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PuenteS
Descripción: PUENTES...
Author:
Joyce Oviedo
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Descripción: Puentes
Ensayo Puentes
ensayo puente
a1
a2
L RA =
11.917 ton
DATOS f´c = fy = L= a1 = a2 = b= d= r= R max =
280 4200 6 0.25 0.25 0.25 0.25 1 0.3 0.04 0.04 11.9167 11.9167
RB =
LUZ EFECTIVA DE CÁLCULO kg/cm2 kg/cm2 kg/cm2 kg/cm2 m m m m m m T
S=
ρ=
WD = RD = Vu = Vc act =
29.99 kg/cm2 kg/cm2 0.0077
0.816 2.448 15.8089 15.8089 7.0262
ESPESOR DE LOSA
t=
6.25 6.25 m
CARGA MUERTA
WD =
Ru =
8.083 ton
E= bo = Vp = Vact= Vc act =
MOMENTOS MD = ML = I= MU =
0.816 T/m
1.595 298 3.3557 7.4713 3.3206
m cm T/m T (m) Kg (cm)
ok
RECALCULO
T/m2 T/m T/m kg/cm2
d= Ru = ρ=
Vcritico
23.77 cm 47.77 kg/cm2 0.0128 8.72 kg/cm2
ok ok
V c act para el recálculo 8.8686 kg/cm2
As = 30.4256 cm2 As min = 7.9233 cm2
% reparto 22.08
As reparto = As min rep =
0.34 m
6.71797 cm2 2.65 cm2
3.9844 3.9844 Tm 11.3063 11.3063 Tm 0.3 24.29 Tm
As As min As rep As min r
22 16 18 10
#
As cal
8 4 3 3
30.426 7.923 6.718 2.650
cal 0.0128 0.0033
As real 30.411 8.042 7.634 2.356
real Sep (cm) 0.0128 0.0034 0.0032 0. 0 .0010
10.30 23.40 31.53 32 3 2.33
ok ok ok ok
VIGA DE BORDE h= r= b= d=
35 4 20 31
cm cm cm cm
35 cm
M= Ru =
6.25 36.1313 0.0094 ρ= As = 5.828 Diámetro varilla = 16 # varillas = 3 Separación = 3.6
3Φ
12 mm
3Φ
16 mm
T/m kg/cm /cm2
ok
cm2 mm
ρ min = 0.0033 As = 2.65 Diám var 12 mm # var = 3 4.2 cm Sep =
cm
4Φ
16 mm
20 cm 24 cm
8Φ
22 mm
DATOS f´c = fy =
a1
a2
280 kg/cm2 4200 kg/cm2
a1 = a2 = x= delta =
0.25 m 0.25 m 0.3 3
L= x= RA = RB = M1 = M2 = M3 =
L
25.6
m
0.3
3.3
6.3
9.3
12.3
15.3
18.3
21.3
24.3
19.75 2.75 5.92 47.34 46.27
17.11 5.39 56.46 86.68 74.39
14.47 8.03 91.18 110.19 86.70
11.84 10.66 110.07 117.88 83.18
9.20 13.30 113.15 109.75 63.84
6.56 15.94 100.41 85.80 28.69
4.04 15.96 73.99 48.67 -
1.70 18.30 36.19 0.92 -
0.51 9.49 12.34 -
CORTANTES SERIE 1 0 0 0.3 0.3 4.55 4.55 8.8 8.8 25.6 25.6
SERIE 2
0 19.75 19.75 9.75 9.75 -0.25 -0.25 -2.75 -2.75 0
0 0 3.3 3.3 7.55 7.55 11.8 11.8 25.6 25.6
SERIE 3
0 17.11 17.11 7.11 7.11 -2.89 -2.89 -5.39 -5.39 0
0 0 6.3 6.3 10.55 10.55 14.8 14.8 25.6 25.6
SERIE 4
0 14.47 14.47 4.47 4.47 -5.53 -5.53 -8.03 -8.03 0
0 0 9.3 9.3 13.55 13.55 17.8 17.8 25.6 25.6
