diseÑo de columnas 2013

53
CALCULO DE PESOS QUE RESISTEN LAS COLUMNAS C-1 at : 14.88 Peso Propio : 2400 Kg/m3 0.30 0.4 Carga de losa : 350 Kg/m2 2.8 4.35 tabiqueria : 120 Kg/m2 14.88 acabados : 150 Kg/m2 14.88 viga principal 2400 Kg/m3 0.4 0.75 viga secundaria : 2400 Kg/m3 0.3 0.6 sobrecarga : 600 14.88 Pu = 1.4xPD + 1.7xPL Pu = 34058.28 Kg Pu = 34.06 Tn C-2 at : 29.04 Peso Propio : 2400 Kg/m3 0.30 0.4 Carga de losa : 350 Kg/m2 8.78 2.8 tabiqueria : 120 Kg/m2 29.04 acabados : 150 Kg/m2 29.04 viga principal 2400 Kg/m3 0.4 0.75 viga secundaria : 2400 Kg/m3 0.3 0.6 sobrecarga : 600 29.04 Pu = 1.4xPD + 1.7xPL Pu = 64397.36 Kg Pu = 64.40 Tn

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Page 1: DISEÑO DE COLUMNAS 2013

CALCULO DE PESOS QUE RESISTEN LAS COLUMNAS

C-1 at : 14.88

Peso Propio : 2400 Kg/m3 0.30 0.4 3Carga de losa : 350 Kg/m2 2.8 4.35tabiqueria : 120 Kg/m2 14.88acabados : 150 Kg/m2 14.88viga principal 2400 Kg/m3 0.4 0.75 4.35viga secundaria : 2400 Kg/m3 0.3 0.6 2.8

PD =

sobrecarga : 600 14.88PL =

Pu = 1.4xPD + 1.7xPL

Pu = 34058.28 KgPu = 34.06 Tn

C-2 at : 29.04

Peso Propio : 2400 Kg/m3 0.30 0.4 3Carga de losa : 350 Kg/m2 8.78 2.8tabiqueria : 120 Kg/m2 29.04acabados : 150 Kg/m2 29.04viga principal 2400 Kg/m3 0.4 0.75 8.78viga secundaria : 2400 Kg/m3 0.3 0.6 2.8

PD=

sobrecarga : 600 29.04PL=

Pu = 1.4xPD + 1.7xPL

Pu = 64397.36 KgPu = 64.40 Tn

C-3 at : 27.90

Peso Propio : 2400 Kg/m3 0.30 0.4 3

Page 2: DISEÑO DE COLUMNAS 2013

Carga de losa : 350 Kg/m2 4.35 5.6tabiqueria : 120 Kg/m2 27.9acabados : 150 Kg/m2 27.9viga principal 2400 Kg/m3 0.4 0.75 4.35viga secundaria : 2400 Kg/m3 0.3 0.6 5.6

PD=

sobrecarga : 600 27.9PL=

Pu = 1.4xPD + 1.7xPL

Pu = 59921.88 KgPu = 59.92 Tn

C-4 at : 54.00

Peso Propio : 2400 Kg/m3 0.30 0.4 3Carga de losa : 350 Kg/m2 8.7 5.6tabiqueria : 120 Kg/m2 54acabados : 100 Kg/m2 54viga principal 2400 Kg/m3 0.4 0.75 8.7viga secundaria : 2400 Kg/m3 0.3 0.6 5.6

PD=

sobrecarga : 600 54PL=

Pu = 1.4xPD + 1.7xPL

Pu = 108950.88 KgPu = 108.95 Tn

Sabiendo que en cada

P = At*Ptotal/Atotal

At portico VP1 = 6 27.3 163.8At portico VP2 = 3.2 27.3 87.36At portico VS central= 9 12.4 111.6At portico VS lateral= 4.65 12.4 57.66

Page 3: DISEÑO DE COLUMNAS 2013

Ptotal = 478901.2Atotal = 12,4x27,3 338.52

Calculo de PAt Ptotal Atotal P

Portico VP1 163.8 478901.2 338.52 231726.4Portico VP2 87.36 478901.2 338.52 123587.4Portico VS1 111.6 478901.2 338.52 157879.5Portico VS2 57.66 478901.2 338.52 81571.08

