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Pgina 1 de 33
DISEO DE ESTRIBOS EN CANTILIVER
PREDIMENSIONAMIENTOh1 = 0.58 B2+B3+B4+B5 = 3.10h2 = 1.90 B2 = 0.30h3 = 1.50 B3 = 0.30h4 = 0.50 B4 = 0.40h = 4.48 B5 = 2.50FSV = 2.00 B1 = -0.71 1.00FSD = 1.50 B = 4.50
FrenadoR3 5% S/C Hs20
t1 t20.40 0.30 S/C = h' = 0.60 Hs20 1.83
Reacciones R1 R2P1
0.580 h1 5% RdFriccin R4 A - A
P20.30 t3 W1
P50.40 t6 P4 W2 Ev E p2=q2= 20.121
M1 p1=q1= 8.1911.900 h2 h = 4.480 FSD= 1.500
W3 /2Eh
2.700 t7 P3
dh1.500 h3
B - BP6
0.500 h4 C - C
0.80 0.30 0.30 0.40 2.50
B1 B2 B3 B4 B54.300
B
q1=P/A(1- 6e/b)q2=P/A(1+ 6e/b)
DIMENSIONES DE LA CAJUELA
Ac4.000
t4 vb Sd t5 t40.30 0.30 3.40 0.30 0.30
0.40 t1
0.30 t2
4.600
Lt
Pgina 2 de 33
VISTA POSTERIOR DEL ESTRIBO
0.880h1+t3
3.100h2+h3-t3
0.500h4
0.300 4.000 0.300
t6 Ln t6
DATOSNUMERO DE VIAS N = 1.00CONCRETO f'c = 210.00 Kg/cm2ACERO fy = 4,200.00 Kg/cm2REACCION DEL PUENTE POR CARGA MUERTA Rd = 26.586 Ton./EstriboREACCION DEL PUENTE POR CARGA VIVA Rl = 48.00 Ton./EstriboIMPACTO I = 0.30ANCHO DE LA CAJUELA A = 4.00 m.LONGITUD DEL PUENTE L = 8.00 m.ANGULO DE FRICCION INTERNA DEL RELLENO = 27.00 FRICCION DEL MATERIAL DE RELLENO f = 0.510PESO ESPECIFICO DEL MATERIAL DE RELLENO Wr = 2.36 Ton/m3PESO ESPECIFICO DEL CONCRETO Wc = 2.40 Ton/m3ANGULO DE FRICCION INTERNA DEL SUELO
MARGEN IZQUIERDA i = 22.83 MARGEN DERECHA d = 22.43
PESO ESPECIFICO DEL SUELO Ws = 2.44 Ton/m3COHESION DEL SUELO
MARGEN IZQUIERDA Ci = 0.097 Kg/Cm2MARGEN DERECHA Cd = 0.061 Kg/Cm2
RESISTENCIA ULTIMA DEL TERRENO (F.S. = 3.00) Qa = 9.23 Ton/m2FRICCION ALBAILERIA SOBRE ALBAILERIA F1 = 0.70FRICCION EN EL SUELO DE CIMENTACION F2i = 0.421FRICCION EN EL SUELO DE CIMENTACION F2d = 0.413COEFICIENTE DE EMPUJE ACTIVO (RELLENO) Ka = 0.376Ka = Tan^2(45-/2)VALORES DE R1, R2, R3 Y R4ANCHO DE LA CAJUELA Ac = 4.00 m.REACCION CARGA MUERTA = Rd/Ac R1 = 6.647 Ton./MlREACCION SOBRECARGA = Rlx(1+I)/Ac R2 = 15.600 Ton./MlFRENADO = 0.05x(960xL+8200)xN/(2 EstribosxAc) R3 = 0.099 Ton./MlFRICCION = 0.05xR1 R4 = 0.332 Ton./Ml
RELACIONES CONCRETO ACEROn = 2.1x10^6/(15000xRAIZ(f'c)) n = 10Fc = 0.4xf'c Fc = 84 Kg/cm2Fs = 0.4xfy Fs = 1,680 Kg/cm2r = Fs/Fc r = 20k = n/(n+r) k = 0.3333j = 1-k/3 j = 0.8889
Pgina 3 de 33
CHEQUEO DE LA SECCION A - A
ESTRIBO CON PUENTE Y CON RELLENO SOBRECARGADO
EMPUJE DE TIERRAh = h1 h = 0.580 m.
h' = 0.600 m.Ka = 0.376B = 0.300 m.E = 0.618 Ton.