SERIE 5
0 11.84 11.84 1.84 1.84 -8.16 -8.16 -10.66 -10.66 0
0 0 12.3 12.3 16.55 16.55 20.8 20.8 25.6 25.6
SERIE 6
0 9.20 9.20 -0.80 -0.80 -10.80 -10.80 -13.30 -13.30 0
0 0 15.3 15.3 19.55 19.55 23.8 23.8 25.6 25.6
SERIE 7
0 6.56 6.56 -3.44 -3.44 -13.44 -13.44 -15.94 -15.94 0
0 0 18.3 18.3 22.55 22.55 25.6 25.6 25.6 25.6
SERIE 8
0 4.04 4.04 -5.96 -5.96 -15.96 -15.96 0.00 0.00 0
0 0 21.3 21.3 25.55 25.55 25.6 25.6 25.6 25.6
SERIE 9
0 1.70 1.70 -8.30 -8.30 -18.30 -18.30 0.00 0.00 0
0 0 24.3 24.3 25.6 25.6 25.6 25.6 25.6 25.6
0 0.51 0.51 -9.49 -9.49 0.00 0.00 0.00 0.00 0
MOMENTOS SERIE 1 0 0.3 4.55 8.8 25.6
SERIE 2
0 -5.92 -47.34 -46.27 0
0 3.3 7.55 11.8 25.6
SERIE 3
0 -56.46 -86.68 -74.39 0
0 6.3 10.55 14.8 25.6
SERIE 4
0 -91.18 -110.19 -86.70 0
0 9.3 13.55 17.8 25.6
SERIE 5
0 -110.07 -117.88 -83.18 0.00
0 12.3 16.55 20.8 25.6
SERIE 6
0 -113.15 -109.75 -63.84 0
0 15.3 19.55 23.8 25.6
SERIE 7
0 -100.41 -85.80 -28.69 0
0 18.3 22.55 25.6
19
21
SERIE 8
0 -73.99 -48.67 0
0 21.3 25.55 25.6
SERIE 9
0 -36.19 -0.92 0
0 24.3 25.6
0 -12.34 0
CORTANTES 25
20
15
10
5
0 0
-5
-10
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
20
22
23
24
25
26
27
28
29
30
CORTANTES 25
20
15
10
5
0 0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
28
29
30
-5
-10
-15
-20
-25 SERIE 1
SERIE 2
SERIE 3
SERIE 4
SERIE 5
SERIE 6
SERIE 7
SERIE 8
SERIE 9
serie 10
MOMENTOS 10
0 0 -10
-20
-30
-40
-50
-60
-70
-80
-90
-100
-110
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
MOMENTOS 10
0 0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
-10
-20
-30
-40
-50
-60
-70
-80
-90
-100
-110
-120
-130
-140
-150 SERIE 1
SERIE 2
SERIE 3
SERIE 4
SERIE 5
SERIE 6
SERIE 7
SERIE 8
SERIE 9
SERIE 10
CALCULO DE PUENTES DE HORMIGON CON VIGAS "T" TIPO DE LOSA
CONTINUA
F'c = Fy = L= # vías = A vía =
280 4200 25.6 2 6.096
Kg/cm2 Kg/cm2 mts vías mts
# vigas = bw = S1 = S2 = asumimos
8.5 mts
3 45 2.83 2.38
vigas cm mts mts
CALCULO DE PUENTES DE HORMIGON CON VIGAS "T" TIPO DE LOSA
CONTINUA
F'c = Fy = L= # vías = A vía = # vered. = A vered: = # postes =
280 4200 25.6 2 6.096 2 1 2
A Post. =
Kg/cm2 Kg/cm2 mts vías mts veredas mts postes
# vigas = bw = S1 = S2 = asumimos
vigas cm mts mts
8.5 mts
A total del puente
10.9 mts
0.2 mts
LOSA INTERIOR
LOSA EXTERIOR
MOMENTOS
MOMENTOS
