Pc-4-ildefonso -campos.xlsx
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80
B
cm
80
20
160
30
20
4800.00 cm2 Ag 3.4% ρ 163.20 cm2 Ast 32.00 φ1" φ1" colocado 32.00 Ast colocado 163.20 cm2
30
Pu Mu x Mu y
280 320 20
Tn Tn.m Tn.m
f´c fy
210 4200
kg/cm2 kg/cm2
Compresion Pura φ 0.7 Po=0.85 x f´c x (Ag - Ast) + Ast x fy 1513.11 ton Po 1210.49 ton 0.8 x Po 1059.18 ton φPo 847.34 ton 0.8 x φ Po
Corte horizontal del diagr
Corte horizontal del diagr
Traccion pura φ 0.9 To = - fy x Ast 685.44 ton To 616.90 ton φTo
5 cm
recubrimiento
N°
N° Acero en la capa
1 2 3 4 5 6 7 8 9 10 11 12 Concreto 1 Concreto 2
N°
30.6 30.6 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 1600 3200
F 123057.9 123057.9 41019.3 41019.3 41019.3 41019.3 41019.3 41019.3 41019.3 41019.3 41019.3 41019.3 285600 571200 1513108.8
espaciamiento
5.00 10.00 10.00 16.67 16.67 16.67 16.67 16.67 16.67 16.67 16.67 16.67
yp
111.6266
cm
N° Acero en la capa
F
espaciamiento
1 2 3 4 5 6 7 8 Concreto 1 Concreto 2
10.2 10.2 10.2 51 51 10.2 10.2 10.2 1600 3200
yp
41019.3 41019.3 41019.3 205096.5 205096.5 41019.3 41019.3 41019.3 285600 571200 1513108.8 40 cm
5 13 13 5 8 5 13 13
orte horizontal del diagrama nominal
orte horizontal del diagrama de diseño
d 175.00 165.00 155.00 138.33 121.67 105.00 88.33 71.67 55.00 38.33 21.67 5.00 170.00 80
F*d 21535132.5 20304553.5 6357991.5 5674336.5 4990681.5 4307026.5 3623371.5 2939716.5 2256061.5 1572406.5 888751.5 205096.5 48552000 45696000 168903126
medidos desde el borde inferior d
F*d
75 62 49 44 36 31 18 5 40 40
3076447.5 2543196.6 2009945.7 9024246 7383474 1271598.3 738347.4 205096.5 11424000 22848000 60524352
medidos desde el borde inferior
Falla balanceada -1 0.0021 0.7 175 0.003 102.94 0.85 87.5 yp 111.626557 cm
α εs1 φ d1 εc c β a
Capa
Asi (cm2)
di (cm)
εsi
1 2 3 4 5 6 7 8 9 10 11 12
30.6 30.6 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2
175.00 165.00 155.00 138.33 121.67 105.00 88.33 71.67 55.00 38.33 21.67 5.00
-0.0021 -0.0018 -0.0015 -0.0010 -0.0005 -0.0001 0.0004 0.0009 0.0014 0.0019 0.0024 0.0029
CC brazo
526575.00 67.88
Pn φPn Mn φMn
402.89 282.02 298.57 209.00
kg cm ton ton ton.m ton.m
fsi real fsi real x Asi fsi (kg/cm2) (kg/cm2) (kg) -4200 -3617 -3034 -2063 -1091 -120 851 1823 2794 3766 4737 5709
-4200 -3617 -3034 -2063 -1091 -120 851 1823 2794 3766 4200 4200
-128520.0 -110684.6 -30949.7 -21041.1 -11132.6 -1224.0 8684.6 18593.1 28501.7 38410.3 42840.0 42840.0 -123682.3
brazo = Yp d
Fx brazo
-63.37 -53.37 -43.37 -26.71 -10.04 6.63 23.29 39.96 56.63 73.29 89.96 106.63
8144754.87 5907616.64 1342395.66 561941.092 111772.236 -8110.906 202291.666 742979.953 1613953.95 2815213.67 3853881.71 4567881.71
