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calculo para vigas
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VIGA DE CINCO CLAROS
VIGA DE UN CLAROVIGA DE DOS CLAROSVIGA DE TRES CLAROS
VIGA DE CUATRO CLAROS
VIGA DE SEIS CLAROS
DA
TO
S D
E L
A V
IGA b = 25 cm VIGA DE SEIS CLAROS Y CARGA UNIFORMEMENTE DISTRIBUIDA
f'c= 250 kg/cm2 f*c= 200 kg/cm2 Carga distribuida f''c= 170 kg/cm2 fy= 4200 kg/cm2 longitudinal
VIGA V-6 Longitud
fy= 2530 kg/cm2 estribosp = 0.008 EIq = 0.198
Carga puntual
P - - - a-b 2.000 1.600 2.000 1.800 2.000 4.000 2.000 6.000
w 2250 3850 3000 2100
EI 1 1 1 1L 3.6 3.8 6 8
METODO DE CROSS PARA VIGAS
A B B C C D D EEI 1 1 1 1L 3.6 3.8 6 8K 0.2083333333 0.2631578947 0.1666666667 0.125
0 0.4714912281 0.4298245614 0.2916666667 0.325FD 0 0.4418604651 0.5581395349 0.612244898 0.387755102 0.5714285714 0.4285714286 0.3846153846
MEP 0 3645 - 4,632.83 4,632.83 - 9,000.00 9,000.00 - 11,200.00 11,200.00 1MDES 0 -987.83 -4367.17 -2200.00 7262.50
1DISTR. 0 436.48 551.35 2673.78 1693.39 1257.142857143 942.8571428571 -2793.269230771TRANS 0 0 1336.89 275.67 628.57 846.70 -1396.63 471.432MDES 0 1336.89 904.25 -549.94 745.62
∑ K
A B C D
2DISTR. 0 -590.72 -746.17 -553.62 -350.63 314.2508783733 235.68815878 -286.7777383912TRANS 0 0 -276.81 -373.08 157.13 -175.31 -143.39 117.843MDES 0 -276.81 -215.96 -318.70 694.52
3DISTR. 0 122.31 154.50 132.22 83.74 182.115336895 136.5865026712 -267.1226989833TRANS 0 0 66.11 77.25 91.06 41.87 -133.56 68.294MDES 0 66.11 168.31 -91.69 127.50
4DISTR. 0 -29.21 -36.90 -103.05 -65.26 52.3952271217 39.2964203413 -49.0380684504MF 0 3583.87 -3583.87 6762.00 -6762.00 11519.16 -11519.16 8461.36
DETERMINACION DE CORTANTES TOTALES
A B B C C D D EVISOST 4050.00 -4050.00 7315.00 -7315.00 9000.00 -9000.00 8400.00 -8400.00-∑M/L -995.52 -995.52 -836.35 -836.35 -792.86 -792.86 382.22 382.22
VTOTAL 3054.48 -5045.52 6478.65 -8151.35 8207.14 -9792.86 8782.22 -8017.78
A B C DREACCION 3054.48 11524.17 16358.49 18575.08
DIAGRAMA CORTANTE SIN CARGAS PUNTUALES
3054.48 6,478.648 8207.14 8782.22 5779.23
2.24 2.12 3.26 3.82
1.36 1.68 2.74 4.18
-5045.52 -8151.35 -9792.86 -8017.78
DIAGRAMA MOMENTOS FLEXIONANTES SIN CARGAS PUNTUALES
2073.301867.16 4464.19 6844.53
0
-3583.87 -6762.00 -11519.16
DISEÑO POR FLEXION
SECCION Mu (kg-m) d (cm) As req.Armados
Principal As Bastones Sobra
A 0.00 - - 2 Var No. 4 2.54 0 bast. No. 1 - 2.54
A B 2073.30 17.62 1.00 2 Var No. 4 2.54 0 bast. No. 1 - 1.54
B 3583.87 23.17 1.72 2 Var No. 4 2.54 0 bast. No. 1 - 0.82
B C 1867.16 16.72 0.90 2 Var No. 4 2.54 0 bast. No. 1 - 1.64
C 6762.00 31.82 3.25 2 Var No. 4 2.54 1 bast. No. 4 1.27 0.56
C D 4464.19 25.85 2.15 2 Var No. 4 2.54 1 bast. No. 3 0.71 1.10
D 11519.16 41.53 5.54 2 Var No. 4 2.54 2 bast. No. 4 2.54 - 0.46
D E 6844.53 32.01 3.29 2 Var No. 4 2.54 0 bast. No. 1 - - 0.75
E 8461.36 35.59 4.07 2 Var No. 4 2.54 1 bast. No. 5 1.98 0.45
E F 374.49 7.49 0.18 2 Var No. 4 2.54 0 bast. No. 1 - 2.36
F 3190.21 21.86 1.53 2 Var No. 4 2.54 2 bast. No. 5 3.96 4.97
F G 3532.11 23.00 1.70 2 Var No. 4 2.54 1 bast. No. 5 1.98 2.82
G 0.00 - - 2 Var No. 4 2.54 0 bast. No. 1 - 2.54
d = 41.53 cm
DISEÑO POR CORTANTE Smax.