S l.int = t l.int = d l.int = WD l.int = MD l.int = P20 = ML = I= Mu =
3 45 2.83 2.38
2.38 0.18 0.14 0.43 0.25 10.00 2.46 0.38 4.47
CORTANTES
mts mts mts T/m T (m) Ton T (m) 30 % T (m)
S l.ext = d l.ext = t l.ext = WD = MD = P20 = ML = I= Mu =
1.19 26.41 30.41 0.63 0.45 10.00 4.80 0.39 8.70
CORTANTES
mts cm cm T/m T (m) Ton T (m) 30 % T (m)
VL = VD = I= Vu = Vu act = V crit =
10 Ton 0.51 Ton (m) 0.38 17.57 T (m) 16.73 Kg/cm2 8.87 Kg/cm2
x= E= VL = VD = I= Vu =
30 %
Vu act = V crit =
26.41 cm 30.41 cm 7.12 Kg/cm2 0.0017
Ru = cuantia =
Revisión por punzonamiento bo = Vp = Vp´=
283.66 cm 35.25 Kg/cm 1.33 Kg/cm2
m m T (m) T (m) 30 % T (m)
recalcular
Recálculo de "d" d= t= Ru = cuantia =
0.89 1.86 5.39 0.87 0.35 10.23
cumple
5.17 Kg/cm2 8.87 Kg/cm2 13.86 Kg/cm2 0.0034
d= t= Vu act = V crit =
13.52 17.52 10.10 8.87
d= t= Ru =
15.39 cm 19.39 40.84 Kg/cm2
cuantia =
cm cm Kg/cm2 Kg/cm2
0.0107
19.39
30.41
ACERO EN LOSA INTERIOR
10.8339 cm2 As = As min = 20.9846 cm2
As As min As rep As min r
12 12 8 8
% reparto 35.76
#
As cal
10 19 8 15
10.834 20.985 3.874 7.503
cal 0.00172 0.0033
As reparto = As min rep =
As real 11.310 21.488 4.021 7.540
real 0.00180 0.0034 0.0006 0.0012
3.87376 cm2 7.50321 cm2
Sep (cm) 22.63 11.34 28.99 15.09
ok ok ok ok
ACERO EN LOSA EXTERIOR
As =
19.6975 cm2
% reparto
As reparto =
3.43835 cm2
cumple
cuantia = Ru =
recalcular
0.0145 52.9282
As min =
As As min As rep As min r
6.1122 cm2
#
As cal
8 8 7 9
19.698 6.112 3.438 2.650
18 10 8 6
As min rep =
17.46
cal
As real
real
2.65 cm2
Sep (cm)
0.01074 0.0033
20.358 6.283 3.519 2.545
0.01110 0.00343 0.00192 0.00139
27.99 28.79 33.25 25.88
ok ok ok ok
x
MD
ML
ML*%P
%I
MI
0.00 13.69 132.74 219.32 273.43 295.07 294.62
0.00 5.92 56.46 91.18 110.07 113.15 117.88
24.02 24.02 24.02 24.02 24.02 24.02 24.02
0.00 2.20 20.99 33.90 40.93 42.07 43.83
%I
VI
VIGA INTERIOR
H= t= bw = B=
WD viga = R1 = M max = V max =
1.73 30.41 45.00 2.83
mts cm cm mts
VD 46.18 45.09 34.27 23.45 12.63 1.80 2.56
3.61 T/m (m) 1.55 P 677.24 T-m 107.96 T
Mu int = Vu act = V crit =
323.508 T-m 19.63 kg/cm2 8.87 Kg/cm2
Ru = Ru min = cuantia =
10.00 Kg/cm2 13.587 0.0033
As =
153.88 cm2
diam.var= # varillas # filas= #var x fila Sep hor = h de acer
0 0.3 3.3 6.3 9.3 12.3 13.51 x 0 0.3 3.3 6.3 9.3 12.3 13.51
32 20 4 5 5.8 30.2