Falla balanceada -1.74986 0.0021 0.7 175 0.003 78.66 0.85 66.8568772917 yp 111.626557 cm
α εs1 φ d1 εc c β a
Capa
Asi (cm2)
di (cm)
εsi
1 2 3 4 5 6 7 8 9 10 11 12
30.6 30.6 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2
175.00 165.00 155.00 138.33 121.67 105.00 88.33 71.67 55.00 38.33 21.67 5.00
-0.0037 -0.0033 -0.0029 -0.0023 -0.0016 -0.0010 -0.0004 0.0003 0.0009 0.0015 0.0022 0.0028
CC brazo
452879.05 78.20
Pn φPn Mn φMn
0.00 0.00 408.32 285.82
kg cm ton ton ton.m ton.m
fsi real fsi real x Asi fsi (kg/cm2) (kg/cm2) (kg) -7349 -6587 -5824 -4552 -3281 -2010 -738 533 1804 3076 4347 5619
-7349 -6587 -5824 -4552 -3281 -2010 -738 533 1804 3076 4200 4200
-224892.0 -201549.6 -59402.4 -46434.4 -33466.4 -20498.4 -7530.4 5437.6 18405.6 31373.6 42840.0 42840.0 -452876.8
brazo = Yp d
Fx brazo
-63.37 -53.37 -43.37 -26.71 -10.04 6.63 23.29 39.96 56.63 73.29 89.96 106.63
14252180.8 10757396.4 2576486.69 1240113.18 336006.336 -135833.83 -175407.32 217285.861 1042245.72 2299472.25 3853881.71 4567881.71
Excluyendo φ P (tn) Drescripcion compresio pura Po 1513.11 Falla balanceada 402.89 Flexion pura 0.00 Traccion pura To -685.44
P (tn) 1210.49 1210.49
M (tn.m) 0.00 298.57 408.32 0.00
Incluyendo φ Drescripcion P (tn) 1059.18 compresio pura φPo 282.02 Falla balanceada 0.00 Flexion pura -616.90 Traccion pura φTo
M (tn.m) 0 79 tanteo
M (tn.m) 0 209.00 285.82 0
P (tn) 847.34 847.34
M (tn.m) 0 57
Pu 280
Muy 20
φ
DIAGRAMA DE INTERACCIÓN-COLUMNA SECCIÓN "T" 2000.00 1500.00
P (TN)
1000.00
tanteo
Nomi na l Di seño 0.8Po φ0.8po Mu,Pu
500.00 0.00 0.00
100.00
200.00
-500.00 -1000.00
M (TN.m)
300.00
400.00
500.00
α εs1 φ d1 εc c β a
-1 0.0021 0.7 75 0.003 44.12 0.85 37.5
f´c fy Base
yp
210 4200 20 30 180
40 cm
Capa
Asi (cm2)
di (cm)
εsi
1 2 3 4 5 6 7 8
10.2 10.2 10.2 51 51 10.2 10.2 10.2
75.00 62.00 49.00 44.00 36.00 31.00 18.00 5.00
-0.0021 -0.0012 -0.0003 0.0000 0.0006 0.0009 0.0018 0.0027
CC brazo
348075.00 21.25
Pn φPn Mn φMn
428.04 299.63 121.85 85.29
kg cm ton ton ton.m ton.m
fsi real fsi real x Asi fsi (kg/cm2) (kg/cm2) (kg) -4200 -2432 -664 16 1104 1784 3552 5320
-4200 -2432 -664 16 1104 1784 3552 4200
-42840.0 -24806.4 -6772.8 816.0 56304.0 18196.8 36230.4 42840.0 79968.0
kg/cm2 kg/cm2
brazo = Xp d -35.00 -22.00 -9.00 -4.00 4.00 9.00 22.00 35.00
Fx brazo 1499400 545740.8 60955.2 -3264 225216 163771.2 797068.8 1499400
α εs1 φ d1 εc c β a
-1.55878 0.0021 0.7 75 0.003 35.87 0.85 30.4856762751
f´c fy Base
yp
210 4200 20 30 180
40 cm
Capa
Asi (cm2)
di (cm)
εsi
1 2 3 4 5 6 7 8
10.2 10.2 10.2 51 51 10.2 10.2 10.2
75.00 62.00 49.00 44.00 36.00 31.00 18.00 5.00
-0.0033 -0.0022 -0.0011 -0.0007 0.0000 0.0004 0.0015 0.0026
