ANÁLISIS ESTRUCTURAL

ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

0.0 -703.2 1649.7 0.0 703.2 811.3

[k] 1, 4 =
-55895 0.0 0.0 55895.3 0.0 0.0
0.0 -401.8 703.2 0.0 401.8 703.2
0.0 -703.2 811.3 0.0 703.2 1649.7

186318 0.0 0.0 -186318 0.0 0.0

0.0 16191.8 -28335.6 0.0 -16191.8 -28335.6
0.0 -28335.6 71945.4 0.0 28335.6 27229.1
[k] 2,3 =
-186318 0.0 0.0 186317.7 0.0 0.0
0.0 -16191.8 28335.6 0.0 16191.8 28335.6
0.0 -28335.6 27229.1 0.0 28335.6 71945.4

65211 0.0 0.0 -65211 0.0 0.0

0.0 633.1 -949.7 0.0 -633.1 -949.7
[k] 0.0 -949.7 1913.6 0.0 949.7 935.4
5,8,9,12,13,16,17,20 = -65211 0.0 0.0 65211.2 0.0 0.0
0.0 -633.1 949.7 0.0 633.1 949.7
0.0 -949.7 935.4 0.0 949.7 1913.6

217371 0.0 0.0 -217371 0.0 0.0

0.0 23499.5 -35249.3 0.0 -23499.5 -35249.3

[k] 0.0 -35249.3 78958.4 0.0 35249.3 26789.5

6,7,10,11,14,15,18,19 = -217371 0.0 0.0 217370.7 0.0 0.0
0.0 -23499.5 35249.3 0.0 23499.5 35249.3
0.0 -35249.3 26789.5 0.0 35249.3 78958.4 Columas
b1= 0 b2= 0.6
[K] =[ST] [K '] [S] 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0
0.0 1013.9 2027.7 0.0 -1013.9 2027.7 0.0 1.0 0.0 0.0 0.0 0.0
[k]' 21, 24, 27, 30, 33 0.0 2027.7 5470.6 0.0 -2027.7 2640.2 0.0 0.0 1.0 0.0 0.0 0.0
[s] 16 =
= 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0
0.0 -1013.9 -2027.7 0.0 1013.9 -2027.7 0.0 0.0 0.0 0.0 1.0 -0.6
0.0 2027.7 2640.2 0.0 -2027.7 5470.6 0.0 0.0 0.0 0.0 0.0 1.0

0.0 0.0 0.0 0.0 0.0 0.0

0.0 1013.9 2027.7 0.0 -1013.9 2636.0
[k] 21, 24, 27, 30, 33 0.0 2027.7 5470.6 0.0 -2027.7 3856.9
= 0.0 0.0 0.0 0.0 0.0 0.0
0.0 -1013.9 -2027.7 0.0 1013.9 -2636.0
0.0 2636.0 3856.9 0.0 -2636.0 8268.8

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

b1= 0.6 b2= 0.6

[K] =[ST] [K '] [S] 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0
0.0 1013.9 2027.7 0.0 -1013.9 2027.7 0.0 1.0 0.6 0.0 0.0 0.0
[k]' 22, 35, 28, 31, 34 0.0 2027.7 5470.6 0.0 -2027.7 2640.2 0.0 0.0 1.0 0.0 0.0 0.0
[s] 15 =
= 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0
0.0 -1013.9 -2027.7 0.0 1013.9 -2027.7 0.0 0.0 0.0 0.0 1.0 -0.6
0.0 2027.7 2640.2 0.0 -2027.7 5470.6 0.0 0.0 0.0 0.0 0.0 1.0

0.0 0.0 0.0 0.0 0.0 0.0

0.0 1013.9 2636.0 0.0 -1013.9 2636.0
[k] 22, 35, 28, 31, 34 0.0 2636.0 8268.8 0.0 -2636.0 5438.5
= 0.0 0.0 0.0 0.0 0.0 0.0
0.0 -1013.9 -2636.0 0.0 1013.9 -2636.0
0.0 2636.0 5438.5 0.0 -2636.0 8268.8

b1= 0.6 b2= 0

[K] =[ST] [K '] [S] 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0
0.0 1013.9 2027.7 0.0 -1013.9 2027.7 0.0 1.0 0.6 0.0 0.0 0.0
[k]' 23, 26, 29, 32, 35 0.0 2027.7 5470.6 0.0 -2027.7 2640.2 0.0 0.0 1.0 0.0 0.0 0.0
[s] 16 =
= 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0
0.0 -1013.9 -2027.7 0.0 1013.9 -2027.7 0.0 0.0 0.0 0.0 1.0 0.0
0.0 2027.7 2640.2 0.0 -2027.7 5470.6 0.0 0.0 0.0 0.0 0.0 1.0

0.0 0.0 0.0 0.0 0.0 0.0

0.0 1013.9 2636.0 0.0 -1013.9 2027.7
[k] 23, 26, 29, 32, 35 0.0 2636.0 8268.8 0.0 -2636.0 3856.9
= 0.0 0.0 0.0 0.0 0.0 0.0
0.0 -1013.9 -2636.0 0.0 1013.9 -2027.7
0.0 2027.7 3856.9 0.0 -2027.7 5470.6 Vigas

6.- Determinar la Matriz deTransformacion de desplazamientos [R] i {𝑑}=[𝑅]{𝑑^∗ }

cos a sen a 0 0 0 0
sen a -cos a 0 0 0 0
0 0 1 0 0 0
[R]i=
0 0 0 cos a sen a 0
0 0 0 sen a -cos a 0
0 0 0 0 0 1

0 1 0 0 0 0
1 0 0 0 0 0
0 0 1 0 0 0
[R]1, 4=
0 0 0 0 1 0
0 0 0 1 0 0
0 0 0 0 0 1

0 1 0 0 0 0
1 0 0 0 0 0
0 0 1 0 0 0
[R] 2, 3=
0 0 0 0 1 0
0 0 0 1 0 0
0 0 0 0 0 1

0 1 0 0 0 0
1 0 0 0 0 0
[R] 5, 8, 9, 12, 13, 16, 0 0 1 0 0 0
17, 20= 0 0 0 0 1 0
0 0 0 1 0 0
0 0 0 0 0 1

0 1 0 0 0 0
1 0 0 0 0 0
[R]6, 7, 10, 11, 14, 15, 0 0 1 0 0 0
18, 19= 0 0 0 0 1 0
0 0 0 1 0 0
0 0 0 0 0 1 Columnas y Placas

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

1 0 0 0 0 0
0 1 0 0 0 0
[R]21, 24, 27, 30, 0 0 1 0 0 0
33= 0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1

1 0 0 0 0 0
0 1 0 0 0 0
[R]22, 25, 28, 31, 0 0 1 0 0 0
34= 0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1

1 0 0 0 0 0
0 1 0 0 0 0
[R]23, 26, 29, 32, 0 0 1 0 0 0
35= 0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1

7.- Matriz de rigidez de la barra [k*]i, {q*}-{d*} [𝑘^∗ ]=[𝑅]^𝑇 [𝑘][𝑅]

401.8 0.0 -703.2 -401.8 0.0 -703.2

0.0 55895.3 0.0 0.0 -55895.3 0.0
-703.2 0.0 1649.7 703.2 0.0 811.3
[k*]1, 4=
-401.8 0.0 703.2 401.8 0.0 703.2
0.0 -55895.3 0.0 0.0 55895.3 0.0
-703.2 0.0 811.3 703.2 0.0 1649.7

16192 0 -28336 -16192 0 -28336

0 186318 0 0 -186318 0
-28336 0 71945 28336 0 27229
[k*] 2, 3=
-16192 0 28336 16192 0 28336
0 -186318 0 0 186318 0
-28336 0 27229 28336 0 71945

633 0 -950 -633 0 -950

0 65211 0 0 -65211 0
[k*] 5, 8, 9, 12, 13, -950 0 1914 950 0 935
16, 17, 20= -633 0 950 633 0 950
0 -65211 0 0 65211 0
-950 0 935 950 0 1914

23500 0 -35249 -23500 0 -35249

0 217371 0 0 ### 0
[k*]6, 7, 10, 11, 14, -35249 0 78958 35249 0 26789
15, 18, 19= -23500 0 35249 23500 0 35249
0 -217371 0 0 217371 0
-35249 0 26789 35249 0 78958

0 0 0 0 0 0
0 1014 2028 0 -1014 2636
[k*]21, 24, 27, 30, 0 2028 5471 0 -2028 3857
33= 0 0 0 0 0 0
0 -1014 -2028 0 1014 -2636
0 2636 3857 0 -2636 8269

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

0 0 0 0 0 0
0 1014 2636 0 -1014 2636
[k*]22, 25, 28, 31, 0 2636 8269 0 -2636 5438
34= 0 0 0 0 0 0
0 -1014 -2636 0 1014 -2636
0 2636 5438 0 -2636 8269

0 0 0 0 0 0
0 1014 2636 0 -1014 2028
[k*] 23, 26, 29, 32, 0 2636 8269 0 -2636 3857
35 = 0 0 0 0 0 0
0 -1014 -2636 0 1014 -2028
0 2028 3857 0 -2028 5471

8.- Ensamblaje de la Matriz de Rigidez Total [𝐾]= 〖 [𝑨_𝒆^∗] 〗 ^𝑻 [𝒌_𝒆^∗ ][𝑨_𝒆^∗ ]

- Ensamblaje [K]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
401.80334885 0 0 0 0 0 703.15586049 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 55895.310307 0 0 0 0 0 0 0 0 0 0
703.15586049 0 0 0 0 0 1649.7375832 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[K]1= 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

1 2 3 4 5 6 7 8 9 10 11 12 … 45
16192 0 0 0 0 0 0 0 28336 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 4
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 5
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 6
0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
[K]2=
0 0 0 0 0 0 0 186318 0 0 0 0 0 0 8
28336 0 0 0 0 0 0 0 71945 0 0 0 0 0 9
0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 0 0 0 12
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 …
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 45

1 2 3 4 5 6 7 8 9 10 11 12 … 45
16192 0 0 0 0 0 0 0 0 0 28336 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 4
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 5
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 6
0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
[K]3=
0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 9
0 0 0 0 0 0 0 0 0 186318 0 0 0 0 10
28336 0 0 0 0 0 0 0 0 0 71945 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 0 0 0 12
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 …
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 45

1 2 3 4 5 6 7 8 9 10 11 12 … 45
401.80334885 0 0 0 0 0 0 0 0 0 0 0 703.156 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
0 0 0 0 0 0 0 0 0 0 0 0 0 0 5
0 0 0 0 0 0 0 0 0 0 0 0 0 0 6
0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
[K]4=
0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 9
0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 55895.3 0 0 12
703.15586049 0 0 0 0 0 0 0 0 0 0 0 1649.74 0 …
0 0 0 0 0 0 0 0 0 0 0 0 0 0 45

Generacion de las formulas excel para obtener el aporte de cada barra y hallar la suma directa por cuestiones de dimensiones grandes de las matrices. Esto con el fin de
hallar directamente la sumatoria de aportes sin la necesidad de hallar cada uno
Fila Fila
Matriz K * del
[K]elem Formula de multiplicacion de matrices inicial final de
elemento
de [A] [A]
[K]1 MMULT(TRANSPOSE(B162:AT167);MMULT(E507:J512;B162:AT167)) 162 167 E507:J512
[K]2 MMULT(TRANSPOSE(B168:AT173);MMULT(E514:J519;B168:AT173)) 168 173 E514:J519
[K]3 MMULT(TRANSPOSE(B174:AT179);MMULT(E514:J519;B174:AT179)) 174 179 E514:J519
[K]4 MMULT(TRANSPOSE(B180:AT185);MMULT(E507:J512;B180:AT185)) 180 185 E507:J512
[K]5 MMULT(TRANSPOSE(B186:AT191);MMULT(E521:J526;B186:AT191)) 186 191 E521:J526
[K]6 MMULT(TRANSPOSE(B192:AT197);MMULT(E528:J533;B192:AT197)) 192 197 E528:J533
[K]7 MMULT(TRANSPOSE(B198:AT203);MMULT(E528:J533;B198:AT203)) 198 203 E528:J533
[K]8 MMULT(TRANSPOSE(B204:AT209);MMULT(E521:J526;B204:AT209)) 204 209 E521:J526
[K]9 MMULT(TRANSPOSE(B210:AT215);MMULT(E521:J526;B210:AT215)) 210 215 E521:J526
[K]10 MMULT(TRANSPOSE(B216:AT221);MMULT(E528:J533;B216:AT221)) 216 221 E528:J533
[K]11 MMULT(TRANSPOSE(B222:AT227);MMULT(E528:J533;B222:AT227)) 222 227 E528:J533
[K]12 MMULT(TRANSPOSE(B228:AT233);MMULT(E521:J526;B228:AT233)) 228 233 E521:J526
[K]13 MMULT(TRANSPOSE(B234:AT239);MMULT(E521:J526;B234:AT239)) 234 239 E521:J526
[K]14 MMULT(TRANSPOSE(B240:AT245);MMULT(E528:J533;B240:AT245)) 240 245 E528:J533
[K]15 MMULT(TRANSPOSE(B246:AT251);MMULT(E528:J533;B246:AT251)) 246 251 E528:J533
[K]16 MMULT(TRANSPOSE(B252:AT257);MMULT(E521:J526;B252:AT257)) 252 257 E521:J526
[K]17 MMULT(TRANSPOSE(B258:AT263);MMULT(E521:J526;B258:AT263)) 258 263 E521:J526
[K]18 MMULT(TRANSPOSE(B264:AT269);MMULT(E528:J533;B264:AT269)) 264 269 E528:J533
[K]19 MMULT(TRANSPOSE(B270:AT275);MMULT(E528:J533;B270:AT275)) 270 275 E528:J533

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

[K]20 MMULT(TRANSPOSE(B276:AT281);MMULT(E521:J526;B276:AT281)) 276 281 E521:J526

[K]21 MMULT(TRANSPOSE(B282:AT287);MMULT(E535:J540;B282:AT287)) 282 287 E535:J540
[K]22 MMULT(TRANSPOSE(B288:AT293);MMULT(E542:J547;B288:AT293)) 288 293 E542:J547
[K]23 MMULT(TRANSPOSE(B294:AT299);MMULT(E549:J554;B294:AT299)) 294 299 E549:J554
[K]24 MMULT(TRANSPOSE(B300:AT305);MMULT(E535:J540;B300:AT305)) 300 305 E535:J540
[K]25 MMULT(TRANSPOSE(B306:AT311);MMULT(E542:J547;B306:AT311)) 306 311 E542:J547
[K]26 MMULT(TRANSPOSE(B312:AT317);MMULT(E549:J554;B312:AT317)) 312 317 E549:J554
[K]27 MMULT(TRANSPOSE(B318:AT323);MMULT(E535:J540;B318:AT323)) 318 323 E535:J540
[K]28 MMULT(TRANSPOSE(B324:AT329);MMULT(E542:J547;B324:AT329)) 324 329 E542:J547
[K]29 MMULT(TRANSPOSE(B330:AT335);MMULT(E549:J554;B330:AT335)) 330 335 E549:J554
[K]30 MMULT(TRANSPOSE(B336:AT341);MMULT(E535:J540;B336:AT341)) 336 341 E535:J540
[K]31 MMULT(TRANSPOSE(B342:AT347);MMULT(E542:J547;B342:AT347)) 342 347 E542:J547
[K]32 MMULT(TRANSPOSE(B348:AT353);MMULT(E549:J554;B348:AT353)) 348 353 E549:J554
[K]33 MMULT(TRANSPOSE(B354:AT359);MMULT(E535:J540;B354:AT359)) 354 359 E535:J540
[K]34 MMULT(TRANSPOSE(B360:AT365);MMULT(E542:J547;B360:AT365)) 360 365 E542:J547
[K]35 MMULT(TRANSPOSE(B366:AT371);MMULT(E549:J554;B366:AT371)) 366 371 E549:J554