VIGA EXTERIOR
mm varillas fila varillas cm cm
cumple
Ru a utilizar 13.587 Kg/cm2
OK OK
VL 20.01 19.75 17.11 14.47 11.84 9.20 8.14
0.00 9.17 87.42 141.17 170.42 175.19 182.51
VL*%P 30.98 30.57 26.49 22.41 18.33 14.24 12.60
24.02 24.13 25.33 26.65 28.12 29.76 30.48
7.44 7.38 6.71 5.97 5.15 4.24 3.84
MU 0.00 32.58 313.49 512.70 630.22 666.03 677.24
VU 109.98 107.96 87.71 67.38 46.94 26.37 24.70
x
H= t= bw = B=
WD viga = R2 = M max = V max =
1.73 19.39 45.00 2.83
mts cm cm mts
ML
0.00 11.30 109.53 180.97 225.62 243.48 243.11
0.00 5.92 56.46 91.18 110.07 113.15 117.88
VD 46.18 45.09 34.27 23.45 12.63 1.80 2.56
2.98 T/m (m) 2.49 P 788.91 T-m 137.91 T
Mu int = Vu act = V crit =
213.426 T-m 25.08 kg/cm2 8.87 Kg/cm2
Ru = Ru min = cuantia =
11.65 Kg/cm2 13.587 0.0033
As =
153.88 cm2
diam.var= # varillas # filas= #var x fila Sep hor = h de acer
0 0.3 3.3 6.3 9.3 12.3 13.51 x 0 0.3 3.3 6.3 9.3 12.3 13.51
MD
32 20 4 5 5.8 33.1
mm varillas fila varillas cm cm
cumple
Ru a utilizar 13.587 Kg/cm2
OK OK
VL 20.01 19.75 17.11 14.47 11.84 9.20 8.14
ML*%P 0.00 14.74 140.49 226.87 273.89 281.54 293.31
VL*%P 49.79 49.13 42.57 36.01 29.45 22.89 20.24
%I
MI
24.02 24.02 24.02 24.02 24.02 24.02 24.02
0.00 3.54 33.74 54.48 65.78 67.61 70.44
%I
VI
24.02 24.13 25.33 26.65 28.12 29.76 30.48
11.96 11.86 10.78 9.60 8.28 6.81 6.17
MU 0.00 38.45 368.88 601.02 734.88 770.43 788.91
VU 140.30 137.91 113.91 89.77 65.47 40.96 37.67
DATOS f´c = fy =
a1
a2
280 kg/cm2 4200 kg/cm2
a1 = a2 = x= delta =
0.25 m 0.25 m 0.3 3
L
L=
30
0.3
3.3
6.3
9.3
12.3
15.3
18.3
21.3
24.3
20.15 2.35 6.05 49.18 49.82
17.90 4.60 59.07 92.65 83.72
15.65 6.85 98.60 122.61 104.12
13.40 9.10 124.62 139.07 111.02
11.15 11.35 137.15 142.03 104.42
8.90 13.60 136.17 131.50 84.32
6.65 15.85 121.70 107.46 50.72
4.38 15.62 93.37 69.49 3.12
2.38 17.62 57.92 25.54 -
x= RA = RB = M1 = M2 = M3 =
m
CORTANTES SERIE 1 0 0 0.3 0.3 4.55 4.55 8.8 8.8 30 30
SERIE 2
0 20.15 20.15 10.15 10.15 0.15 0.15 -2.35 -2.35 0
0 0 3.3 3.3 7.55 7.55 11.8 11.8 30 30
SERIE 3
0 17.90 17.90 7.90 7.90 -2.10 -2.10 -4.60 -4.60 0
0 0 6.3 6.3 10.55 10.55 14.8 14.8 30 30
SERIE 4
0 15.65 15.65 5.65 5.65 -4.35 -4.35 -6.85 -6.85 0
0 0 9.3 9.3 13.55 13.55 17.8 17.8 30 30
SERIE 5
0 13.40 13.40 3.40 3.40 -6.60 -6.60 -9.10 -9.10 0