CC brazo
122704.78 24.76
kg cm
Pn φPn Mn φMn
0.00 0.00 90.76 63.53
ton ton.m ton.m
fsi real fsi real x Asi fsi (kg/cm2) (kg/cm2) (kg) -6547 -4372 -2197 -1361 -23 814 2989 5164
-6547 -4372 -2197 -1361 -23 814 2989 4200
-66778.1 -44595.3 -22412.4 -69402.5 -1147.5 8302.4 30485.2 42840.0 -122708.2
kg/cm2 kg/cm2
brazo = Xp d
Fx brazo
-35.00 -22.00 -9.00 -4.00 4.00 9.00 22.00 35.00
2337234.73 981095.686 201711.435 277610.12 -4590.0979 74721.3371 670675.446 1499400
Excluyendo φ P (tn) Drescripcion compresio pura Po 1513.11 Falla balanceada 428.04 Flexion pura 0.00 Traccion pura To -685.44
P (tn) 1210.49 1210.49
M (tn.m) 0.00 121.85 90.76 0.00
Incluyendo φ P (tn) Drescripcion compresio pura φPo 1059.18 299.63 Falla balanceada 0.00 Flexion pura -616.90 Traccion pura φTo
M (tn.m) 0 85.29 63.53 0
P (tn) 847.34 847.34
M (tn.m) 0 25
Pu 280
Mux 320
M (tn.m) 0 36 tanteo
φ
Nota: el valor asumido de b no es el adecuado es por ello que el punto (Mux, Pu) sale fuera del diagrama, para corregir esta falla debemos aumentar el valor de b. Sin embargo la columna en el otro eje obtendra una gran dimension y no seria el mas optimo.
DIAGRAMA DE INTERACCIÓN - COLUMNA SECCIÓN "T" 2000.00 1500.00
P (TN)
1000.00
tanteo
Nomi na l Di seño 0.8Po φ0.8Po Mu,Pu
500.00 0.00 0.00
50.00
100.00 150.00 200.00 250.00 300.00 350.00
-500.00 -1000.00
M (TN.m)
B
cm
80
20
160
30
20
4800.00 cm2 Ag 3.4% ρ 163.20 cm2 Ast 32.00 φ1" φ1" colocado 32.00 Ast colocado 163.20 cm2
30
Pu Mu x Mu y
280 320 20
Tn Tn.m Tn.m
f´c fy
210 4200
kg/cm2 kg/cm2
Compresion Pura φ 0.7 Po=0.85 x f´c x (Ag - Ast) + Ast x fy 1513.11 ton Po 1210.49 ton 0.8 x Po 1059.18 ton φPo 847.34 ton 0.8 x φ Po
Corte horizontal del diagr
Corte horizontal del diagr
Traccion pura φ 0.9 To = - fy x Ast 685.44 ton To 616.90 ton φTo
5 cm
recubrimiento
N°
N° Acero en la capa
1 2 3 4 5 6 7 8 9 10 11 12 Concreto 1 Concreto 2
N°
30.6 30.6 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 1600 3200
F 123057.9 123057.9 41019.3 41019.3 41019.3 41019.3 41019.3 41019.3 41019.3 41019.3 41019.3 41019.3 285600 571200 1513108.8
espaciamiento
5.00 10.00 10.00 16.67 16.67 16.67 16.67 16.67 16.67 16.67 16.67 16.67
yp
111.6266
cm
N° Acero en la capa
F
espaciamiento
1 2 3 4 5 6 7 8 Concreto 1 Concreto 2
10.2 10.2 10.2 51 51 10.2 10.2 10.2 1600 3200
yp
41019.3 41019.3 41019.3 205096.5 205096.5 41019.3 41019.3 41019.3 285600 571200 1513108.8 40 cm
5 13 13 5 8 5 13 13
orte horizontal del diagrama nominal
orte horizontal del diagrama de diseño
d 175.00 165.00 155.00 138.33 121.67 105.00 88.33 71.67 55.00 38.33 21.67 5.00 170.00 80
F*d 21535132.5 20304553.5 6357991.5 5674336.5 4990681.5 4307026.5 3623371.5 2939716.5 2256061.5 1572406.5 888751.5 205096.5 48552000 45696000 168903126