SECCION Vu (kg) Vcr (kg) Vre (kg)Separacion de estribos
Estribos Av Sreq
A 3,054.48 5,168.58 - 2,114.10 Estribo No. 2 2 0.64 - 47.52
B 5,045.52 5,168.58 - 123.06 Estribo No. 2 0.64 - 816.43
B 6,478.65 5,168.58 1,310.07 Estribo No. 2 0.64 76.69
C 8,151.35 5,168.58 2,982.77 Estribo No. 2 0.64 33.68
C 8,207.14 5,168.58 3,038.56 Estribo No. 2 0.64 33.07
D 9,792.86 5,168.58 4,624.28 Estribo No. 2 0.64 21.73
D 8,782.22 5,168.58 3,613.64 Estribo No. 2 0.64 27.80
E 8,017.78 5,168.58 2,849.19 Estribo No. 2 0.64 35.26
E 5,779.23 5,168.58 610.65 Estribo No. 2 0.64 164.53
F 3,670.77 5,168.58 - 1,497.81 Estribo No. 2 0.64 - 67.08
F 5,797.55 5,168.58 628.97 Estribo No. 2 0.64 159.74
G 4,202.45 5,168.58 - 966.13 Estribo No. 2 0.64 - 103.99
2 Varillas No. 4
0 baston No.1
0 baston No. 1
- baston No. 1
2 varillas No. 4
90 180 90 0.95 1.9
Estribos @ 14.80 Estribos @ 14.80 Estribos @ 14.80 Estribos @ 14.80 Estribos @
BBA
AA
Carga distribuida
Lado aLado b
- 2.000 3.000 3.000 1.000
2100 1890 2500
1 15 4
METODO DE CROSS PARA VIGAS
E E F F G1 1 18 5 4
0.125 0.2 0.18750.325 0.3875 0
0.3846153846 0.6153846154 0.5161290323 0.4838709677 0 11,200.00 - 3,937.50 3,937.50 -5000 0
7262.50 -1062.50 0-2793.26923077 -4469.23076923 548.39 514.11 0
471.43 274.19 -2234.62 0 0745.62 -2234.62 0
E F G
-286.777738391 -458.844381425 1153.35 1081.27 0117.84 576.67 -229.42 0 0
694.52 -229.42 0-267.122698983 -427.396318372 118.41 111.01 0
68.29 59.21 -213.70 0 0127.50 -213.70 0
-49.0380684504 -78.4609095207 110.30 103.40 08461.36 -8461.36 3190.21 -3190.21 0
DETERMINACION DE CORTANTES TOTALES
E E F F G-8400.00 4725.00 -4725.00 5000.00 -5000.00382.22 1054.23 1054.23 797.55 797.55
-8017.78 5779.23 -3670.77 5797.55 -4202.45
E F G13797.01 9468.32 4202.45
5779.23 5797.55
1.94 1.68
3.06 2.32
-8017.78 -3670.77 -4202.45
3532.11374.49
-
-8461.36 -3190.21
LS
LI
LS
LI
LS
LI
LS
LI
LS
LI
LS
LI
LS
Vrestriccion: 17,620.16 kg
Smax. 14.80 20.77
Separacion de estribos
Smax.