Ev = ExSen(/2) Ev = 0.144 Ton.Eh = ExCos(/2) Eh = 0.601 Ton.Punto de Aplicacin de Ehdh = (h+h')/3 dh = 0.393 m.
DISEO DEL PARAPETO
ESPESOR POR MOMENTO FLECTORPi(Ton.) Xi(m.) Mi(Ton-m.)
Eh 0.601 0.393 0.236R3 0.099 2.410 0.239
TOTAL 0.700 0.475
d = RAIZ(2xMix10^5/(Fcxkxjxb)) b = 100 Cm. d = 0.062 m."d" debe ser menor que t2 = 0.300 m.
ESPESOR POR CORTE
Vu = R3+Eh Vu = 0.700 Ton.Vumax = 2.10xbxRAIZ(f'c) Vumax = Vu/ = 0.824 Ton.d = Vumax/(2.10x100xRAIZ(f'c)) d = 0.003 m.
"d" debe ser menor que t2 = 0.300 m.
DISEO POR FLEXION
REFUERZO PRINCIPAL
As = Mix10^5/(Fsxjxd) d = 0.250 m. As = 1.27 Cm2.Cuanta MnimaAsmin = 0.0018xbxd b = 1.000 m. Asmin = 4.50 Cm2.
Escoger el mayor As = 4.50 Cm2.S = 100xAv/As Usar 3/8" @ S = 15.80 Cm.
1/2" @ S = 28.70 Cm. 5/8" @ S = 44.40 Cm. 3/4" @ S = 63.10 Cm.
ACERO DE REPARTICION VERTICAL
As = 0.0015xbxd As = 3.75 Cm2.Usar 3/8" @ S = 18.90 Cm.
1/2" @ S = 34.40 Cm.
REFUERZO HORIZONTAL
As = 0.0025xbxd As = 6.25 Cm2.Usar 3/8" @ S = 11.40 Cm.
1/2" @ S = 20.60 Cm. 5/8" @ S = 32.00 Cm.
E = 0.5xWrx(h+h')2xKa
Pgina 4 de 33
DISEO DE LA CAJUELA
ESPESOR POR MOMENTO FLECTOR
Pi(Ton.) Xi(m.) Mi(Ton-m.)P1 0.418 0.250 0.104p2' 0.288 0.200 0.058P5 0.192 0.133 0.026
TOTAL 0.898 0.188
d = RAIZ(2xMix10^5/(Fcxkxjxb)) b = 100 Cm. d = 0.039 m."d" debe ser menor que t3+ t6 = 0.700 m.
ESPESOR POR CORTE
Vu = P1+ p2 + P5 Vu = 0.898 Ton.Vumax = 2.10xbxRAIZ(f'c) Vumax = Vu/ = 1.056 Ton.d = Vumax/(2.10x100xRAIZ(f'c)) d = 0.003 m.
"d" debe ser menor que t3+ t6 = 0.700 m.
DISEO POR FLEXION
REFUERZO PRINCIPAL
As = Mix10^5/(Fsxjxd) d = 0.650 m. As = 0.19 Cm2.Cuanta MnimaAsmin = 0.0018xbxd b = 1.000 m. Asmin = 11.70 Cm2.
Escoger el mayor As = 11.70 Cm2.S = 100xAv/As Usar 3/8" @ S = 6.10 Cm.
1/2" @ S = 11.00 Cm. 5/8" @ S = 17.10 Cm. 3/4" @ S = 24.30 Cm.
ACERO DE REPARTICION TRANSVERSAL
As = 0.0015xbxd As = 9.75 Cm2.Usar 3/8" @ S = 7.30 Cm.
1/2" @ S = 13.20 Cm. 5/8" @ S = 20.50 Cm.