medidos desde el borde inferior d
F*d
75 62 49 44 36 31 18 5 40 40
3076447.5 2543196.6 2009945.7 9024246 7383474 1271598.3 738347.4 205096.5 11424000 22848000 60524352
medidos desde el borde inferior
Falla balanceada -1 0.0021 0.7 175 0.003 102.94 0.85 87.5 yp 111.626557 cm
α εs1 φ d1 εc c β a
Capa
Asi (cm2)
di (cm)
εsi
1 2 3 4 5 6 7 8 9 10 11 12
30.6 30.6 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2
175.00 165.00 155.00 138.33 121.67 105.00 88.33 71.67 55.00 38.33 21.67 5.00
-0.0021 -0.0018 -0.0015 -0.0010 -0.0005 -0.0001 0.0004 0.0009 0.0014 0.0019 0.0024 0.0029
CC brazo
526575.00 67.88
Pn φPn Mn φMn
402.89 282.02 298.57 209.00
kg cm ton ton ton.m ton.m
fsi real fsi real x Asi fsi (kg/cm2) (kg/cm2) (kg) -4200 -3617 -3034 -2063 -1091 -120 851 1823 2794 3766 4737 5709
-4200 -3617 -3034 -2063 -1091 -120 851 1823 2794 3766 4200 4200
-128520.0 -110684.6 -30949.7 -21041.1 -11132.6 -1224.0 8684.6 18593.1 28501.7 38410.3 42840.0 42840.0 -123682.3
brazo = Yp d
Fx brazo
-63.37 -53.37 -43.37 -26.71 -10.04 6.63 23.29 39.96 56.63 73.29 89.96 106.63
8144754.87 5907616.64 1342395.66 561941.092 111772.236 -8110.906 202291.666 742979.953 1613953.95 2815213.67 3853881.71 4567881.71
Falla balanceada -1.74986 0.0021 0.7 175 0.003 78.66 0.85 66.8568772917 yp 111.626557 cm
α εs1 φ d1 εc c β a
Capa
Asi (cm2)
di (cm)
εsi
1 2 3 4 5 6 7 8 9 10 11 12
30.6 30.6 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2
175.00 165.00 155.00 138.33 121.67 105.00 88.33 71.67 55.00 38.33 21.67 5.00
-0.0037 -0.0033 -0.0029 -0.0023 -0.0016 -0.0010 -0.0004 0.0003 0.0009 0.0015 0.0022 0.0028
CC brazo
452879.05 78.20
Pn φPn Mn φMn
0.00 0.00 408.32 285.82
kg cm ton ton ton.m ton.m
fsi real fsi real x Asi fsi (kg/cm2) (kg/cm2) (kg) -7349 -6587 -5824 -4552 -3281 -2010 -738 533 1804 3076 4347 5619
-7349 -6587 -5824 -4552 -3281 -2010 -738 533 1804 3076 4200 4200
-224892.0 -201549.6 -59402.4 -46434.4 -33466.4 -20498.4 -7530.4 5437.6 18405.6 31373.6 42840.0 42840.0 -452876.8
brazo = Yp d
Fx brazo
-63.37 -53.37 -43.37 -26.71 -10.04 6.63 23.29 39.96 56.63 73.29 89.96 106.63
14252180.8 10757396.4 2576486.69 1240113.18 336006.336 -135833.83 -175407.32 217285.861 1042245.72 2299472.25 3853881.71 4567881.71
Excluyendo φ P (tn) Drescripcion compresio pura Po 1513.11 Falla balanceada 402.89 Flexion pura 0.00 Traccion pura To -685.44
P (tn) 1210.49 1210.49
M (tn.m) 0.00 298.57 408.32 0.00
Incluyendo φ Drescripcion P (tn) 1059.18 compresio pura φPo 282.02 Falla balanceada 0.00 Flexion pura -616.90 Traccion pura φTo
M (tn.m) 0 79 tanteo
M (tn.m) 0 209.00 285.82 0
P (tn) 847.34 847.34