14.80
14.80
14.80
14.80
14.80
14.80
14.80
14.80
14.80
14.80
14.80
14.80
1 baston No. 4.00
1.00 baston No. 3
2 Baston No. 4 - baston No. 1
0.95 1.5 3 1.5 2 4
Estribos @ 14.80 E @ 14.80 Estribos @ 14.80 E @ 14.80 Estribos @ 14.80
CA
DA
0 Baston No. 0#REF!
2 20
E @ 0.00
EA
Varilla As cm2
1 0.012 0.32
2.5 0.493 0.714 1.275 1.98 1.58756 2.857 3.888 5.07
10 7.9212 11.4
DA
TO
S D
E L
A V
IGA b = 20 cm
f'c= 200 kg/cm2 f*c= 160 kg/cm2 VIGA DE UN CLARO Y CARGA UNIFORMEMENTE DISTRIBUIDA f''c= 136 kg/cm2 fy= 4200 kg/cm2 longitudinal
VIGA V-1 fy= 2530 kg/cm2 estribos 1220.4p = 0.008q = 0.247
DISEÑO POR FLEXION
Dif
ere
n
Le
ch
o
SECCION COEF. w (kg/m) L (m) d (cm) As req.Armados
Principal As Bastones As
A 0 1,220.40 7.3 - - - 2 Var No. 3.0 1.42 0 bast. No. 1 - 1.42 LS
A B 0.125 1,220.40 7.3 812,938.95 39.16 6.27 2 Var No. 4.0 2.54 2 bast. No. 5 3.96 0.23 LI
B 0 1,220.40 7.3 - - - 2 Var No. 3.0 1.42 0 bast. No. 1 - 1.42 LS
Peralte efectivo de la viga 39.16
Vrestriccion: 11,888.46 kg
DISEÑO POR CORTANTE Smax. 18.51 20.83
SECCION COEF. w (kg/m) L (m) Vcr VreSeparacion de estribos
Estribos Av Sreq Smax.
A 0.5 1,220.40 7.3 4,454.46 3,487.28 967.18 Estribo No. 2 0.64 52.45 18.51
B 0.5 1,220.40 7.3 4,454.46 3,487.28 967.18 Estribo No. 2 0.64 52.45 18.51
2 Varillas No. 3
2 bast. del No. 5
42
2 varillas No. 4
182.5 365 182.5 20
Estribos @ 18.51 Estribos @ 18.51 Estribos @ 18.51
Mu (kg-cm)
Vu (kg)
BA
AA
DA
TO
S D
E L
A V
IGA b = 20 cm
f'c= 200 kg/cm2 f*c= 160 kg/cm2 VIGA DE DOS CLAROS Y CARGA UNIFORMEMENTE DISTRIBUIDA f''c= 136 kg/cm2 fy= 4200 kg/cm2 longitudinal
VIGA V-2 fy= 2530 kg/cm2 estribosp = 0.008q = 0.247
W a-b 1,250.00 kg/m L a-b 5.00 mts. EI a-b = 1.00 K a-b = 0.20 W b-c 1,250.00 kg/m L b-c 4.00 mts. EI b-c = 1.00 K b-c = 0.25
1,250.00 kg/m 1,250.00 kg/m
A 5.00 B 4.00 C
NODO TRAMO
K
DISEÑO POR FLEXION
Dif
ere
n
Le
ch
o
SECCION COEF. w (kg/m) L (m) d (cm) As req.Armados
Principal As Bastones As
A 0 1,194.00 6 - - - 2 Var No. 4 2.54 0 bast. No. 1 - 2.54 LS
A B 0.071 1,194.00 6 305,186.40 23.99 3.84 2 Var No. 4 2.54 2 bast. No. 3 1.42 0.12 LI
B 0.125 1,194.00 6 537,300.00 31.84 5.09 2 Var No. 4 2.54 4 bast. No. 3 2.84 0.29 LS
B C 0.071 1,142.00 4 129,731.20 15.64 2.50 2 Var No. 4 2.54 0 bast. No. 2.5 - 0.04 LI
C 0 1,142.00 4 - - - 2 Var No. 4 2.54 0 bast. No. 1 - 2.54 LS
Peralte efectivo de la viga 32.00
Vrestriccion: 9,714.52 kg
DISEÑO POR CORTANTE Smax. 18.51 16.00
SECCION COEF. w (kg/m) L (m) Vcr VreSeparacion de estribos
Mu (kg-cm)
Vu (kg)
SECCION COEF. w (kg/m) L (m) Vcr VreEstribos Av Sreq Smax.