Pgina 5 de 33
DISEO DEL CUERPO DE LA PANTALLASOPORTARA SOLO EL EMPUJE DEL SUELO
h
ALTURA DE LA ARMADURAAL DISEO EN LA FRANJA INFERIOR
0.500h4 Lc
4.600Lt
PRESION DEL SUELOh = h1+h2+h3 h = 3.980 m.
h' = 0.600 m.Ka = 0.376
B = B3+B2 B = 0.600 m.E = 9.307 Ton.
Ev = ExSen(/2) Ev = 2.173 Ton.Eh = ExCos(/2) Eh = 9.050 Ton.Punto de Aplicacin de Ehdh = (h+h')/3 dh = 1.527 m.
ESPESOR POR MOMENTO FLECTOR
Pi(Ton.) Xi(m.) Mi(Ton-m.)Eh 9.050 1.527 13.819R3 0.099 5.810 0.575
TOTAL 9.149 14.394
d = RAIZ(2xMix10^5/(Fcxkxjxb)) b = 100 Cm. d = 0.340 m."d" debe ser menor que B2+B3 = 0.600 m.
ESPESOR POR CORTE
Vu = Eh+ R3 Vu = 9.149 Ton.Vumax = 2.10xbxRAIZ(f'c) Vumax = Vu/ = 10.764 Ton.d = Vumax/(2.10x100xRAIZ(f'c)) d = 0.035 m.
"d" debe ser menor que B2+B3 = 0.600 m.
DISEO POR FLEXION
REFUERZO PRINCIPAL
As = Mix10^5/(Fsxjxd) d = 0.550 m. As = 17.52 Cm2.Cuanta MnimaAsmin = 0.0018xbxd b = 1.000 m. Asmin = 9.90 Cm2.
Escoger el mayor As = 17.52 Cm2.S = 100xAv/As Usar 3/8" @ S = 4.10 Cm.
1/2" @ S = 7.40 Cm. 5/8" @ S = 11.40 Cm. 3/4" @ S = 16.20 Cm. 1" @ S = 28.50 Cm.
E = 0.5xWrx(h+h')2xKa
Pgina 6 de 33
AREA DE ACERO PARA DISTINTOS VALORES DE "d" y "Y".
B3 Y d dh Eh M As Asmin 1" 3/4" 5/8"0.580 h1 0.300 0.000 0.250 0.393 0.601 0.475 1.27 4.50 112.70 63.10 44.40 53.75
0.500 0.294 0.560 1.218 0.970 2.21 5.29 95.80 53.70 37.80 45.751.000 0.338 0.727 2.050 1.828 3.62 6.08 83.30 46.70 32.90 39.81.500 0.382 0.893 3.099 3.154 5.53 6.88 73.70 41.30 29.10 35.2
Y 2.000 0.426 1.060 4.363 5.061 7.96 7.67 66.10 37.00 26.10 31.552.500 0.471 1.227 5.842 7.655 10.88 8.48 59.80 33.50 23.60 28.55
3.400 H d 3.000 0.515 1.393 7.538 11.036 14.35 9.27 54.70 30.60 21.60 26.13.500 0.559 1.560 9.449 15.326 18.36 10.06 50.40 28.20 19.90 04.000 0.603 1.727 11.576 20.626 22.91 10.85 46.70 26.20 18.40
dh 3.400 0.550 1.527 9.050 14.394 17.52 9.90 51.20 16.20 20.20
0.600B2+B3
d = YxB2/H+B3-.05dh = (h1+y+h')/3REFUERZO VERTICAL POR MONTAJE EN CARA ANTERIOR
"As"montaje = (0.0018xbxd)/2 b = 100 m "As"mont. = 4.95 Cm2.
As = 4.95 Cm2. 3/8" @ S = 14.30 Cm. 1/2" @ S = 26.10 Cm. 5/8" @ S = 40.40 Cm.
REFUERZO HORIZONTAL POR REPARTICION
TERCIO INFERIOR
"As"reparticin = 0.002xbxt 100.0 cm Asr. = 12.00 Cm2.60.0 cm
Cara Anterior Asr / 3 = 4.00 Cm2.
As = 4.00 Cm2. 3/8" @ S = 17.80 Cm. 1/2" @ S = 32.30 Cm. 5/8" @ S = 50.00 Cm.
