Diseño de Alas de Puente PDF
April 10, 2023 | Author: Anonymous | Category: N/A
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DISEÑO DE ALAS DE UN PUENTE PUE NTE 1.-DATOS GEOMETRICOS EN EL FIN DE LA ALA DE ESTRIBO DESCRIPCION Espesor parcial - pantalla Espesor parcial - pantalla Espesor total en la base - pantalla Profundidad del Estribo Altura deL peralte de la zapata Altura de la pantalla del ala Largo de zapata Largo de Pie de zapata Largo de Talón de zapata solado
SIMBOLOS E1 = E2 = T=E= Hf = hz = hp = B= B1 = B2 = e=
PROPIEDADES Y CARACTERISTICAS DE LOS MATERIALES Resistencia del terreno Angulo de fricción Coeficiente de fricción Esfuerzo fluencia del Acero de refuerzo Peso especifico del concreto Peso especifico del terreno Coef. de fricción : Concreto./concreto Coef. de fricción : concreto./grava Coef. de fricción : concreto./arena Coef. de fricción : concreto./arcilla Anguo entre la horizontal y la linea accion de E altura adicional por sobrecarga PARAMETROS PARA ALA DEL ESTRIBO f'c = 210.00 Kg/cm² Es= 2.040E+06 Kg/cm² Ec= 217370.65 Kg/cm² fs=0.40*fy fs = 1680.00 Kg/cm² fc=0.40*fc fc= 84.00 K Kg g/cm² r=fs/fc r= 20.00 n=Es/Ec n= 9 .3 8 k=n/(n+r) k= 0 .3 2 j=1-k/3 0.89 fc*j*k= 23.97
VALORES 0.30 0.30 0.60 3.65 0.60 3.05 1.80 0.40 0.80 0.20
σ = Φ =
fi = fy = ɣC = ɣr =
f = f = f = f = Φw = Φ/2 = h' =
UNIDAD m m m m m m m m m m
1.8 Kg/cm² 35 ° 0.7 4200 Kg/cm² 2400 Kg/m³ 1750 Kg/m³ 0.7 0.5 0.4 0.3 17.5 ° 0 m PARAMETROS PARA LA ZAPATAS f'c = 175.00 Kg/cm² Es= 2.040E+06 Kg/cm² Ec= 198431.35 Kg/cm² fs=0.40*fy fs = 1680.00 Kg/cm² fc=0.40*fc fc= 70.00 Kg K g/cm² r=fs/fc r= 24.00 n=Es/Ec n= 10.28 k=n/(n+r) k= 0.30 j=1-k/3 j= 0.90 fc*j*k= 18.89
2.- CONTROL DE ESTABILIDAD DE LAS ALAS DEL ESTRIBO SECCION B - B (AL INICIO DE LA PANTALLA) 2.1 CHEQUEO EN LA SECCION 2.1.1 FUERZ FUERZAS AS HORIZON HORIZONTALES TALES Y VERTIC VERTICALES ALES EMPUJE DE TIERRAS C= E= EH = EV =
C= E= EH = EV=
(Tan(45°-Φ/2))² (1/2)* ɣr*hp²*C E*Cos(Φw) E*Sen(Φw)
FV
DESCRIPCION
Xi
(Kg) 663.313 2196.000 1098.000 4270.000
Empuje de Tierras (4) E1*hp*ɣC (5) (1/2)*E2*hp*ɣC (7) B2*hp*ɣr
Mr
(m) 0 .6 0 0 .4 5 0 .2 0 1 .0 0
8227.313
SUB-TOTAL
0.271 2205.855 Kg 2103.761 Kg/m 663.313 Kg/m
FH
Yi
Mv
(Kg-m) 397.988 988.200 219.600 4270.000
(Kg) 2103.761
(m) 1.017
(Kg-m) 2139.525
5875.788
2103.761
2.1.2 EXCEN EXCENTRICI TRICIDAD DAD ((e) e) :
2139.525
Ancho de la base de la pantalla T= Xo=(Mr-Mv)/ΣFV= e = E/2 E/2 - Xo Xo= = ABS (e) =
Debe cumplir: e < E/6