A 0.375 1,199.00 6 2,697.75 2,849.59 - 151.84 Estribo No. 2 0.64 - 272.99 16.00
B 0.625 1,199.00 6 4,496.25 2,849.59 1,646.66 Estribo No. 2 0.64 25.17 16.00
B 0.625 1,142.00 4 2,855.00 2,849.59 5.41 Estribo No. 2 0.64 7,664.35 16.00
C 0.375 1,142.00 4 1,713.00 2,849.59 - 1,136.59 Estribo No. 2 0.64 - 36.47 16.00
2 Varillas No. 4
2 baston No. 3
4 baston No. 3
0 baston No. 2.5
34.5
2 varillas No. 4
150 300 150 100 200 100 20
Estribos @ 16.00 Estribos @ 16.00 Estribos @ 16.00 Estribos @ 16.00
Vu (kg)
BBA
CA
AA
DA
TO
S D
E L
A V
IGA b = 15 cm
f'c= 200 kg/cm2 f*c= 160 kg/cm2 VIGA DE TRES CLAROS Y CARGA UNIFORMEMENTE DISTRIBUIDA f''c= 136 kg/cm2 fy= 4200 kg/cm2 longitudinal
VIGA V-3 fy= 2530 kg/cm2 estribosp = 0.008q = 0.247
DISEÑO POR FLEXION
SECCION COEF. w (kg/m) L (m) d (cm) As req.Armados
Principal As Bastones
A 0 1,533.84 3 - - - 2 Var No. 3 1.42 bast. No.
A B 0.080 1,533.84 3 110,436.48 16.67 2.00 2 Var No. 3 1.42 1 bast. No.
B 0.100 1,533.84 3 138,045.60 18.63 2.24 2 Var No. 3 1.42 1 bast. No.
B C 0.025 1,533.84 1.03 4,068.13 3.20 0.38 2 Var No. 3 1.42 bast. No.
C 0.100 1,533.84 1.97 59,526.80 12.24 1.47 2 Var No. 3 1.42 1 bast. No.
C D 0.080 1,533.84 1.97 47,621.44 10.94 1.31 2 Var No. 3 1.42 bast. No.
D 0.0 1,533.84 1.97 - - - 2 Var No. 3 1.42 bast. No.
Peralte efectivo de la viga 23.00
Vrestriccion:DISEÑO POR CORTANTE Smax. 24.67
SECCION COEF. w (kg/m) L (m) Vcr VreSeparacion de estribos
Estribos Av Sreq
A 0.4 1,533.84 3 1,840.61 2,331.48 - 490.88 Estribo No. 2 0.64 - 84.44
B 0.6 1,533.84 3 2,760.91 2,331.48 429.43 Estribo No. 2 0.64 96.53
B 0.500 1,533.84 1.03 789.93 2,331.48 - 1,541.56 Estribo No. 2 0.64 - 26.89
C 0.5 1,533.84 1.03 789.93 2,331.48 - 1,541.56 Estribo No. 2 0.64 - 26.89
C 0.600 1,533.84 1.97 1,813.00 2,331.48 - 518.49 Estribo No. 2 0.64 - 79.95
D 0.4 1,533.84 1.97 1,208.67 2,331.48 - 1,122.82 Estribo No. 2 0.64 - 36.92
2 Varillas No. 3
1 baston No. 3
1 baston No. 4
0 baston No. 1
1 baston No.
2 varillas No. 3
75 150 75 25.75 51.5 25.75
Estribos @ 15.00 Estribos @ 15.00 Estribos @ 15.00 Estribos @ 15.00 Estribos @
Mu (kg-cm)
Vu (kg)
BBA
CA
AA
VIGA DE TRES CLAROS Y CARGA UNIFORMEMENTE DISTRIBUIDA
DISEÑO POR FLEXION
Dif
ere
n
Le
ch
o
Armados
Bastones As
1 - 1.42 LS
3 0.71 0.13 LI 1533.844 1.27 0.45 LS
1 - 1.04 LI
3 0.71 0.66 LS
1 - 0.11 LI
1 - 1.42 LS
5,236.73 kg
11.50
Separacion de estribos
Smax.
