-
Pretensado v2.02
Una Colaboracin de: RAUL PIA GUERRA, RONALD VEGA ROMERO
L (m) = 35.00
1.58
1.83 Ok !!
106.68 cm
h (cm) =
Ac (cm2)=
20.32 cm Ic(cm4)=
182.88 cm C1 --> Ct (cm) =
C2 --> Cb (cm) =
25.40 Ic/A --> r2 (cm2) =
Wo(Kg/m)=
20.32
Ic/Cb--> Sb (cm3) =
71.12 cm Ic/Ct--> St (cm3) =
Tablero: ts (cm) = 17 ------> ts (cm) = 20
Ec (losa) =
L/4 = 8.75 Ec (viga) =
12ts+bi/2= 2.93 bef (m) = 2.10
S = 2.10 n=
be (m) = 1.71
be (m) = 171 cm
1 20 cm
106.68 cm 2.5 cm 1 3420.0
ESPESOR DE ASFALTO (m)
N CARRILES
DIM. CARRILES (m)
DIM. TABLERO (m)
VEREDAS (m)
LONGITUD DEL PUENTE
Ancho transfomado: (b ef ) x(n) ---->
PROPIEDADES DE LA SECCIN COMPUESTA
hmin Peralte (m)
GEOMETRIA DE LA VIGA POSTENSADA AASHTO
h Peralte (m) =
BERMA CENTRAL (m)
N DE VIGAS (Nb)
S (m) =
Seccion Compuesta
Ancho efectivo del Ala
TIPO VIGA AASHTO:
A (cm2)
Lh 045.0min
30
)3(
St s
-
2 7000.0
10420.0
eg = 102.97205.38 195.38 Yc (cm) = 126.21
2 Ic (cm4) = 5.488E+07
Sbc (cm3)= 4.349E+05
C2 = 92.41 Stc (cm3)= 6.932E+05
rc2 (cm2)= 5267.11
71.12 cm
1) Losa = 1.008 t/m
2) Silla = 0.064 t/m
3) Viga = 1.680 t/m
4) Vereda = 0.144 t/m WDC = 2.97 t/m
5) Berma C. = 0.000 t/m
6) Baranda = 0.075 t/m
WDW = 0.203 t/m
MC de D = 246.69 t.m
MC de C = 145.78 t.m
M HL-93 = 392.46 t.m
n = 1.225 m = 1.00
Kg = 1.28E+08 cm4 mg = 0.622
MLL = 244.11 t.m
MIM = 50.63 t.m
Sb = 3.303E+05 cm3
Sbc = 4.349E+05 cm3
VIGA PROPIA: MD = 257.25 t.m
LOSA Y SILLA: MS = 164.15 t.m
BARANDAS, VEREDAS: Mb = 33.53 t.m
CARPETA ASFALTICA: Mws = 31.01 t.m
Carpeta Asfaltica------------------>
Linea de Influencia ----------------->
Carga repartida----------------->
DISTRIBUCIN DE CARGAS VIVAS VEHICULARES
CALCULO DE ESFUERZOS FIBRARIOS
Para la combinacin de Servicio III el esfuerzo fibrario en la fibra inferior fb es -->
CALCULO DE MOMENTOS y CARGAS W DC - W DW
1.0
3
2.0
6.0
)*
()(2900
075.0tsL
Kg
L
SSmg
-
32.59 kg/cm2 ------->
164.06 kg/cm2
9.14 cm
12 cm
ec = 80.41 cm
Pe = 4.25E+05 kg
* Asumiendo perdida del 25%
Pi = 5.66E+05 kg
* Considerando Diametro de Torones, fpi=75%fpu
fpu = 18900 kg/cm2
fpi = 14175 kg/cm2
39.95 cm2
40.47
42
Asp = 41.46 cm2
Pi = 587669.985 kg
Pe = 440752 kg
203.2
mm
1.00 254 mm
51
yt= 139.64 mm 203 mm
51
e = 784.46
711.2 mm e = 78.45
fpi = 13230 kg/cm2
Distancia del centroide a la fibra inferior aprox. 0.05h-->
Esfuerzo de compresin requerido en la fibra interior-->
Esfuerzo de traccin mximo --------------------------------->
Nmero de torones aprox. -------->
Se toma ----->
fbp debido al pretensado ------------------------------------->
Nmero de torones para el diseo
CHEKEO DE ESFUERZO EN LA SECCIN
Asp (area requerida de torones) ->
a) Esfuerzo en la transferencia
Pi=(fbi)x(Asp)
Sb
ecPe
A
Pefb p
*
-
Perdida por relajacin inicial = 10%
Pi = 528902.9865 kg
ft = -28.853 kg/cm2 ---> Compresin Ok !!!!
