diseno de columnas y la diagrama de interaccion xls
DESCRIPTION
PLANILHATRANSCRIPT
PREDIMENCIONAMIENTO DE COLUNNA
1.0 ESTRUCTURACION EN PLANTA Y ELEVACION PREDIMENSIONAMIENTO
A. ESTRUCTURACION EN PLANTA B m. H m.VP 0.25 0.50
E VS 0.25 0.40C4 C2 C2 C2 C4C1 0.40 0.04
4 C2 0.25 0.35C3 0.25 0.25
D C4 0.25 0.25C3 C1 C1 C1 C3LOSA ALIG. 0.20
4.3
CC3 C1 C1 C1 C3
3.8
BC3 C1 C1 C1 C3
4
AC4 C2 C2 C2 C45.3 5 3.8 5
1 ### 3 4 5Calculo de area trubutaria para la columna C1
Atri= 21.3725Analizando el antepenultimo piso
Ac= 769.41 b= 30t3= 27.7382408 cm h= 30
Analizando el segundo pisoAc= 1025.88 b= 35t2= 32.0293615 cm h= 35
Analizando el primer pisot1= 39.0293615 cm b= 40
h= 40las seccciones de las columnas será:primer piso 40 X 40.00 ### 40x40segundo piso 35 X 35.00tercer y 30 X 30.00cuarto
Elemento primer piso segundo piso tercer piso cuarto piso totallosa aligerada 4515 6020 6020 6020 22575viga principal 1987.5 1987.5 1987.5 1987.5 7950viga secundaria 1032 1032 1032 3096
columna 1584 1080 1080 1080 4824acabado 2279 2279 2279 2279 9116 0.297719
sobrecarga 11395 3418.5 3418.5 3418.5 21650.5muros 7560 5670 5670 5670 24570 93781.5
B. ESTRUCTURACION EN ELEVACION
0.200.400.50
2.40 2.202.6 2.10
0.200.400.50
2.40 2.202.6 2.10
0.200.400.50
2.40 2.202.6 2.10
0.200.400.50
2.78 2.73 2.832.975
1 1 1 1
HECHO POR : EST. ING CIVIL UNA-PUNO BORIS CHIQUE
ESTIMACION DE CUANTIA DE ACERO PARA COLUMNAS
Columna: C101 Nivel: 1
HECHO POR : EST. ING CIVIL UNA-PUNO BORIS CHIQUE
Datos:
b= 40 cmh= 40 cmr= 5 cm
f'c= 210 Kg/cm2
fy= 4200 Kg/cm2Es= 2000000 Kg/cm2
f= 0.7 Columnas Con Estribos
Momentos De Diseño
Pu= 93.7815 TnMu= 14 Tn-m
Mn= 20Pn= 133.9736
Cuantia Asumida:
r = 0.011
As= 17.6 cm²
r
r
h
b
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00
-800
-600
-400
-200
0
200
400
600
800
1000
1200
1
DIAGRAMA DE INTERACCION
Mn (Tn-m)
Pn
(T
n)
diseño de la columna principal
acero de: 4 3/4"+ 4 5/8"
40 cm 4 3/4" 11.419.312
4 5/8" 7.912
19.36 mas el 10% 19.31240 cm 16.72 menos el 5%
19.312 esta dentro del margen establecido
ESTIMACION DE CUANTIA DE ACERO PARA COLUMNAS
Diagrama de interaccion para ColumnasHECHO POR : EST. ING CIVIL UNA-PUNO BORIS CHIQUE
b= 40 cm r= 5 cm f'c= 210 Kg/cm2 Es= 2000000 Kg/cm2 r= 0.0201
h= 40 cm fy= 4200 Kg/cm2
0.7 Columnas Con Estribos
Condicion de Carga Concentrica
Ag= 1600 cm2
Pno= 414.75 Tn
Condicion Balanceada
0.0021
35.00 Cb= 20.59
f=
ey=
Ag=bh
Pno=0 . 85fC, (A g−Ast )+Ast f Y
ε y=f YES
0 .003
Cb
dc
ey
f Si=0 . 003×ES×(c−d i )c
(Kg/cm2)
0.00 5.00 10.00 15.00 20.00 25.00 30.00
-200
-100
0
100
200
300
400
500
r
r
h
b
fs Fs (Tn) Brazo (m) M(Tn-m)
fs1 4542.86 Fluye 4200 44.96 Compresion 0.15 6.74421
fs2 171.43 171.429 1.84 Compresion 0.00 0
fs3 -4200.00 -4200 -44.96 Traccion -0.15 6.74421
fs4 6000.00 Fluye 4200 0 Compresion 0.20 0
fs5 6000.00 Fluye 4200 0 Compresion 0.20 0
fs6 6000.00 Fluye 4200 0 Compresion 0.20 0
Cc 16.47 cm 117.60 0.11765 13.8353
Fnb= 119.44 Tn Mnb= 27.3237 Tn-m
Punto de falla en la zona de fluencia del acero en traccion: 2.1
# varC Pn Mn a Calculado Asumido Fuerza (kg)
cm Tn Tn-m cm fs1 fs2 fs3 fs4 fs5 fs6 fs1 fs2 fs3 fs4 fs5 fs6 Fs1 Fs2 Fs3 Fs4
1 2.10 -122.8889 2.30 1.68 -8285.714 -51142.86 -94000 6000 6000 6000 -4200 -4200 -4200 4200 4200 4200 -44961.37 -44961.37 -44961.37 0