COMBINACION DE CARGASVP1 VS2 VP2 VS1 VP1C1 C1 C2 C2 C3

1 1,4WD + 1,7 WL 34058.28 34058.28 64397.36 64397.36 59921.882 1,25(Wd +Wl) +P 259744.137 109588.83 176417.91 210710 280744.13713 1,25(Wd +Wl) -P -203708.64 -53553.33 176417.91 134401.6 -182708.6374 0,9Wd + P 243863.967 93708.664 145943.77 52830.5 476695.16715 0,9Wd - P -219588.81 -69433.5 -101231 52830.5 13242.3929

Page 4: DISEÑO DE COLUMNAS 2013

41.2520.2517.60

864 Kg 8.644263 Kg

1785.6 Kg2232 Kg3132 Kg

1209.6 Kg13486.2 Kg

8928 Kg8928 Kg

864 Kg8604.4 Kg3484.8 Kg

4356 Kg6321.6 Kg1209.6 Kg

24840.4 Kg

17424 Kg17424 Kg

864 Kg

Page 5: DISEÑO DE COLUMNAS 2013

8526 Kg3348 Kg4185 Kg3132 Kg

2419.2 Kg22474.2 Kg

16740 Kg16740 Kg

864 Kg17052 Kg

6480 Kg5400 Kg6264 Kg

2419.2 Kg38479.2 Kg

32400 Kg32400 Kg

Page 6: DISEÑO DE COLUMNAS 2013

C3, C4C1, C2C2, C4C1, C3

VS2 VP1 VS1C3 C4 C4

59921.88 108950.88 108950.88130588.834 320325.3871 246478.516-32553.334 -143127.3871 -69280.516326539.864 266357.6671 192510.796163397.696 -197095.1071 -123248.24

Page 7: DISEÑO DE COLUMNAS 2013

b = 30 cmh = 40 cmr = 4 cmnºc = 1f'c = 210 Kg/cm2fy = 4200 Kg/cm2

Calculo de Cuantia

0.6Kn = Pn/f'c.Ag = 0.08 ABACORn = Mn/f'c.Ag.h = 0.34 se acerca al 2.5%

As= 0.025x30x40 = 60Ø 1 5.07 12 60.8

Datos

DIAMETRO (puAREA (cm2) 24.73 1/4 0.32 24.73 3/8 0.71 5.27 1/2 1.27 30 cm 5/8 1.98 3/4 2.85 As = 30.40 cm2 30.40 cm2 12 Ø1'' 7/8 3.881 5.07

1 1/4 7.921 1/2 11.401 3/4 15.52

40 c

m

ϒ = yh/h =

Page 8: DISEÑO DE COLUMNAS 2013

c=14.55 cm

0.0021Punto 2

0.003

c=5.27 cm 0.0021Punto 3

0.003

c=24.73 cm 0.0021

Punto 4

0.003

Page 9: DISEÑO DE COLUMNAS 2013

CURVA - Pn Y Mn CURVA - Pn Y MnPu (Tn) Mu (Tn-m) Pn (Tn) Mn (Tn-m)

P5 -255.38 0.00 -340.51 0.00 C-2P3 -95.71 0.21 -127.61 0.28 C-4P2 76.93 30.53 102.57 40.70

C2 P4 293.63 27.15 391.50 36.20C3 P1 458.73 0.00 611.64 0.00C4

Punto 1 Pn Maximo

Pn =

Page 10: DISEÑO DE COLUMNAS 2013

Pn = 458726.8953 Kg

Pn = 458.73 Tn

Punto 5 Falla por traccion

Pn =

Pn = 255380.57 Kg

Pn = -255.38 Tn

Punto 2 Falla balanceada

c = 14.55 cm

x Es 2.00E+06 fy As C o T 5.27 0.0019 2.00E+06 3826.36 30.40 116330.86 C1

24.73 -0.0021 2.00E+06 -4200.00 0.00 0.00 C224.73 -0.0021 2.00E+06 -4200.00 30.40 -127690.28 T1

Para el Concreto :

Cc 0.85xCxhx0.85f'c 88286.1

Por lo tanto :