fb = -123.264 kg/cm2
fb = 123.264 kg/cm2
Ok !!: Cumple Lmite en Tracin: f'ti > fb
f'ti = 336.000 kg/cm2
Pe = 440752.4888 kg
ft = -86.818 kg/cm2 ---> Compresin Ok !!!!
ft = 86.818 kg/cm2
---> Ok !!!! : f'ci > fb
f'ci = 189.000 kg/cm2
fb = -58.724 kg/cm2 Compresin Ok !!!! Perdera su Traccin
c) Incluyendo los Esfuerzos debido a LL + IM
b) Esfuerzo en Servicio
Fibra Superior
Fibra Inferior
Fibra Superior
Fibra Inferior
Fibra Superior
St
M
r
Cte
A
Pift D )
*1(
2
Sb
M
r
Cbe
A
Pifb D )
*1(
2
C
bwsSD
St
MM
St
MM
r
Cte
A
Pift
)()()
*1(
2
C
bwsSD
Sb
MM
Sb
MM
r
Cbe
A
Pift
)()()
*1(
2
C
impLL
C
bwsSD
St
MM
St
MM
St
MM
r
Cte
A
Pift
)(*8.0)()()
*1(
2
-
ft = -120.834 kg/cm2
ft = 120.834 kg/cm2
---> Ok !!!! : f'ci > ft
f'ci = 252.000 kg/cm2
fb= -4.502 kg/cm2
---> Ok !!!! : f'ti > fb
f'ti = 32.585 kg/cm2
Fibra Inferior
C
impLL
C
bwsSD
Sb
MM
Sb
MM
Sb
MM
r
Cbe
A
Pifb
)(*8.0)()()
*1(
2
-
23.60 f'c = 280
8.40 ( 8.40 ) fy = 4200
0.60
0.00
4 f'c = 420
0.05 fy = 4200
2.10
VI
182.88
6999.99
30523082.9
90.47
92.41
4361.28
1681.63
3.303E+05
3.374E+05
Silla: -------> Silla (cm) 2.5
254512 Kg/cm2
311712 Kg/cm2
0.816
(cm) 2 (cm2)
Y - Yc (Y - Yc)2
195.38 668199.6 69.17 4785 16364700
A*Y (cm3) A*2 (cm4)
ESPESOR DE ASFALTO (m)
N CARRILES
DIM. CARRILES (m)
DIM. TABLERO (m)
VEREDAS (m)
VIGA
LOSA
BERMA CENTRAL (m)
N DE VIGAS (Nb)
S (m) =
TIPO VIGA AASHTO:
Y (cm)
-
92.41 646868.7 -33.80 1142.2 7995384
1315068.3 24360084
3.63 14.51 14.51
13.2 13.2
6.6 6.6
L/4 = 8.75 m
fb= 196.65 Kg/cm2
4.3 4.3
1.0
3
2.0
6.0
)*
()(2900
075.0tsL
Kg
L
SSmg
Sbc
MMMM
Sb
MMfb IMPLLwsbSD
))(*8.0()(
-
kg/cm2 ------->
ACERO: GRADO 270
Toron: 0.5"
As 0.5" 0.9871 cm2
D 0.5" 12.7 mm
Distancia: # Torones:
510
459
408 Distancia
357 51
306 102
255 153
204 204
153 255
102 306
51 357
408
459
mm 510
cm
DISEO A FLEXION
f'c = 490
Aps (cm2) = 39.95 a (cm) = 12.74
+ + + + + + + + + +
+ + + + + + + + + +
+ + + + + +
+ + + + + +
+ +
Combinaciones
Sb
ecPe
A
Pefb p
*
cft '*59.1max
-
fps (Kg/cm2) = 14175 Mn(T-m) = 929.61
b (cm) = 106.68 Mn = 836.65d (cm) = 170.54
e (cm) = 12.34
Mdc (T-m) 454.94 Mu (T-m) = 1074.44
Mdw (T-m) 31.01
M LL (T-m) 244.11 Mn > Mu ERROR