0 0 12.3 12.3 16.55 16.55 20.8 20.8 30 30
SERIE 6
0 11.15 11.15 1.15 1.15 -8.85 -8.85 -11.35 -11.35 0
0 0 15.3 15.3 19.55 19.55 23.8 23.8 30 30
SERIE 7
0 8.90 8.90 -1.10 -1.10 -11.10 -11.10 -13.60 -13.60 0
0 0 18.3 18.3 22.55 22.55 30 30 30 30
SERIE 8
0 6.65 6.65 -3.35 -3.35 -13.35 -13.35 0.00 0.00 0
0 0 21.3 21.3 25.55 25.55 30 30 30 30
SERIE 9
0 4.38 4.38 -5.62 -5.62 -15.62 -15.62 0.00 0.00 0
0 0 24.3 24.3 30 30 30 30 30 30
0 2.38 2.38 -7.62 -7.62 0.00 0.00 0.00 0.00 0
MOMENTOS SERIE 1 0 0.3 4.55 8.8 30
SERIE 2
0 -6.05 -49.18 -49.82 0
0 3.3 7.55 11.8 30
SERIE 3
0 -59.07 -92.65 -83.72 0
0 6.3 10.55 14.8 30
SERIE 4
0 -98.60 -122.61 -104.12 0
0 9.3 13.55 17.8 30
SERIE 5
0 -124.62 -139.07 -111.02 0.00
0 12.3 16.55 20.8 30
SERIE 6
0 -137.15 -142.03 -104.42 0
0 15.3 19.55 23.8 30
SERIE 7
0 -136.17 -131.50 -84.32 0
0 18.3 22.55 30
19
21
SERIE 8
0 -121.70 -107.46 0
0 21.3 25.55 30
SERIE 9
0 -93.37 -69.49 0
0 24.3 30
0 -57.92 0
CORTANTES 25
20
15
10
5
0 0
-5
-10
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
20
22
23
24
25
26
27
28
29
30
CORTANTES 25
20
15
10
5
0 0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
28
29
30
-5
-10
-15
-20
-25 SERIE 1
SERIE 2
SERIE 3
SERIE 4
SERIE 5
SERIE 6
SERIE 7
SERIE 8
SERIE 9
serie 10
MOMENTOS 10
0 0 -10
-20
-30
-40
-50
-60
-70
-80
-90
-100
-110
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
MOMENTOS 10
0 0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
-10
-20
-30
-40
-50
-60
-70
-80
-90
-100
-110
-120
-130
-140
-150 SERIE 1
27.3 0.90 9.10 24.57 -
SERIE 10 0 0 27.3 27.3 30 30 30 30
0 0.90 0.90 -9.10 -9.10 0.00 0.00 0 00
SERIE 2
SERIE 3
SERIE 4
SERIE 5
SERIE 6
SERIE 7
SERIE 8
SERIE 9
SERIE 10
28
29
30
27.3 0.90 9.10 24.57 -
SERIE 10 0 0 27.3 27.3 30 30 30 30 30 30
0 0.90 0.90 -9.10 -9.10 0.00 0.00 0.00 0.00 0
SERIE 10 0 27.3 30
0 -24. 57 0
CALCULO DE PUENTES DE HORMIGON CON VIGAS "T" TIPO DE LOSA
CONTINUA
F'c = Fy = L= # vías = A vía =
280 4200 30 2 6.096 2
Kg/cm2 Kg/cm2 mts vías mts d
# vigas = bw = S1 = S2 = asumimos
8.5 mts
4 45 2.73 2.28
vigas cm mts mts
CALCULO DE PUENTES DE HORMIGON CON VIGAS "T" TIPO DE LOSA
CONTINUA
F'c = Fy = L= # vías = A vía = # aceras = A acera = # postes =
280 4200 30 2 6.096 2 1.2 2
A Post. =
Kg/cm2 Kg/cm2 mts vías mts veredas mts postes