Pn = 116330.857865944 + 0 + -127690.284732569 + 8828 76926.67 Kg

Mn = C1*(30/2-5.27)+C2*(30/2-24.73)+T1*(30/2-24.73)+Cc *(-1 3052626.6578 Kg-m

Pn = 76.93 TnMn = 30.53 Tn-m

Punto 3

c = 5.27 cm

x Es 2.00E+06 fy As C o T 5.27 0.0000 2.00E+06 0.00 30.40 0 C1

24.73 -0.0021 2.00E+06 -4200.00 0.00 0 C224.73 -0.0021 2.00E+06 -4200.00 30.40 -127690.28473 C3

Para el Concreto :

Page 11: DISEÑO DE COLUMNAS 2013

Cc 0.85xCxhx0.85f'c 31983.63

Por lo tanto :

Pn = 0 + 0 + -127690.284732569 + 31983.63 = -95706.654733 Kg

Mn = C1*(30/2-5.27)+C2*(30/2-24.73)+C3*(30/2-24.73)+Cc *(-5. 21185.629397 Kg-m

Pn = -95.71 TnMn = 0.21 Tn-m

Punto 4

c = 24.73 cm

x Es 2.00E+06 fy As C o T 5.27 0.0024 2.00E+06 4721.39 30.40 143541.84859 C1

24.73 0.0000 2.00E+06 0.00 0.00 0 C224.73 0.0000 2.00E+06 0.00 30.40 0 C3

Para el Concreto :

Cc 0.85xCxhx0.85f'c 150086.37

Por lo tanto :

Pn = 143541.848587361 + 0 + 0 + 150086.37 = 293628.21859 Kg

Mn = C1*(30/2-5.27)+C2*(30/2-24.73)+C3*(30/2-24.73)+Cc *(-24 2714979.4812 Kg-m

Pn = 293.63 TnMn = 27.15 Tn-m

Punto 5

c = 24.73 cm

x Es 2.00E+06 fy As C o T 5.27 0.0024 2.00E+06 4721.39 30.40 143541.84859 T1

24.73 0.0000 2.00E+06 0.00 0.00 0 T224.73 0.0000 2.00E+06 0.00 30.40 0 T3

Para el Concreto :

Page 12: DISEÑO DE COLUMNAS 2013

Cc 0.85xCxhx0.85f'c 150086.37

Por lo tanto :

Pn = 143541.848587361 + 0 + 0 + 150086.37 = 293628.21859 Kg

Mn = T1*(30/2-5.27)+T2*(30/2-24.73)+T3*(30/2-24.73)+Cc *(-24 2714979.4812 Kg-m

Pn = 293.63 TnMn = 2714.98 Tn-m

Punto 6

c = 3.85 cm

x Es 2.00E+06 fy As C o T 5.27 -0.0011 2.00E+06 -2219.27 30.40 -67471.122492 C1

24.73 -0.0021 2.00E+06 -4200.00 0.00 0 T124.73 -0.0021 2.00E+06 -4200.00 30.40 -127690.28473 T2

Para el Concreto :

Cc 0.85xCxhx0.85f'c 23347.8

Por lo tanto :

Pn = -67471.1224919365 + 0 + -127690.284732569 + 233-171813.60722 Kg

Mn = C1*(30/2-5.27)+T1*(30/2-24.73)+T2*(30/2-24.73)+Cc *(-3 -1710356.412 Kg-m

Pn = -171.81 TnMn = -1710.36 Tn-m

Page 13: DISEÑO DE COLUMNAS 2013

PUNTOSMu (Tn-m) Pu (Tn)

16.57 12.899.25 7.29

0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00

-400.00

-200.00

0.00

200.00

400.00

600.00

800.00

1; -340.51

2; -127.61

3; 102.57

391.50

611.64

P5: 0.00, -255.38

P3: 21.19, -95.71

P2: 3052.63, 76.93

P4: 2714.98, 293.63

P1: 0.00, 458.73

C-2: 16.57, 12.89

C-4: 9.25, 7.29

DIAGRAMA DE INTERACCION

PuntosMu y PuMn y Pn

MOMENTOS (Tn-m)

P (T

n)

Page 14: DISEÑO DE COLUMNAS 2013

0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00

-400.00

-200.00

0.00

200.00

400.00

600.00

800.00

1; -340.51

2; -127.61

3; 102.57

391.50

611.64

P5: 0.00, -255.38

P3: 21.19, -95.71

P2: 3052.63, 76.93

P4: 2714.98, 293.63

P1: 0.00, 458.73

C-2: 16.57, 12.89

C-4: 9.25, 7.29

DIAGRAMA DE INTERACCION

PuntosMu y PuMn y Pn

MOMENTOS (Tn-m)