M im (T-m) 50.63
Ok !!: Cumple Lmite en Tracin: f'ti > fb
Compresin Ok !!!! Perdera su Traccin
-
kg/cm2
kg/cm2
kg/cm2
kg/cm2
VIGA
LOSA
-
w = 0.952 t/m
-
Tramo # aprox # torones Acum #t
1 24.0 15 ( 15.00 )
1 24.0 15 ( 30.00 )
1 24.0 10 ( 40.00 )
2 24.0 10 ( 50.00 )
2 21.9 0 ( 50.00 )
2 19.9 0 ( 50.00 )
2 17.9 0 ( 50.00 )
2 15.9 0 ( 50.00 )
3 4.0 0 ( 50.00 )
3 4.0 0 ( 50.00 )
TOTAL: 50 -----> Hacer Nueva Combinacin
Combinaciones
-
30.48 cm
10.16 h (cm) = 71.12
7.62 Ac (cm2)= 1780.64
Ic(cm4)= 946926.49
15.24 cm C1 (cm) = 39.14
71.12 cm C2 (cm) = 31.98
r2 (cm2) = 529.03
12.7 Wo(Kg/m)= 428.59
12.7
40.6 cm
30.48 cm
15.24 h (cm) = 91.44
7.62 Ac (cm2)= 2380.64
Ic(cm4)= 2121906.18
15.24 cm C1 (cm) = 51.23
91.44 cm C2 (cm) = 40.21
r2 (cm2) = 890.32
15.24 Wo(Kg/m)= 571.45
15.24
45.72 cm
40.64 cm
17.78 h (cm) = 114.30
11.43 Ac (cm2)= 3612.90
Ic(cm4)= 5219125.85
17.78 cm C1 (cm) = 62.81
114.3 cm C2 (cm) = 51.49
r2 (cm2) = 1445.16
19.05 Wo(Kg/m)= 867.60
17.78
55.88 cm
50.8 cm
TIPO I
TIPO II
TIPO III
TIPO IV
De 10.67 a 13.72 metros
De 12.20 a 15.24 metros
De 16.76 a 24.38 metros
De 21.34 a 30.48 metros
-
20.32 h (cm) = 137.16
15.24 Ac (cm2)= 5090.31
Ic(cm4)= 10852859.81
20.32 cm C1 (cm) = 74.35
137.16 cm C2 (cm) = 62.81
r2 (cm2) = 2129.03
22.86 Wo(Kg/m)= 1223.27
20.32
66.04 cm
106.68 cm
12.7 h (cm) = 160.02
7.6 Ac (cm2)= 6535.47
Ic(cm4)= 21693149.44
20.32 cm Ct =C1 (cm) = 78.84
160.02 cm Cb =C2 (cm) = 81.18
r2 (cm2) = 3316.12
25.4 Wo(Kg/m)= 1570.01
Sb(cm3) = 267228.1
20.32 St (cm3) = 275148.52
71.12 cm
106.68 cm
12.7 h (cm) = 182.88
7.6 Ac (cm2)= 6999.99
Ic(cm4)= 30523082.90
20.32 cm C1 (cm) = 90.47
182.88 cm C2 (cm) = 92.41
r2 (cm2) = 4361.28
25.4 Wo(Kg/m)= 1681.63
20.32
71.12 cm
De 33.53 a 42.67 metros
TIPO V
TIPO VI
De 27.43 a 36.58 metros
-
Bs Bi h1
(cm) (cm) (cm)
I 30.48 40.6 12.7
h (plg) = 28 II 30.48 45.72 15.24
Ac(plg2) = 276 III 40.64 55.88 17.78
Ic (plg4)= 22750 IV 50.8 66.04 20.32
C1 (plg) = 15.41 V 106.68 71.12 20.32
C2 (plg) = 12.59 VI 106.68 71.12 20.32
r2 (plg2) = 82 OTRO 150 97.5 13
Wo(lb/pie)= 288
Bs: 150
h4: 7.62
h3: 7.62
h (plg) = 36
Ac(plg2) = 369 Htotal: 200 cm
Ic (plg4)= 50979
