FACULTAD DE INGENIERIA CIVIL
PREGUNTA 1 :
Datos:
L = 12 m
Ancho Trib = 5 m
g con = 2.4 Ton/m3f'c = 350 Kg/cm2
f'ci = 280 Kg/cm2
s/c 0.25 Ton/m2
Alig = 0.30 Ton/m2
Carga Muerta = 0.15 Ton/m2
Cota fondo = 0.075 m
R = 1.15
K = 110.0% Incrementamos la Carga a Balancear para cumplir los esfuerzos admisiblesfpu = 18900 Kg/cm2
A acero = cm2
Propiedades seccion Viga:
b = 0.40 m
h = 0.60 m
A = 0.240 m2
I = 0.00720 m4
Yb = 0.300 m
Yt = 0.300 m
Zb = 0.0240 m3
Zt = 0.0240 m3
exc = 0.225 m
PARABOLA 2 PARABOLA 1
y1 = 0.300 m y = k*x^2
y0 = 0.075 m dy = 0.450 m 0.225 m
y2 = 0.525 m dx= 0.6 7.2 0.4 4.8
e1= 0.000 m k = dy/dx^2 = 0.009 0.010
e2= 0.225 m x = 0.1 1.2
e3=(e1+e2)/2= 0.1125 m y(L/2) = y0+k*x^2= 0.088 m
e=yb-y(L/2)= 0.213 m a 0.12435 rad 0.09348 rad
7.1250 g 5.3558 g
f = e + e3 = 0.3250 m
Carga Actuantes
Wpp = 0.576 Ton/m
Walig = 1.500 Ton/m
Wcm = 0.750 Ton/m
Ws/c = 1.250 Ton/m
Calculo de Fuerza Final Efectiva (Pe):
Wbalanc = Wpresf= 3.109 Ton/m
Reacc.=Wbalanc*L/2 = 18.65 Ton 21.35 Ton 16.07 Ton
Despejando Pe la ecuacin de Carga Equivalente
Pe = 172.2 Ton 10.1275656
Excentricidad en el extremo = 0.000 m
Mto en los Extremos = 0.000 Ton.m
UNIVESIDAD NACIONAL DE INGENIERIA
Departamento de Estructuras
CONCRETO PRESFORZADO 2010-1
SOLUCIONARIO DE PRACTICA DIRIGIDA - PASO 2
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balanccmaligppK = )(*
2
8
L
fPepresf =
PREGUNTA 2 :
DIAGRAMA DE MOMENTOS
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VERIFICANDO ESFUERZOS ADMISIBLES:
ESTADO FINAL
Ubicacin: 0.4 L1 Ubicacin: 1.0 L1
Momentos
CARGA
EQUIVALENTE
s t s bMomentos
CARGA
EQUIVALENTE
s t s b
Ton.m kg/cm2 kg/cm2 Ton.m kg/cm2 kg/cm2
pp+alig 20.930 -87.2 87.2 pp+alig -37.350 155.6 -155.6
cm 7.560 -31.5 31.5 cm -13.490 56.2 -56.2
s/c 17.220 -71.8 71.8 s/c -22.490 93.7 -93.7
Axial -71.7 -71.7 Axial -71.7 -71.7
-34.490 143.7 -143.7 49.420 -205.9 205.9
Hiperestticos 4.272 Hiperestticos 10.680
Los esfuerzos Finales sern: Los esfuerzos Finales sern:
Combinacin s t s b Combinacin s t s bpresf 72.0 -215.4 presf -277.7 134.2
pp+alig -87.2 87.2 pp+alig 155.6 -155.6
cm -31.5 31.5 cm 56.2 -56.2
s/c -71.8 71.8 s/c 93.7 -93.7
S = -118.5 -25.0 S = 27.9 -171.4
OK OK OK OK
Esfuerzos Admisibles:
s adm (comp.) = -210.0 kg/cm2
s adm (traccin) = 29.9 kg/cm2
ESTADO INICIAL:
Pi = 198.0 Ton
Ubicacin: 0.4 L1 Ubicacin: 1.0 L1
Combinacin s t s b Combinacin s t s bpresf 82.8 -247.8 presf -319.3 154.3
pp+alig -87.2 87.2 pp+alig 155.6 -155.6
S = -4.4 -160.6 S = -163.7 -1.3
OK OK OK OK
Esfuerzos Admisibles:
s adm (comp.) = -168.0 kg/cm2
s adm (traccin) = 13.4 kg/cm2
-160.6
0
Estados de carga Estados de carga
pretensado pretensado
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DIAGRAMA DE ESFUERZOS FINALES
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DIAGRAMA DE ESFUERZOS FINALES
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DIAGRAMA DE ESFUERZOS INICIALES
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DIAGRAMA DE ESFUERZOS INICIALES
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P os t -T ens ioning S ec ondary
cfcadm '6.0_ =s cftadm '6.1_ =s
cifcadm '6.0_ =s icftadm '8.0_ =s
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