P (T

n)

Page 15: DISEÑO DE COLUMNAS 2013

0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00

-400.00

-200.00

0.00

200.00

400.00

600.00

800.00

1; -340.51

2; -127.61

3; 102.57

391.50

611.64

P5: 0.00, -255.38

P3: 21.19, -95.71

P2: 3052.63, 76.93

P4: 2714.98, 293.63

P1: 0.00, 458.73

C-2: 16.57, 12.89

C-4: 9.25, 7.29

DIAGRAMA DE INTERACCION

PuntosMu y PuMn y Pn

MOMENTOS (Tn-m)

P (T

n)

Page 16: DISEÑO DE COLUMNAS 2013

I 0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00

-400.00

-200.00

0.00

200.00

400.00

600.00

800.00

1; -340.51

2; -127.61

3; 102.57

391.50

611.64

P5: 0.00, -255.38

P3: 21.19, -95.71

P2: 3052.63, 76.93

P4: 2714.98, 293.63

P1: 0.00, 458.73

C-2: 16.57, 12.89

C-4: 9.25, 7.29

DIAGRAMA DE INTERACCION

PuntosMu y PuMn y Pn

MOMENTOS (Tn-m)

P (T

n)

Page 17: DISEÑO DE COLUMNAS 2013

Datosb = 30 cmh = 40 cmr = 4 cmnºc = 2f'c = 210 Kg/cm2fy = 4200 Kg/cm2

DIAMETRO (puAREA (cm2) 24.73 1/4 0.32 15.00 3/8 0.71 5.27 1/2 1.27 30 cm 5/8 1.98 3/4 2.85 As = 15.20 15.20 cm2 7/8 3.881 5.07

1 1/4 7.921 1/2 11.401 3/4 15.52 40 cm

c=15.29 cm

0.0021Punto 2

0.003

c=5.27 cm 0.0021Punto 3

0.003

c=15.00 cm 0.0021

Punto 4

Page 18: DISEÑO DE COLUMNAS 2013

0.003

c=24.73 cm 0.0021

Punto 5

0.003

c=8.82 cm 0.0021

Punto 6

0.003

Page 19: DISEÑO DE COLUMNAS 2013

Pu (Tn) Mu (Tn-m) Pn (Tn)

-127.69 0.00 -170.25-31.86 214.65 -42.4826.44 1276.04 35.25

C2 91.04 1936.49 121.38C3 96.33 1947.96 128.44C4 221.86 1694.41 295.81

336.46 0.00 448.62

Punto 1 Pn Maximo

Pn =

Pn = 336463.4476 Kg

Pn = 336.46 Tn

Punto 7 Falla por traccion

Pn =

Pn = 127690.28 Kg

Pn = -127.69 Tn

Punto 2 Falla balanceada

c = 15.29 cm

x Es 2.00E+06 fy As C o T5.27 0.0020 2.00E+06 3932.54 15.20 59779.40

15.00 0.0001 2.00E+06 115.38 0.00 0.0024.73 -0.0019 2.00E+06 -3701.77 15.20 -56271.42

Page 20: DISEÑO DE COLUMNAS 2013

Para el Concreto :

Cc 0.85xCxhx0.85f'c 92820

Por lo tanto :

Pn = 59779,3995090032 + 0 + -56271,4246537128 + 92820 = 96327.97486

Mn = C1*(30/2-5,27)+C2*(30/2-15)+T1*(30/2-24,73)+Cc *(-15,294117647 1947962.305

Pn = 96.33Mn = 1947.96

Punto 3

c = 5.27 cm

x Es 2.00E+06 fy As C o T5.27 0.0000 2.00E+06 0.00 15.20 0

15.00 -0.0021 2.00E+06 -4200.00 0.00 024.73 -0.0021 2.00E+06 -4200.00 15.20 -63845.1424

Para el Concreto :

Cc 0.85xCxhx0.85f'c 31983.63

Por lo tanto :