0.60 0.60 m 0.454 m -0. -0.154 154 m 0.15 0.154 4m
0.154 m
<
NO CUMPLE
0.100
Se controlará con la armadura 2.1.3 CHEQU CHEQUEO EO DE TRACCI TRACCIONES ONES Y COMPR COMPRESION ESIONES ES (p) : SABEMOS QUE LOS ESFUERZOS ADMISIBLES SON: Padm: Esfuerzo admisible a la compresion tadm: Esfuerzo admisible a la traccion
padm = tadm =
0.40*f'c 0.03*f'c
Kg/cm² Kg/cm² Kg/cm² Kg/cm²
≥
= =
84.000 Kg/cm² -6.300 Kg/cm²
VERIFICANDO: p1= p2 = p1= p2 =
(ΣFV/(ar*L))*(1+6*e/ar) (ΣFV/(ar*L))*(1-6*e/ar) (ΣFV/(ar*L))*(1+6*e/ar) (ΣFV/(ar*L))*(1-6*e/ar)
= = = =
3.483 -0.74 3.483 -0.74
≥ ≤ ≤
CUMPLE CUMPLE CUMPLE CUMPLE
-6.300 -6.300 84.000 84.000
2.1.4 CHEQU CHEQUEO EO AL VO VOLTEO LTEO (Cv) (Cv) : Cv = Mr/Mv > 2
Cv = 2.746
2.746 >
2.000
CUMPLE
CHEQUEO EN LA SECCION - C (BASE DE LA LA ZAPATA) 2.2 FUERZ 2.2.1 FUERZAS AS HORIZON HORIZONTALES TALES YCVERTIC VERTICALES ALES EMPUJE DE TIERRAS C = (Tan(45°-Φ/2))² E = (1/2)* ɣr*Hf²*C EH = E*CO E*COS( S(Φw) EV = E*Sen(Φw)
DESCRIPCION E; Empuje de Tierras (4) E1*hp*ɣC (5) (1/2)*E2*hp*ɣC (6) Zapata : B*hz* ɣC (7) B2*hp*ɣr
SUB-TOTAL
C= E= EH = EV =
FV (Kg) 949.959 2196.000 1098.000 2592.000 4270.000
11105.959
Xi (m) 1 .8 0 0 .8 5 0 .6 0 0 .9 0 1 .4 0
0.271 3159.098 Kg 3012.885 Kg/m 949.959 Kg/m
FH
Yi
Mv
(Kg-m) 1709.926 1866.600 658.800 2332.800 5978.000
Mr
(Kg) 3012.885
(m) 1.217
(Kg-m) 3666.681
12546.126
3012.885
3666.681
2.2.2 EXCEN EXCENTRICI TRICIDAD DAD ((e) e) : B= Xo=(Mr-Mv)/ΣFV= e = B /2 - X o
1.800 0.800 .800 m e= ABS ABS (e) =
Debe cumplir: e < B/6
0.100
0.100 m 0.1 0.100 00 m <
CUMPLE
0.300
2.2.3 CHEQU CHEQUEO EO DE TRACCI TRACCIONES ONES Y COMPR COMPRESION ESIONES ES (p) : p1 = ΣFV/(B*L)*(1+6*e/B) p2 = ΣFV/(B*L)*(1-6*e/B)
0.823 Kg/cm² 0.411 Kg/cm²
= =
VERIFICANDO: 0.000 0.000
≤ ≤
p1 = p2 =
0.823 0.411
1.8 1.8
≤ ≤
CUMPLE CUMPLE
2.2.4 CHEQU CHEQUEO EO AL VO VOLTEO LTEO (Cv) (Cv) : Cv = Mr/Mv > 2
Cv = 3.422
3.422 >
CUMPLE
2.000
2.2.5 CHEQU CHEQUEO EO AL DESL DESLIZAMIE IZAMIENTO NTO (Cd) : Coef. de fricción: Cd = ΣFV*f/ΣFH
concreto/suelo
fi = Cd = 2.580
>
0.700 2.580
CUMPLE
1.500
3.- CALCULO DE ACERO DE REFUERZO EN FIN DE LA ALAS 3.1 DISEÑ DISEÑO O DEL CUERPO CUERPO - PANTALLA PANTALLA 3.1.1 CALC CALCULO ULO DEL ACERO ACERO POR RO ROTURA TURA MD = Mv
MD =
2139.525 2139 .525 KgKg-m/m m/m
VERIFICACION DEL PERALTE Ms = MD + ML + MI
Hallando los momentos por servicio Ms = MD + ML + MI
Ms =
2139.525
d req. = Mu = d' = d=
13.361 2781.382 10.000 50.000
b= 100.00 cm
El peralte mínimo es : (1/2)
d = (2*Ms/(fc*j*k*b)) Mu = 1,3*(MD + 1,67*(ML + MI)) d = E - d'