2 4.20 -78.16672 9.30 3.36 -1142.857 -22571.43 -44000 6000 6000 6000 -1142.857 -4200 -4200 4200 4200 4200 -12234.39 -44961.37 -44961.37 0
3 6.30 -40.68322 15.02 5.04 1238.0952 -13047.62 -27333.33 6000 6000 6000 1238.0952 -4200 -4200 4200 4200 4200 13253.918 -44961.37 -44961.37 0
4 8.40 -15.94387 18.63 6.72 2428.5714 -8285.714 -19000 6000 6000 6000 2428.5714 -4200 -4200 4200 4200 4200 25998.07 -44961.37 -44961.37 0
5 10.50 3.6978253 21.27 8.40 3142.8571 -5428.571 -14000 6000 6000 6000 3142.8571 -4200 -4200 4200 4200 4200 33644.561 -44961.37 -44961.37 0
6 12.60 28.029364 23.32 10.08 3619.0476 -3523.81 -10666.67 6000 6000 6000 3619.0476 -3523.81 -4200 4200 4200 4200 38742.222 -37722.69 -44961.37 0
7 14.70 58.230496 24.96 11.76 3959.1837 -2163.265 -8285.714 6000 6000 6000 3959.1837 -2163.265 -4200 4200 4200 4200 42383.408 -23157.94 -44961.37 0
8 16.80 83.727214 26.23 13.44 4214.2857 -1142.857 -6500 6000 6000 6000 4200 -1142.857 -4200 4200 4200 4200 44961.368 -12234.39 -44961.37 0
9 18.90 104.21852 26.92 15.12 4412.6984 -349.2063 -5111.111 6000 6000 6000 4200 -349.2063 -4200 4200 4200 4200 44961.368 -3738.285 -44961.37 0
10 21.00 125.15161 27.08 16.80 4571.4286 285.71429 -4000 6000 6000 6000 4200 285.71429 -4000 4200 4200 4200 44961.368 3058.5965 -42820.35 0
ab=
D c:
f Si=0 . 003×ES×(c−d i )c
(Kg/cm2)
ab=0 . 8Cb
C<Cb
Diagrama de interaccion para ColumnasHECHO POR : EST. ING CIVIL UNA-PUNO BORIS CHIQUE
b= 40 cm r= 5 cm f'c= 210 Kg/cm2 Es= 2E+06 Kg/cm2 r= 0.030
h= 40 cm fy= 4200 Kg/cm2
0.7 Columnas Con Estribos
a) Condicion de Carga Concentrica
Ag= 1600 cm2
Pno= 479.33 Tn
b) Condicion Balanceada
0.0021
35.00 Cb= 20.59
f=
ey=
Ag=bh
Pno=0 . 85fC, (A g−Ast )+Ast f Y
ε y=f YES
0 .003
Cb
dc
ey
f Si=0 . 003×ES×(c−d i )c
(Kg/cm2)
0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00
-300
-200
-100
0
100
200
300
400
500
600
r
r
h
b
fs Fs (Tn) Brazo (m) M(Tn-m)
fs1 4542.86 Fluye 4200 67.44 Compresion 0.15 10.1163
fs2 171.43 171.429 2.75 Compresion 0.00 0
fs3 -4200.00 -4200 -67.44 Traccion -0.15 10.1163
fs4 6000.00 Fluye 4200 0 Compresion 0.20 0
fs5 6000.00 Fluye 4200 0 Compresion 0.20 0
fs6 6000.00 Fluye 4200 0 Compresion 0.20 0
Cc 16.47 cm 117.60 0.11765 13.8353
Fnb= 120.35 Tn Mnb= 34.0679 Tn-m
c) Punto de falla en la zona de fluencia del acero en traccion: 2.1
# varC Pn Mn a Calculado Asumido Fuerza (kg)
cm Tn Tn-m cm fs1 fs2 fs3 fs4 fs5 fs6 fs1 fs2 fs3 fs4 fs5 fs6 Fs1 Fs2 Fs3 Fs4
1 2.10 -190.331 2.30 1.68 -8285.714 -51142.86 -94000 6000 6000 6000 -4200 -4200 -4200 4200 4200 4200 -67442.05 -67442.05 -67442.05 0
2 4.20 -129.2453 11.76 3.36 -1142.857 -22571.43 -44000 6000 6000 6000 -1142.857 -4200 -4200 4200 4200 4200 -18351.58 -67442.05 -67442.05 0
3 6.30 -79.01763 19.39 5.04 1238.0952 -13047.62 -27333.33 6000 6000 6000 1238.0952 -4200 -4200 4200 4200 4200 19880.877 -67442.05 -67442.05 0
4 8.40 -47.9062 23.95 6.72 2428.5714 -8285.714 -19000 6000 6000 6000 2428.5714 -4200 -4200 4200 4200 4200 38997.105 -67442.05 -67442.05 0
5 10.50 -24.44126 27.16 8.40 3142.8571 -5428.571 -14000 6000 6000 6000 3142.8571 -4200 -4200 4200 4200 4200 50466.841 -67442.05 -67442.05 0
6 12.60 6.0584464 29.60 10.08 3619.0476 -3523.81 -10666.67 6000 6000 6000 3619.0476 -3523.81 -4200 4200 4200 4200 58113.333 -56584 -67442.05 0