Pn = 0 + 0 + -63845,1423662847 + 31983,63 = -31861.5124

Mn = C1*(30/2-5,27)+C2*(30/2-15)+C3*(30/2-24,73)+Cc *(-5,27*0.85/2+30214652.3721

Pn = -31.86Mn = 214.65

Punto 4

c = 15.00 cm

x Es 2.00E+06 fy As C o T5.27 0.0019 2.00E+06 3892.00 15.20 59163.16526

15.00 0.0000 2.00E+06 0.00 0.00 024.73 -0.0019 2.00E+06 -3892.00 15.20 -59163.1653

Page 21: DISEÑO DE COLUMNAS 2013

Para el Concreto :

Cc 0.85xCxhx0.85f'c 91035

Por lo tanto :

Pn = 59163,1652594238 + 0 + -59163,1652594238 + 91035 = 91035

Mn = C1*(30/2-5,27)+C2*(30/2-15)+C3*(30/2-24,73)+Cc *(-15*0.85/2+30/1936492.071

Pn = 91.04Mn = 1936.49

Punto 5

c = 24.73 cm

x Es 2.00E+06 fy As C o T5.27 0.0024 2.00E+06 4721.39 15.20 71770.92429

15.00 0.0012 2.00E+06 2360.70 0.00 024.73 0.0000 2.00E+06 0.00 15.20 0

Para el Concreto :

Cc 0.85xCxhx0.85f'c 150086.37

Por lo tanto :

Pn = 71770,9242936803 + 0 + 0 + 150086,37 = 221857.2943

Mn = T1*(30/2-5,27)+T2*(30/2-15)+T3*(30/2-24,73)+Cc *(-24,73*0.85/2+3 1694414.88

Pn = 221.86Mn = 1694.41

Punto 6

c = 8.82 cm

x Es 2.00E+06 fy As C o T5.27 0.0012 2.00E+06 2416.40 15.20 36732.23857

15.00 -0.0021 2.00E+06 -4200.00 0.00 024.73 -0.0021 2.00E+06 -4200.00 15.20 -63845.1424

Para el Concreto :

Page 22: DISEÑO DE COLUMNAS 2013

Cc 0.85xCxhx0.85f'c 53550

Por lo tanto :

Pn = 36732,2385747358 + 0 + -63845,1423662847 + 53550 = 26437.09621

Mn = C1*(30/2-5,27)+T1*(30/2-15)+T2*(30/2-24,73)+Cc *(-8,8235294117 1276035.249

Pn = 26.44Mn = 1276.04

Page 23: DISEÑO DE COLUMNAS 2013

Mn (Tn-m) Mu (Tn-m) Pu (Tn)

0.00 C-3 165.71 59.92286.20 C-4 9.25 108.95

1701.38 C-4 9.25 108.952581.99 C-3 165.71 59.922597.282259.22 C-1 9.296 34.06

0.00 C-2 5.053 64.40C-2 5.053 64.40C-1 9.296 34.06

C1C2T1

0.00 500.00 1000.00 1500.00 2000.00 2500.00 3000.00

-300.00

-200.00

-100.00

0.00

100.00

200.00

300.00

400.00

500.00

7; 448.62

7; 336.46

DIAGRAMA DE INTERACCION

Column NMn y PnPUNTOS

MOMENTOS

P

Page 24: DISEÑO DE COLUMNAS 2013

Kg

Kg-m

TnTn-m

C1C2C3

Kg

Kg-m

TnTn-m

C1C2C3

Page 25: DISEÑO DE COLUMNAS 2013

Kg

Kg-m

TnTn-m

T1T2T3

Kg

Kg-m

TnTn-m

C1T1T2

Page 26: DISEÑO DE COLUMNAS 2013

Kg

Kg-m

TnTn-m

Page 27: DISEÑO DE COLUMNAS 2013

I 0.00 500.00 1000.00 1500.00 2000.00 2500.00 3000.00

-300.00

-200.00

-100.00

0.00

100.00

200.00

300.00

400.00

500.00

7; 448.62

7; 336.46

DIAGRAMA DE INTERACCION

Column NMn y PnPUNTOS

MOMENTOS

P

Page 28: DISEÑO DE COLUMNAS 2013

Datosb = 40 cmh = 30 cmr = 4 cmnºc = 2f'c = 210 Kg/cm2fy = 4200 Kg/cm2

DIAMETRO (puAREA (cm2) 34.73 1/4 0.32 20.00 3/8 0.71 5.27 1/2 1.27 40 cm 5/8 1.98 3/4 2.85 As = 10.13 10.13 10.13 cm2 7/8 3.881 5.07

