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 = 100%
fpu = 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= 2.826 Ton/m
Reacc.=Wbalanc*L/2 = 16.96 Ton 19.41 Ton 14.61 Ton
Despejando Pe la ecuacin de Carga Equivalente
Pe = 156.5 Ton 9.20687783
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
29. 27
-50. 69
0. 000
-15. 52
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40
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20
10
0
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S pan 1 S pan 2
M o m en t D iag ram s (N o R ed i s t rib u t io n )Fi l e : 2VC 12MSIMPL E
Mo
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P os t -T ens ioning S ec ondary
37. 35
-20. 93
13. 49
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M o m en t D iag ram s (N o R ed i s t rib u t io n )Fi l e : 2VC 12MSIMPL E
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D ead Load S uperim pos ed D ead Load
22. 49
0. 000
11. 24
-17. 2215
10
5
0
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M o m en t D iag ram s (N o R ed i s t rib u t io n )Fi l e : 2VC 12MSIMPL E
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L iv e Load M in Liv e Load M ax
37. 35
-20. 93
13. 49
-7. 560
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10
0
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M o m en t D iag ram s (N o R ed i s t rib u t io n )Fi l e : 2VC 12MSIMPL E
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D ead Load S uperim pos ed D ead Load
22. 49
0. 000
11. 24
-17. 2215
10
5
0
-5
-10
-15
-20
S pan 1 S pan 2
M o m en t D iag ram s (N o R ed i s t rib u t io n )Fi l e : 2VC 12MSIMPL E
Mo
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L iv e Load M in Liv e Load M ax
31. 34
-44. 92
0. 000
-9. 700
40
30
20
10
0
-10
-20
-30
S pan 1 S pan 2
M o m en t D iag ram s (N o R ed i s t rib u t io n )Fi l e : 2VC 12Mre ve rsa
Mo
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nt
[
Tm
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P os t -T ens ioning S ec ondary
balanccmaligppK = )(*
2
8
L
fPepresf =
DIAGRAMA DE MOMENTOS
VERIFICANDO ESFUERZOS ADMISIBLES:
ESTADO FINAL
Ubicacin: 0.4 L1 Ubicacin: 1.0 L1
Momentos SAP s t s b Momentos SAP s t s bTon.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 -65.2 -65.2 Axial -65.2 -65.2
-29.270 122.0 -122.0 50.690 -211.2 211.2
Hiperestticos 6.208 Hiperestticos 15.520
Los esfuerzos Finales sern: Los esfuerzos Finales sern:
Combinacin s t s b Combinacin s t s bpresf 56.7 -187.2 presf -276.4 146.0
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 = -133.7 3.3 S = 29.1 -159.5
OK OK OK OK
Esfuerzos Admisibles:
s adm (comp.) = -210.0 kg/cm2
s adm (traccin) = 29.9 kg/cm2
Estados de carga
pretensado
Estados de carga
pretensado
0
0.1
0.2
0.3
0.4
0.5
0.6
-150-100-50050
h (
m)
ESF (kg/cm2)
DIAGRAMA DE ESFUERZOS FINALES
29. 27
-50. 69
0. 000
-15. 52
50
40
30
20
10
0
-10
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-30
S pan 1 S pan 2
M o m en t D iag ram s (N o R ed i s t rib u t io n )Fi l e : 2VC 12MSIMPL E
Mo
me
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[
Tm
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P os t -T ens ioning S ec ondary
0
0.1
0.2
0.3
0.4
0.5
0.6
-200-150-100-50050
h (
m)
ESF (kg/cm2)
DIAGRAMA DE ESFUERZOS FINALES
37. 35
-20. 93
13. 49
-7. 560
20
10
0
-10
-20
-30
-40
S pan 1 S pan 2
M o m en t D iag ram s (N o R ed i s t rib u t io n )Fi l e : 2VC 12MSIMPL E
Mo
me
nt
[
Tm
]