M (tn.m) 0 57
Pu 280
Muy 20
φ
DIAGRAMA DE INTERACCIÓN-COLUMNA SECCIÓN "T" 2000.00 1500.00
P (TN)
1000.00
tanteo
Nomi na l Di seño 0.8Po φ0.8po Mu,Pu
500.00 0.00 0.00
100.00
200.00
-500.00 -1000.00
M (TN.m)
300.00
400.00
500.00
α εs1 φ d1 εc c β a
-1 0.0021 0.7 75 0.003 44.12 0.85 37.5
f´c fy Base
yp
210 4200 20 30 180
40 cm
Capa
Asi (cm2)
di (cm)
εsi
1 2 3 4 5 6 7 8
10.2 10.2 10.2 51 51 10.2 10.2 10.2
75.00 62.00 49.00 44.00 36.00 31.00 18.00 5.00
-0.0021 -0.0012 -0.0003 0.0000 0.0006 0.0009 0.0018 0.0027
CC brazo
348075.00 21.25
Pn φPn Mn φMn
428.04 299.63 121.85 85.29
kg cm ton ton ton.m ton.m
fsi real fsi real x Asi fsi (kg/cm2) (kg/cm2) (kg) -4200 -2432 -664 16 1104 1784 3552 5320
-4200 -2432 -664 16 1104 1784 3552 4200
-42840.0 -24806.4 -6772.8 816.0 56304.0 18196.8 36230.4 42840.0 79968.0
kg/cm2 kg/cm2
brazo = Xp d -35.00 -22.00 -9.00 -4.00 4.00 9.00 22.00 35.00
Fx brazo 1499400 545740.8 60955.2 -3264 225216 163771.2 797068.8 1499400
α εs1 φ d1 εc c β a
-1.55878 0.0021 0.7 75 0.003 35.87 0.85 30.4856762751
f´c fy Base
yp
210 4200 20 30 180
40 cm
Capa
Asi (cm2)
di (cm)
εsi
1 2 3 4 5 6 7 8
10.2 10.2 10.2 51 51 10.2 10.2 10.2
75.00 62.00 49.00 44.00 36.00 31.00 18.00 5.00
-0.0033 -0.0022 -0.0011 -0.0007 0.0000 0.0004 0.0015 0.0026
CC brazo
122704.78 24.76
kg cm
Pn φPn Mn φMn
0.00 0.00 90.76 63.53
ton ton.m ton.m
fsi real fsi real x Asi fsi (kg/cm2) (kg/cm2) (kg) -6547 -4372 -2197 -1361 -23 814 2989 5164
-6547 -4372 -2197 -1361 -23 814 2989 4200
-66778.1 -44595.3 -22412.4 -69402.5 -1147.5 8302.4 30485.2 42840.0 -122708.2
kg/cm2 kg/cm2
brazo = Xp d
Fx brazo
-35.00 -22.00 -9.00 -4.00 4.00 9.00 22.00 35.00
2337234.73 981095.686 201711.435 277610.12 -4590.0979 74721.3371 670675.446 1499400
Excluyendo φ P (tn) Drescripcion compresio pura Po 1513.11 Falla balanceada 428.04 Flexion pura 0.00 Traccion pura To -685.44
P (tn) 1210.49 1210.49
M (tn.m) 0.00 121.85 90.76 0.00
Incluyendo φ P (tn) Drescripcion compresio pura φPo 1059.18 299.63 Falla balanceada 0.00 Flexion pura -616.90 Traccion pura φTo
M (tn.m) 0 85.29 63.53 0
P (tn) 847.34 847.34
M (tn.m) 0 25
Pu 280
Mux 320
M (tn.m) 0 36 tanteo
φ
Nota: el valor asumido de b no es el adecuado es por ello que el punto (Mux, Pu) sale fuera del diagrama, para corregir esta falla debemos aumentar el valor de b. Sin embargo la columna en el otro eje obtendra una gran dimension y no seria el mas optimo.
DIAGRAMA DE INTERACCIÓN - COLUMNA SECCIÓN "T" 2000.00 1500.00
P (TN)
1000.00
tanteo
Nomi na l Di seño 0.8Po φ0.8Po Mu,Pu
500.00 0.00 0.00
50.00
100.00 150.00 200.00 250.00 300.00 350.00
-500.00 -1000.00
M (TN.m)
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