1 1/4 7.921 1/2 11.401 3/4 15.52 30 cm

c=21.18 cm

0.0021Punto 2

0.003

c=5.27 cm 0.0021Punto 3

0.003

c=20.00 cm 0.0021

Punto 4

Page 29: DISEÑO DE COLUMNAS 2013

0.003

c=34.73 cm 0.0021

Punto 5

0.003

c=11.76 cm 0.0021

Punto 6

0.003

Page 30: DISEÑO DE COLUMNAS 2013

CURVA - Pn Y Mn CURVA - Pn Y MnPu (Tn) Mu (Tn-m) Pn (Tn) Mn (Tn-m)

-61.14 -458.89 -81.52 -611.85-127.69 0.00 -170.25 0.00

1.99 1151.26 2.65 1535.02C2 93.25 2359.04 124.34 3145.38C3 106.52 2417.77 142.03 3223.70C4 235.45 1993.44 313.93 2657.93

336.46 0.00 448.62 0.00

Punto 1 Pn Maximo

Pn =

Pn = 336463.4476 Kg

Pn = 336.46 Tn

Punto 7 Falla por traccion

Pn =

Pn = 127690.28 Kg

Pn = -127.69 Tn

Punto 2 Falla balanceada

c = 21.18 cm

x Es 2.00E+06 fy As C o T 5.27 0.0023 2.00E+06 4506.83 10.13 45672.92 C1

20.00 0.0002 2.00E+06 333.33 10.13 3378.05 C234.73 -0.0019 2.00E+06 -3840.17 10.13 -38916.82 T1

Page 31: DISEÑO DE COLUMNAS 2013

Para el Concreto :

Cc 0.85xCxhx0.85f'c 96390

Por lo tanto :

Pn = 45672,9231409181 + 3378,04986064999 + -38916,8234196 106524.1496 Kg

Mn = C1*(40/2-5,27)+C2*(40/2-20)+T1*(40/2-34,73)+Cc *(-21,176470588 2417772.612 Kg-m

Pn = 106.52 TnMn = 2417.77 Tn-m

Punto 3

c = 5.27 cm

x Es 2.00E+06 fy As C o T 5.27 0.0000 2.00E+06 0.00 10.13 0 C1

20.00 -0.0021 2.00E+06 -4200.00 10.13 -42563.4282 C234.73 -0.0021 2.00E+06 -4200.00 10.13 -42563.4282 C3

Para el Concreto :

Cc 0.85xCxhx0.85f'c 23987.7225

Por lo tanto :

Pn = 0 + -42563,4282441898 + -42563,4282441898 + 23987,7225 -61139.134 Kg

Mn = C1*(40/2-5,27)+C2*(40/2-20)+C3*(40/2-34,73)+Cc *(-5,27*0.85/2+40-458887.006 Kg-m

Pn = -61.14 TnMn = -458.89 Tn-m

Punto 4

c = 20.00 cm

x Es 2.00E+06 fy As C o T 5.27 0.0022 2.00E+06 4419.00 10.13 44782.807 C1

20.00 0.0000 2.00E+06 0.00 10.13 0 C234.73 -0.0021 2.00E+06 -4200.00 10.13 -42563.4282 C3

Page 32: DISEÑO DE COLUMNAS 2013

Para el Concreto :

Cc 0.85xCxhx0.85f'c 91035

Por lo tanto :

Pn = 44782,8070026368 + 0 + -42563,4282441898 + 91035 = 93254.37876 Kg

Mn = C1*(40/2-5,27)+C2*(40/2-20)+C3*(40/2-34,73)+Cc *(-20*0.85/2+40/2359035.401 Kg-m

Pn = 93.25 TnMn = 2359.04 Tn-m

Punto 5

c = 34.73 cm

x Es 2.00E+06 fy As C o T 5.27 0.0025 2.00E+06 5089.55 10.13 51578.24014 T1

20.00 0.0013 2.00E+06 2544.77 10.13 25789.12007 T234.73 0.0000 2.00E+06 0.00 10.13 0 T3

Para el Concreto :

Cc 0.85xCxhx0.85f'c 158082.2775

Por lo tanto :