d req. <
cm Kg-m/m ccm m cm
CUMPLE
ACERO PRINCIPAL ω = ρ*fy/f'c
Mu = Φ*f'c*b*d²* ω*(1+ω/1,70) 0.5
ω1 = (1,7+(( (1,7+((1,7²-4* 1,7²-4*(1,7*Mu (1,7*Mu/( /(Φ*f'c*b*d²))) )/2 ω2 = (1,7-( (1,7-((1,7²(1,7²-4*(1,7*M 4*(1,7*Mu/( u/(Φ*f'c*b*d²)))
Refuerzo principal mínimo : Tomamos:
0.5
)/2
ω1 = ω2 =
1.700
ρ = As/(b*d) ρ1 =
0.085
ρ2 = 0.00000 0.000 As 1 = 425.00 cm² As 2 = 0 cm² As = 0 cm² Asmín = 0,0018*b*d = 9.00 ccm m² As mín < As NO CUMPLE USAR As mín As = 9.00cm²/m
DISTRIBUCION DE REFUERZO VERTICAL ACERO PRINCIPAL Ø = 5/8 ''
As =
1.99 cm²
@ 22.11 cm
Asm = 0,0018*b*d/2 = Ø = 1/2 '' As =
4.50 cm² 1.29 cm²
@ 28.67 cm
USAR:
Ø 5/8 @ 20cm
ACERO DE MONTAJE (CARA ANTERIOR)
USAR:
Ø 1/2 @ 25cm
DISTRIBUCION DE REFUERZO HORIZONTAL ACERO HORIZONTAL (ARRIBA) : CARA ANTERIOR : As = Ash/3 Ø = 3/8 '' USAR:
Ash= 0.002*b*t= 0.002*b*E1= As = As =
0.71 cm²
@ 35.50 cm
Ø 3/8 @ 35cm
CARA POSTERIOR : As = (2/3)*Ash Ø = 1/2 ''
USAR:
6.000 cm² 2.000 cm²
As = As =
1.29 cm²
4.000 cm²
@ 32.25 cm
Ø 1/2 @ 30cm
ACERO HORIZONTAL (INTERMEDIO) : Ash= 0.002*b*(E1+E)/2= As =
CARA ANTERIOR : As = Ash/3 Ø = 3/8 '' USAR:
As =
0.71 cm²
Ø = 5/8 ''
As = As =
1.99 cm²
CARA ANTERIOR : As = Ash/3 Ø = 1/2 ''
@ 33.17 cm
Ash= 0 0..002*b*t= 0.002*b*E As = As =
1.29 cm²
12.000 cm² 4.000 cm²
@ 32.25 cm
Ø 1/2 @ 30cm
CARA POSTERIOR : As = (2/3)*Ash Ø = 5/8 '' USAR:
6.000 cm²
Ø 5/8 @ 30cm
ACERO HORIZONTAL (INTERMEDIO) :
USAR:
@ 23.67 cm
Ø 3/8 @ 20cm
CARA POSTERIOR : As = (2/3)*Ash
USAR:
9.000 cm² 3.000 cm²
Ø 5/8 @ 20cm
As = As =
1.99 cm²
8.000 cm²
@ 24.88 cm
3.2.-DISEÑO DE ZAPATA EN EL FIN DEL ALA 3.2.1 CALC CALCULO ULO DEL ACERO ACERO POR RO ROTURA TURA
B= q1 q2 Wss = Wpp =
q1 p1*b q2 p2*b Wss = ɣr*(Hf - hz)*b Wpp = ɣC*hz*b
1.80 m 8226.636 4113.318 5337.500 1440.000
3.2.2 ZAPAT ZAPATA A ANTERIOR ANTERIOR (PIE)
Largo de la zapata Kg/m Kg/m Kg/m Kg/m
B1 = 0 .4 0 m qpie = 7312.6 7312.6 Kg/m Kg/m
qpie = q1 - (B1/B)*(q1-q2) MD = Mpp= Wpp*B1*(B1/2)
MD =
ML=Mq= qpie*B1*(B1/2)+(q1-q pie)*(B1/2)*(2*B1/3)
115.2 Kg-m/m
ML = 633. 633.76 76 Kg-m/m
VERIFICACION DEL PERALTE Ms = ML- MD
Hallando los momentos por servicio Ms = ML- MD
Ms =
518.556 K Kg g - m /m
b= 1 10 00 cm
El peralte mínimo es : d = (2*Ms/(fc*j*k*b))
(1/2)
d = hz-d'
d req. = 0.741cm d' = 8.000cm d = 52.000cm
d req. ≤
CUMPLE
ACERO PRINCIPAL
ρ =
Mumáx.= Mu =1,7*ML - 0,9*MD Mu = Φ*f'c*b*d²* ω*(1+ω/1,70) 2
2
ω = ρ*fy/f'c
r = As/(b*d)
)/2
ω1 = 1.7000
ρ1 = 0.123791
)/2
ω2 =
ρ2 = 0.000167
0.5)
w1 = (1, (1,7+(( 7+((1,7 1,7 -4*(1,7*Mu/(f*f'c*b*d ))) 2