𝐾]=∑_(𝑒=1)^𝑚▒ 〖〖 [𝐴_𝑒^∗] 〗 ^𝑇 [𝑘_𝑒^∗ ][𝐴_𝑒^∗ ] 〗

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
81452.426389 -48265.29652 0 0 0 0 -246.5217418 0 -6913.7 0 -6913.7 0 -246.52 0 -949.68 0
-48265.29652 96530.593041 -48265.29652 0 0 0 949.6776023 0 35249 0 35249 0 949.678 0 0 0
0 -48265.29652 96530.593041 -48265 0 0 0 0 0 0 0 0 0 0 949.678 0
0 0 -48265.29652 96531 -48265 0 0 0 0 0 0 0 0 0 0 0
0 0 0 -48265 48265 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 122120.36131 2027.7112984 -1014 2636 0 0 0 0 -65211 0 0
-246.5217418 949.6776023 0 0 0 2027.7112984 9033.934059 -2028 3856.88 0 0 0 0 0 935.432 0
[K]T=
0 0 0 0 0 -1013.855649 -2027.711298 405716 0 -1013.856 2636 0 0 0 0 ###
-6913.712013 35249.294788 0 0 0 2636.024688 3856.8758656 0 167441 -2636.025 5438.49 0 0 0 0 0
0 0 0 0 0 0 0 -1014 -2636 405716.06 0 -1013.9 2027.71 0 0 0
-6913.712013 35249.294788 0 0 0 0 0 2636 5438.49 0 167441 -2636 3856.88 0 0 0
0 0 0 0 0 0 0 0 0 -1013.856 -2636 122120 -2027.7 0 0 0
-246.5217418 949.6776023 0 0 0 0 0 0 0 2027.7113 3856.88 -2027.7 9033.93 0 0 0
0 0 0 0 0 -65211.19536 0 0 0 0 0 0 0 131436 2027.71 ###
-949.6776023 0 949.6776023 0 0 0 935.43243826 0 0 0 0 0 0 2027.71 9297.8 ###
0 0 0 0 0 0 0 -2E+05 0 0 0 0 0 -1013.9 -2027.7 ###
-35249.29479 0 35249.294788 0 0 0 0 0 26789 0 0 0 0 2636 3856.88 0
0 0 0 0 0 0 0 0 0 -217370.7 0 0 0 0 0 ###
-35249.29479 0 35249.294788 0 0 0 0 0 0 0 26789 0 0 0 0 ###
0 0 0 0 0 0 0 0 0 0 0 -65211 0 0 0 0
-949.6776023 0 949.6776023 0 0 0 0 0 0 0 0 0 935.432 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 -65211 0 0
0 -949.6776023 0 949.68 0 0 0 0 0 0 0 0 0 0 935.432 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ###
0 -35249.29479 0 35249 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 -35249.29479 0 35249 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 -949.6776023 0 949.68 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 -949.6776023 0 949.678 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 -35249.29479 0 35249 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 -35249.29479 0 35249 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 -949.6776023 0 949.678 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 -949.68 949.678 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 -35249 35249 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 -35249 35249 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 -949.68 949.678 0 0 0 0 0 0 0 0 0 0 0
* Estructura del K ordenado

Kuu Kur
[K]T=

Kru Krr
ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

Kru Krr

- GDLE 1-5
1 2 3 4 5
67249.8 -45483.5 13720.6 -2055.9 287.7 1
[K]L5=
-45483.5 67981.0 -46048.5 13544.1 -1557.3 2
13720.6 -46048.5 67966.1 -44479.6 10596.7 3
-2055.9 13544.1 -44479.6 57449.5 -24717.4 4
287.7 -1557.3 10596.7 -24717.4 15403.7 5

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

06.- Condensacion de la matriz de rigidez del portico 6

VISTA EN ELEVACION DEL

PORTICO 06

0.25x0.50 0.25x0.50 0.25x0.50

30x30

r=0.17
r=0.17

30x30

3.0m
0.25x0.50 0.25x0.50 0.25x0.50
30x30

r=0.17
r=0.17

30x30

3.0m
0.25x0.50 0.25x0.50 0.25x0.50
30x30

r=0.17
30x1.2

30x30

3.0m
0.25x0.50 0.25x0.50 0.25x0.50
30x30

r=0.17

r=0.17

30x30

3.0m
0.25x0.50 0.25x0.50 0.25x0.50
30x30

r=0.17
r=0.17

30x30

3.5m

4m 4m 4m

Dato
E= 2173706.5119 Tn/m²

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

1.- Determinacion de Cordenadas Globales Generalizadas y GDL

38 40 42 44
5 5 5 5
39 41 43 45
30 32 34 36
4 4 4 4

31 33 35 37
22 24 26 28
3 3 3 3
23 25 27 29
14 16 18 20
2 2 2 2

15 17 19 21
6 8 10 12
1 1 1 1
7 9 11 13

47 50 53 56
46 49 52 55

48 51 54 57

33 34 35
GDL: 45

17 18 19 20
30 31 32

13 14 15 16
27 28 29

9 10 11 12
24 25 26

5 6 7 8
21 22 23

1 2 3 4

2.- Determinacion de Cordenadas Locales Generalizadas: {q} - {d}

1 3

Vigas
(12𝐸𝐼/𝐿^3 @6𝐸𝐼/𝐿^2 @(−12𝐸𝐼)/𝐿^3 e: 7, 8, 9, 10) █(6𝐸𝐼/𝐿^2 @4𝐸𝐼/𝐿@(−6𝐸𝐼)/𝐿^2 @2𝐸𝐼/𝐿) █((−12𝐸𝐼)/𝐿^3 @(−6𝐸𝐼)/𝐿^2 @12𝐸𝐼/𝐿^3 @(−6𝐸𝐼)/𝐿^2 ) █(6𝐸𝐼/𝐿^2 @2𝐸𝐼/𝐿@(−6𝐸𝐼)/𝐿^2 @4𝐸𝐼/𝐿)]
@6𝐸𝐼/𝐿^2
2 4
+ m.transformcion

&0&0@0&12𝐸𝐼/𝐿^3 &−6𝐸𝐼/𝐿^2 @0&−6𝐸𝐼/𝐿^2 &4𝐸𝐼/𝐿)&■8(−𝐸𝐴/𝐿&0&0@0&−12𝐸𝐼/𝐿^3 &−6𝐸𝐼/𝐿^2 @0&6𝐸𝐼/𝐿^2 &2𝐸𝐼/𝐿)@■8(−𝐸𝐴/𝐿&0&0@0&−12𝐸𝐼/𝐿^3 &6𝐸𝐼/𝐿^2 @0&−6𝐸𝐼/𝐿^2 &2𝐸𝐼/𝐿)&■8(𝐸𝐴/𝐿&0&0@0&12𝐸𝐼/𝐿^3 &6𝐸𝐼/𝐿^2 @0&6𝐸𝐼/𝐿^2 &4𝐸𝐼/𝐿))]

2 5

4
1
3 6
Columnas y placas
e: 1-14

b1 b2
23,26,29,32,35

21,24,27,30,33

22,25,28,31,34

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

3.- Cálculos previos - Datos de las barras

Columnas
Vigas
Placas
0.34 0.50 21,24,27,30,33 22,25, 23,26,29,32,35

1.20
0.25 28,31,34

0.25 33 34 35
30x30

r=0.17

30x30
r=0.1
7

3.0m 18 19
17 20
0.25x0.50 0.25x0.50 0.25x0.50
30 31 32
30x30

r=0.17
r=0.17

30x30
3.0m
13 14 15 16
27 28 29
30x30

r=0.17
30x1.2

30x30 3.0m 9 10 11 12
24 25 26
30x3

r=0.17

r=0.17

30x30

6 7
0

3.0m 5 8
21 22 23
30x30

2 3
r=0.17

1 4
r=0.17

30x30

3.5m

4m 4m 4m

(2−)𝐸𝐼/(1+)𝐿 (12.𝐸𝐼)/((1+)
Barra b h A E I EA EI AX AY L EA/L (4+)𝐸𝐼/(1+)𝐿(6.𝐸𝐼)/((1+) 𝐿^2 ) 𝐿^3 )
f

1 1.20 0.25 0.3 2.2E+06 1.6E-03 6.5E+05 3396 0 3.5 3.50 186318 3837.7 1896.9 1638.5 936.3 0.02
2 3.14 0.17 0.09 2.2E+06 6.6E-04 2.0E+05 1426 0 3.5 3.50 56387 1621.0 806.2 693.5 396.3 0.01
3 3.14 0.17 0.09 2.2E+06 6.6E-04 2.0E+05 1426 0 3.5 3.50 56387 1621.0 806.2 693.5 396.3 0.01
4 1.20 0.25 0.30 2.2E+06 1.6E-03 6.5E+05 3396 0 3.5 3.50 186318 3837.7 1896.9 1638.5 936.3 0.02
5 1.20 0.25 0.30 2.2E+06 1.6E-03 6.5E+05 3396 0 3 3.00 217371 4459.2 2195.0 2218.1 1478.7 0.02
6 3.14 0.17 0.09 2.2E+06 6.6E-04 2.0E+05 1426 0 3 3.00 65785 1887.6 937.0 941.5 627.7 0.01
7 3.14 0.17 0.09 2.2E+06 6.6E-04 2.0E+05 1426 0 3 3.00 65785 1887.6 937.0 941.5 627.7 0.01
8 1.20 0.25 0.30 2.2E+06 1.6E-03 6.5E+05 3396 0 3 3.00 217371 4459.2 2195.0 2218.1 1478.7 0.02
9 1.20 0.25 0.30 2.2E+06 1.6E-03 6.5E+05 3396[𝑘𝑒]=[■8(■8(𝐸𝐴/𝐿&0&0@0&12𝐸𝐼/𝐿^3
0 3 3.00 &−6𝐸𝐼/𝐿^2
217371 @0&−6𝐸𝐼/𝐿^2
4459.2 2195.0 &4𝐸𝐼/𝐿)&■8(−𝐸𝐴/𝐿&0&0@0&−12𝐸𝐼/𝐿^3
2218.1 1478.7 0.02 &−6𝐸𝐼/𝐿^2 @0&6𝐸𝐼/𝐿^2 &2𝐸𝐼/𝐿

10 3.14 0.17 0.09 2.2E+06 6.6E-04 2.0E+05 1426 0 3 3.00 65785 1887.6 937.0 941.5 627.7 0.01
11 3.14 0.17 0.09 2.2E+06 6.6E-04 2.0E+05 1426 0 3 3.00 65785 1887.6 937.0 941.5 627.7 0.01
12 1.20 0.25 0.30 2.2E+06 1.6E-03 6.5E+05 3396 0 3 3.00 217371 4459.2 2195.0 2218.1 1478.7 0.02
13 1.20 0.25 0.30 2.2E+06 1.6E-03 6.5E+05 3396 0 3 3.00 217371 4459.2 2195.0 2218.1 1478.7 0.02
14 3.14 0.17 0.09 2.2E+06 6.6E-04 2.0E+05 1426 0 3 3.00 65785 1887.6 937.0 941.5 627.7 0.01
15 3.14 0.17 0.09 2.2E+06 6.6E-04 2.0E+05 1426 0 3 3.00 65785 1887.6 937.0 941.5 627.7 0.01
16 1.20 0.25 0.30 2.2E+06 1.6E-03 6.5E+05 3396 0 3 3.00 217371 4459.2 2195.0 2218.1 1478.7 0.02
17 1.20 0.25 0.30 2.2E+06 1.6E-03 6.5E+05 3396 0 3 3.00 217371 4459.2 2195.0 2218.1 1478.7 0.02
18 3.14 0.17 0.09 2.2E+06 6.6E-04 2.0E+05 1426 0 3 3.00 65785 1887.6 937.0 941.5 627.7 0.01
19 3.14 0.17 0.09 2.2E+06 6.6E-04 2.0E+05 1426 0 3 3.00 65785 1887.6 937.0 941.5 627.7 0.01
20 1.20 0.25 0.3 2.2E+06 1.6E-03 6.5E+05 3396 0 3 3.00 217371 4459.2 2195.0 2218.1 1478.7 0.02
21 0.25 0.50 0.125 2.2E+06 2.6E-03 2.7E+05 5661 4 0 4.00 0 ∞ 5470.6 2640.2 2027.7 1013.9 0.05
22 0.25 0.50 0.125 2.2E+06 2.6E-03 2.7E+05 5661 4 0 4.00 0 ∞ 5470.6 2640.2 2027.7 1013.9 0.05
23 0.25 0.50 0.125 2.2E+06 2.6E-03 2.7E+05 5661 4 0 4.00 0 ∞ 5470.6 2640.2 2027.7 1013.9 0.05
24 0.25 0.50 0.125 2.2E+06 2.6E-03 2.7E+05 5661 4 0 4.00 0 ∞ 5470.6 2640.2 2027.7 1013.9 0.05
25 0.25 0.50 0.125 2.2E+06 2.6E-03 2.7E+05 5661 4 0 4.00 0 ∞ 5470.6 2640.2 2027.7 1013.9 0.05
26 0.25 0.50 0.125 2.2E+06 2.6E-03 2.7E+05 5661 4 0 4.00 0 ∞ 5470.6 2640.2 2027.7 1013.9 0.05
27 0.25 0.50 0.125 2.2E+06 2.6E-03 2.7E+05 5661 4 0 4.00 0 ∞ 5470.6 2640.2 2027.7 1013.9 0.05
28 0.25 0.50 0.125 2.2E+06 2.6E-03 2.7E+05 5661 4 0 4.00 0 ∞ 5470.6 2640.2 2027.7 1013.9 0.05
29 0.25 0.50 0.125 2.2E+06 2.6E-03 2.7E+05 5661 4 0 4.00 0 ∞ 5470.6 2640.2 2027.7 1013.9 0.05
30 0.25 0.50 0.125 2.2E+06 2.6E-03 2.7E+05 5661 4 0 4.00 0 ∞ 5470.6 2640.2 2027.7 1013.9 0.05
31 0.25 0.50 0.125 2.2E+06 2.6E-03 2.7E+05 5661 4 0 4.00 0 ∞ 5470.6 2640.2 2027.7 1013.9 0.05
32 0.25 0.50 0.125 2.2E+06 2.6E-03 2.7E+05 5661 4 0 4.00 0 ∞ 5470.6 2640.2 2027.7 1013.9 0.05
33 0.25 0.50 0.125 2.2E+06 2.6E-03 2.7E+05 5661 4 0 4.00 0 ∞ 5470.6 2640.2 2027.7 1013.9 0.05
34 0.25 0.50 0.125 2.2E+06 2.6E-03 2.7E+05 5661 4 0 4.00 0 ∞ 5470.6 2640.2 2027.7 1013.9 0.05
35 0.25 0.50 0.125 2.2E+06 2.6E-03 2.7E+05 5661 4 0 4.00 0 ∞ 5470.6 2640.2 2027.7 1013.9 0.05