Pn = 51578,240141246 + 25789,120070623 + 0 + 158082,2775 = 235449.6377 Kg

Mn = T1*(40/2-5,27)+T2*(40/2-20)+T3*(40/2-34,73)+Cc *(-34,73*0.85/2+41993444.716 Kg-m

Pn = 235.45 TnMn = 1993.44 Tn-m

Punto 6

c = 11.76 cm

x Es 2.00E+06 fy As C o T 5.27 0.0017 2.00E+06 3312.30 10.13 33567.34366 C1

20.00 -0.0021 2.00E+06 -4200.00 10.13 -42563.4282 T134.73 -0.0021 2.00E+06 -4200.00 10.13 -42563.4282 T2

Para el Concreto :

Page 33: DISEÑO DE COLUMNAS 2013

Cc 0.85xCxhx0.85f'c 53550

Por lo tanto :

Pn = 33567,3436602928 + -42563,4282441898 + -42563,42824411990.487172 Kg

Mn = C1*(40/2-5,27)+T1*(40/2-20)+T2*(40/2-34,73)+Cc *(-11,764705882 1151263.578 Kg-m

Pn = 1.99 TnMn = 1151.26 Tn-m

Page 34: DISEÑO DE COLUMNAS 2013

PUNTOSMu (Tn-m) Pu (Tn)

C-1 853.89 34.06C-3 252.44 59.92C-1 853.89 34.06

-1000.00 -500.00 0.00 500.00 1000.00 1500.00 2000.00 2500.00 3000.00 3500.00

-300.00

-200.00

-100.00

0.00

100.00

200.00

300.00

400.00

500.00

7; 448.62

7; 336.46

DIAGRAMA DE INTERACCION

Mu y PuMn y PnPUNTOS

MOMENTOS

P

Page 35: DISEÑO DE COLUMNAS 2013

I -1000.00 -500.00 0.00 500.00 1000.00 1500.00 2000.00 2500.00 3000.00 3500.00

-300.00

-200.00

-100.00

0.00

100.00

200.00

300.00

400.00

500.00

7; 448.62

7; 336.46

DIAGRAMA DE INTERACCION

Mu y PuMn y PnPUNTOS

MOMENTOS

P

Page 36: DISEÑO DE COLUMNAS 2013

CALCULO DE PESOS QUE RESISTEN LAS COLUMNAS

C-1 at : 14.88

Peso Propio : 2400 Kg/m3 0.30 0.4 3Carga de losa : 350 Kg/m2 2.8 4.35tabiqueria : 120 Kg/m2 14.88acabados : 150 Kg/m2 14.88viga principal 2400 Kg/m3 0.4 0.75 4.35viga secundaria : 2400 Kg/m3 0.3 0.6 2.8

PD =

sobrecarga : 600 14.88PL =

Pu = 1.4xPD + 1.7xPL

Pu = 34058.28 KgPu = 34.06 Tn

C-2 at : 29.04

Peso Propio : 2400 Kg/m3 0.30 0.4 3Carga de losa : 350 Kg/m2 8.78 2.8tabiqueria : 120 Kg/m2 29.04acabados : 150 Kg/m2 29.04viga principal 2400 Kg/m3 0.4 0.75 8.78viga secundaria : 2400 Kg/m3 0.3 0.6 2.8

PD=

sobrecarga : 600 29.04PL=

Pu = 1.4xPD + 1.7xPL

Pu = 64397.36 KgPu = 64.40 Tn

Page 37: DISEÑO DE COLUMNAS 2013

41.2520.2517.60

864 Kg 8.644263 Kg

1785.6 Kg2232 Kg3132 Kg

1209.6 Kg13486.2 Kg

8928 Kg8928 Kg

864 Kg8604.4 Kg3484.8 Kg

4356 Kg6321.6 Kg1209.6 Kg

24840.4 Kg

17424 Kg17424 Kg

Page 38: DISEÑO DE COLUMNAS 2013

COMBINACION DE CARGAS

1.- 1,4WD + 1,7 WL2.- 1,25(Wd +Wl) +P3.- 1,25(Wd +Wl) -P4.- 0,9Wd + P5.- 0,9Wd - P

Para columnas 30 x 40

METRADO DE CARGAS

VIGA PRINCIPAL VP1

WD Carga Muerta

- Peso VP : 0.4 0.75 2400 Kg/m3 = 720 Kg/m- Losa : 6 0.4 350 Kg/m2 = 1960 Kg/m- Tabiqueria : 6 150 Kg/m2 = 900 Kg/m- Acabados : 6 120 Kg/m2 = 720 Kg/m