7 14.70 45.362543 31.51 11.76 3959.1837 -2163.265 -8285.714 6000 6000 6000 3959.1837 -2163.265 -4200 4200 4200 4200 63575.112 -34736.92 -67442.05 0
8 16.80 77.610021 32.98 13.44 4214.2857 -1142.857 -6500 6000 6000 6000 4200 -1142.857 -4200 4200 4200 4200 67442.052 -18351.58 -67442.05 0
9 18.90 102.34937 33.66 15.12 4412.6984 -349.2063 -5111.111 6000 6000 6000 4200 -349.2063 -4200 4200 4200 4200 67442.052 -5607.427 -67442.05 0
10 21.00 127.75142 33.67 16.80 4571.4286 285.71429 -4000 6000 6000 6000 4200 285.71429 -4000 4200 4200 4200 67442.052 4587.8947 -64230.53 0
ab=
D c:
f Si=0 . 003×ES×(c−d i )c
(Kg/cm2)
ab=0 . 8Cb
C<Cb
Diagrama de interaccion para ColumnasHECHO POR : EST. ING CIVIL UNA-PUNO BORIS CHIQUE
b= 40 cm r= 5 cm f'c= 210 Kg/cm2 Es= 2E+06 Kg/cm2 r= 0.040
h= 40 cm fy= 4200 Kg/cm2
0.7 Columnas Con Estribos
a) Condicion de Carga Concentrica
Ag= 1600 cm2
Pno= 543.90 Tn
b) Condicion Balanceada
0.0021
35.00 Cb= 20.59
f=
ey=
Ag=bh
Pno=0 . 85fC, (A g−Ast )+Ast f Y
ε y=f YES
0 .003
Cb
dc
ey
f Si=0 . 003×ES×(c−d i )c
(Kg/cm2)
0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00
-300
-200
-100
0
100
200
300
400
500
600
r
r
h
b
fs Fs (Tn) Brazo (m) M(Tn-m)
fs1 4542.86 Fluye 4200 89.92 Compresion 0.15 13.4884
fs2 171.43 171.429 3.67 Compresion 0.00 0
fs3 -4200.00 -4200 -89.92 Traccion -0.15 13.4884
fs4 6000.00 Fluye 4200 0 Compresion 0.20 0
fs5 6000.00 Fluye 4200 0 Compresion 0.20 0
fs6 6000.00 Fluye 4200 0 Compresion 0.20 0
Cc 16.47 cm 117.60 0.11765 13.8353
Fnb= 121.27 Tn Mnb= 40.8121 Tn-m
c) Punto de falla en la zona de fluencia del acero en traccion: 2.1
# varC Pn Mn a Calculado Asumido Fuerza (kg)
cm Tn Tn-m cm fs1 fs2 fs3 fs4 fs5 fs6 fs1 fs2 fs3 fs4 fs5 fs6 Fs1 Fs2 Fs3 Fs4
1 2.10 -257.773 2.30 1.68 -8285.714 -51142.86 -94000 6000 6000 6000 -4200 -4200 -4200 4200 4200 4200 -89922.74 -89922.74 -89922.74 0
2 4.20 -180.3238 14.21 3.36 -1142.857 -22571.43 -44000 6000 6000 6000 -1142.857 -4200 -4200 4200 4200 4200 -24468.77 -89922.74 -89922.74 0
3 6.30 -117.352 23.75 5.04 1238.0952 -13047.62 -27333.33 6000 6000 6000 1238.0952 -4200 -4200 4200 4200 4200 26507.836 -89922.74 -89922.74 0
4 8.40 -79.86853 29.27 6.72 2428.5714 -8285.714 -19000 6000 6000 6000 2428.5714 -4200 -4200 4200 4200 4200 51996.14 -89922.74 -89922.74 0
5 10.50 -52.58035 33.06 8.40 3142.8571 -5428.571 -14000 6000 6000 6000 3142.8571 -4200 -4200 4200 4200 4200 67289.122 -89922.74 -89922.74 0
6 12.60 -15.91247 35.88 10.08 3619.0476 -3523.81 -10666.67 6000 6000 6000 3619.0476 -3523.81 -4200 4200 4200 4200 77484.443 -75445.38 -89922.74 0
7 14.70 32.494591 38.06 11.76 3959.1837 -2163.265 -8285.714 6000 6000 6000 3959.1837 -2163.265 -4200 4200 4200 4200 84766.816 -46315.89 -89922.74 0
8 16.80 71.492828 39.72 13.44 4214.2857 -1142.857 -6500 6000 6000 6000 4200 -1142.857 -4200 4200 4200 4200 89922.736 -24468.77 -89922.74 0
9 18.90 100.48023 40.41 15.12 4412.6984 -349.2063 -5111.111 6000 6000 6000 4200 -349.2063 -4200 4200 4200 4200 89922.736 -7476.569 -89922.74 0
10 21.00 130.35123 40.25 16.80 4571.4286 285.71429 -4000 6000 6000 6000 4200 285.71429 -4000 4200 4200 4200 89922.736 6117.1929 -85640.7 0
ab=
D c:
f Si=0 . 003×ES×(c−d i )c
(Kg/cm2)
ab=0 . 8Cb
C<Cb
Diagrama de interaccion para ColumnasHECHO POR : EST. ING CIVIL UNA-PUNO BORIS CHIQUE
b= 40 cm r= 5 cm f'c= 210 Kg/cm2 Es= 2E+06 Kg/cm2 r= 0.050
h= 40 cm fy= 4200 Kg/cm2