Cara Posterior 2xAsr / 3 = 8.00 Cm2.
As = 8.00 Cm2. 3/8" @ S = 8.90 Cm. 1/2" @ S = 16.10 Cm. 5/8" @ S = 25.00 Cm.
TERCIO MEDIO
"As"reparticin = 0.002xbxt 100.0 cm Asr. = 9.00 Cm2.45.0 cm
Cara Anterior Asr / 3 = 3.00 Cm2.
As = 3.00 Cm2. 3/8" @ S = 23.70 Cm. 1/2" @ S = 43.00 Cm. 5/8" @ S = 66.70 Cm.
Cara Posterior 2xAsr / 3 = 6.00 Cm2.
As = 6.00 Cm2. 3/8" @ S = 11.80 Cm. 1/2" @ S = 21.50 Cm. 5/8" @ S = 33.30 Cm.
TERCIO SUPERIOR
"As"reparticin = 0.002xbxt 100.0 cm Asr. = 6.00 Cm2.30.0 cm
b =t =
b =t =
b =t =
Pgina 7 de 33
Cara Anterior Asr / 3 = 2.00 Cm2.
As = 2.00 Cm2. 3/8" @ S = 35.50 Cm. 1/2" @ S = 64.50 Cm. 5/8" @ S = 100.00 Cm.
Cara Posterior 2xAsr / 3 = 4.00 Cm2.
As = 4.00 Cm2. 3/8" @ S = 17.80 Cm. 1/2" @ S = 32.30 Cm. 5/8" @ S = 50.00 Cm.
CHEQUEO DE LA SECCION C - C
ESTRIBO SIN PUENTE Y CON RELLENO SOBRECARGADO
EMPUJE DE TIERRAh = h1+h2+h3+h4 h = 4.480 m.
h' = 0.600 m.B = 4.300 m.E = 11.450 Ton.
Ev = ExSen(/2) Ev = 2.673 Ton.Eh = ExCos(/2) Eh = 11.133 Ton.Punto de Aplicacin de Ehdh = (h+h')/3 dh = 1.693 m.
FUERZAS VERTICALES ESTABILIZADORASPi(Ton.) Xi(m.) Mi(Ton-m.)
P1 = t2xh1xWc P1 0.418 1.650 0.690P2 = (t1+t2)xt3xWc P2 0.504 1.450 0.731P3 = B2x(h2+h3)xWc/2 P3 1.224 1.000 1.224P4 = B3x(h2+h3-t3)xWc P4 2.232 1.250 2.790P5 = B4xt6xWc/2 P5 0.192 1.533 0.294P6 = B4xh4Wc P6 5.160 2.150 11.094W1 = B5x(h-h4)xWr W1 23.482 3.050 71.620W2 = B4xt6xWr/2 W2 0.189 1.667 0.315W3 = B4x(h2+h3-t3-t6)xWr W3 2.549 1.600 4.078
Ev 2.673 4.300 11.494TOTAL 38.623 104.330
Xv = SUMA Mi/SUMA Pi Xv = 2.701 m.z = Ehxdh/SUMA Pi z = 0.488 m.e = B/2-(Xv-z) e = -0.063 m.
"e" debe ser menor que B/6 = 0.717 m.CHEQUEOS
a) Compresiones y Tracciones
p = SUMA Pix(1+6xABS(e)/B)/(Bxa) a = 1.0 p = 9.772 Ton/m2.Comparar con Qa = 9.230 Ton/m2.p debe ser menor
Chequeo al Volteo
FSV = SUMA Mi/(Ehxdh) Debe ser mayor FSV = 5.5o igual que 1.5
Chequeo al Deslizamiento
FSD = SUMA PixF1/Eh Debe ser mayor FSD = 1.5o igual que 1.3
E = 0.5xWrx(h+h')2xKa
Pgina 8 de 33
ESTRIBO CON PUENTE Y CON RELLENO SOBRECARGADO
FUERZAS VERTICALES ESTABILIZADORASPi(Ton.) Xi(m.) Mi(Ton-m.)