15.00
15.00
15.00
15.00
15.00
15.00
3
0 baston No. 1 25.00
49.25 98.5 49.25 20
15.00 Estribos @ 15.00 Estribos @ 15.00
CA
DA
DA
TO
S D
E L
A V
IGA b = 20 cm
f'c= 250 kg/cm2 f*c= 200 kg/cm2 VIGA DE TRES CLAROS Y CARGA UNIFORMEMENTE DISTRIBUIDA f''c= 170 kg/cm2 fy= 4200 kg/cm2 longitudinal
VIGA V-3 fy= 2530 kg/cm2 estribosp = 0.008q = 0.198
DISEÑO POR FLEXION
SECCION COEF. w (kg/m) L (m) d (cm) As req.Armados
Principal As Bastones
A 0 750.00 7.2 - - - 2 Var No. 4 2.54 0 bast. No.
A B 0.0772 908.50 7.2 363,586.06 25.83 4.13 2 Var No. 4 2.54 2 bast. No.
B 0.1071 750.00 7.2 416,404.80 27.64 4.42 2 Var No. 4 2.54 2 bast. No.
B C 0.0364 750.00 7.2 141,523.20 16.11 2.58 2 Var No. 4 2.54 0 bast. No.
C 0.0711 750.00 7.2 276,436.80 22.52 3.60 2 Var No. 4 2.54 2 bast. No.
C D 0.0364 750.00 7.2 141,523.20 16.11 2.58 2 Var No. 4 2.54 2 bast. No.
D 0.1071 750.00 7.2 416,404.80 28.03 4.48 2 Var No. 4 2.54 0 bast. No.
D E 0.0772 750.00 7.2 300,153.60 23.47 3.75 2 Var No. 4 2.54 2 bast. No.
E 0.0 750.00 7.2 - - - 2 Var No. 4 2.54 0 bast. No.
Peralte efectivo de la viga 29.50
Vrestriccion:DISEÑO POR CORTANTE Smax. 18.51
SECCION COEF. w (kg/m) L (m) Vcr VreSeparacion de estribos
Estribos Av Sreq
A 0.393 908.50 3.5 1,249.64 2,849.59 - 1,599.95 Estribo No. 2 0.64 - 25.91
B 0.607 908.50 3.5 1,930.11 2,849.59 - 919.48 Estribo No. 2 0.64 - 45.08
B 0.536 908.50 3.5 1,704.35 2,849.59 - 1,145.25 Estribo No. 2 0.64 - 36.19
C 0.46 908.50 3.5 1,475.40 2,849.59 - 1,374.19 Estribo No. 2 0.64 - 30.16
C 0.464 908.50 3.5 1,475.40 2,849.59 - 1,374.19 Estribo No. 2 0.64 - 30.16
D 0.536 908.50 3.5 1,704.35 2,849.59 - 1,145.25 Estribo No. 2 0.64 - 36.19
E 0.607 908.50 3.5 1,930.11 2,849.59 - 919.48 Estribo No. 2 0.64 - 45.08
F 0.393 908.50 3.5 1,249.64 2,849.59 - 1,599.95 Estribo No. 2 0.64 - 25.91
2 Varillas No. 4
2 baston No. 3
2 baston No. 4
0 baston No. 1
2 baston No.
2 varillas No. 4
180 360 180 180 360 180
Estribos @ 14.75 Estribos @ 14.75 Estribos @ 14.75 Estribos @ 14.75 Estribos @
Mu (kg-cm)
Vu (kg)
BBA
CA
AA
VIGA DE TRES CLAROS Y CARGA UNIFORMEMENTE DISTRIBUIDA
DISEÑO POR FLEXION
Dif
ere
n
Le
ch
o
Armados
Bastones As
1 - 2.54 LS
3 1.42 - 0.17 LI
4 2.54 0.66 LS
1 - - 0.04 LI
4 2.54 1.48 LS
3 1.42 1.38 LI
1 - - 1.94 LS
3 1.42 0.21 LI
1 - 2.54 LS
10,012.63 kg
14.75
Separacion de estribos
Smax.
14.75
14.75
14.75
14.75
14.75
14.75
14.75
14.75
4
2 baston No. 3 0
180 360 180 100 200
14.75 Estribos @ 14.75 Estribos @ 0.00 Estribos @ 0.00
CA
DA
31.50
100 20
Estribos @ 0.00
DA
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