# vigas = bw = S1 = S2 = asumimos
A total del puente
10.9 mts
0.2 mts
PESOS EN VIGA
POSTES
POSTES 2 4 20 1.05 18.26 36.52 766.92
m postes postes m kg/m kg/m kg
4 C/6m
200*100*6mm
RIELES Sep = # rieles = Largo = perfil C = doble C =
vigas cm mts mts
8.5 mts
PESOS EN LOSA
Sep. = # postes # total Altura = perfil C = doble C = Peso =
4 45 2.73 2.28
Sep. = # postes # total Altura = perfil C = doble C = Peso =
2 4 20 1.05 18.26 36.52 766.92
m postes postes m kg/m kg/m kg
4 C/6m
200*100*6mm
RIELES 0.4 2 60 2.59 5.18
m rieles m kg/m kg/m
60*30*3mm
Sep = # rieles = Largo = perfil C = doble C =
0.4 2 60 2.59 5.18
m rieles m kg/m kg/m
60*30*3mm
Peso riel Riel+post
310.8 kg 35.924 kg/m
0.03592 tn/m
ACERA
Peso riel = Riel+post
310.8 kg/m 35.924 kg
ACERA
Ancho = Espesor = Peso =
1.2 m 0.2 m 0.48 t/m2 (m)
MOMENTO= CORTANTE=
Ancho = 1.2 Espesor = 0.2 Peso = 0.48 Asfalto = 3 peso = 44 peso capa asfalto =
0.34781 tn-m 0.58192 tn
WD =
LOSA EXTERIOR
MOMENTOS
MOMENTOS
2.28 0.18 0.14 0.56 0.29 10.00 2.37 0.38 4.38
mts mts mts T/m T (m) Ton T (m) 30 % T (m)
CORTANTES VL = VD = I= Vu = Vu act = V crit =
10 Ton 0.64 Ton (m) 0.38 17.73 T (m) 16.89 Kg/cm2 8.87 Kg/cm2
26.66 30.66 6.85 13.59 0.0033
30 %
x= E= VL = VD = I= Vu =
mts cm cm T/m T (m) Ton T (m) 30 % T (m)
cm cm Kg/cm2 Kg/cm2
284.65 cm 35.13 Kg/cm
0.84 1.81 5.52 1.42 0.35 11.17
m m T (m) T (m) 30 % T (m)
recalcular
Vu act = V crit =
Revisión por punzonamiento bo = Vp =
1.14 26.66 30.66 0.74 0.82 10.00 4.62 0.39 8.88
CORTANTES
Recálculo de "d" d= t= Ru = Ru min = cuantia =
S l.ext = d l.ext = t l.ext = WD = MD = P20 = ML = I= Mu =
m m t/m2 (m) " kg (1m2 de espesor 1") 0.132 tn/m
0.63337 tn-m
LOSA INTERIOR
S l.int = t l.int = d l.int = WD l.int = MD l.int = P20 = ML = I= Mu =
0.03592 tn/m
Ru a utilizar 13.587 Kg/cm2
Ru = cuantia =
d= t= Vu act = V crit =
5.58 Kg/cm2 8.87 Kg/cm2 13.88 Kg/cm2 0.00341
13.65 17.65 10.91 8.87
cm cm Kg/cm2 Kg/cm2
cumple
cuantia = Ru =
recalcular
0.0145 52.9282
Vp´=
1.32 Kg/cm2
cumple
d= t= Ru = cuantia =
16.79 cm 20.79 35.00 Kg/cm2 13.587 Kg/cm2 0.0091
Ru a utilizar 35.0012 Kg/cm2
20.79
30.66
ACERO EN LOSA INTERIOR
8.88646 cm2 As = As min = 8.8873 cm2
As As min As rep As min r
20 20 12 12
% reparto
As reparto = As min rep =
36.60
#
As cal
3 3 3 3
8.886 8.887 3.252 3.253
cal 0.00333 0.0033