0.7 Columnas Con Estribos
a) Condicion de Carga Concentrica
Ag= 1600 cm2
Pno= 608.48 Tn
b) Condicion Balanceada
0.0021
35.00 Cb= 20.59
fs Fs (Tn) Brazo (m) M(Tn-m)
fs1 4542.86 Fluye 4200 112.40 Compresion 0.15 16.8605
f=
ey=
Ag=bh
Pno=0 . 85fC, (A g−Ast )+Ast f Y
ε y=f YES
0 .003
Cb
dc
ey
f Si=0 . 003×ES×(c−d i )c
(Kg/cm2)0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00
-400
-200
0
200
400
600
800
r
r
h
b
fs2 171.43 171.429 4.59 Compresion 0.00 0
fs3 -4200.00 -4200 -112.40 Traccion -0.15 16.8605
fs4 6000.00 Fluye 4200 0 Compresion 0.20 0
fs5 6000.00 Fluye 4200 0 Compresion 0.20 0
fs6 6000.00 Fluye 4200 0 Compresion 0.20 0
Cc 16.47 cm 117.60 0.11765 13.8353
Fnb= 122.19 Tn Mnb= 47.5563 Tn-m
c) Punto de falla en la zona de fluencia del acero en traccion: 2.1
# varC Pn Mn a Calculado Asumido Fuerza (kg)
cm Tn Tn-m cm fs1 fs2 fs3 fs4 fs5 fs6 fs1 fs2 fs3 fs4 fs5 fs6 Fs1 Fs2
1 2.10 -325.2151 2.30 1.68 -8285.714 -51142.86 -94000 6000 6000 6000 -4200 -4200 -4200 4200 4200 4200 -112403 -112403
2 4.20 -231.4024 16.67 3.36 -1142.857 -22571.43 -44000 6000 6000 6000 -1142.857 -4200 -4200 4200 4200 4200 -30586 -112403
3 6.30 -155.6864 28.12 5.04 1238.0952 -13047.62 -27333.33 6000 6000 6000 1238.0952 -4200 -4200 4200 4200 4200 33134.795 -112403
4 8.40 -111.8309 34.59 6.72 2428.5714 -8285.714 -19000 6000 6000 6000 2428.5714 -4200 -4200 4200 4200 4200 64995.175 -112403
5 10.50 -80.71944 38.95 8.40 3142.8571 -5428.571 -14000 6000 6000 6000 3142.8571 -4200 -4200 4200 4200 4200 84111.402 -112403
6 12.60 -37.88339 42.16 10.08 3619.0476 -3523.81 -10666.67 6000 6000 6000 3619.0476 -3523.81 -4200 4200 4200 4200 96855.554 -94306.72
7 14.70 19.626639 44.61 11.76 3959.1837 -2163.265 -8285.714 6000 6000 6000 3959.1837 -2163.265 -4200 4200 4200 4200 105958.52 -57894.86
8 16.80 65.375635 46.46 13.44 4214.2857 -1142.857 -6500 6000 6000 6000 4200 -1142.857 -4200 4200 4200 4200 112403.42 -30586
9 18.90 98.611089 47.15 15.12 4412.6984 -349.2063 -5111.111 6000 6000 6000 4200 -349.2063 -4200 4200 4200 4200 112403.42 -9345.711
10 21.00 132.95103 46.83 16.80 4571.4286 285.71429 -4000 6000 6000 6000 4200 285.71429 -4000 4200 4200 4200 112403.42 7646.4911
ab=
D c:
ab=0 . 8Cb
C<Cb
0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00
-400
-200
0
200
400
600
800
0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00
-400
-200
0
200
400
600
800
Fuerza (kg)
Fs3 Fs4
-112403 0
-112403 0
-112403 0
-112403 0
-112403 0
-112403 0
-112403 0
-112403 0
-112403 0
-107051 0
0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00
-400
-200
0
200
400
600
800
Diagrama de interaccion para ColumnasHECHO POR : EST. ING CIVIL UNA-PUNO BORIS CHIQUE
b= 40 cm r= 5 cm f'c= 210 Kg/cm2 Es= 2E+06 Kg/cm2 r= 0.060
h= 40 cm fy= 4200 Kg/cm2
0.7 Columnas Con Estribos
a) Condicion de Carga Concentrica
Ag= 1600 cm2
Pno= 673.05 Tn
b) Condicion Balanceada
0.0021
35.00 Cb= 20.59
fs Fs (Tn) Brazo (m) M(Tn-m)
fs1 4542.86 Fluye 4200 134.88 Compresion 0.15 20.2326
f=
ey=
Ag=bh
Pno=0 . 85fC, (A g−Ast )+Ast f Y
ε y=f YES
0 .003
Cb
dc
ey
f Si=0 . 003×ES×(c−d i )c
(Kg/cm2)0.00 10.00 20.00 30.00 40.00 50.00 60.00
-600
-400
-200
0
200
400
600
800
r
r
h
b
fs2 171.43 171.429 5.51 Compresion 0.00 0
fs3 -4200.00 -4200 -134.88 Traccion -0.15 20.2326
fs4 6000.00 Fluye 4200 0 Compresion 0.20 0