2
0.5)
w2 = (1,7-((1,7 -4*(1,7*Mu/(f*f'c*b*d )))
As 1 = Usamos: Acero mínimo = Asmín. = 0.0018*b*d Tomamos:
643.714 ccm m² As = 0.869 ccm m² As m i n = 9.36 cm cm² As mín < As As = 9.36 cm²/m
DISTRIBUCION DE REFUERZO VERTICAL ACERO PRINCIPAL Ø = 5/8 ''
As =
1.99 cm²
@ 21.26 cm
As =
10.80 cm² 1.99 cm²
@ 18.43 cm
Ø 5/8 @ 20cm
USAR:
ACERO TRANSVERSAL Asm = 0,0018*b*hz = Ø = 5/8 ''
Ø 5/8 @ 15cm
USAR:
VERIFICACION DEL CORTANTE VL = Vq = qpie *B1 + (q1-qpie)*(B1/2)
Vq = 3107.8403 Kg
VD = Vpp = Wpp*B1
Vpp =
Vumáx.= Vu =1.7*VL - 0.9*VD
576.000 Kg
Vu = 4764.9285 Kg
Fuerza cortante que absorbe el concreto: Vc = 0.53*(f'c)
1/2
*b*d Vc =
Φ = 0.85 ΦVc > Vu
ΦVc =
30.9896851
≥
0.000
36. 6.4 45845 58453 31 30.9896851 4.765
CUMPLE
As 2 =
NO CUMPLE
0.869 ccm m²
USAR As mín
3.2.3 ZAPAT ZAPATA A POSTERIOR POSTERIOR (TAL (TALON) ON)
B2 = 0.80 m qtalón = 5941.46 Kg/m
qtalón = q2 + (B2/B)*(q1-q2)
Mss = 1708.00 Kg-m/m Mpp = 460.80 Kg-m/m
Mss = Wss*B2*(B2/2) Mpp = Wpp*B2*(B2/2) MD = Mss + Mpp ML = Mq =
MD = 2168.80 Kg-m/m
q2*B q2*B2* 2*(B (B2/ 2/2) 2)+( +(q qtalón-q2)*(B2/2)*(B2/3)
ML = 1511.26 Kg-m/m
VERIFICACION DEL PERALTE Ms = MD + ML
Hallando los momentos por servicio Ms = ML - MD
Ms =
-657.536 Kg-m/m
b=
100.00 cm
El peralte mínimo es : d req. = (2*Ms/(fc*j*k*b))
(1/2)
d = hz-d'
d req. req. = 0.834 0.834 ccm m d' = 8.00 cm d= 52.00 cm
d req. <
CUMPLE
ACERO PRINCIPAL Mumáx =
Mu =1.7*ML - 0.9*MD
Mu =
2
Mu = Φ*f'c*b*d *ω*(1+ω/1,70)
ω= ρ*fy/f'c
2
2
0,5
ω1 = (1,7+((1,7 -4*(1,7*Mu/(Φ*f'c*b*d ))) )/2 2
2
0,5
ω2 = (1,7-((1,7 -4*(1,7*Mu/( Φ*f'c*b*d ))) )/3
ρ = As/(b*d)
ω1 =
1.7
ρ1 = 0.123853
ω2 =
0.0014 644.04 0.546 0.546 9 .3 6
ρ2 = 0.000105
As 1 = As 2 = As = Asmin =
Usamos: Asmín. = 0.0018*b*d
Acero mínimo =
617.23 Kg-m/m
NO CUMPLE
As min < As As = 9.36 cm²/m
Tomamos:
cm c m² cm cm² cm² cm² cm
USAR As mín
DISTRIBUCION DE REFUERZO HORIZONTAL ACERO PRINCIPAL Ø = 5/8 ''
As =
1.99 cm²
@ 21.26 cm
As =
10.80 cm² 1.99 cm²
@ 18.43 cm
Ø 5/8 @ 20cm
USAR:
ACERO TRANSVERSAL Asm = 0,0018*b*hz = Ø = 5/8 '' USAR:
Ø 5/8 @ 15cm
VERIFICACION DEL CORTANTE V = Vq = L
VL = 402 4021.9 1.9109 109 Kg
qtalón *B2 - (qtalón-q2)*(B2/2)
Vss = Wss*B2 Vpp = Wpp*B2 VD = Vss + Vpp
Vss = Vpp = VD =
Vumáx = Vu =1.7*VL - 0.9*VD
4270 Kg 1152 Kg 5422 542 2 Kg-m Kg-m/m /m
Vu = 1957.4486 Kg
Fuerza cortante que absorbe el concreto: Vc = 0,53*(f'c)
ΦVc > Vu
1/2
*b*d
Vc = 36.4 36.458 5845 453 3 ΦVc = 30.989685 30.9896851
≥
1.9574486
CUMPLE
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