R1 6.647 1.300 8.641R2 15.600 1.300 20.28
SUM Pivert 38.623 2.701 104.320TOTAL 60.870 133.241
Xv = SUMA Mi/SUMA Pi Xv = 2.189 m.
FUERZAS HORIZONTALESPi(Ton.) Xi(m.) Mi(Ton-m.)
Eh 11.133 1.693 18.848R3 0.099 6.310 0.625R4 0.332 3.900 1.295
TOTAL 11.564 20.768
Yh = SUMA Mi/SUMA Pi Yh = 1.796 m.Punto de aplicacin de la resultantez = SUMA Mi./SUMA Pvert z = 0.341 m.e = B/2-(Xv-z) e = 0.302 m.
CHEQUEOS
Compresiones y Tracciones
p2 = SUMA Pivertx(1+6xABS(e)/B)/(Bxa) a = 1.0 p2 = 20.121 Ton/m2.Comparar con Qa = 9.230 Ton/m2.p debe ser menorNota: La resistencia ltima del terreno presenta un CS = 3
p1 = SUMA Pivertx(1-6xABS(e)/B)/(Bxa) a = 1.0 p1 = 8.191 Ton/m2.
Chequeo al Volteo
FSV = SUMA Mivert/SUMA Mihor) FSV = 6.4Debe ser mayoro igual que 1.5
Chequeo al Deslizamiento
FSD = SUMA PivertxF1/SUMA Pihor FSD = 2.2Debe ser mayoro igual que 1.5
Pgina 9 de 33
DISEO DE LA ZAPATA ANTERIOR ( Pie )
0.500h4
0.800 0.600 2.900
L1 L2 L3
8.191 Ton/m2
20.121 17.901 16.237 8.191 p1p2 p3 p4
11.930
Pp = h4xWc Pp = 1.200 Ton./m2/mM = -PpxL1^2/2+p3xL1^2/2+(p2-p3)xL1^2/3 M = 5.818 Ton.-mV = -PpxL1+p3xL1+ (p2-p3)xL1/2 V = 14.249 Ton.
ESPESOR POR MOMENTO FLECTOR
d = RAIZ(2xMix10^5/(Fcxkxjxb)) b = 100 Cm. d = 0.216 m.d debe ser menor que h4 = 0.500 m.
ESPESOR POR CORTE
Vu = 14.249 Ton.Vumax = 2.10xbxRAIZ(f'c) Vumax = Vu/ = 16.764 Ton.d = Vumax/(2.10xbxRAIZ(f'c)) d = 0.055 m.
d debe ser menor que h4 = 0.500 m.
DISEO POR FLEXION
REFUERZO PRINCIPAL
As = Mix10^5/(Fsxjxd) d = 0.450 m. As = 8.66 Cm2.Cuanta MnimaPmin = 0.0018xbxd b = 1.000 m. Asmin = 8.10 Cm2.
Escoger el mayor As = 8.66 Cm2.S = 100xAv/As Usar 3/8" @ S = 8.20 Cm.
1/2" @ S = 14.90 Cm. 5/8" @ S = 23.10 Cm. 3/4" @ S = 32.80 Cm. 1" @ S = 58.90 Cm.
ACERO DE REPARTICION TRANSVERSAL
As = 0.0015xbxd d = 0.450 m. As = 6.75 Cm2.Usar 3/8" @ S = 10.50 Cm.
1/2" @ S = 19.10 Cm. 5/8" @ S = 29.60 Cm.
Pgina 10 de 33
DISEO DE LA ZAPATA POSTERIOR ( Taln )
0.500h4
0.800 0.600 2.900
L1 L2 L3
8.191 Ton/m220.121 17.901 16.237 p1p2 p3 p4
h = h1+h2+h3 h = 3.980 m.p = Wrxh p = 9.393 Ton./m2Pp = h4xWc Pp = 1.200 Ton./m2/mM = -PpxL3^2/2-pxL3^2/2+p1xL3^2/2+(p4-p1)xL3^2/6 M = 11.269 Ton.-mV = -PpxL3-pxL3+p1xL3+ (p4-p1)xL3/2 V = 4.701 Ton.
ESPESOR POR MOMENTO FLECTOR
d = RAIZ(2xMix10^5/(Fcxkxjxb)) b = 100 Cm. d = 0.301 m."d" debe ser menor que h4 = 0.500 m.