C1 (plg) = 20.17 h2: 130
C2 (plg) = 15.83
r2 (plg2) = 138 h1: 13
Wo(lb/pie)= 384
Bi: 97.5
h (plg) = 45
Ac(plg2) = 560
Ic (plg4)= 125390
C1 (plg) = 24.73
C2 (plg) = 20.27
r2 (plg2) = 224
Wo(lb/pie)= 583
OTRO (cm)
TIPODe 10.67 a 13.72 metros
De 12.20 a 15.24 metros
De 16.76 a 24.38 metros
De 21.34 a 30.48 metros
-
h (plg) = 54
Ac(plg2) = 789
Ic (plg4)= 260741
C1 (plg) = 29.27
C2 (plg) = 24.73
r2 (plg2) = 330
Wo(lb/pie)= 822
h (plg) = 63
Ac(plg2) = 1013
Ic (plg4)= 521180
C1 (plg) = 31.04
C2 (plg) = 31.96
r2 (plg2) = 514
Wo(lb/pie)= 1055
h (plg) = 72
Ac(plg2) = 1085
Ic (plg4)= 733320
C1 (plg) = 35.62
C2 (plg) = 36.38
r2 (plg2) = 676
Wo(lb/pie)= 1130
De 33.53 a 42.67 metros
De 27.43 a 36.58 metros
-
h2 h3 h4 Htotal tw h(cm) Ac Ic
(cm) (cm) (cm) (cm) (cm) h(cm) (cm2) (cm4)
12.7 7.62 10.16 71.12 15.24 71.12 1780.6416 946926.4932
15.24 7.62 15.24 91.44 15.24 91.44 2380.6404 2121906.185
19.05 11.43 17.78 114.3 17.78 114.30 3612.896 5219125.846
22.86 15.24 20.32 137.16 20.32 137.16 5090.3124 10852859.81
25.40 7.60 12.70 160.02 20.32 160.02 6535.4708 21693149.44
25.40 7.60 12.70 182.88 20.32 182.88 6999.986 30523082.9
130 7.62 7.62 200 15.6 200.00 11044.39 45304145.46
cm
h (cm) = 200.00 A (cm2) (cm)
tw: Ac (cm2)= 11044.39 5 1143.000 196.19
15.6 cm Ic(cm4)= 45304145.46 4 630.936 189.60
C1 (cm) = 116.98 3 651.456 163.88
C2 (cm) = 83.02 2 7351.500 62.31
r2 (cm2) = 4102.00 1 1267.500 6.5
h' (cm)= 41.76 11044.39
cm
OTRO (cm)
-
Ct =c1 Cb =c2 r2 wo
(cm) (cm) (cm) (Kg/m)
39.14 31.98 529.03 428.59
51.23 40.21 890.32 571.45
62.81 51.49 1445.16 867.6
74.35 62.81 2129.03 1223.27
78.84 81.19 3316.12 1570.01
90.47 92.41 4361.28 1681.63
116.98 83.02 4102.00 -
Ay = - c2 A2 Ip
224245.17 113.17 14637988.2 5530.6
119625.92 106.58 7166605.2 2382.6
106760.61 80.86 4259063.5 94672.7
458074.5 -20.71 3154073.4 8543678.4
8238.75 -76.52 7422300.2 17850.625
916944.95 36640030.4 8664115.0
-
(pulg) (mm) (pulg2) (mm2)
0.25" 0.25 6.35 0.036 23.22
0.313" 0.313 7.94 0.058 37.42
0.375" 0.375 9.53 0.085 54.84
0.438" 0.438 11.11 0.115 74.19
0.5" 0.5 12.7 0.153 98.71
0.6" 0.6 15.24 0.217 140
DIAMETRODiametro Nominal Area Nominal