WL = 4300 Kg/mWL Carga Viva

- Sobre carga : 6 600 Kg/m2 = 3600 Kg/mWD = 3600 Kg/m

P Carga Lateral

- Peso propio : 4 3 0.4 0.3 2400 Kg/m3 = 3456 Kg- P viga CM : 4300.00 27.00 = 116100 Kg- P viga CV : 3600.00 27.00 = 97200 Kg

P = 216756 Kg

VIGA PRINCIPAL VP2

WD Carga Muerta

- Peso VP : 0.4 0.75 2400 Kg/m2 = 720 Kg/m- Losa : 3.2 0.4 350 Kg/m2 = 980 Kg/m- Tabiqueria : 3.2 150 Kg/m2 = 480 Kg/m- Acabados : 3.2 120 Kg/m2 = 384 Kg/m

WL = 2564 Kg/mWL Carga Viva

- Sobre carga : 3.2 600 Kg/m2 = 1920 Kg/m

Page 39: DISEÑO DE COLUMNAS 2013

WD = 1920 Kg/m

P Carga Lateral

- Peso propio : 4 3 0.4 0.3 2400 Kg/m3 = 3456 Kg- P viga CM : 2564.00 27.00 = 69228 Kg- P viga CV : 1920.00 27.00 = 51840 Kg

P = 124524 Kg

VIGA SECUNDARIA VS

WD Carga Muerta

- Peso VS : 0.3 0.6 2400 Kg/m2 = 432 Kg/m- Tabiqueria : 0.3 150 Kg/m2 = 45 Kg/m- Acabados : 0.3 120 Kg/m2 = 36 Kg/m

WL = 513 Kg/mWL Carga Viva

- Sobre carga : 0.3 600 Kg/m2 = 180 Kg/mWD = 180 Kg/m

P Carga Lateral

- Peso propio : 3 3 0.4 0.3 2400 Kg/m3 = 2592 Kg- P viga CM : 513.00 12.00 = 6156 Kg- P viga CV : 180.00 12.00 = 2160 Kg

P = 10908 Kg

Page 40: DISEÑO DE COLUMNAS 2013

C3 C4

Mu Pu Mu PuCM 5206.28 4043.69 1360.84 1082.21CV 5460.16 4250.52 4320.87 3399.25P 3845.80 2796.25 2730.25 2390.69

1.- 1,4WD + 1,7 WL 16571.06 12887.05 9250.65 7293.822.- 1,25(Wd +Wl) +P 17178.85 13164.01 9832.39 7992.513.- 1,25(Wd +Wl) -P 9487.25 7571.51 4371.89 3211.134.- 0,9Wd + P 8531.45 6435.57 3955.01 3364.685.- 0,9Wd - P 839.85 843.07 -1505.49 -1416.70

25493.94 19826.23

C1 C2

Mu Pu Mu PuCM 3104.40 2411.17 811.44 645.29CV 2912.09 2266.95 2304.46 1812.93P 2051.09 1491.33 1456.13 1242.50

1.- 1,4WD + 1,7 WL 9296.71 7229.45 5053.60 3985.392.- 1,25(Wd +Wl) +P 9571.70 7338.98 5351.01 4315.283.- 1,25(Wd +Wl) -P 5469.52 4356.32 2438.75 1830.284.- 0,9Wd + P 4845.05 3661.38 2186.43 1823.26

Page 41: DISEÑO DE COLUMNAS 2013

5.- 0,9Wd - P 742.87 678.72 -725.83 -661.74

C1 C3

Mu Pu Mu PuCM 408.42 284.13 0.00 0.00CV 165.94 106.46 148.49 113.22P 5816.82 3467.60 6391.76 4148.13

1.- 1,4WD + 1,7 WL 853.89 578.76 252.43 192.472.- 1,25(Wd +Wl) +P 6534.77 3955.84 6577.37 4289.663.- 1,25(Wd +Wl) -P -5098.87 -2979.36 -6206.15 -4006.614.- 0,9Wd + P 6184.40 3723.32 6391.76 4148.135.- 0,9Wd - P -5449.24 -3211.88 -6391.76 -4148.13