ESPESOR POR CORTE
Vu = 4.701 Ton.Vumax = 2.10xbxRAIZ(f'c) Vumax = Vu/ = 5.531 Ton.d = Vumax/(2.10xbxRAIZ(f'c)) d = 0.018 m.
"d" debe ser menor que h4 = 0.500 m.
DISEO POR FLEXION
REFUERZO PRINCIPAL
As = Mix10^5/(Fsxjxd) d = 0.450 m. As = 16.77 Cm2.Cuanta MnimaPmin = 0.0018xbxd b = 1.000 m. Asmin = 8.10 Cm2.
Escoger el mayor As = 16.77 Cm2.S = 100xAv/As Usar 3/8" @ S = 4.20 Cm.
1/2" @ S = 7.70 Cm. 5/8" @ S = 11.90 Cm. 3/4" @ S = 16.90 Cm. 1" @ S = 30.40 Cm.
ACERO DE REPARTICION TRANSVERSAL
As = 0.0015xbxd d = 0.450 m. As = 6.75 Cm2.Usar 3/8" @ S = 10.50 Cm.
1/2" @ S = 19.10 Cm. 5/8" @ S = 29.60 Cm. 3/4" @ S = 42.10 Cm.
DISEO DE LAS ALAS DEL ESTRIBO
ELEVACION 1.0H = 3.980 2.0
ha = 1.99
L = 5.97
PLANTA
45
PERFIL DE PRUEBA PARA EL INICIO (H = Estribo : 3.98 m)
h4 0.00 = 0 W1
W2P2
2.480 h1Ev E
h = 4.480P1 /2
Eh
1.500 h2dh
B -BP3
0.500 h3 C - C
0.800 0.300 0.300 2.900
B1 B2 B3 B44.300
B
q1=P/A(1- 6e/b)q2=P/A(1+ 6e/b)
DATOS
CONCRETO f'c = 210.00 Kg/cm2ACERO fy = 4,200.00 Kg/cm2ANGULO DE FRICCION INTERNA DEL RELLENO = 27.00 ANGULO SOBRE LA HORIZ. DEL TALUD DEL MATERIAL = 0.00 PESO ESPECIFICO DEL MATERIAL DE RELLENO Wr = 2.360 Ton/m3PESO ESPECIFICO DEL CONCRETO Wc = 2.400 Ton/m3RESISTENCIA ULTIMA DEL TERRENO Qa = 9.230 Ton/m2FRICCION ALBAILERIA SOBRE ALBAILERIA F1 = 0.70FRICCION ALBAILERIA SOBRE ARCILLA HUMEDA F2i = 0.421FRICCION ALBAILERIA SOBRE ARCILLA HUMEDA F2d 0.413
Si = 0 Ka = Tan^2(45-/2)Ka = Cos x Cos - Cos2 - Cos2
Cos + Cos2 - Cos2
A = 0.894X = 0.891
Y = RAIZ(A^2-X^2) Y = 0.073Ka = Ax(A-Y)/(A+Y) Ka = 0.376
RELACIONES CONCRETO ACERO.
n = 2.1x10^6/(15000xRAIZ(f'c)) n = 10Fc = 0.4xf'c Fc = 84 Kg/cm2Fs = 0.4xfy Fs = 1,680 Kg/cm2r = Fs/Fc r = 20k = n/(n+r) k = 0.3333j = 1-k/3 j = 0.8889
DISEO DE LA PANTALLA
SOPORTARA SOLO EL EMPUJE DEL SUELO
PRESION DEL SUELOh = (h1+h2) h = 3.980 m.B = B2+B3 B = 0.600 m.E = 0.5xWrxh^2xKa E = 7.019 Ton.
Ev = 3.187 Ton.Eh = 6.254 Ton.
Punto de Aplicacin de Ehdh = h/3 dh = 1.327 m.
ESPESOR POR MOMENTO FLECTOR
Pi(Ton.) Xi(m.) Mi(Ton-m.)Eh 6.254 1.327 8.299
TOTAL 6.254 8.299
d = RAIZ(2xMix10^5/(Fcxkxjxb)) b = 100 Cm. d = 0.258 m."d" debe ser menor que B2+B3 = 0.600 m.