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

4.- Matriz de Transformacion de desplazamientos [A*]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]2
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]3
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]4
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
[A*]5
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
[A*]6
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
[A*]7
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
[A*]8
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
[A*]9
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]10
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]11
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]12
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

[A*]12

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]13
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]14
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]15
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]16
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]17
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]18
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]19
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]20
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
[A*]21
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
[A*]22
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
[A*]23
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
[A*]24
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]25
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]26
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]27
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]28
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]29
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]30
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]31
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]32
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]33
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

[A*]34

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]34
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]35
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

5.- Matriz de rigidez de la barra [k]i, {q}-{d}

186318 0.0 0.0 -186318 0.0 0.0

0.0 936.3 -1638.5 0.0 -936.3 -1638.5
0.0 -1638.5 3837.7 0.0 1638.5 1896.9
[k] 1, 4 =
### 0.0 0.0 186317.7 0.0 0.0
0.0 -936.3 1638.5 0.0 936.3 1638.5
0.0 -1638.5 1896.9 0.0 1638.5 3837.7

56387 0.0 0.0 -56387 0.0 0.0

0.0 396.3 -693.5 0.0 -396.3 -693.5
0.0 -693.5 1621.0 0.0 693.5 806.2
[k] 2,3 =
-56387&−6𝐸𝐼/𝐿^2
[𝑘𝑒]=[■8(■8(𝐸𝐴/𝐿&0&0@0&12𝐸𝐼/𝐿^3 0.0 0.0
@0&−6𝐸𝐼/𝐿^2 56387.2 0.0 0.0
&4𝐸𝐼/𝐿)&■8(−𝐸𝐴/𝐿&0&0@0&−12𝐸𝐼/𝐿^3 &−6𝐸𝐼/𝐿^2 @0&6𝐸𝐼/𝐿^2 &2𝐸𝐼/𝐿)@■8(−𝐸𝐴/𝐿&0&0@0&−12𝐸𝐼/𝐿^3 &6𝐸𝐼/𝐿^2 @0&−6𝐸𝐼/𝐿^2 &2𝐸𝐼/𝐿)&■8(𝐸𝐴/
0.0 -396.3 693.5 0.0 396.3 693.5
0.0 -693.5 806.2 0.0 693.5 1621.0

217371 0.0 0.0 -217371 0.0 0.0

0.0 1478.7 -2218.1 0.0 -1478.7 -2218.1
[k] 0.0 -2218.1 4459.2 0.0 2218.1 2195.0
5,8,9,12,13,16,17,20 = ### 0.0 0.0 217370.7 0.0 0.0
0.0 -1478.7 2218.1 0.0 1478.7 2218.1
0.0 -2218.1 2195.0 0.0 2218.1 4459.2

65785 0.0 0.0 -65785 0.0 0.0

0.0 627.7 -941.5 0.0 -627.7 -941.5

[k] 0.0 -941.5 1887.6 0.0 941.5 937.0

6,7,10,11,14,15,18,19 = -65785 0.0 0.0 65785.1 0.0 0.0
0.0 -627.7 941.5 0.0 627.7 941.5
0.0 -941.5 937.0 0.0 941.5 1887.6 Columas
b1= 0.15 b2= 0
[K] =[ST] [K '] [S] 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0
0.0 1013.9 2027.7 0.0 -1013.9 2027.7 0.0 1.0 0.2 0.0 0.0 0.0
[k]' 21, 24, 27, 30, 33 0.0 2027.7 5470.6 0.0 -2027.7 2640.2 0.0 0.0 1.0 0.0 0.0 0.0
[s] 16 =
= 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0
0.0 -1013.9 -2027.7 0.0 1013.9 -2027.7 0.0 0.0 0.0 0.0 1.0 0.0
0.0 2027.7 2640.2 0.0 -2027.7 5470.6 0.0 0.0 0.0 0.0 0.0 1.0

0.0 0.0 0.0 0.0 0.0 0.0

0.0 1013.9 2179.8 0.0 -1013.92027.7
[k] 21, 24, 27, 30, 33 0.0 2179.8 6101.7 0.0 -2179.8 2944.4
= 0.0 0.0 0.0 0.0 0.0 0.0
0.0 -1013.9 -2179.8 0.0 1013.9 -2027.7
0.0 2027.7 2944.4 0.0 -2027.7 5470.6

b1= 0 b2= 0
[K] =[ST] [K '] [S] 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0
0.0 1013.9 2027.7 0.0 -1013.9 2027.7 0.0 1.0 0.0 0.0 0.0 0.0
[k]' 22, 35, 28, 31, 34 0.0 2027.7 5470.6 0.0 -2027.7 2640.2 0.0 0.0 1.0 0.0 0.0 0.0
[s] 15 =
= 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0
0.0 -1013.9 -2027.7 0.0 1013.9 -2027.7 0.0 0.0 0.0 0.0 1.0 0.0
0.0 2027.7 2640.2 0.0 -2027.7 5470.6 0.0 0.0 0.0 0.0 0.0 1.0

0.0 0.0 0.0 0.0 0.0 0.0

0.0 1013.9 2027.7 0.0 -1013.92027.7
[k] 22, 35, 28, 31, 34 0.0 2027.7 5470.6 0.0 -2027.7 2640.2
= 0.0 0.0 0.0 0.0 0.0 0.0
0.0 -1013.9 -2027.7 0.0 1013.9 -2027.7
0.0 2027.7 2640.2 0.0 -2027.7 5470.6

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

b1= 0 b2= 0.15

[K] =[ST] [K '] [S] 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0
0.0 1013.9 2027.7 0.0 -1013.9 2027.7 0.0 1.0 0.0 0.0 0.0 0.0
[k]' 23, 26, 29, 32, 35 0.0 2027.7 5470.6 0.0 -2027.7 2640.2 0.0 0.0 1.0 0.0 0.0 0.0
[s] 16 =
= 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0
0.0 -1013.9 -2027.7 0.0 1013.9 -2027.7 0.0 0.0 0.0 0.0 1.0 -0.2
0.0 2027.7 2640.2 0.0 -2027.7 5470.6 0.0 0.0 0.0 0.0 0.0 1.0

0.0 0.0 0.0 0.0 0.0 0.0

0.0 1013.9 2027.7 0.0 -1013.9 2179.8
[k] 23, 26, 29, 32, 35 0.0 2027.7 5470.6 0.0 -2027.7 2944.4
= 0.0 0.0 0.0 0.0 0.0 0.0
0.0 -1013.9 -2027.7 0.0 1013.9 -2179.8
0.0 2179.8 2944.4 0.0 -2179.8 6101.7 Vigas

6.- Determinar la Matriz deTransformacion de desplazamientos [R] i {𝑑}=[𝑅]{𝑑^∗ }

cos a sen a 0 0 0 0
sen a -cos a 0 0 0 0
0 0 1 0 0 0
[R]i=
0 0 0 cos a sen a 0
0 0 0 sen a -cos a 0
0 0 0 0 0 1

0 1 0 0 0 0
1 0 0 0 0 0
0 0 1 0 0 0
[R]1, 4=
0 0 0 0 1 0
0 0 0 1 0 0
0 0 0 0 0 1

0 1 0 0 0 0
1 0 0 0 0 0
0 0 1 0 0 0
[R] 2, 3=
0 0 0 0 1 0
0 0 0 1 0 0
0 0 0 0 0 1

0 1 0 0 0 0
1 0 0 0 0 0
[R] 5, 8, 9, 12, 13, 16, 0 0 1 0 0 0
17, 20= 0 0 0 0 1 0
0 0 0 1 0 0
0 0 0 0 0 1

0 1 0 0 0 0
1 0 0 0 0 0
[R]6, 7, 10, 11, 14, 15, 0 0 1 0 0 0
18, 19= 0 0 0 0 1 0
0 0 0 1 0 0
0 0 0 0 0 1 Columnas y Placas

1 0 0 0 0 0
0 1 0 0 0 0
[R]21, 24, 27, 30, 0 0 1 0 0 0
33= 0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1

1 0 0 0 0 0
0 1 0 0 0 0
[R]22, 25, 28, 31, 0 0 1 0 0 0
34= 0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

1 0 0 0 0 0
0 1 0 0 0 0
[R]23, 26, 29, 32, 0 0 1 0 0 0
35= 0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1

7.- Matriz de rigidez de la barra [k*]i, {q*}-{d*} [𝑘^∗ ]=[𝑅]^𝑇 [𝑘][𝑅]

936.3 0.0 -1638.5 -936.3 0.0 -1638.5

0.0 186317.7 0.0 0.0 ### 0.0
-1638.5 0.0 3837.7 1638.5 0.0 1896.9
[k*]1, 4=
-936.3 0.0 1638.5 936.3 0.0 1638.5
0.0 ### 0.0 0.0 186317.7 0.0
-1638.5 0.0 1896.9 1638.5 0.0 3837.7

396 0 -693 -396 0 -693

0 56387 0 0 -56387 0
-693 0 1621 693 0 806
[k*] 2, 3=
-396 0 693 396 0 693
0 -56387 0 0 56387 0
-693 0 806 693 0 1621

1479 0 -2218 -1479 0 -2218

0 217371 0 0 -217371 0
[k*] 5, 8, 9, 12, 13, -2218 0 4459 2218 0 2195
16, 17, 20= -1479 0 2218 1479 0 2218
0 ### 0 0 217371 0
-2218 0 2195 2218 0 4459

628 0 -942 -628 0 -942

0 65785 0 0 -65785 0
[k*]6, 7, 10, 11, 14, -942 0 1888 942 0 937
15, 18, 19= -628 0 942 628 0 942
0 -65785 0 0 65785 0
-942 0 937 942 0 1888

0 0 0 0 0 0
0 1014 2180 0 -1014 2028
[k*]21, 24, 27, 30, 0 2180 6102 0 -2180 2944
33= 0 0 0 0 0 0
0 -1014 -2180 0 1014 -2028
0 2028 2944 0 -2028 5471

0 0 0 0 0 0
0 1014 2028 0 -1014 2028
[k*]22, 25, 28, 31, 0 2028 5471 0 -2028 2640
34= 0 0 0 0 0 0
0 -1014 -2028 0 1014 -2028
0 2028 2640 0 -2028 5471

0 0 0 0 0 0
0 1014 2028 0 -1014 2180
[k*] 23, 26, 29, 32, 0 2028 5471 0 -2028 2944
35 = 0 0 0 0 0 0
0 -1014 -2028 0 1014 -2180
0 2180 2944 0 -2180 6102

8.- Ensamblaje de la Matriz de Rigidez Total [𝐾]= 〖 [𝑨_𝒆^∗] 〗 ^𝑻 [𝒌_𝒆^∗ ][𝑨_𝒆^∗ ]

- Ensamblaje [K]
NOTA: LA MATRIZ COMPLETA SE PUEDE APRECIAR EN EL EXCEL
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
936.26985438 0 0 0 0 0 1638.4722452 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 186317.70102 0 0 0 0 0 0 0 0 0 0

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

1638.4722452 0 0 0 0 0 3837.7311219 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[K]1= 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 … 45
396 0 0 0 0 0 0 0 693 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 4
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 5
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 6
0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
[K]2=
0 0 0 0 0 0 0 56387 0 0 0 0 0 0 8
693 0 0 0 0 0 0 0 1621 0 0 0 0 0 9
0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 0 0 0 12
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 …
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 45

1 2 3 4 5 6 7 8 9 10 11 12 … 45
396 0 0 0 0 0 0 0 0 0 693 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 4
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 5
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 6
0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
[K]3=
0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 9
0 0 0 0 0 0 0 0 0 56387 0 0 0 0 10
693 0 0 0 0 0 0 0 0 0 1621 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 0 0 0 12
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 …
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 45

1 2 3 4 5 6 7 8 9 10 11 12 … 45

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

936.26985438 0 0 0 0 0 0 0 0 0 0 0 1638.47 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
0 0 0 0 0 0 0 0 0 0 0 0 0 0 5
0 0 0 0 0 0 0 0 0 0 0 0 0 0 6
0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
[K]4=
0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 9
0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 186318 0 0 12
1638.4722452 0 0 0 0 0 0 0 0 0 0 0 3837.73 0 …
0 0 0 0 0 0 0 0 0 0 0 0 0 0 45