As real 9.425 9.425 3.393 3.393
real 0.00353 0.0035 0.0013 0.0013
3.2522 cm2 3.25251 cm2
Sep (cm) 31.33 31.33 32.13 32.13
ok ok ok ok
ACERO EN LOSA EXTERIOR
15.2055 cm2 As = As min = 5.5959 cm2
As As min As rep As min r
20 16 12 12
% reparto
As reparto = As min rep =
50.00
#
As cal
5 3 7 3
15.205 5.596 7.603 2.798
cal
As real
real
7.60273 cm2 2.79795 cm2
Sep (cm)
0.00906 0.0033
15.708 6.032 7.917 3.393
0.00936 0.00359 0.00472 0.00202
18.00 31.73 13.09 32.13
ok ok ok ok
x
MD
ML
ML*%P
%I
MI
0.00 17.66 174.65 295.96 381.59
0.00 6.05 59.07 98.60 124.62
22.46 22.46 22.46 22.46 22.46
0.00 2.02 19.76 32.98 41.69
VIGA INTERIOR
0 0.3 3.3 6.3 9.3
0.00 9.00 87.96 146.81 185.57
MU 0.00 37.29 367.08 618.48 791.49
H= t= bw = B=
WD viga = R1 = M max = V max =
2.00 30.66 45.00 2.73
12.3 15.3 15.71 x 0 0.3 3.3 6.3 9.3 12.3 15.3 15.71
mts cm cm mts
3.96 T/m (m) 1.49 P
431.54 445.81 444.99
VD 59.47 58.28 46.38 34.49 22.60 10.70 1.19 2.81
137.15 136.17 142.56
VL 20.38 20.15 17.90 15.65 13.40 11.15 8.90 8.22
204.22 202.77 212.29
VL*%P 30.34 30.00 26.65 23.30 19.95 16.60 13.25 12.24
22.46 22.46 22.46
45.87 45.55 47.69
%I
VI
22.46 22.56 23.61 24.75 26.02 27.41 28.97 29.20
6.82 6.77 6.29 5.77 5.19 4.55 3.84 3.57
886.12 902.36 916.45
VU 125.61 123.57 103.13 82.63 62.06 41.42 23.77 24.22
916.45 T-m 123.57 T
Mu int = Vu act = V crit =
366.897 T-m 19.29 kg/cm2 8.87 Kg/cm2
Ru = Ru min = cuantia =
10.37 Kg/cm2 13.587 0.0033
As =
172.42 cm2
diam.var= # varillas # filas= #var x fila Sep hor = h de acer
32 22 4 5 5.8 30.2
mm varillas fila varillas cm cm
cumple
Ru a utilizar 13.587 Kg/cm2
OK OK
VIGA EXTERIOR x
H= t= bw = B=
WD viga =
2.00 20.79 45.00 2.73
mts cm cm mts
3.29 T/m (m)
0 0.3 3.3 6.3 9.3 12.3 15.3 15.71 x 0 0.3 3.3 6.3 9.3 12.3 15.3
MD
0.00 17.49 172.99 293.14 377.95 427.43 441.56 440.75
ML 0.00 6.05 59.07 98.60 124.62 137.15 136.17 142.56
VD
VL
58.90 57.72 45.94 34.16 22.38 10.60 1.18
20.38 20.15 17.90 15.65 13.40 11.15 8.90
ML*%P 0.00 14.56 142.26 237.44 300.12 330.28 327.93 343.33
VL*%P 49.07 48.53 43.11 37.69 32.27 26.85 21.43
%I
MI
MU
22.46 22.46 22.46 22.46 22.46 22.46 22.46 22.46
0.00 0.00 3.27 45.92 31.96 451.36 53.34 759.10 67.42 969.13 74.19 1081.47 73.67 1096.11 77.12 1119.57
%I
VI
22.46 22.56 23.61 24.75 26.02 27.41 28.97