fs5 6000.00 Fluye 4200 0 Compresion 0.20 0
fs6 6000.00 Fluye 4200 0 Compresion 0.20 0
Cc 16.47 cm 117.60 0.11765 13.8353
Fnb= 123.11 Tn Mnb= 54.3005 Tn-m
c) Punto de falla en la zona de fluencia del acero en traccion: 2.1
# varC Pn Mn a Calculado Asumido Fuerza (kg)
cm Tn Tn-m cm fs1 fs2 fs3 fs4 fs5 fs6 fs1 fs2 fs3 fs4 fs5 fs6 Fs1 Fs2
1 2.10 -392.6571 2.30 1.68 -8285.714 -51142.86 -94000 6000 6000 6000 -4200 -4200 -4200 4200 4200 4200 -134884 -134884
2 4.20 -282.481 19.12 3.36 -1142.857 -22571.43 -44000 6000 6000 6000 -1142.857 -4200 -4200 4200 4200 4200 -36703.16 -134884
3 6.30 -194.0209 32.49 5.04 1238.0952 -13047.62 -27333.33 6000 6000 6000 1238.0952 -4200 -4200 4200 4200 4200 39761.754 -134884
4 8.40 -143.7932 39.92 6.72 2428.5714 -8285.714 -19000 6000 6000 6000 2428.5714 -4200 -4200 4200 4200 4200 77994.21 -134884
5 10.50 -108.8585 44.85 8.40 3142.8571 -5428.571 -14000 6000 6000 6000 3142.8571 -4200 -4200 4200 4200 4200 100933.68 -134884
6 12.60 -59.85431 48.43 10.08 3619.0476 -3523.81 -10666.67 6000 6000 6000 3619.0476 -3523.81 -4200 4200 4200 4200 116226.67 -113168
7 14.70 6.7586867 51.16 11.76 3959.1837 -2163.265 -8285.714 6000 6000 6000 3959.1837 -2163.265 -4200 4200 4200 4200 127150.22 -69473.83
8 16.80 59.258443 53.21 13.44 4214.2857 -1142.857 -6500 6000 6000 6000 4200 -1142.857 -4200 4200 4200 4200 134884.1 -36703.16
9 18.90 96.741946 53.90 15.12 4412.6984 -349.2063 -5111.111 6000 6000 6000 4200 -349.2063 -4200 4200 4200 4200 134884.1 -11214.85
10 21.00 135.55084 53.42 16.80 4571.4286 285.71429 -4000 6000 6000 6000 4200 285.71429 -4000 4200 4200 4200 134884.1 9175.7894
ab=
D c:
ab=0 . 8Cb
C<Cb
0.00 10.00 20.00 30.00 40.00 50.00 60.00
-600
-400
-200
0
200
400
600
800
0.00 10.00 20.00 30.00 40.00 50.00 60.00
-600
-400
-200
0
200
400
600
800
Fuerza (kg)
Fs3 Fs4
-134884 0
-134884 0
-134884 0
-134884 0
-134884 0
-134884 0
-134884 0
-134884 0
-134884 0
-128461 0
0.00 10.00 20.00 30.00 40.00 50.00 60.00
-600
-400
-200
0
200
400
600
800
Diagrama de interaccion para ColumnasHECHO POR : EST. ING CIVIL UNA-PUNO BORIS CHIQUE
b= 40 cm r= 5 cm f'c= 210 Kg/cm2 Es= 2E+06 Kg/cm2 r= 0.070
h= 40 cm fy= 4200 Kg/cm2
0.7 Columnas Con Estribos
a) Condicion de Carga Concentrica
Ag= 1600 cm2
Pno= 737.63 Tn
b) Condicion Balanceada
0.0021
35.00 Cb= 20.59
fs Fs (Tn) Brazo (m) M(Tn-m)
fs1 4542.86 Fluye 4200 157.36 Compresion 0.15 23.6047
f=
ey=
Ag=bh
Pno=0 . 85fC, (A g−Ast )+Ast f Y
ε y=f YES
0 .003
Cb
dc
ey
f Si=0 . 003×ES×(c−d i )c
(Kg/cm2) 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00
-600
-400
-200
0
200
400
600
800
1000
r
r
h
b
fs2 171.43 171.429 6.42 Compresion 0.00 0
fs3 -4200.00 -4200 -157.36 Traccion -0.15 23.6047
fs4 6000.00 Fluye 4200 0 Compresion 0.20 0
fs5 6000.00 Fluye 4200 0 Compresion 0.20 0
fs6 6000.00 Fluye 4200 0 Compresion 0.20 0
Cc 16.47 cm 117.60 0.11765 13.8353
Fnb= 124.02 Tn Mnb= 61.0447 Tn-m
c) Punto de falla en la zona de fluencia del acero en traccion: 2.1
# varC Pn Mn a Calculado Asumido Fuerza (kg)
cm Tn Tn-m cm fs1 fs2 fs3 fs4 fs5 fs6 fs1 fs2 fs3 fs4 fs5 fs6 Fs1 Fs2
1 2.10 -460.0992 2.30 1.68 -8285.714 -51142.86 -94000 6000 6000 6000 -4200 -4200 -4200 4200 4200 4200 -157365 -157365
2 4.20 -333.5595 21.58 3.36 -1142.857 -22571.43 -44000 6000 6000 6000 -1142.857 -4200 -4200 4200 4200 4200 -42820.35 -157365