Generacion de las formulas excel para obtener el aporte de cada barra y hallar la suma directa por cuestiones de dimensiones grandes de las matrices. Esto con el fin de
hallar directamente la sumatoria de aportes sin la necesidad de hallar cada uno
Fila Fila
Matriz K * del
[K]elem Formula de multiplicacion de matrices inicial final de
elemento
de [A] [A]
[K]1 MMULT(TRANSPOSE(B162:AT167);MMULT(E507:J512;B162:AT167)) 162 167 E507:J512
[K]2 MMULT(TRANSPOSE(B168:AT173);MMULT(E514:J519;B168:AT173)) 168 173 E514:J519
[K]3 MMULT(TRANSPOSE(B174:AT179);MMULT(E514:J519;B174:AT179)) 174 179 E514:J519
[K]4 MMULT(TRANSPOSE(B180:AT185);MMULT(E507:J512;B180:AT185)) 180 185 E507:J512
[K]5 MMULT(TRANSPOSE(B186:AT191);MMULT(E521:J526;B186:AT191)) 186 191 E521:J526
[K]6 MMULT(TRANSPOSE(B192:AT197);MMULT(E528:J533;B192:AT197)) 192 197 E528:J533
[K]7 MMULT(TRANSPOSE(B198:AT203);MMULT(E528:J533;B198:AT203)) 198 203 E528:J533
[K]8 MMULT(TRANSPOSE(B204:AT209);MMULT(E521:J526;B204:AT209)) 204 209 E521:J526
[K]9 MMULT(TRANSPOSE(B210:AT215);MMULT(E521:J526;B210:AT215)) 210 215 E521:J526
[K]10 MMULT(TRANSPOSE(B216:AT221);MMULT(E528:J533;B216:AT221)) 216 221 E528:J533
[K]11 MMULT(TRANSPOSE(B222:AT227);MMULT(E528:J533;B222:AT227)) 222 227 E528:J533
[K]12 MMULT(TRANSPOSE(B228:AT233);MMULT(E521:J526;B228:AT233)) 228 233 E521:J526
[K]13 MMULT(TRANSPOSE(B234:AT239);MMULT(E521:J526;B234:AT239)) 234 239 E521:J526
[K]14 MMULT(TRANSPOSE(B240:AT245);MMULT(E528:J533;B240:AT245)) 240 245 E528:J533
[K]15 MMULT(TRANSPOSE(B246:AT251);MMULT(E528:J533;B246:AT251)) 246 251 E528:J533
[K]16 MMULT(TRANSPOSE(B252:AT257);MMULT(E521:J526;B252:AT257)) 252 257 E521:J526
[K]17 MMULT(TRANSPOSE(B258:AT263);MMULT(E521:J526;B258:AT263)) 258 263 E521:J526
[K]18 MMULT(TRANSPOSE(B264:AT269);MMULT(E528:J533;B264:AT269)) 264 269 E528:J533
[K]19 MMULT(TRANSPOSE(B270:AT275);MMULT(E528:J533;B270:AT275)) 270 275 E528:J533
[K]20 MMULT(TRANSPOSE(B276:AT281);MMULT(E521:J526;B276:AT281)) 276 281 E521:J526
[K]21 MMULT(TRANSPOSE(B282:AT287);MMULT(E535:J540;B282:AT287)) 282 287 E535:J540
[K]22 MMULT(TRANSPOSE(B288:AT293);MMULT(E542:J547;B288:AT293)) 288 293 E542:J547
[K]23 MMULT(TRANSPOSE(B294:AT299);MMULT(E549:J554;B294:AT299)) 294 299 E549:J554
[K]24 MMULT(TRANSPOSE(B300:AT305);MMULT(E535:J540;B300:AT305)) 300 305 E535:J540
[K]25 MMULT(TRANSPOSE(B306:AT311);MMULT(E542:J547;B306:AT311)) 306 311 E542:J547
[K]26 MMULT(TRANSPOSE(B312:AT317);MMULT(E549:J554;B312:AT317)) 312 317 E549:J554
[K]27 MMULT(TRANSPOSE(B318:AT323);MMULT(E535:J540;B318:AT323)) 318 323 E535:J540
[K]28 MMULT(TRANSPOSE(B324:AT329);MMULT(E542:J547;B324:AT329)) 324 329 E542:J547
[K]29 MMULT(TRANSPOSE(B330:AT335);MMULT(E549:J554;B330:AT335)) 330 335 E549:J554
[K]30 MMULT(TRANSPOSE(B336:AT341);MMULT(E535:J540;B336:AT341)) 336 341 E535:J540
[K]31 MMULT(TRANSPOSE(B342:AT347);MMULT(E542:J547;B342:AT347)) 342 347 E542:J547
[K]32 MMULT(TRANSPOSE(B348:AT353);MMULT(E549:J554;B348:AT353)) 348 353 E549:J554
[K]33 MMULT(TRANSPOSE(B354:AT359);MMULT(E535:J540;B354:AT359)) 354 359 E535:J540
[K]34 MMULT(TRANSPOSE(B360:AT365);MMULT(E542:J547;B360:AT365)) 360 365 E542:J547
[K]35 MMULT(TRANSPOSE(B366:AT371);MMULT(E549:J554;B366:AT371)) 366 371 E549:J554

𝐾]=∑_(𝑒=1)^𝑚▒ 〖〖 [𝐴_𝑒^∗] 〗 ^𝑇 [𝑘_𝑒^∗ ][𝐴_𝑒^∗ ] 〗

NOTA: LA MATRIZ COMPLETA SE PUEDE VER EN EL ARCHIVO EXCEL ADJUNTO

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
6877.8865625 -4212.78956 0 0 0 0 -579.5956241 0 -248.04 0 -248.04 0 -579.6 0 -2218.1 0
-4212.78956 8425.5791208 -4212.78956 0 0 0 2218.0678693 0 941.524 0 941.524 0 2218.07 0 0 0
0 -4212.78956 8425.5791208 -4213 0 0 0 0 0 0 0 0 0 0 2218.07 0
0 0 -4212.78956 8425.6 -4213 0 0 0 0 0 0 0 0 0 0 0
0 0 0 -4213 4212.79 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 404702.20786 2179.7896458 -1014 2027.71 0 0 0 0 -217371 0 0
-579.5956241 2218.0678693 0 0 0 2179.7896458 14398.692983 -2180 2944.41 0 0 0 0 0 2195 0
[K]T=
0 0 0 0 0 -1013.855649 -2179.789646 124200 0 -1013.856 2027.71 0 0 0 0 ###
-248.0366693 941.52430099 0 0 0 2027.7112984 2944.4057813 0 14450 -2027.711 2640.25 0 0 0 0 0
0 0 0 0 0 0 0 -1014 -2027.7 124200 0 -1013.9 2179.79 0 0 0
-248.0366693 941.52430099 0 0 0 0 0 2027.7 2640.25 0 14450 -2027.7 2944.41 0 0 0
0 0 0 0 0 0 0 0 0 -1013.856 -2027.7 404702 -2179.8 0 0 0
-579.5956241 2218.0678693 0 0 0 0 0 0 0 2179.7896 2944.41 -2179.8 14399 0 0 0

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
 “ANÁLISIS PSEUDO-TRIDIMENCIONAL DE UNA EDIFICACIÓN DE CINCO NIVELES UTILIZANDO EL MÉTODO ESTÁTICO DE LA NORMA E-030 DEL R.N.E”

0 0 0 0 0 -217370.6512 0 0 0 0 0 0 0 435755 2179.79 ###

-2218.067869 0 2218.0678693 0 0 0 2194.9629957 0 0 0 0 0 0 2179.79 15020 ###
0 0 0 0 0 0 0 -65785 0 0 0 0 0 -1013.9 -2179.8 ###
-941.524301 0 941.52430099 0 0 0 0 0 936.989 0 0 0 0 2027.71 2944.41 0
0 0 0 0 0 0 0 0 0 -65785.07 0 0 0 0 0 ###
-941.524301 0 941.52430099 0 0 0 0 0 0 0 936.989 0 0 0 0 ###
0 0 0 0 0 0 0 0 0 0 0 -217371 0 0 0 0
-2218.067869 0 2218.0678693 0 0 0 0 0 0 0 0 0 2195 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 -217371 0 0
0 -2218.067869 0 2218.1 0 0 0 0 0 0 0 0 0 0 2195 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ###
0 -941.524301 0 941.52 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 -941.524301 0 941.52 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 -2218.067869 0 2218.1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 -2218.067869 0 2218.07 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 -941.524301 0 941.524 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 -941.524301 0 941.524 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 -2218.067869 0 2218.07 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 -2218 2218.07 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 -941.52 941.524 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 -941.52 941.524 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 -2218 2218.07 0 0 0 0 0 0 0 0 0 0 0
* Estructura del K ordenado

- GDLE 1-5
Kuu Kur 1 2 3 4 5
[K]T= 6160.69 -4029.22 675.80 -91.53 18.89 1
[K]L=
-4029.22 7009.14 -4116.94 678.24 -68.31 2
Kru Krr 675.80 -4116.94 7016.65 -4083.36 578.63 3
-91.53 678.24 -4083.36 6763.75 -3276.87 4
18.89 -68.31 578.63 -3276.87 2746.00 5

ANÁLISIS ESTRUCTURAL
ING. HUGO OLAZA HENOSTROZA
07.- Condensacion de la matriz de rigidez del portico 7

VISTA ELEVACIÓN DEL PORTICO 07

1.20m 1.20m

3.0m 26 27 28
0.25x0.50 0.25x0.50 0.25x0.50
17 18 19 20
25x120

13 14 15 16
25x120
30x30

30x30

3.0m 23 24 25
0.25x0.50 0.25x0.50 0.25x0.50
13 14 15 16
9 10 11 12
25x120

25x120
30x30

30x30

3.0m 20 21 22
0.25x0.50 0.25x0.50 0.25x0.50
9 10 11 12
5 6 7 8
25x120
25x120
30x30

30x30

3.0m 17 18 19
0.25x0.50 0.25x0.50 0.25x0.50 5 6 7 8
1 2 3 4
25x120

25x120
30x30

30x30

3.5m
1 2 3 4
4m 4m 4m

Dato
E= 2509980 Tn/m²

1.- Determinacion de Cordenadas Globales Generalizadas y GDL

29 31 33 35
4 4 4 4

30 32 34 36
21 23 25 27
3 3 3 3

22 24 26 28
13 15 17 19
2 2 2 2

14 16 18 20
5 7 9 11
1 1 1 1

6 8 10 12

38 41 44 47
37 40 43 46

39 42 45 48
 GDL: 1, 2, 3, 4, 5, 6, 7..., 8, 9, …,36

42 43 44 45

21 22 23 24 25
38 39 40 41

16 17 18 19 20
34 35 36 37

11 12 13 14 15
30 31 32 33

6 7 8 9 10
26 27 28 29

1 2 3 4 5

2.- Determinacion de Cordenadas Locales Generalizadas: {q} - {d}

1 3
2 5
Vigas
[𝑘𝑒]=[■8(■8(𝐸𝐴/𝐿&0&0@0&12𝐸𝐼/𝐿^3 &−6𝐸𝐼/𝐿^2 @0&−6𝐸𝐼/𝐿^2 &4𝐸𝐼/𝐿)&■8(−𝐸𝐴/𝐿&0&0@0&−12𝐸𝐼/𝐿^3 &−6𝐸𝐼/𝐿^2 @0&6𝐸𝐼/𝐿^2 &2𝐸𝐼/𝐿)@■8(−𝐸𝐴/𝐿&0&0@0&−12𝐸𝐼/𝐿^3 &6𝐸𝐼/𝐿^2 @
e: 7, 8, 9, 10 4
2 4 1
+ m.transformcion 3 6
𝐸𝐼/𝐿^2 ) █(6𝐸𝐼/𝐿^2 @4𝐸𝐼/𝐿@(−6𝐸𝐼)/𝐿^2 @2𝐸𝐼/𝐿) █((−12𝐸𝐼)/𝐿^3 @(−6𝐸𝐼)/𝐿^2 @12𝐸𝐼/𝐿^3
Columnas @(−6𝐸𝐼)/𝐿^2 ) █(6𝐸𝐼/𝐿^2 @2𝐸𝐼/𝐿@(−6𝐸𝐼)/𝐿^2 @4𝐸𝐼/𝐿)]
y placas
b1 b2 e: 1-14

3.- Cálculos previos - Datos de las barras

Columnas Vigas Placas

0.30 0.50 0.25

1.20
0.30 0.25

17, 20, 23, 26 18, 21, 24, 27 19, 22, 25, 28

(2−)𝐸𝐼/(1+
(4+)𝐸𝐼/(1+)𝐿 )𝐿 (12.𝐸𝐼)/((1+)
(6.𝐸𝐼)/((1+) 𝐿^2 ) 𝐿^3 )
Barra b h A E I EA EI AX AY L EA/L f

1 0.30 0.30 0.09 2.5E+06 6.8E-04 2.3E+05 1694 0 3.5 3.50 64542 1905.0 936.8 811.9 464.0 0.02
2 0.25 1.20 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3.5 3.50 215141 83075.4 31441.5 32719.1 18696.6 0.35
3 0.25 1.20 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3.5 3.50 215141 83075.4 31441.5 32719.1 18696.6 0.35
4 0.30 0.30 0.09 2.5E+06 6.8E-04 2.3E+05 1694 0 3.5 3.50 64542 1905.0 936.8 811.9 464.0 0.02
5 0.30 0.30 0.09 2.5E+06 6.8E-04 2.3E+05 1694 0 3.5 3.50 64542 1905.0 936.8 811.9 464.0 0.02
6 0.25 1.20 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3 3.00 250998 91173.3 30933.8 40702.4 27134.9 0.48
7 0.25 1.20 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3 3.00 250998 91173.3 30933.8 40702.4 27134.9 0.48
 8 0.30 0.30 0.09 2.5E+06 6.8E-04 2.3E+05 1694 0 3 3.00 75299 2209.6 1080.1 1096.6 731.1 0.03
9 0.30 0.30 0.09 2.5E+06 6.8E-04 2.3E+05 1694 0 3 3.00 75299 2209.6 1080.1 1096.6 731.1 0.03
10 0.25 1.20 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3 3.00 250998 91173.3 30933.8 40702.4 27134.9 0.48
11 0.25 1.20 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3 3.00 250998 91173.3 30933.8 40702.4 27134.9 0.48
12 0.30 0.30 0.09 2.5E+06 6.8E-04 2.3E+05 1694 0 3 3.00 75299 2209.6 1080.1 1096.6 731.1 0.03
13 0.30 0.30 0.09 2.5E+06 6.8E-04 2.3E+05 1694 0 3 3.00 75299 2209.6 1080.1 1096.6 731.1 0.03
14 0.25 1.20 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3 3.00 250998 91173.3 30933.8 40702.4 27134.9 0.48
15 0.25 1.20 0.3 2.5E+06 3.6E-02 7.5E+05 90359 0 3 3.00 250998 91173.3 30933.8 40702.4 27134.9 0.48
16 0.30 0.30 0.09 2.5E+06 6.8E-04 2.3E+05 1694 0 3 3.00 75299 2209.6 1080.1 1096.6 731.1 0.03
17 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 5 0 5.00 0 ∞ 5114.9 2500.3 1523.0 609.2 0.03
18 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 5 0 5.00 0 ∞ 5114.9 2500.3 1523.0 609.2 0.03
19 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 5 0 5.00 0 ∞ 5114.9 2500.3 1523.0 609.2 0.03
20 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 5 0 5.00 0 ∞ 5114.9 2500.3 1523.0 609.2 0.03
21 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 5 0 5.00 0 ∞ 5114.9 2500.3 1523.0 609.2 0.03
22 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 5 0 5.00 0 ∞ 5114.9 2500.3 1523.0 609.2 0.03
23 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 5 0 5.00 0 ∞ 5114.9 2500.3 1523.0 609.2 0.03
24 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 5 0 5.00 0 ∞ 5114.9 2500.3 1523.0 609.2 0.03
25 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 5 0 5.00 0 ∞ 5114.9 2500.3 1523.0 609.2 0.03
26 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 5 0 5.00 0 ∞ 5114.9 2500.3 1523.0 609.2 0.03
27 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 5 0 5.00 0 ∞ 5114.9 2500.3 1523.0 609.2 0.03
28 0.25 0.50 0.125 2.5E+06 2.6E-03 3.1E+05 6536 5 0 5.00 0 ∞ 5114.9 2500.3 1523.0 609.2 0.03

4.- Matriz de Transformacion de desplazamientos [A*]

NOTA: LA MATRIZ COMPLETA SE PUEDE VER EN EL ARCHIVO EXCEL ADJUNTO
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]2
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]3
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]4
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
[A*]5
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
[A*]6
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
[A*]6

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
[A*]7
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
[A*]8
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
[A*]9
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
[A*]10
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]11
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]12
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]13
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]14
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]15
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]16
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]16