D ead Load S uperim pos ed D ead Load
22. 49
0. 000
11. 24
-17. 2215
10
5
0
-5
-10
-15
-20
S pan 1 S pan 2
M o m en t D iag ram s (N o R ed i s t rib u t io n )Fi l e : 2VC 12MSIMPL E
Mo
me
nt
[
Tm
]
L iv e Load M in Liv e Load M ax
37. 35
-20. 93
13. 49
-7. 560
20
10
0
-10
-20
-30
-40
S pan 1 S pan 2
M o m en t D iag ram s (N o R ed i s t rib u t io n )Fi l e : 2VC 12MSIMPL E
Mo
me
nt
[
Tm
]
D ead Load S uperim pos ed D ead Load
22. 49
0. 000
11. 24
-17. 2215
10
5
0
-5
-10
-15
-20
S pan 1 S pan 2
M o m en t D iag ram s (N o R ed i s t rib u t io n )Fi l e : 2VC 12MSIMPL E
Mo
me
nt
[
Tm
]
L iv e Load M in Liv e Load M ax
31. 34
-44. 92
0. 000
-9. 700
40
30
20
10
0
-10
-20
-30
S pan 1 S pan 2
M o m en t D iag ram s (N o R ed i s t rib u t io n )Fi l e : 2VC 12Mre ve rsa
Mo
me
nt
[
Tm
]
P os t -T ens ioning S ec ondary
cfcadm '6.0_ =s cftadm '6.1_ =s
ESTADO INICIAL:
Pi = 180.0 Ton
Ubicacin: 0.4 L1 Ubicacin: 1.0 L1
Combinacin s t s b Combinacin s t s bpresf 65.3 -215.2 presf -317.9 167.9
pp+alig -87.2 87.2 pp+alig 155.6 -155.6
S = -22.0 -128.0 S = -162.3 12.3
OK OK OK OK
Esfuerzos Admisibles:
s adm (comp.) = -168.0 kg/cm2
s adm (traccin) = 13.4 kg/cm2
ES
0
-22.0
-128.0
0
29. 27
-50. 69
0. 000
-15. 52
50
40
30
20
10
0
-10
-20
-30
S pan 1 S pan 2
M o m en t D iag ram s (N o R ed i s t rib u t io n )Fi l e : 2VC 12MSIMPL E
Mo
me
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[
Tm
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P os t -T ens ioning S ec ondary
0
0.1
0.2
0.3
0.4
0.5
0.6
-140-120-100-80-60-40-200
h (
m)
ESF (kg/cm2)
DIAGRAMA DE ESFUERZOS INICIALES
-0.1
6E-16
0.1
0.2
0.3
0.4
0.5
0.6
-200-150-100-50050
h (
m)
ESF (kg/cm2)
DIAGRAMA DE ESFUERZOS INICIALES
37. 35
-20. 93
13. 49
-7. 560
20
10
0
-10
-20
-30
-40
S pan 1 S pan 2
M o m en t D iag ram s (N o R ed i s t rib u t io n )Fi l e : 2VC 12MSIMPL E
Mo
me
nt
[
Tm
]
D ead Load S uperim pos ed D ead Load
22. 49
0. 000
11. 24
-17. 2215
10
5
0
-5
-10
-15
-20
S pan 1 S pan 2
M o m en t D iag ram s (N o R ed i s t rib u t io n )Fi l e : 2VC 12MSIMPL E
Mo
me
nt
[
Tm
]
L iv e Load M in Liv e Load M ax
37. 35
-20. 93
13. 49
-7. 560
20
10
0
-10
-20
-30
-40
S pan 1 S pan 2
M o m en t D iag ram s (N o R ed i s t rib u t io n )Fi l e : 2VC 12MSIMPL E
Mo
me
nt
[
Tm
]
D ead Load S uperim pos ed D ead Load
22. 49
0. 000
11. 24
-17. 2215
10
5
0
-5
-10
-15
-20
S pan 1 S pan 2
M o m en t D iag ram s (N o R ed i s t rib u t io n )Fi l e : 2VC 12MSIMPL E
Mo
me
nt
[
Tm
]
L iv e Load M in Liv e Load M ax
31. 34
-44. 92
0. 000
-9. 700
40
30
20
10
0
-10
-20
-30
S pan 1 S pan 2
M o m en t D iag ram s (N o R ed i s t rib u t io n )Fi l e : 2VC 12Mre ve rsa
Mo
me
nt
[
Tm
]
P os t -T ens ioning S ec ondary
cifcadm '6.0_ =s icftadm '8.0_ =s
PREGUNTA 2 :
-3.26
16.302
Colocando estos valores en el SAP2000 se obtiene
DIAGRAMA DE MOMENTOS
29. 27
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40
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-10
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M o m en t D iag ram s (N o R ed i s t rib u t io n )Fi l e : 2VC 12MSIMPL E
Mo
me
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[
Tm
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P os t -T ens ioning S ec ondary
37. 35
-20. 93
13. 49
-7. 560
20
10
0
-10
-20
-30
-40
S pan 1 S pan 2
M o m en t D iag ram s (N o R ed i s t rib u t io n )Fi l e : 2VC 12MSIMPL E
Mo
me
nt
[
Tm
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D ead Load S uperim pos ed D ead Load