3 6.30 -232.3553 36.85 5.04 1238.0952 -13047.62 -27333.33 6000 6000 6000 1238.0952 -4200 -4200 4200 4200 4200 46388.713 -157365
4 8.40 -175.7555 45.24 6.72 2428.5714 -8285.714 -19000 6000 6000 6000 2428.5714 -4200 -4200 4200 4200 4200 90993.244 -157365
5 10.50 -136.9976 50.74 8.40 3142.8571 -5428.571 -14000 6000 6000 6000 3142.8571 -4200 -4200 4200 4200 4200 117756 -157365
6 12.60 -81.82522 54.71 10.08 3619.0476 -3523.81 -10666.67 6000 6000 6000 3619.0476 -3523.81 -4200 4200 4200 4200 135597.78 -132029
7 14.70 -6.109266 57.71 11.76 3959.1837 -2163.265 -8285.714 6000 6000 6000 3959.1837 -2163.265 -4200 4200 4200 4200 148341.93 -81052.81
8 16.80 53.14125 59.95 13.44 4214.2857 -1142.857 -6500 6000 6000 6000 4200 -1142.857 -4200 4200 4200 4200 157364.79 -42820.35
9 18.90 94.872804 60.64 15.12 4412.6984 -349.2063 -5111.111 6000 6000 6000 4200 -349.2063 -4200 4200 4200 4200 157364.79 -13084
10 21.00 138.15065 60.00 16.80 4571.4286 285.71429 -4000 6000 6000 6000 4200 285.71429 -4000 4200 4200 4200 157364.79 10705.088
ab=
D c:
ab=0 . 8Cb
C<Cb
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00
-600
-400
-200
0
200
400
600
800
1000
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00
-600
-400
-200
0
200
400
600
800
1000
Fuerza (kg)
Fs3 Fs4
-157365 0
-157365 0
-157365 0
-157365 0
-157365 0
-157365 0
-157365 0
-157365 0
-157365 0
-149871 0
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00
-600
-400
-200
0
200
400
600
800
1000
Diagrama de interaccion para ColumnasHECHO POR : EST. ING CIVIL UNA-PUNO BORIS CHIQUE
b= 40 cm r= 5 cm f'c= 210 Kg/cm2 Es= 2E+06 Kg/cm2 r= 0.080
h= 40 cm fy= 4200 Kg/cm2
0.7 Columnas Con Estribos
a) Condicion de Carga Concentrica
Ag= 1600 cm2
Pno= 802.21 Tn
b) Condicion Balanceada
0.0021
35.00 Cb= 20.59
fs Fs (Tn) Brazo (m) M(Tn-m)
fs1 4542.86 Fluye 4200 179.85 Compresion 0.15 26.9768
f=
ey=
Ag=bh
Pno=0 . 85fC, (A g−Ast )+Ast f Y
ε y=f YES
0 .003
Cb
dc
ey
f Si=0 . 003×ES×(c−d i )c
(Kg/cm2) 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00
-600
-400
-200
0
200
400
600
800
1000
r
r
h
b
fs2 171.43 171.429 7.34 Compresion 0.00 0
fs3 -4200.00 -4200 -179.85 Traccion -0.15 26.9768
fs4 6000.00 Fluye 4200 0 Compresion 0.20 0
fs5 6000.00 Fluye 4200 0 Compresion 0.20 0
fs6 6000.00 Fluye 4200 0 Compresion 0.20 0
Cc 16.47 cm 117.60 0.11765 13.8353
Fnb= 124.94 Tn Mnb= 67.7889 Tn-m
c) Punto de falla en la zona de fluencia del acero en traccion: 2.1
# varC Pn Mn a Calculado Asumido Fuerza (kg)
cm Tn Tn-m cm fs1 fs2 fs3 fs4 fs5 fs6 fs1 fs2 fs3 fs4 fs5 fs6 Fs1 Fs2
1 2.10 -527.5412 2.30 1.68 -8285.714 -51142.86 -94000 6000 6000 6000 -4200 -4200 -4200 4200 4200 4200 -179845 -179845
2 4.20 -384.6381 24.03 3.36 -1142.857 -22571.43 -44000 6000 6000 6000 -1142.857 -4200 -4200 4200 4200 4200 -48937.54 -179845
3 6.30 -270.6897 41.22 5.04 1238.0952 -13047.62 -27333.33 6000 6000 6000 1238.0952 -4200 -4200 4200 4200 4200 53015.672 -179845
4 8.40 -207.7179 50.56 6.72 2428.5714 -8285.714 -19000 6000 6000 6000 2428.5714 -4200 -4200 4200 4200 4200 103992.28 -179845
5 10.50 -165.1367 56.64 8.40 3142.8571 -5428.571 -14000 6000 6000 6000 3142.8571 -4200 -4200 4200 4200 4200 134578.24 -179845
6 12.60 -103.7961 60.99 10.08 3619.0476 -3523.81 -10666.67 6000 6000 6000 3619.0476 -3523.81 -4200 4200 4200 4200 154968.89 -150891