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
[A*]17
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
[A*]18
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
[A*]19
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
[A*]20
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
[A*]21
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]22
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]23
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]24
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]25
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]26
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]26

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]27
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[A*]28
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

5.- Matriz de rigidez de la barra [k]i, {q}-{d}

64542 0.0 0.0 -64542 0.0 0.0

0.0 464.0 -811.9 0.0 -464.0 -811.9
0.0 -811.9 1905.0 0.0 811.9 936.8
[k] 1, 4 =
-64542 0.0 0.0 64542.3 0.0 0.0
0.0 -464.0 811.9 0.0 464.0 811.9
0.0 -811.9 936.8 0.0 811.9 1905.0

215141 0.0 0.0 -215141 0.0 0.0

0.0 18696.6 -32719.1 0.0 -18696.6 -32719.1
0.0 -32719.1 83075.4 0.0 32719.1 31441.5
[k] 2, 3 =
-215141 0.0 0.0 215141.1 0.0 0.0
0.0 -18696.6 32719.1 0.0 18696.6 32719.1
0.0 -32719.1 31441.5 0.0 32719.1 83075.4

64542 0.0 0.0 -64542 0.0 0.0

0.0 464.0 -811.9 0.0 -464.0 -811.9

[k] 5, 8, 9, 0.0 -811.9 1905.0 0.0 811.9 936.8

12, 13, 16 = -64542 0.0 0.0 64542.3 0.0 0.0
0.0 -464.0 811.9 0.0 464.0 811.9
0.0 -811.9 936.8 0.0 811.9 1905.0

250998 0.0 0.0 -250998 0.0 0.0

0.0 27134.9 -40702.4 0.0 -27134.9 -40702.4
[k] 6, 7, 0.0 -40702.4 91173.3 0.0 40702.4 30933.8
10, 11, 14, 15
= -250998 0.0 0.0 250998.0 0.0 0.0
0.0 -27134.9 40702.4 0.0 27134.9 40702.4
0.0 -40702.4 30933.8 0.0 40702.4 91173.3 Columas
b1= 0 b2= 0.6
[K] =[ST] [K '] [S] 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0
0.0 609.2 1523.0 0.0 -609.2 1523.0 0.0 1.0 0.0 0.0 0.0 0.0
[k]' 17, 0.0 1523.0 5114.9 0.0 -1523.0 2500.3 0.0 0.0 1.0 0.0 0.0 0.0
[s] 17 =
20, 23, 26 = 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0
0.0 -609.2 -1523.0 0.0 609.2 -1523.0 0.0 0.0 0.0 0.0 1.0 -0.6
0.0 1523.0 2500.3 0.0 -1523.0 5114.9 0.0 0.0 0.0 0.0 0.0 1.0

0.0 0.0 0.0 0.0 0.0 0.0

0.0 609.2 1523.0 0.0 -609.2 1888.6
[k] 17, 20, 0.0 1523.0 5114.9 0.0 -1523.0 3414.2
23, 26 = 0.0 0.0 0.0 0.0 0.0 0.0
0.0 -609.2 -1523.0 0.0 609.2 -1888.6
0.0 1888.6 3414.2 0.0 -1888.6 7161.9
b1= 0.6 b2= 0.6
[K] =[ST] [K '] [S] 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0

[k]' 18,
[s] 18 =
=
21, 24, 27
 0.0 609.2 1523.0 0.0 -609.2 1523.0 0.0 1.0 0.6 0.0 0.0 0.0
[k]' 18, 0.0 1523.0 5114.9 0.0 -1523.0 2500.3 0.0 0.0 1.0 0.0 0.0 0.0
[s] 18 =
=
21, 24, 27 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0
0.0 -609.2 -1523.0 0.0 609.2 -1523.0 0.0 0.0 0.0 0.0 1.0 -0.6
0.0 1523.0 2500.3 0.0 -1523.0 5114.9 0.0 0.0 0.0 0.0 0.0 1.0

0.0 0.0 0.0 0.0 0.0 0.0

0.0 609.2 1888.6 0.0 -609.2 1888.6
[k] 18, 21, 0.0 1888.6 7161.9 0.0 -1888.6 4547.3
24, 27 = 0.0 0.0 0.0 0.0 0.0 0.0
0.0 -609.2 -1888.6 0.0 609.2 -1888.6
0.0 1888.6 4547.3 0.0 -1888.6 7161.9

b1= 0.6 b2= 0

[K] =[ST] [K '] [S] 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0
0.0 609.2 1523.0 0.0 -609.2 1523.0 0.0 1.0 0.6 0.0 0.0 0.0
[k]' 19, 0.0 1523.0 5114.9 0.0 -1523.0 2500.3 0.0 0.0 1.0 0.0 0.0 0.0
[s] 15 =
=
22, 25, 28 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0
0.0 -609.2 -1523.0 0.0 609.2 -1523.0 0.0 0.0 0.0 0.0 1.0 0.0
0.0 1523.0 2500.3 0.0 -1523.0 5114.9 0.0 0.0 0.0 0.0 0.0 1.0

0.0 0.0 0.0 0.0 0.0 0.0

0.0 609.2 1888.6 0.0 -609.2 1523.0
[k] 19, 22, 0.0 1888.6 7161.9 0.0 -1888.6 3414.2
25, 28 = 0.0 0.0 0.0 0.0 0.0 0.0
0.0 -609.2 -1888.6 0.0 609.2 -1523.0
0.0 1523.0 3414.2 0.0 -1523.0 5114.9 Vigas

6.- Determinar la Matriz deTransformacion de desplazamientos [R]i {𝑑}=[𝑅]{𝑑^∗ }

cos a sen a 0 0 0 0
sen a -cos a 0 0 0 0
0 0 1 0 0 0
[R]i=
0 0 0 cos a sen a 0
0 0 0 sen a -cos a 0
0 0 0 0 0 1

0 1 0 0 0 0
1 0 0 0 0 0
[R]1, 0 0 1 0 0 0
4= 0 0 0 0 1 0
0 0 0 1 0 0
0 0 0 0 0 1

0 1 0 0 0 0
1 0 0 0 0 0
[R]2, 0 0 1 0 0 0
3= 0 0 0 0 1 0
0 0 0 1 0 0
0 0 0 0 0 1
 0 1 0 0 0 0
1 0 0 0 0 0
[R] 5, 8, 9, 0 0 1 0 0 0
12, 13, 16= 0 0 0 0 1 0
0 0 0 1 0 0
0 0 0 0 0 1

0 1 0 0 0 0
1 0 0 0 0 0
[R] 6, 7, 0 0 1 0 0 0
10, 11, 14,
= 0 0 0 0 1 0
15
0 0 0 1 0 0
0 0 0 0 0 1 Columnas y Placas

1 0 0 0 0 0
0 1 0 0 0 0
[R] 17, 0 0 1 0 0 0
20, 23,
0 0 0 1 0 0
26 =
0 0 0 0 1 0
0 0 0 0 0 1

1 0 0 0 0 0
0 1 0 0 0 0
[R]18, 0 0 1 0 0 0
21, 24,
0 0 0 1 0 0
27 =
0 0 0 0 1 0
0 0 0 0 0 1

1 0 0 0 0 0
0 1 0 0 0 0
[R]19, 0 0 1 0 0 0
22, 25,
0 0 0 1 0 0
28 =
0 0 0 0 1 0
0 0 0 0 0 1

7.- Matriz de rigidez de la barra [k*]i, {q*}-{d*} [𝑘^∗ ]=[𝑅]^𝑇 [𝑘][𝑅]

464.0 0.0 -811.9 -464.0 0.0 -811.9

0.0 64542.3 0.0 0.0 -64542.3 0.0

[k*] 1, 4 -811.9 0.0 1905.0 811.9 0.0 936.8

= -464.0 0.0 811.9 464.0 0.0 811.9
0.0 -64542.3 0.0 0.0 64542.3 0.0
-811.9 0.0 936.8 811.9 0.0 1905.0

18696.6 0.0 -32719.1 -18696.6 0.0 -32719.1

0.0 215141.1 0.0 0.0 -215141.1 0.0

[k*] 2, 3 -32719.1 0.0 83075.4 32719.1 0.0 31441.5

= -18696.6 0.0 32719.1 18696.6 0.0 32719.1
0.0 ### 0.0 0.0 215141.1 0.0
-32719.1 0.0 31441.5 32719.1 0.0 83075.4

464.0 0.0 -811.9 -464.0 0.0 -811.9

0.0 64542.3 0.0 0.0 -64542.3 0.0
[k*] 5, 8, -811.9 0.0 1905.0 811.9 0.0 936.8
9, 12, 13, 16
= -464.0 0.0 811.9 464.0 0.0 811.9
0.0 -64542.3 0.0 0.0 64542.3 0.0
-811.9 0.0 936.8 811.9 0.0 1905.0
 27134.9 0.0 -40702.4 -27134.9 0.0 -40702.4
0.0 250998.0 0.0 0.0 ### 0.0
[k*] 6, 7, -40702.4 91173.3 40702.4 0.0 30933.8
0.0
10, 11, 14, 15
-27134.9 0.0 40702.4 27134.9 0.0 40702.4
=
0.0 ### 0.0 0.0 250998.0 0.0
-40702.4 0.0 30933.8 40702.4 0.0 91173.3

0.0 0.0 0.0 0.0 0.0 0.0

0.0 609.2 1523.0 0.0 -609.2 1888.6 E433:J438
[k*] 17, 0.0 1523.0 5114.9 0.0 -1523.0 3414.2 E440:J445
=
20, 23, 26 0.0 0.0 0.0 0.0 0.0 0.0 E447:J452
0.0 -609.2 -1523.0 0.0 609.2 -1888.6 E454:J459
0.0 1888.6 3414.2 0.0 -1888.6 7161.9 E461:J466
E468:J473
0.0 0.0 0.0 0.0 0.0 0.0 E475:J480
0.0 609.2 1888.6 0.0 -609.2 1888.6

[k*] 18, 0.0 1888.6 7161.9 0.0 -1888.6 4547.3

=
21, 24, 27 0.0 0.0 0.0 0.0 0.0 0.0
0.0 -609.2 -1888.6 0.0 609.2 -1888.6
0.0 1888.6 4547.3 0.0 -1888.6 7161.9

0.0 0.0 0.0 0.0 0.0 0.0

0.0 609.2 1888.6 0.0 -609.2 1523.0

[k*] 19, 0.0 1888.6 7161.9 0.0 -1888.6 3414.2

=
22, 25, 28 0.0 0.0 0.0 0.0 0.0 0.0
0.0 -609.2 -1888.6 0.0 609.2 -1523.0
0.0 1523.0 3414.2 0.0 -1523.0 5114.9

8.- Ensamblaje de la Matriz de Rigidez Total [𝐾]= 〖 [𝑨_𝒆^∗] 〗 ^𝑻 [𝒌_𝒆^∗ ][𝑨_𝒆^∗ ]

- Ensamblaje [K]
1 2 3 4 5 6 7 8 9 10 11 12 … 55 …
464 0 0 0 0 812 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 4
0 0 0 0.0 64542.3 0.0 0 0 0 0 0 0 0.0 0.0 5
812 0 0 0.0 0.0 1905.0 0 0 0 0 0 0 0.0 0.0 6
0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
[K]1=
0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 9
0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 0 0 0 12
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 …
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 55

1 2 3 4 5 6 7 8 9 10 11 12 … 55
18697 0 0 0 0 0 0 32719 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 4
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 5
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 6
0 0 0 0 0 0 215141 0 0 0 0 0 0 0 7
[K]2=
32719 0 0 0 0 0 0 83075 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 9
0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 0 0 0 12
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 …
 0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 55

1 2 3 4 5 6 7 8 9 10 11 12 … 55
18697 0 0 0 0 0 0 0 0 32719 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 4
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 5
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 6
0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
[K]3=
0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 215141 0 0 0 0 0 9
32719 0 0 0 0 0 0 0 0 83075 0 0 0 0 10
0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 0 0 0 12
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 …
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 55

1 2 3 4 5 6 7 8 9 10 11 12 … 55
18697 0 0 0 0 0 0 0 0 0 0 32719 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 4
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 5
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 6
0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
[K]4=
0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 9
0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
0 0 0 0 0 0 0 0 0 0 215141 0 0 0 11
32719 0 0 0 0 0 0 0 0 0 0 83075 0 0 12
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 …
0 0 0 0.0 0.0 0.0 0 0 0 0 0 0 0.0 0.0 1455

Generacion de las formulas excel para obtener el aporte de cada barra y hallar la suma directa por cuestiones de dimensiones grandes de las
matrices. Esto con el fin de hallar directamente la sumatoria de aportes sin la necesidad de hallar cada uno
Fila Fila
Matriz K * del
[K]elem Formula de multiplicacion de matrices inicial final de
elemento
de [A] [A]
[K]1 MMULT(TRANSPOSE(B131:AK136);MMULT(E433:J438;B131:AK136)) 131 136 E433:J438
[K]2 MMULT(TRANSPOSE(B137:AK142);MMULT(E440:J445;B137:AK142)) 137 142 E440:J445
[K]3 MMULT(TRANSPOSE(B143:AK148);MMULT(E440:J445;B143:AK148)) 143 148 E440:J445
[K]4 MMULT(TRANSPOSE(B149:AK154);MMULT(E433:J438;B149:AK154)) 149 154 E433:J438[k*] 5, 8,
9, 12, 13, 16
[K]5 MMULT(TRANSPOSE(B155:AK160);MMULT(E447:J452;B155:AK160)) 155 160 E447:J452 =
[K]6 MMULT(TRANSPOSE(B161:AK166);MMULT(E454:J459;B161:AK166)) 161 166 E454:J459
[K]7 MMULT(TRANSPOSE(B167:AK172);MMULT(E454:J459;B167:AK172)) 167 172 E454:J459
[K]8 MMULT(TRANSPOSE(B173:AK178);MMULT(E447:J452;B173:AK178)) 173 178 E447:J452
[K]9 MMULT(TRANSPOSE(B179:AK184);MMULT(E447:J452;B179:AK184)) 179 184 E447:J452
[K]10 MMULT(TRANSPOSE(B185:AK190);MMULT(E454:J459;B185:AK190)) 185 190 E454:J459
[K]11 MMULT(TRANSPOSE(B191:AK196);MMULT(E454:J459;B191:AK196)) 191 196 E454:J459[k*] 6, 7,
10, 11, 14, 15
[K]12 MMULT(TRANSPOSE(B197:AK202);MMULT(E447:J452;B197:AK202)) 197 202 E447:J452 =
[K]13 MMULT(TRANSPOSE(B203:AK208);MMULT(E447:J452;B203:AK208)) 203 208 E447:J452
[K]14 MMULT(TRANSPOSE(B209:AK214);MMULT(E454:J459;B209:AK214)) 209 214 E454:J459
[K]15 MMULT(TRANSPOSE(B215:AK220);MMULT(E454:J459;B215:AK220)) 215 220 E454:J459
[K]16 MMULT(TRANSPOSE(B221:AK226);MMULT(E447:J452;B221:AK226)) 221 226 E447:J452
[K]17 MMULT(TRANSPOSE(B227:AK232);MMULT(E461:J466;B227:AK232)) 227 232 E461:J466
[K]18 MMULT(TRANSPOSE(B233:AK238);MMULT(E468:J473;B233:AK238)) 233 238 E468:J473[k*] 17,
[K]19 MMULT(TRANSPOSE(B239:AK244);MMULT(E475:J480;B239:AK244)) 239 244 E475:J48020, 23, 26 =
[K]20 MMULT(TRANSPOSE(B245:AK250);MMULT(E461:J466;B245:AK250)) 245 250 E461:J466
 [k*] 17,
=
20, 23, 26