11.02 10.95 10.18 9.33 8.40 7.36 6.21
VU 154.69 152.36 128.99 105.53 81.96 58.26 37.47
WD total R2 = M max = V max = Mu int = Vu act = V crit =
2.79
8.22
19.80
29.20
1119.57 T-m 152.36 T 255.4 T-m 23.78 kg/cm2 8.87 Kg/cm2
Ru = Ru min = cuantia =
12.67 Kg/cm2 13.587 0.0033
As =
172.42 cm2
diam.var= # varillas # filas= #var x fila Sep hor = h de acer
15.71
3.93 T/m (m) 2.41 P
35 18 4 4.5 6.5 36.75
cumple
Ru a utilizar 13.587 Kg/cm2
mm varillas fila varillas cm cm
OK OK
ESTRIBOS EN VIGA INTERIOR Vu 125.61 123.57 103.13 82.63 62.06 41.42 23.77 24.22
vu 19.6049 19.2864 16.0965 12.8972 9.68707 6.46432 3.70946 3.77991
Vc 8.8686 8.8686 8.8686 8.8686 8.8686 8.8686 8.8686 8.8686
Vs Diseño Diseño Diseño Diseño Diseño E. min. E. min. E. min.
10.74 10.42 7.23 4.03 0.82 -
Diam.Var.Area estr. 12 12 12 12 12 12 12 12
2.26195 2.26195 2.26195 2.26195 2.26195 2.26195 2.26195 2.26195
Sep. 19.66 20.26 29.21 52.40 257.94 94.92 94.92 94.92
Sep. real 19.66 20.26 29.21 52.40 94.92 94.92 94.92 94.92
ESTRIBOS EN VIGA EXTERIOR Vu 154.69 152.36 128.99 105.53 81.96 58.26 37.47 36.87
vu 24.1438 23.7799 20.1335 16.472 12.7928 9.09332 5.84801 5.75522
Vc 8.8686 8.8686 8.8686 8.8686 8.8686 8.8686 8.8686 8.8686
Vs Diseño Diseño Diseño Diseño Diseño Diseño E. min. E. min.
CALCULO DE LA CONTRAFLECHA DATOS
15.28 14.91 11.26 7.60 3.92 0.22 -
Diam.Var.Area estr. 12 12 12 12 12 12 12 12
2.26195 2.26195 2.26195 2.26195 2.26195 2.26195 2.26195 2.26195
Sep. 13.82 14.16 18.74 27.77 53.80 939.46 94.92 94.92
Sep. real 13.82 14.16 18.74 27.77 53.80 94.92 94.92 94.92
5.78
36.87
Ea = F´c = Fy = Es = Ec = L=
280 4200 2100000 ###### 30
As = B= t= bw =
172.42 2.73 200.00 45.00
h= n= At =
kg/cm2 kg/cm2 kg/cm2 kg/cm2 m
Es1 = Es2 = Es3 =
cm2 m cm cm
2.00 m 8.96421 1545.57 cm2
52.5 G Pa 1.7E+07 250998 1552.37
profundidad del eje neutro
USO DE LA FORMULA GENERAL DE LA ECUACION CUADRATICA a= b= c=
136.25 1545.57 -309114
c1 = c2 =
42.2959 -53.64
Cálculo de la Inercia sección agrietada de la viga
Icg =
-1E+07 cm4
Cálculo de las deformaciones WM = f WM =
13.0782 T/m 1.41974 cm
Def total centro de la luz 1.56401 cm
WD = f WV = WP = f WP =
0.8595 0.09331 7.335 0.05096
T/m cm T/m cm
Def Inm = 1.56401 cm Def dif = 0 cm
Contraflecha 3.94036 cm
c 42.2959
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