7 14.70 -18.97722 64.26 11.76 3959.1837 -2163.265 -8285.714 6000 6000 6000 3959.1837 -2163.265 -4200 4200 4200 4200 169533.63 -92631.78
8 16.80 47.024057 66.70 13.44 4214.2857 -1142.857 -6500 6000 6000 6000 4200 -1142.857 -4200 4200 4200 4200 179845.47 -48937.54
9 18.90 93.003662 67.38 15.12 4412.6984 -349.2063 -5111.111 6000 6000 6000 4200 -349.2063 -4200 4200 4200 4200 179845.47 -14953.14
10 21.00 140.75046 66.58 16.80 4571.4286 285.71429 -4000 6000 6000 6000 4200 285.71429 -4000 4200 4200 4200 179845.47 12234.386
ab=
D c:
ab=0 . 8Cb
C<Cb
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00
-600
-400
-200
0
200
400
600
800
1000
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00
-600
-400
-200
0
200
400
600
800
1000
Fuerza (kg)
Fs3 Fs4
-179845 0
-179845 0
-179845 0
-179845 0
-179845 0
-179845 0
-179845 0
-179845 0
-179845 0
-171281 0
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00
-600
-400
-200
0
200
400
600
800
1000
Diagrama de interaccion para ColumnasHECHO POR : EST. ING CIVIL UNA-PUNO BORIS CHIQUE
b= 40 cm r= 5 cm f'c= 210 Kg/cm2 Es= 2E+06 Kg/cm2 r= 0.090
h= 40 cm fy= 4200 Kg/cm2
0.7 Columnas Con Estribos
a) Condicion de Carga Concentrica
Ag= 1600 cm2
Pno= 866.78 Tn
b) Condicion Balanceada
0.0021
35.00 Cb= 20.59
fs Fs (Tn) Brazo (m) M(Tn-m)
fs1 4542.86 Fluye 4200 202.33 Compresion 0.15 30.3489
f=
ey=
Ag=bh
Pno=0 . 85fC, (A g−Ast )+Ast f Y
ε y=f YES
0 .003
Cb
dc
ey
f Si=0 . 003×ES×(c−d i )c
(Kg/cm2)0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00
-800
-600
-400
-200
0
200
400
600
800
1000
r
r
h
b
fs2 171.43 171.429 8.26 Compresion 0.00 0
fs3 -4200.00 -4200 -202.33 Traccion -0.15 30.3489
fs4 6000.00 Fluye 4200 0 Compresion 0.20 0
fs5 6000.00 Fluye 4200 0 Compresion 0.20 0
fs6 6000.00 Fluye 4200 0 Compresion 0.20 0
Cc 16.47 cm 117.60 0.11765 13.8353
Fnb= 125.86 Tn Mnb= 74.5331 Tn-m
c) Punto de falla en la zona de fluencia del acero en traccion: 2.1
# varC Pn Mn a Calculado Asumido Fuerza (kg)
cm Tn Tn-m cm fs1 fs2 fs3 fs4 fs5 fs6 fs1 fs2 fs3 fs4 fs5 fs6 Fs1 Fs2
1 2.10 -594.9833 2.30 1.68 -8285.714 -51142.86 -94000 6000 6000 6000 -4200 -4200 -4200 4200 4200 4200 -202326 -202326
2 4.20 -435.7166 26.49 3.36 -1142.857 -22571.43 -44000 6000 6000 6000 -1142.857 -4200 -4200 4200 4200 4200 -55054.74 -202326
3 6.30 -309.0241 45.59 5.04 1238.0952 -13047.62 -27333.33 6000 6000 6000 1238.0952 -4200 -4200 4200 4200 4200 59642.631 -202326
4 8.40 -239.6802 55.88 6.72 2428.5714 -8285.714 -19000 6000 6000 6000 2428.5714 -4200 -4200 4200 4200 4200 116991.31 -202326
5 10.50 -193.2758 62.54 8.40 3142.8571 -5428.571 -14000 6000 6000 6000 3142.8571 -4200 -4200 4200 4200 4200 151400.52 -202326
6 12.60 -125.7671 67.27 10.08 3619.0476 -3523.81 -10666.67 6000 6000 6000 3619.0476 -3523.81 -4200 4200 4200 4200 174340 -169752
7 14.70 -31.84517 70.81 11.76 3959.1837 -2163.265 -8285.714 6000 6000 6000 3959.1837 -2163.265 -4200 4200 4200 4200 190725.34 -104211
8 16.80 40.906864 73.44 13.44 4214.2857 -1142.857 -6500 6000 6000 6000 4200 -1142.857 -4200 4200 4200 4200 202326.16 -55054.74
9 18.90 91.13452 74.13 15.12 4412.6984 -349.2063 -5111.111 6000 6000 6000 4200 -349.2063 -4200 4200 4200 4200 202326.16 -16822.28
10 21.00 143.35026 73.17 16.80 4571.4286 285.71429 -4000 6000 6000 6000 4200 285.71429 -4000 4200 4200 4200 202326.16 13763.684