[K]21 MMULT(TRANSPOSE(B251:AK256);MMULT(E468:J473;B251:AK256)) 251 256 E468:J473

[K]22 MMULT(TRANSPOSE(B257:AK262);MMULT(E475:J480;B257:AK262)) 257 262 E475:J480
[K]23 MMULT(TRANSPOSE(B263:AK268);MMULT(E461:J466;B263:AK268)) 263 268 E461:J466
[K]24 MMULT(TRANSPOSE(B269:AK274);MMULT(E468:J473;B269:AK274)) 269 274 E468:J473
[K]25 MMULT(TRANSPOSE(B275:AK280);MMULT(E475:J480;B275:AK280)) 275 280 E475:J480[k*] 18,
[K]26 MMULT(TRANSPOSE(B281:AK286);MMULT(E461:J466;B281:AK286)) 281 286 E461:J46621, 24, 27 =
[K]27 MMULT(TRANSPOSE(B287:AK292);MMULT(E468:J473;B287:AK292)) 287 292 E468:J473
[K]28 MMULT(TRANSPOSE(B293:AK298);MMULT(E475:J480;B293:AK298)) 293 298 E475:J480

[𝐾]=∑_(𝑒=1)^𝑚▒ 〖〖 [𝐴_𝑒^∗] 〗 ^𝑇 [𝑘_𝑒^∗ ][𝐴_𝑒^∗ ] 〗

NOTA: LA MATRIZ COMPLETA SE PUEDE VER EN EL ARCHIVO EXCEL ADJUNTO

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
93518.9614 -55198 0 0 0 0 0 -7983 0 -7983 0 0 0 -812 0 ###

-55198 110396 -55198 0 0 812 0 40702 0 40702 0 812 0 0 0 0

0 -55198 83261 -28063 0 0 0 0 0 0 0 0 0 812 0 ###

0 0 -28063 28063 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 129694 1523 -609 1889 0 0 0 0 -64542 0 0 0

0 812 0 0 1523 8924.8 -1523.0 3414.2 0.0 0.0 0.0 0.0 0.0 936.8 0.0 0.0

0 0 0 0 -609 -1523.0 467357.6 0.0 -609.2 1888.6 0.0 0.0 0.0 0.0 -250998.0 0.0
[K]T=
-7983 40702 0 0 1889 3414.2 0.0 188572.5 -1888.6 4547.3 0.0 0.0 0.0 0.0 0.0 ###

0 0 0 0 0 0.0 -609.2 -1888.6 467357.6 0.0 -609.2 1523.0 0.0 0.0 0.0 0.0

-7983 40702 0 0 0 0.0 1888.6 4547.3 0.0 188572.5 -1888.6 3414.2 0.0 0.0 0.0 0.0

0 0 0 0 0 0.0 0.0 0.0 -609.2 -1888.6 129693.9 -1523.0 0.0 0.0 0.0 0.0

0 812 0 0 0 0.0 0.0 0.0 1523.0 3414.2 -1523.0 8924.8 0.0 0.0 0.0 0.0

0 0 0 0 -64542 0.0 0.0 0.0 0.0 0.0 0.0 0.0 129693.9 1523.0 -609.2 ###

-812 0 812 0 0 936.8 0.0 0.0 0.0 0.0 0.0 0.0 1523.0 8924.8 -1523.0 ###

0 0 0 0 0 0.0 -250998.0 0.0 0.0 0.0 0.0 0.0 -609.2 -1523.0 503214.5 0.0

-40702 0 40702 0 0 0.0 0.0 30933.8 0.0 0.0 0.0 0.0 1888.6 3414.2 0.0 ###

0 0 0 0 0 0.0 0.0 0.0 -250998.0 0.0 0.0 0.0 0.0 0.0 -609.2 ###

-40702 0 40702 0 0 0.0 0.0 0.0 0.0 30933.8 0.0 0.0 0.0 0.0 1888.6 ###

0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 -64542.3 0.0 0.0 0.0 0.0 0.0

-812 0 812 0 0 0.0 0.0 0.0 0.0 0.0 0.0 936.8 0.0 0.0 0.0 0.0

0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -64542.3 0.0 0.0 0.0

0 -812 0 812 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 936.8 0.0 0.0

0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -250998.0 0.0

0 -40702 0 40702 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 ###

0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0 -40702 40702 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0 -812 0 812 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0 0 -812 812 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0 0 -40702 40702 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0 0 -812 812 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

* Estructura del K ordenado

Kuu Kur
 Kuu Kur
[K]T=

Kru Krr

- GDLE 1-5
1 2 3 4 5
76595.06 -51827.71 15049.59 -949.01 377.45 1
[K]L7=
-51827.71 76004.88 -44193.83 6220.24 -82.05 2
15049.59 -44193.83 44105.24 -12971.55 227.68 3
-949.01 6220.24 -12971.55 7572.32 -852.84 4
377.45 -82.05 227.68 -852.84 65941.56 5
 𝑃4

𝑃3

𝑃7 𝑃6 𝑃5

𝑃2

[KE]= [G]T[KL][G]
𝑃1
[KE]= S[G]T[KL][G]

[DL]= [G][DE]
1 4 5 2 6 7 3 8 9 10 11 12 13 14 15
cos a sen a r 0 0 0 0 0 0 0 0 0 0 0 0 1
[Gi] =
0 0 0 cos a sen a r 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 cos a sen a r 0 0 0 0 0 0 3
0 0 0 0 0 0 0 0 0 cos a sen a r 0 0 0 4
0 0 0 0 0 0 0 0 0 0 0 0 cos a sen a r 5

Ensamblar la matriz de Rigidez del Edificio [KE]= [G]T[KL][G]

Portico 1
1 4 5 2 6 7 3 8 9 10 11 12 13 14 15
1 0 4.85571 0 0 0 0 0 0 0 0 0 0 0 0 1
[GC] =
0 0 0 1 0 4.85571 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 1 0 4.85571 0 0 0 0 0 0 3
0 0 0 0 0 0 0 0 0 1 0 4.85571 0 0 0 4
0 0 0 0 0 0 0 0 0 0 0 0 1 0 4.85571 5

1 4 5 2 6 7 3 8 9 10 11 12 13 14 15
39426.1515908904 0 191441.958541 -26972.13493 0 -130968.8653 8363.53014 0 40610.8769334 -1146.10698 0 -5565.163133 209.29049207 0 1016.25394 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
191441.958541403 0 929586.632509 -130968.8653 0 -635946.829 40610.8769 0 197194.641234 -5565.16313 0 -27022.81828 1016.2539352 0 4934.6344 5
-26972.134933826 0 -130968.86532 39474.36327 0 191676.0605 -27168.8317 0 -131923.96795 8455.37946 0 41056.870583 -894.7585106 0 -4344.68785 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6
[KE]1C =
-130968.865319529 0 -635946.82902 191676.0605 0 930723.3637 -131923.968 0 -640584.5304 41056.8706 0 199360.25706 -4344.687848 0 -21096.5442 7
8363.53013944684 0 40610.8769334 -27168.83174 0 -131923.9679 39615.9982 0 192363.798451 -25763.831 0 -125101.6921 6083.3844607 0 29539.1508 3
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
40610.8769334134 0 197194.641234 -131923.9679 0 -640584.5304 192363.798 0 934062.819777 -125101.692 0 -607457.5371 29539.15076 0 143433.55 9
-1146.10698193278 0 -5565.1631332 8455.379457 0 41056.87058 -25763.831 0 -125101.69206 30242.7484 0 146850.01574 -11939.31765 0 -57973.8641 10
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
-5565.16313324084 0 -27022.818278 41056.87058 0 199360.2571 -125101.692 0 -607457.53714 146850.016 0 713061.08991 -57973.86412 0 -281504.272 12
209.29049206581 0 1016.25393523 -894.7585106 0 -4344.687848 6083.38446 0 29539.1507598 -11939.3177 0 -57973.86412 6565.8339438 0 31881.7855 13
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 14
1016.25393522888 0 4934.63439583 -4344.687848 0 -21096.54423 29539.1508 0 143433.549736 -57973.8641 0 -281504.2717 31881.785539 0 154808.705 15

Portico 2
1 4 5 2 6 7 3 8 9 10 11 12 13 14 15
1 0 0.8571 0 0 0 0 0 0 0 0 0 0 0 0 1
[GC] 2=
0 0 0 1 0 0.8571 1 0 8.8571 0 0 0 0 0 0 2
0 0 0 0 0 0 1 0 0.8571 0 0 0 0 0 0 3
0 0 0 0 0 0 0 0 0 1 0 0.8571 1 0 8.8571 4
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0.8571 5

1 4 5 2 6 7 3 8 9 10 11 12 13 14 15
92253.9192322301 0 79070.8341739 -54184.63029 0 -46441.64663 -40160.6829 0 -467898.76367 -3246.12478 0 -2782.253546 -3150.049221 0 -28668.9054 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
79070.8341739444 0 67771.6119705 -46441.64663 0 -39805.13532 -34421.7213 0 -401036.03034 -2782.25355 0 -2384.669514 -2699.907187 0 -24572.1188 5
[KE]2C =
-54184.6302943547 0 -46441.646625 74354.08991 0 63728.89046 16417.3914 0 608904.065421 20330.4303 0 17425.211785 18604.919785 0 178589.719 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6
-46441.6466252914 0 -39805.135323 63728.89046 0 54622.03201 14071.3462 0 521891.674472 17425.2118 0 14935.149021 15946.276748 0 153069.248 7
-40160.6829052525 0 -34421.721318 16417.39139 0 14071.34616 42591.6431 0 167844.428404 -25452.8928 0 -21815.67445 -18678.81538 0 -219632.755 3
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
-467898.763672929 0 -401036.03034 608904.0654 0 521891.6745 167844.428 0 5015091.98295 140827.768 0 120703.47971 132829.74562 0 1240470.52 9
-3246.12477611371 0 -2782.2535456 20330.43027 0 17425.21179 -25452.8928 0 140827.76772 42025.1116 0 36019.723195 28014.566822 0 360212.178 10
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
-2782.25354560706 0 -2384.6695139 17425.21179 0 14935.14902 -21815.6744 0 120703.479713 36019.7232 0 30872.50475 24011.285223 0 308737.858 12
-3150.04922096955 0 -2699.9071873 18604.91978 0 15946.27675 -18678.8154 0 132829.745617 28014.5668 0 24011.285223 21159.704999 0 242252.518 13
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 14
-28668.9053962027 0 -24572.118815 178589.7189 0 153069.2481 -219632.755 0 1240470.51673 360212.178 0 308737.85812 242252.51773 0 3089332.06 15

Portico 3
1 4 5 2 6 7 3 8 9 10 11 12 13 14 15
1 0 -3.1329 0 0 0 0 0 0 0 0 0 0 0 0 1
[GC] 3=
0 0 0 1 0 -3.1329 1 0 4.85571 0 0 0 0 0 0 2
0 0 0 0 0 0 1 0 -3.1329 0 0 0 0 0 0 3
0 0 0 0 0 0 0 0 0 1 0 -3.1329 1 0 4.85571 4
0 0 0 0 0 0 0 0 0 0 0 0 1 0 -3.1329 5

1 4 5 2 6 7 3 8 9 10 11 12 13 14 15
92253.9192322301 0 -289022.30356 -54184.63029 0 169755.0282 -40160.6829 0 -307040.47594 -3246.12478 0 10169.784311 -3150.049221 0 -16063.2356 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
-289022.303562654 0 905477.974831 169755.0282 0 -531825.528 125819.403 0 961927.107078 10169.7843 0 -31860.91727 9868.7892044 0 50324.5109 5
[KE]3C =
-54184.6302943547 0 169755.028249 74354.08991 0 -232943.9283 16417.3914 0 542551.780684 20330.4303 0 -63693.205 18604.919785 0 104124.525 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6
169755.028249184 0 -531825.528 -232943.9283 0 729790.0329 -51434.0455 0 -1699760.4737 -63693.205 0 199544.44193 -58287.35319 0 -326211.726 7
-40160.6829052525 0 125819.403474 16417.39139 0 -51434.04549 42591.6431 0 -2283.2215076 -25452.8928 0 79741.367964 -18678.81538 0 -144814.374 3
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
-307040.475941919 0 961927.107078 542551.7807 0 -1699760.474 -2283.22151 0 4341387.68535 242153.247 0 -758641.9061 207146.30894 0 1285499.18 9
-3246.12477611371 0 10169.7843111 20330.43027 0 -63693.205 -25452.8928 0 242153.246533 42025.1116 0 -131660.4723 28014.566822 0 247955.391 10
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
10169.7843110867 0 -31860.917268 -63693.205 0 199544.4419 79741.368 0 -758641.90606 -131660.472 0 412479.09362 -87766.8364 0 -776819.444 12
-3150.04922096955 0 9868.78920438 18604.91978 0 -58287.35319 -18678.8154 0 207146.308943 28014.5668 0 -87766.8364 21159.704999 0 157506.209 13
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 14
-16063.2356433343 0 50324.510947 104124.5254 0 -326211.7255 -144814.374 0 1285499.1755 247955.391 0 -776819.4438 157506.20887 0 1487367.71 15
Portico 4
1 4 5 2 6 7 3 8 9 10 11 12 13 14 15
1 0 -7.1429 0 0 0 0 0 0 0 0 0 0 0 0 1
[GC] 4=
0 0 0 1 0 -7.1429 1 0 0.8571 1 0 8.8571 0 0 0 2
0 0 0 0 0 0 1 0 -7.1429 0 0 0 0 0 0 3
0 0 0 0 0 0 0 0 0 1 0 -7.1429 1 0 0.8571 4
0 0 0 0 0 0 0 0 0 0 0 0 1 0 -7.1429 5

