7/28/2019 Mathcad - Pregunta 1
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Diseñar el muro de contencion en voladizo con pantalla de seccion variable que se1.muestra en la Fig. 1.
Materiales:
wsc 1t
m2
f'c 210
kg
cm2
fy 4200kg
cm2
B2max 0.5m
Datos:
h p 6.5m 1 32° 2 35° t1 25cm
t 2.50kg
cm2
s1 1.70t
m3
s2 1.90t
m3
DIMENSIONAMIENTO DE LA PANTALLA
K a1 tan
4
1
2
2
0.31 h1 0.6 h p 3.9 m
h2 0.4 h p 2.6 mK
a2tan
4
2
2
2
0.27
P1 K a1 wsc 0.31t
m2
P2 K a1 s1 h1
wsc
s1
2.34
t
m2
P3 K a2 s1 h1
wsc
s1
2.07
t
m2
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7/28/2019 Mathcad - Pregunta 1
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he
wsc s1 h1 s2
4.02 m
P4 K a2 s2 he h2 3.41t
m2
Mu 1.7 P1 h1h1
2h2
P3
h22
2
P2 P1
2h1
h1
3h2
P4 P3 2
h22
3
Mu 50.05 t m
Hallando el valor de t2 mediante la ecuacion
Si: 0.90 b 100cm 0.1275
Mu b d
2
f'c 1 0.59 ( ) d
d Mu
b f'c 1 0.59 ( )
d min d 0.45 m ; usamos: t2 50cm d t2 5cm 45 cm
DIMENSIONAMIENTO DE LA ZAPATA: FSD 1.5 FSV 1.75
hz t2 10cm 60 cm µ tan 2 0.7 h h p hz 7.1 m
m
2.4t
m3
3 0.60 s1 0.4 s2
41.94
t
m3
FA
P1 P2 2
h1P3 P4
2h2
FA 12.29 t
B1 FSD
FA
µ m h 1. m 1.92m usamos: B1 3.00m
B2µ
3
FSV
FSD
B1
2 h 0.06 usamos: B2 0.50m
B B1 B2 3.5 m
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7/28/2019 Mathcad - Pregunta 1
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VERIFICACION POR ESTABILIDAD
PESO(t) BRAZO DEGIRO X (m)
M (t-m)
P1 2.4t
m3
B hz 1 m 5.04 tx1
B
21.75m M1 P1 x1 8.82 t m
P2 2.4t
m3
h p t1 1 m 3.9 tx2 B2 t2
t1
2 0.88m M2 P2 x2 3.41 t m
P3 2.4t
m3
h pt2 t1
2 1 m 1.95 t x3 B2
2 t2 t1 3
0.67m M3 P3 x3 1.3 t m
P4 s1 h1 B1 t2 1 m 16.57 t x4 BB1 t2
2 2.25m M4 P4 x4 37.29 t m
P5 s2 h2 B1 t2 1 m 12.35 t x5 BB1 t2
2 2.25m M5 P5 x5 27.79 t m
Ptotal P1 P2 P3 P4 P5 39.81 t
Mtotal M1 M2 M3 M4 M5 78.61 t m
Deslizamiento:
FA 12.29 t FR µ Ptotal 27.88 t
FR
FA
2.27 >FSD CORRECTO!
Momento de Volteo:
Para hallar el momento de nuestro desarrollo de presiones, actualizamos la presion P3para un hz=0.50m:
P4 K a2 s2 he h2 hz 3.72t
m2
MA P1 h1h1
2h2
P3
h22
2
P2 P1
2h1
h1
3h2
P4 P3 2
h22
3
MA 29.79 t m
MR Mtotal 78.61m t
MR
MA
2.64 >FSV CORRECTO!
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7/28/2019 Mathcad - Pregunta 1
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Presiones en el Terreno:
Condición para que no se registren tracciones:
xo
MR MA
Ptotal
1.23m xo
B
3
B
31.17m e
B
2xo 0.52m CORRECTO!
Hallando esfuerzo maximo en el terreno
max
Ptotal
B 1 m1 6
e
B
21.59t
m2
max t CORRECTO!
DISEÑO DE LA PANTALLA
Refuerzo Vertical:
Hi Mu (t-m) As (cm2) Asmin (cm2) ϕ , s
6.5 51.11 32.78 4.50 ϕ1 @ 0.15m
6.0 41.00 27.20 4.33 ϕ1 @ 0.17m
5.5 32.31 22.18 4.15 ϕ1 @ 0.22m
5.0 24.93 17.76 3.98 ϕ1 @ 0.28m
4.5 18.75 13.90 3.81 ϕ1 @ 0.36m
4.0 13.65 10.58 3.63 ϕ1 @ 0.46m
3.5 9.54 7.29 3.46 ϕ1 @ 0.69m
Refuerzo horizontal:
Arriba: Asmin1 0.002 100 cm 25 cm 5 cm2
2
3Asmin1 3.33 cm
2 ϕ3/8 @ 0.22m ó ϕ1/[email protected]
1
3Asmin1 1.67 cm
2 ϕ3/8 @ 0.40m ó ϕ1/[email protected]
Medio: Asmin2 0.002 100 cm 40 cm 8 cm2
2
3Asmin2 5.33 cm
2 ϕ3/8 @ 0.13m ó ϕ1/[email protected]
1
3Asmin2 2.67 cm
2 ϕ3/8 @ 0.25m ó ϕ1/[email protected]
Abajo:Asmin3 0.002 100 cm 55 cm 11 cm
2
2
3Asmin3 7.33 cm
2 ϕ3/8 @ 0.10m ó ϕ1/[email protected]
1
3Asmin3 3.67 cm
2 ϕ3/8 @ 0.20m ó ϕ1/[email protected]
Distribución de acero:
Interno: ϕ3/8: [email protected], [email protected], [email protected], [email protected]
Externo: ϕ1/2: [email protected], [email protected], [email protected], [email protected]
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7/28/2019 Mathcad - Pregunta 1
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DISEÑO DE LA ZAPATA:
Ws wsc 1 m 1.7 h1 1 m s1 h2 1 m s2 1.4 17.9t
m
W pp
2.4t
m3h
z1 m 1.4 2.02
t
m
Zapata Interior:
Verificacion por Corte:
Min
Ptotal
B 1 m1 6
e
B
1.7 1.98t
m2
Max
Ptotal
B 1 m1 6
e
B
1.7 36.7t
m2
Ld
B1
t2
d 2.05m
Vud Ws W pp 1m Min Ld 12Ptotal e Ld
B3
1.7 1m Min
Ld
2 17.95 t
Vc 0.85 0.53 210 10t
m2
1 m d 29.38 t Vud Vc CORRECTO!
Hallando el Mu:
Li B1 t2 2.5 m
Mui Ws W pp
1m Min
Li2
2
12
Ptotal e Li
B3
1.7
1m Min
Li2
6
32.28 t m
d z hz 9cm 0.51m
As 17.62cm2
ϕ3/4 @ 0.15 m
Zapata exterior:
Wc 12Ptotal e B1
B3
1.7 29.76t
m Wz Max 1 m 36.7
t
m
Mue Wc
B2
2
2 2 Wz Wc
B2
2
3 4.88 t m
As 2.57cm2
Asmin 0.0018 b d z 9.18 cm2
ϕ5/8 @ 0.20 m
Refuerzo Transversal: Asmin 0.0018 100 cm hz 10.8 cm2
ϕ5/8 @ 0.15 m
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7/28/2019 Mathcad - Pregunta 1
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t 1000kg
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7/28/2019 Mathcad - Pregunta 1
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Mu Mu 1 m
FA FA 1 m
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