22. 49
0. 000
11. 24
-17. 2215
10
5
0
-5
-10
-15
-20
S pan 1 S pan 2
M o m en t D iag ram s (N o R ed i s t rib u t io n )Fi l e : 2VC 12MSIMPL E
Mo
me
nt
[
Tm
]
L iv e Load M in Liv e Load M ax
37. 35
-20. 93
13. 49
-7. 560
20
10
0
-10
-20
-30
-40
S pan 1 S pan 2
M o m en t D iag ram s (N o R ed i s t rib u t io n )Fi l e : 2VC 12MSIMPL E
Mo
me
nt
[
Tm
]
D ead Load S uperim pos ed D ead Load
22. 49
0. 000
11. 24
-17. 2215
10
5
0
-5
-10
-15
-20
S pan 1 S pan 2
M o m en t D iag ram s (N o R ed i s t rib u t io n )Fi l e : 2VC 12MSIMPL E
Mo
me
nt
[
Tm
]
L iv e Load M in Liv e Load M ax
31. 34
-44. 92
0. 000
-9. 700
40
30
20
10
0
-10
-20
-30
S pan 1 S pan 2
M o m en t D iag ram s (N o R ed i s t rib u t io n )Fi l e : 2VC 12Mre ve rsa
Mo
me
nt
[
Tm
]
P os t -T ens ioning S ec ondary
VERIFICANDO ESFUERZOS ADMISIBLES:
ESTADO FINAL
Ubicacin: 0.4 L1 Ubicacin: 1.0 L1
Momentos SAP s t s b Momentos SAP s t s bTon.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 -65.2 -65.2 Axial -65.2 -65.2
-31.340 130.6 -130.6 44.920 -187.2 187.2
Hiperestticos 3.880 Hiperestticos 9.700
Los esfuerzos Finales sern: Los esfuerzos Finales sern:
Combinacin s t s b Combinacin s t s bpresf 65.4 -195.8 presf -252.4 122.0
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 = -125.1 -5.3 S = 53.2 -183.6
OK OK NO CUMPLE OK
Esfuerzos Admisibles:
s adm (comp.) = -210.0 kg/cm2
s adm (traccin) = 29.9 kg/cm2
ESTADO INICIAL:
Pi = 180.0 Ton
Ubicacin: 0.4 L1 Ubicacin: 1.0 L1
Combinacin s t s b Combinacin s t s bpresf 75.2 -225.2 presf -290.2 140.2
pp+alig -87.2 87.2 pp+alig 155.6 -155.6
S = -12.0 -138.0 S = -134.6 -15.4
OK OK OK OK
Esfuerzos Admisibles:
s adm (comp.) = -168.0 kg/cm2
s adm (traccin) = 13.4 kg/cm2
ES
0
-12.0
-138.0
0
Estados de carga Estados de carga
pretensado pretensado
29. 27
-50. 69
0. 000
-15. 52
50
40
30
20
10
0
-10
-20
-30
S pan 1 S pan 2
M o m en t D iag ram s (N o R ed i s t rib u t io n )Fi l e : 2VC 12MSIMPL E
Mo
me
nt
[
Tm
]
P os t -T ens ioning S ec ondary
37. 35
-20. 93
13. 49
-7. 560
20
10
0
-10
-20
-30
-40
S pan 1 S pan 2
M o m en t D iag ram s (N o R ed i s t rib u t io n )Fi l e : 2VC 12MSIMPL E
Mo
me
nt
[
Tm
]
D ead Load S uperim pos ed D ead Load
22. 49
0. 000
11. 24
-17. 2215
10
5
0
-5
-10
-15
-20
S pan 1 S pan 2
M o m en t D iag ram s (N o R ed i s t rib u t io n )Fi l e : 2VC 12MSIMPL E
Mo
me
nt
[
Tm
]
L iv e Load M in Liv e Load M ax
0
0.1
0.2
0.3
0.4
0.5
0.6
-140-120-100-80-60-40-200
h (
m)
ESF (kg/cm2)
DIAGRAMA DE ESFUERZOS FINALES
-0.1
6E-16
0.1
0.2
0.3
0.4
0.5
0.6
-200-150-100-50050100
h (
m)
ESF (kg/cm2)
DIAGRAMA DE ESFUERZOS FINALES
-0.10
0.00
0.10
0.20
0.30
0.40
0.50
0.60
-150-100-500
h (
m)
ESF (kg/cm2)
DIAGRAMA DE ESFUERZOS INICIALES
-0.1
6E-16
0.1
0.2
0.3
0.4
0.5
0.6
-150-100-500
h (
m)
ESF (kg/cm2)
DIAGRAMA DE ESFUERZOS INICIALES
37. 35
-20. 93
13. 49
-7. 560
20
10
0
-10
-20
-30
-40
S pan 1 S pan 2
M o m en t D iag ram s (N o R ed i s t rib u t io n )Fi l e : 2VC 12MSIMPL E
Mo
me
nt
[
Tm
]
D ead Load S uperim pos ed D ead Load
22. 49
0. 000
11. 24
-17. 2215
10
5
0
-5
-10
-15
-20
S pan 1 S pan 2
M o m en t D iag ram s (N o R ed i s t rib u t io n )Fi l e : 2VC 12MSIMPL E
Mo
me
nt
[
Tm
]
L iv e Load M in Liv e Load M ax
31. 34
-44. 92
0. 000
-9. 700
40
30
20
10
0
-10
-20
-30
S pan 1 S pan 2
M o m en t D iag ram s (N o R ed i s t rib u t io n )Fi l e : 2VC 12Mre ve rsa
Mo
me
nt
[
Tm
]
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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