1 4 5 2 6 7 3 8 9 10 11 12 13 14 15
39608.1948051093 0 -282917.37467 -27047.5571 0 193197.9956 -18884.3086 0 -81491.728561 -28107.0576 0 -231995.0121 -833.1199364 0 -2525.11131 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
-282917.374673415 0 2020850.51555 193197.9956 0 -1379993.963 134888.728 0 582087.26794 200765.901 0 1657117.172 5950.8923939 0 18036.6176 5
[KE]4C =
-27047.5570976406 0 193197.995593 39898.17928 0 -284988.7048 12669.241 0 228690.312719 48179.0594 0 294232.66493 7451.6865251 0 13020.3895 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6
193197.995592737 0 -1379993.9627 -284988.7048 0 2035645.819 -90495.1215 0 -1633512.0347 -344138.204 0 -2101674.502 -53226.65168 0 -93003.3399 7
-18884.3086449266 0 134888.72822 12669.241 0 -90495.12153 25529.0286 0 -80997.37033 -4971.44339 0 238218.37894 -12490.47646 0 -51907.2508 3
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
-81491.7285612789 0 582087.26794 228690.3127 0 -1633512.035 -80997.3703 0 2408078.61828 420942.998 0 652291.26056 148831.71652 0 474931.417 9
-28107.0575606208 0 200765.90145 48179.05942 0 -344138.2036 -4971.44339 0 420942.998353 87264.6952 0 147541.95924 26018.936437 0 126834.425 10
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
-231995.012112492 0 1657117.17202 294232.6649 0 -2101674.502 238218.379 0 652291.260563 147541.959 0 3653845.1783 -66623.67667 0 -697639.385 12
-833.119936431903 0 5950.89239394 7451.686525 0 -53226.65168 -12490.4765 0 148831.716521 26018.9364 0 -66623.67667 13212.172397 0 54164.7731 13
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 14
-2525.11130990175 0 18036.6175755 13020.38946 0 -93003.3399 -51907.2508 0 474931.417135 126834.425 0 -697639.3854 54164.773078 0 523618.729 15

Portico 5
1 4 5 2 6 7 3 8 9 10 11 12 13 14 15
0 1 4.6429 0 0 0 0 0 0 0 0 0 0 0 0 1
[GC]5 =
0 0 0 0 1 4.6429 1 0 -3.1329 1 0 4.85571 0 0 0 2
0 0 0 0 0 0 0 1 4.6429 0 0 0 0 0 0 3
0 0 0 0 0 0 0 0 0 0 1 4.6429 1 0 -3.1329 4
0 0 0 0 0 0 0 0 0 0 0 0 0 1 4.6429 5

1 4 5 2 6 7 3 8 9 10 11 12 13 14 15
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 67249.842831847 312234.295284 0 -45483.50322 -211175.3571 -45483.5032 13720.6308 206198.783958 -45483.5032 -2055.90602 -230400.0675 -2055.906018 287.69569116 7776.69029 4
0 312234.29528399 1449672.60957 0 -211175.3571 -980466.0655 -211175.357 63703.5167 957360.334041 -211175.357 -9545.36605 -1069724.473 -9545.36605 1335.7423245 36106.3953 5
[KE]5C =
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 -45483.50321993 -211175.3571 0 67980.96262 315628.8114 67980.9626 -46048.4823 -426776.05622 67980.9626 13544.1077 392979.77769 13544.107709 -1557.346314 -49662.9382 6
0 -211175.3570998 -980466.06548 0 315628.8114 1465433.008 315628.811 -213798.498 -1981478.5514 315628.811 62883.9377 1824565.8098 62883.937682 -7230.603199 -230580.056 7
0 -45483.50321993 -211175.3571 0 67980.96262 315628.8114 67980.9626 -46048.4823 -426776.05622 67980.9626 13544.1077 392979.77769 13544.107709 -1557.346314 -49662.9382 3
0 13720.630795566 63703.5167207 0 -46048.48229 -213798.4984 -46048.4823 67966.0876 459825.038082 -46048.4823 -44479.6163 -430112.4863 -44479.61627 10596.711363 188549.661 8
0 206198.78395845 957360.334041 0 -426776.0562 -1981478.551 -426776.056 459825.038 3471968.37585 -426776.056 -248946.745 -3228135.608 -248946.7454 54078.481452 1031006.24 9
0 -45483.50321993 -211175.3571 0 67980.96262 315628.8114 67980.9626 -46048.4823 -426776.05622 67980.9626 13544.1077 392979.77769 13544.107709 -1557.346314 -49662.9382 10
0 -2055.906017775 -9545.3660499 0 13544.10771 62883.93768 13544.1077 -44479.6163 -248946.7454 13544.1077 57449.4599 332498.35671 57449.459921 -24717.39144 -294743.79 11
0 -230400.06747 -1069724.4733 0 392979.7777 1824565.81 392979.778 -430112.486 -3228135.6082 392979.778 332498.357 3451952.4567 332498.35671 -122322.3988 -1609614.77 12
0 -2055.906017775 -9545.3660499 0 13544.10771 62883.93768 13544.1077 -44479.6163 -248946.7454 13544.1077 57449.4599 332498.35671 57449.459921 -24717.39144 -294743.79 13
0 287.69569115687 1335.74232447 0 -1557.346314 -7230.603199 -1557.34631 10596.7114 54078.4814521 -1557.34631 -24717.3914 -122322.3988 -24717.39144 15403.726417 148955.077 14
0 7776.6902875583 36106.3953361 0 -49662.93824 -230580.056 -49662.9382 188549.661 1031006.24021 -49662.9382 -294743.79 -1609614.767 -294743.7897 148955.07703 1614986.35 15

Portico 6
1 4 5 2 6 7 3 8 9 10 11 12 13 14 15
0 1 -0.3645 0 0 0 0 0 0 0 0 0 0 0 0 1
[GC]6 =
0 0 0 0 1 -0.3645 1 0 -7.1429 1 0 0.8571 1 0 8.8571 2
0 0 0 0 0 0 0 1 -0.3645 0 0 0 0 0 0 3
0 0 0 0 0 0 0 0 0 0 1 -0.3645 1 0 -7.1429 4
0 0 0 0 0 0 0 0 0 0 0 0 0 1 -0.3645 5

1 4 5 2 6 7 3 8 9 10 11 12 13 14 15
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 6160.6895422147 -2245.5713381 0 -4029.219282 1468.650428 -4029.21928 675.796796 28533.9824775 -4029.21928 -91.5332549 -3420.079975 -4120.752537 18.894756029 -35040.2724 4
0 -2245.571338137 818.510752751 0 1468.650428 -535.3230811 1468.65043 -246.327932 -10400.636613 1468.65043 33.3638714 1246.619151 1502.0142997 -6.887138573 12772.1793 5
[KE]6C =
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 -4029.219282025 1468.6504283 0 7009.143924 -2554.83296 7009.14392 -4116.93519 -48564.991259 7009.14392 678.237907 5760.3195404 7687.3818308 -68.31229042 57261.0029 6
0 1468.650428298 -535.32308111 0 -2554.83296 931.2366141 -2554.83296 1500.62288 17701.9393138 -2554.83296 -247.217717 -2099.636472 -2802.050677 24.899829858 -20871.6356 7
0 -4029.219282025 1468.6504283 0 7009.143924 -2554.83296 7009.14392 -4116.93519 -48564.991259 7009.14392 678.237907 5760.3195404 7687.3818308 -68.31229042 57261.0029 3
0 675.79679591294 -246.32793211 0 -4116.935192 1500.622877 -4116.93519 7016.64573 26849.2890114 -4116.93519 -4083.35793 -2040.241189 -8200.293117 578.63298287 -7508.00108 8
0 28533.982477464 -10400.636613 0 -48564.99126 17701.93931 -48564.9913 26849.289 337108.310217 -48564.9913 -3356.20158 -40401.71853 -51921.19284 277.03613697 -406272.951 9
0 -4029.219282025 1468.6504283 0 7009.143924 -2554.83296 7009.14392 -4116.93519 -48564.991259 7009.14392 678.237907 5760.3195404 7687.3818308 -68.31229042 57261.0029 10
0 -91.53325488898 33.363871407 0 678.2379067 -247.217717 678.237907 -4083.35793 -3356.2015796 678.237907 6763.75055 -1884.069366 7441.9884575 -3276.870084 -41111.1537 11
0 -3420.079975216 1246.61915097 0 5760.31954 -2099.636472 5760.31954 -2040.24119 -40401.718532 5760.31954 -1884.06937 5623.913162 3876.2501744 1135.8686814 64063.4211 12
0 -4120.752536914 1502.01429971 0 7687.381831 -2802.050677 7687.38183 -8200.29312 -51921.192838 7687.38183 7441.98846 3876.2501744 15129.370288 -3345.182374 16149.8492 13
0 18.894756028941 -6.8871385725 0 -68.31229042 24.89982986 -68.3122904 578.632983 277.036136973 -68.3122904 -3276.87008 1135.8686814 -3345.182374 2745.9999496 21800.3896 14
0 -35040.27235505 12772.1792734 0 57261.00294 -20871.63557 57261.0029 -7508.00108 -406272.95149 57261.0029 -41111.1537 64063.421142 16149.849236 21800.389552 792873.047 15

Portico 7
1 4 5 2 6 7 3 8 9 10 11 12 13 14 15
0 1 -5.3571 0 0 0 0 0 0 0 0 0 0 0 0 1
[GC] 7=
0 0 0 0 1 -5.3571 0 1 4.6429 1 0 -3.1329 1 0 4.85571 2
0 0 0 0 0 0 0 1 -5.3571 0 0 0 0 0 0 3
0 0 0 0 0 0 0 0 0 0 1 -5.3571 0 1 4.6429 4
0 0 0 0 0 0 0 0 0 0 0 0 0 1 -5.3571 5

1 4 5 2 6 7 3 8 9 10 11 12 13 14 15
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 76595.057845896 -410327.38439 0 -51827.71214 277646.2367 0 -36778.1227 -321253.0405 -51827.7121 -949.006211 167454.96054 -51827.71214 -571.554293 -258088.529 4
0 -410327.3843862 2198164.8309 0 277646.2367 -1487378.655 0 197024.081 1720984.66329 277646.237 5083.92117 -897072.9691 277646.23672 3061.8735031 1382606.06 5
[KE]7C =
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 -51827.71214191 277646.236715 0 76004.88294 -407165.7584 0 31811.0522 589633.84192 76004.8829 6220.24136 -271438.1528 76004.882942 6138.1962769 398377.152 6
0 277646.2367154 -1487378.6547 0 -407165.7584 2181227.684 0 -170414.988 -3158727.4545 -407165.758 -33322.455 1454121.3281 -407165.7584 -32882.93128 -2134146.24 7
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
0 -36778.12266236 197024.080915 0 31811.05216 -170414.9875 0 31722.4598 148170.13225 31811.0522 -6751.30515 -63493.42849 31811.052155 -6605.669826 122339.426 8
0 -321253.0405045 1720984.66329 0 589633.8419 -3158727.455 0 148170.132 5102576.20372 589633.842 98369.8304 -2374240.882 589633.84192 96769.196594 3328386.98 9
0 -51827.71214191 277646.236715 0 76004.88294 -407165.7584 0 31811.0522 589633.84192 76004.8829 6220.24136 -271438.1528 76004.882942 6138.1962769 398377.152 10
0 -949.0062113047 5083.92117458 0 6220.24136 -33322.45499 0 -6751.30515 98369.8303997 6220.24136 7572.32296 -60053.08548 6220.2413596 6719.4868083 69929.955 11
0 167454.96054396 -897072.96913 0 -271438.1528 1454121.328 0 -63493.4285 -2374240.8818 -271438.153 -60053.0855 1172098.973 -271438.1528 -55227.3179 -1622697.54 12
0 -51827.71214191 277646.236715 0 76004.88294 -407165.7584 0 31811.0522 589633.84192 76004.8829 6220.24136 -271438.1528 76004.882942 6138.1962769 398377.152 13
0 -571.5542930075 3061.87350307 0 6138.196277 -32882.93128 0 -6605.66983 96769.1965943 6138.19628 6719.48681 -55227.3179 6138.1962769 71808.209258 -287683.589 14
0 -258088.5287345 1382606.05728 0 398377.1525 -2134146.244 0 122339.426 3328386.98347 398377.152 69929.955 -1622697.543 398377.15247 -287683.5887 4174853.23 15

FINALMENTE SUMAMOS
y se obtiene la matriz de Rigidez del Edificio [KE]

1 4 5 2 6 7 3 8 9 10 11 12 13 14 15
263542.18486046 0 -301426.88552 -162388.9526 0 185542.5119 -90842.1443 0 -815820.09124 -35745.4141 0 -230172.6445 -6923.927886 0 -46240.9984 1
0 150005.59021996 -100338.66044 0 -101340.4346 67939.53004 -49512.7225 -22381.6951 -86520.274069 -101340.435 -3096.44548 -66365.1869 -58004.3707 -264.9638458 -285352.111 4
-301426.885520722 -100338.6604404 7572342.68609 185542.5119 67939.53004 -5055951.498 57190.5806 260481.27 4008117.34662 270527.799 -4428.081 -369702.0563 283738.91331 4390.728689 1480208.28 5
-162388.952620176 0 185542.511897 228080.7224 0 -262527.6821 18335.192 0 1248222.19088 97295.2994 0 289021.54231 43766.767584 0 291389.946 2
0 -101340.4346439 67939.5300439 0 150994.9895 -94091.78002 74990.1065 -18354.3653 114292.794439 150994.989 20442.587 127301.94448 97236.372482 4512.537673 405975.217 6
[KE] = 185542.511897101 67939.530043892 -5055951.4983 -262527.6821 -94091.78002 7398373.177 53292.1896 -382712.863 -8574469.431 -443441.106 29314.265 1588752.8472 -446996.2874 -40088.63464 -2672840.3 7
-90842.1443159848 -49512.72250195 57190.5806375 18335.19205 74990.10655 53292.18959 225318.419 -50165.4175 -198413.41246 -6650.95356 14222.3456 569782.47763 -22533.23322 -1625.658604 -379217.164 3
0 -22381.69507088 260481.269703 0 -18354.36533 -382712.8631 -50165.4175 106705.193 634844.459343 -18354.3653 -55314.2793 -495646.156 -20868.85723 4569.6745197 303381.086 8
-815820.091242714 -86520.2740686 4008117.34662 1248222.191 114292.7944 -8574469.431 -198413.412 634844.459 21610273.9961 793115.115 -153933.117 -6235882.911 807112.82552 151124.71418 7097454.93 9
-35745.414094781 -101340.4346439 270527.799126 97295.29942 150994.9895 -443441.1062 -6650.95356 -18354.3653 793115.114988 352552.656 20442.587 326053.17036 167345.12491 4512.537673 1083003.35 10
 0 -3096.445483968 -4428.0810039 0 20442.58698 29314.26498 14222.3456 -55314.2793 -153933.11658 20442.587 71785.5334 270561.20187 71111.689739 -21274.77472 -265924.988 11
-230172.644480253 -66365.18690123 -369702.05628 289021.5423 127301.9445 1588752.847 569782.478 -495646.156 -6235882.9114 326053.17 270561.202 9439933.2094 -123416.6378 -176413.848 -4615474.13 12
-6923.9278863052 -58004.37069659 283738.913311 43766.76758 97236.37248 -446996.2874 -22533.2332 -20868.8572 807112.825518 167345.125 71111.6897 -123416.6378 210681.12949 -21924.37754 605588.497 13
0 -264.9638458217 4390.72868897 0 4512.537673 -40088.63464 -1625.6586 4569.67452 151124.714183 4512.53767 -21274.7747 -176413.848 -21924.37754 89957.935625 -116928.122 14
-46240.9984142099 -285352.110802 1480208.276 291389.9459 405975.2172 -2672840.297 -379217.164 303381.086 7097454.93129 1083003.35 -265924.988 -4615474.132 605588.49723 -116928.1221 11837839.8 15
 15.8667115599784 Tn
15.8667115599784 Tn
22.41 Tn.m
23.877090211618 Tn
23.877090211618 Tn
1.59 Tn.m
18.1003748378394 Tn
18.1003748378394 Tn
[QE] =
1.46 Tn.m
12.4006823357113 Tn
12.4006823357113 Tn
1.19 Tn.m
6.85503557688387 Tn
6.85503557688387 Tn
0.68 Tn.m