ab=
D c:
ab=0 . 8Cb
C<Cb
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00
-800
-600
-400
-200
0
200
400
600
800
1000
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00
-800
-600
-400
-200
0
200
400
600
800
1000
Fuerza (kg)
Fs3 Fs4
-202326 0
-202326 0
-202326 0
-202326 0
-202326 0
-202326 0
-202326 0
-202326 0
-202326 0
-192692 0
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00
-800
-600
-400
-200
0
200
400
600
800
1000
Diagrama de interaccion para ColumnasHECHO POR : EST. ING CIVIL UNA-PUNO BORIS CHIQUE
b= 40 cm r= 5 cm f'c= 210 Kg/cm2 Es= 2E+06 Kg/cm2 r= 0.100
h= 40 cm fy= 4200 Kg/cm2
0.7 Columnas Con Estribos
a) Condicion de Carga Concentrica
Ag= 1600 cm2
Pno= 931.36 Tn
b) Condicion Balanceada
0.0021
35.00 Cb= 20.59
fs Fs (Tn) Brazo (m) M(Tn-m)
fs1 4542.86 Fluye 4200 224.81 Compresion 0.15 33.721
f=
ey=
Ag=bh
Pno=0 . 85fC, (A g−Ast )+Ast f Y
ε y=f YES
0 .003
Cb
dc
ey
f Si=0 . 003×ES×(c−d i )c
(Kg/cm2) 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00
-800
-600
-400
-200
0
200
400
600
800
1000
1200
r
r
h
b
fs2 171.43 171.429 9.18 Compresion 0.00 0
fs3 -4200.00 -4200 -224.81 Traccion -0.15 33.721
fs4 6000.00 Fluye 4200 0 Compresion 0.20 0
fs5 6000.00 Fluye 4200 0 Compresion 0.20 0
fs6 6000.00 Fluye 4200 0 Compresion 0.20 0
Cc 16.47 cm 117.60 0.11765 13.8353
Fnb= 126.78 Tn Mnb= 81.2773 Tn-m
c) Punto de falla en la zona de fluencia del acero en traccion: 2.1
# varC Pn Mn a Calculado Asumido Fuerza (kg)
cm Tn Tn-m cm fs1 fs2 fs3 fs4 fs5 fs6 fs1 fs2 fs3 fs4 fs5 fs6 Fs1 Fs2
1 2.10 -662.4253 2.30 1.68 -8285.714 -51142.86 -94000 6000 6000 6000 -4200 -4200 -4200 4200 4200 4200 -224807 -224807
2 4.20 -486.7952 28.94 3.36 -1142.857 -22571.43 -44000 6000 6000 6000 -1142.857 -4200 -4200 4200 4200 4200 -61171.93 -224807
3 6.30 -347.3585 49.95 5.04 1238.0952 -13047.62 -27333.33 6000 6000 6000 1238.0952 -4200 -4200 4200 4200 4200 66269.59 -224807
4 8.40 -271.6425 61.20 6.72 2428.5714 -8285.714 -19000 6000 6000 6000 2428.5714 -4200 -4200 4200 4200 4200 129990.35 -224807
5 10.50 -221.4149 68.43 8.40 3142.8571 -5428.571 -14000 6000 6000 6000 3142.8571 -4200 -4200 4200 4200 4200 168222.8 -224807
6 12.60 -147.738 73.54 10.08 3619.0476 -3523.81 -10666.67 6000 6000 6000 3619.0476 -3523.81 -4200 4200 4200 4200 193711.11 -188613
7 14.70 -44.71312 77.36 11.76 3959.1837 -2163.265 -8285.714 6000 6000 6000 3959.1837 -2163.265 -4200 4200 4200 4200 211917 -115790
8 16.80 34.789671 80.19 13.44 4214.2857 -1142.857 -6500 6000 6000 6000 4200 -1142.857 -4200 4200 4200 4200 224806.84 -61171.93
9 18.90 89.265377 80.87 15.12 4412.6984 -349.2063 -5111.111 6000 6000 6000 4200 -349.2063 -4200 4200 4200 4200 224806.84 -18691.42
10 21.00 145.95007 79.75 16.80 4571.4286 285.71429 -4000 6000 6000 6000 4200 285.71429 -4000 4200 4200 4200 224806.84 15292.982
ab=
D c:
ab=0 . 8Cb
C<Cb
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00
-800
-600
-400
-200
0
200
400
600
800
1000
1200
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00
-800
-600
-400
-200
0
200
400
600
800
1000
1200
Fuerza (kg)
Fs3 Fs4
-224807 0
-224807 0
-224807 0
-224807 0
-224807 0
-224807 0
-224807 0
-224807 0
-224807 0
-214102 0
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00
-800
-600
-400
-200
0
200
400
600
800
1000
1200