Los desplazamientos del centro de masa

[QE]= [KE][DE]

0.00067596434120894 m
0.0011152065379476 m
-7.373022534451E-06 rad
0.0010676633421572 m
0.00039761776641186 m
3.0757816243184E-05 rad
[DE] =
0.00089282842108509 m
0.00249672104925633 m
-9.8368089980275E-05 rad
0.00041369575034514 m
0.0028884306867099 m
-7.2656384793769E-05 rad
-0.0007149901930306 m
0.00055421674651607 m
6.1882927539424E-05 rad

6.Calcular los desplazamientos laterales y fuerza cortante en la base

Portico 1
[DL]= [G][DE]
Los desplazamientos de cada pótico
0.00064016308195818 m
[DL]C =
0.00121701437806739 m
0.000415182 m
0.000060897 m
-0.000414505 m
5 0.640163082 mm Desplazamiento relativo de entrepiso
D = (D5-D4)/h -1.92E-04 OK
Desplazamiento relativo de entrepiso
4 1.22E+00 mm D = (D4-D3)/h 0.00026727763 OK

3 4.15E-01 mm Desplazamiento relativo de entrepiso

D = (D3-D2)/h 0.0001180947 OK

2 6.09E-02 mm Desplazamiento relativo de entrepiso

D = (D2-D1)/h 0.00015846735 OK

1 -4.15E-01 mm Desplazamiento relativo de entrepiso

D = (D1-0.00)/h -1.18E-04 OK

Deriva inelastica
4.80E-04 OK
9.13E-04 OK
3.11E-04 OK
[QL]= [KL][DL] 4.57E-05 OK
-3.11E-04 OK
1 2 3 4 5
39426.1515908904 -26972.13493383 8363.53013945 -1146.106982 209.2904921 1
[KLC] =
-26972.134933826 39474.363272132 -27168.831736 8455.379457 -894.7585106 2
8363.53013944684 -27168.8317357 39615.9981653 -25763.83105 6083.384461 3
-1146.10698193278 8455.3794568788 -25763.831048 30242.74838 -11939.31765 4
209.29049206581 -894.7585106383 6083.38446073 -11939.31765 6565.833944 5

-4.27047313123314
[QL]C =
20.3800985676654
-15.3535478153474
5.65056473227988 5 -4.27 Tn
-1.87788747284862

4 20.38 Tn

3 -15.35 Tn

2 5.650564732 Tn

1 -1.877887473 Tn

V = Q1+Q2+Q3+Q4+Q5 Fuerza de Cortante en Portico

V= 4.53 Tn
Portico 2
[DL]= [G][DE]
0.00066964492359466 m
[DL]C =
0.00111559827778003 m
0.000808517131163 m
0.000184535 m
-0.0006619503358365 m
5 0.669644924 mm Desplazamiento relativo de entrepiso
D = (D5-D4)/h -1.49E-04 OK
Desplazamiento relativo de entrepiso
4 1.12E+00 mm D = (D4-D3)/h 0.00010236038 OK

3 8.09E-01 mm Desplazamiento relativo de entrepiso

D = (D3-D2)/h 0.00020799403 OK

2 1.85E-01 mm Desplazamiento relativo de entrepiso

D = (D2-D1)/h 0.00028216179 OK

1 -6.62E-01 mm Desplazamiento relativo de entrepiso

D = (D1-0.00)/h -1.89E-04 OK

Deriva inelastica
5.02E-04 OK
8.37E-04 OK
6.06E-04 OK
[QL]= [KL][DL] 1.38E-04 OK
-4.96E-04 OK
1 2 3 4 5
92253.9192322301 -54184.63029435 14023.9473891 -3246.124776 96.07555514 1
[KLC]2 =
-54184.6302943547 74354.089907411 -57936.698516 20330.43027 -1725.510486 2
14023.9473891021 -57936.69851566 84110.9501874 -45783.32311 8499.587943 3
-3246.12477611371 20330.430271153 -45783.323107 42025.11165 -14010.54483 4
96.0755551441619 -1725.510486353 8499.587943 -14010.54483 7155.683003 5

12.0050691321865
[QL]C =
4.71589792023968
-1.31280455527444
0.519631790349381 5 12.01 Tn
-2.31072088035931

4 4.72 Tn

3 -1.31 Tn

2 0.51963179 Tn

1 -2.31072088 Tn

V = Q1+Q2+Q3+Q4+Q5 Fuerza de Cortante en Portico

V= 13.62 Tn

Portico 3
[DL]= [G][DE]
0.00069906328350712 m
[DL]C =
0.0013864836825359 m
0.00120100581018429 m
0.00023 m
-0.0009088632167188 m
5 0.699063284 mm Desplazamiento relativo de entrepiso
D = (D5-D4)/h -2.29E-04 OK
Desplazamiento relativo de entrepiso
4 1.39E+00 mm D = (D4-D3)/h 6.1825957E-05 OK

3 1.20E+00 mm Desplazamiento relativo de entrepiso

D = (D3-D2)/h 0.00032472984 OK

2 2.27E-01 mm Desplazamiento relativo de entrepiso

D = (D2-D1)/h 0.00037855984 OK

1 -9.09E-01 mm Desplazamiento relativo de entrepiso

D = (D1-0.00)/h -2.60E-04 OK

Deriva inelastica
5.24E-04 OK
1.04E-03 OK
9.01E-04 OK
[QL]= [KL][DL] 1.70E-04 OK
-6.82E-04 OK
1 2 3 4 5
92253.9192322301 -54184.63029435 14023.9473891 -3246.124776 96.07555514 1
[KLC]3 =
-54184.6302943547 74354.089907411 -57936.698516 20330.43027 -1725.510486 2
14023.9473891021 -57936.69851566 84110.9501874 -45783.32311 8499.587943 3
-3246.12477611371 20330.430271153 -45783.323107 42025.11165 -14010.54483 4
96.0755551441619 -1725.510486353 8499.587943 -14010.54483 7155.683003 5

5.38447070959792
[QL]C =
1.80946116446486
12.3837128997846
-6.8018249015068 5 5.38 Tn
-1.79853168165141

4 1.81 Tn

3 12.38 Tn

2 -6.801824902 Tn

1 -1.798531682 Tn

V = Q1+Q2+Q3+Q4+Q5 Fuerza de Cortante en Portico

V= 10.98 Tn
Portico 4
[DL]= [G][DE]
0.00072862910387027 m
[DL]4C =
0.00142665135226501 m
0.00159546185100519 m
0.000271 m
-0.0011570137561519 m
5 0.728629104 mm Desplazamiento relativo de entrepiso
D = (D5-D4)/h -2.33E-04 OK
Desplazamiento relativo de entrepiso
4 1.43E+00 mm D = (D4-D3)/h -5.627017E-05 OK

3 1.60E+00 mm Desplazamiento relativo de entrepiso

D = (D3-D2)/h 0.00044157972 OK

2 2.71E-01 mm Desplazamiento relativo de entrepiso

D = (D2-D1)/h 0.00047591215 OK

1 -1.16E+00 mm Desplazamiento relativo de entrepiso

D = (D1-0.00)/h -3.31E-04 OK

Deriva inelastica
5.46E-04 OK
1.07E-03 OK
1.20E-03 OK
[QL]= [KL][DL] 2.03E-04 OK
-8.68E-04 OK
1 2 3 4 5
39608.1948051093 -27047.55709764 8163.24845271 -1059.500463 226.3805265 1
[KLC]4 =
-27047.5570976406 39898.179280754 -27228.938282 8280.880143 -829.1936179 2
8163.24845271404 -27228.93828235 40088.7258741 -25921.56453 5979.40154 3
-1059.50046298015 8280.8801430014 -25921.564528 30804.75566 -12237.50575 4
226.380526548245 -829.1936178922 5979.40154043 -12237.50575 6882.428234 5

2.74764484942707
[QL]C =
-3.02836744075207
17.1260056568183
-7.81641205627723 5 2.75 Tn
-2.75415051262851

4 -3.03 Tn

3 17.13 Tn

2 -7.816412056 Tn

1 -2.754150513 Tn

V = Q1+Q2+Q3+Q4+Q5 Fuerza de Cortante en Portico

V= 6.27 Tn

Portico 5
[DL]= [G][DE]
0.0010809743316224 m
[DL]5C =
0.00180232645776982 m
0.00204000784428691 m
0.00164223114103209 m
0.00084153299078886 m
5 1.080974332 mm Desplazamiento relativo de entrepiso
D = (D5-D4)/h -2.40E-04 OK
Desplazamiento relativo de entrepiso
4 1.80E+00 mm D = (D4-D3)/h -7.922713E-05 OK

3 2.04E+00 mm Desplazamiento relativo de entrepiso

D = (D3-D2)/h 0.00013259223 OK RESULTADOS

2 1.64E+00 mm Desplazamiento relativo de entrepiso

D = (D2-D1)/h 0.00026689938 OK

1 8.42E-01 mm Desplazamiento relativo de entrepiso

D = (D1-0.00)/h 2.40E-04 OK

Deriva inelastica RESULTADOS

0.000811 OK
0.001352 OK PORTICO CRITICO 5
0.001530 OK
[QL]= [KL][DL] 0.001232 OK
0.000631 OK
1 2 3 4 5
67249.8428318474 -45483.50321993 13720.6307956 -2055.906018 287.6956912 1
[KLC]5 =
-45483.5032199286 67980.962621373 -46048.48229 13544.10771 -1557.346314 2
13720.6307955656 -46048.48229027 67966.0875562 -44479.61627 10596.71136 3
-2055.90601777461 13544.107708906 -44479.616266 57449.45992 -24717.39144 4
287.695691156867 -1557.346313512 10596.7113628 -24717.39144 15403.72642 5

15.5752596430415
[QL]C =
0.350120130660427
6.36027472398594
4.99454771811194 5 15.58 Tn
-8.50740649069039

4 0.35 Tn

3 6.36 Tn

2 4.994547718 Tn

1 -8.507406491 Tn

V = Q1+Q2+Q3+Q4+Q5 Fuerza de Cortante en Portico

V= 18.77 Tn
Portico 6
[DL]= [G][DE]
0.00111789400466141 m
[DL]6C =
0.00216640344081369 m
0.00253257621805414 m
0.00175790018281532 m
0.00053166041942795 m
5 1.117894005 mm Desplazamiento relativo de entrepiso
D = (D5-D4)/h -3.50E-04 OK
Desplazamiento relativo de entrepiso
4 2.17E+00 mm D = (D4-D3)/h -0.0001220576 OK

3 2.53E+00 mm Desplazamiento relativo de entrepiso

D = (D3-D2)/h 0.00025822535 OK

2 1.76E+00 mm Desplazamiento relativo de entrepiso

D = (D2-D1)/h 0.00040874659 OK

1 5.32E-01 mm Desplazamiento relativo de entrepiso

D = (D1-0.00)/h 1.52E-04 OK

Deriva inelastica
8.38E-04 OK
1.62E-03 OK
1.90E-03 OK
[QL]= [KL][DL] 1.32E-03 OK
3.99E-04 OK
1 2 3 4 5
6160.68954221472 -4029.219282025 675.796795913 -91.53325489 18.89475603 1
[KLC]6 =
-4029.21928202465 7009.1439241775 -4116.9351916 678.2379067 -68.31229042 2
675.796795912936 -4116.935191609 7016.64573057 -4083.357925 578.6329829 3
-91.5332548889839 678.23790665753 -4083.3579255 6763.750551 -3276.870084 4
18.8947560289408 -68.31229041842 578.63298287 -3276.870084 2745.99995 5

-0.281270450570388
[QL]C =
1.40989687724572
2.73621734024392
1.173413492737 5 -0.28 Tn
-2.96190854943694

4 1.41 Tn

3 2.74 Tn

2 1.173413493 Tn

1 -2.961908549 Tn

V = Q1+Q2+Q3+Q4+Q5 Fuerza de Cortante en Portico

V= 2.08 Tn

Portico 7
[DL]= [G][DE]
0.00115470455696691 m
[DL]7C =
0.00249966920861985 m
0.00302368874408966 m
0.00411919119647746 m
0.000223 m
5 1.154704557 mm Desplazamiento relativo de entrepiso
D = (D5-D4)/h -4.48E-04 OK
Desplazamiento relativo de entrepiso
4 2.50E+00 mm D = (D4-D3)/h -0.0001746732 OK

3 3.02E+00 mm Desplazamiento relativo de entrepiso RESULTADOS

D = (D3-D2)/h -0.0003651675 OK

2 4.12E+00 mm Desplazamiento relativo de entrepiso

D = (D2-D1)/h 0.00129882916 OK

1 2.23E-01 mm Desplazamiento relativo de entrepiso

D = (D1-0.00)/h 6.36E-05 OK

Deriva inelastica
8.66E-04 OK
1.87E-03 OK RESULTADOS
2.27E-03 OK
[QL]= [KL][DL] 3.09E-03 OK PORTICO CRITICO 7
1.67E-04 OK
1 2 3 4 5
76595.0578458958 -51827.71214191 15049.5894795 -949.0062113 377.4519183 1
[KLC]7 =
-51827.7121419052 76004.882942169 -44193.830787 6220.24136 -82.0450827 2
15049.5894795424 -44193.8307867 44105.2384144 -12971.54651 227.6804037 3
-949.00621130473 6220.2413596282 -12971.546507 7572.322959 -852.8361508 4
377.451918297198 -82.04508269897 227.68040375 -852.8361508 65941.5586 5

0.572722367507349
[QL]C =
22.1170732037119
-13.1131904301023
6.23272112486233 5 0.57 Tn
12.0916294921489

4 22.12 Tn

3 -13.11 Tn

2 6.232721125 Tn

1 12.09162949 Tn

V = Q1+Q2+Q3+Q4+Q5 Fuerza de Cortante en Portico

V= 27.90 Tn
 CUADRO DE RESUMEN DE LAS CORTANTES BASALES

PORTICOS FUERZA CORTANTE EN LOS PORTICOS

1 4.53
2 13.62
3 10.98 RESULTADOS
4 6.27
5 18.77 PORTICO CRITICO 1
6 2.08
7 27.90 PORTICO CRITICO 2