ESPESOR POR CORTE
Vu = Eh Vu = 6.254 Ton.Vumax = 2.10xbxRAIZ(f'c) Vumax = Vu/ = 7.358 Ton.d = Vumax/(2.10x100xRAIZ(f'c)) d = 0.024 m.
"d" debe ser menor que B2+B3 = 0.600 m.
DISEO POR FLEXION
REFUERZO PRINCIPAL
As = Mix10^5/(Fsxjxd) d = 0.550 m. As = 10.10 Cm2.Cuanta MnimaAsmin = 0.0018xbxd b = 1.000 m. Asmin = 9.90 Cm2.
Escoger el mayor As = 10.10 Cm2.S = 100xAv/As Usar 3/8" @ S = 7.00 Cm.
1/2" @ S = 12.80 Cm. 5/8" @ S = 19.80 Cm. 3/4" @ S = 28.10 Cm. 1" @ S = 49.50 Cm.
A = Cos X = Cos
Ev = ExSenEh = ExCos
AREA DE ACERO PARA DISTINTOS VALORES DE "d" y "Y".
B3 Y d dh Eh M As Asmin 1" 3/4" 5/8"0.300 0.000 0.250 0.000 0.000 0.000 0.00 4.50 111.10 63.10 44.40
0.500 0.288 0.167 0.099 0.016 0.04 5.18 96.60 54.80 38.601.000 0.325 0.333 0.395 0.132 0.27 5.86 85.40 48.50 34.101.500 0.363 0.500 0.888 0.444 0.82 6.54 76.50 43.50 30.60
Y dh 2.000 0.401 0.667 1.579 1.053 1.76 7.21 69.30 39.40 27.702.500 0.438 0.833 2.468 2.056 3.14 7.89 63.40 36.00 25.30
3.980 H d 3.000 0.476 1.000 3.553 3.553 5.00 8.57 58.30 33.10 23.303.500 0.514 1.167 4.837 5.643 7.35 9.25 54.10 30.70 21.604.000 0.552 1.333 6.317 8.423 10.23 9.93 50.40 28.60 20.104.500 0.589 1.500 7.995 11.993 13.63 10.61 47.10 26.80 18.905.000 0.627 1.667 9.871 16.451 17.57 11.28 44.30 25.20 17.70
0.600 5.500 0.665 1.833 11.943 21.896 22.06 11.96 41.80 23.70 16.70B2+B3 3.980 0.550 1.327 6.254 8.297 10.10 9.90 50.50 28.70 20.20
d = YxB2/H+B3-.05dh = y/3
REFUERZO VERTICAL POR MONTAJE EN CARA ANTERIOR
"As"montaje = (0.0018xbxd)/2 b = 100 m "As"mont. = 4.95 Cm2.
As = 4.95 Cm2. 3/8" @ S = 14.30 Cm. 1/2" @ S = 26.10 Cm. 5/8" @ S = 40.40 Cm.
REFUERZO HORIZONTAL POR REPARTICION
TERCIO INFERIOR
"As"reparticin = 0.002xbxt 100.0 cm Asr. = 12.00 Cm2.60.0 cm
Cara Anterior Asr / 3 = 4.00 Cm2.
As = 4.00 Cm2. 3/8" @ S = 17.80 Cm. 1/2" @ S = 32.30 Cm. 5/8" @ S = 50.00 Cm.
Cara Posterior 2xAsr / 3 = 8.00 Cm2.
As = 8.00 Cm2. 3/8" @ S = 8.90 Cm. 1/2" @ S = 16.10 Cm. 5/8" @ S = 25.00 Cm.
TERCIO MEDIO
"As"reparticin = 0.002xbxt 100.0 cm Asr. = 9.00 Cm2.45.0 cm
Cara Anterior Asr / 3 = 3.00 Cm2.
As = 3.00 Cm2. 3/8" @ S = 23.70 Cm. 1/2" @ S = 43.00 Cm. 5/8" @ S = 66.70 Cm.
Cara Posterior 2xAsr / 3 = 6.00 Cm2.
As = 6.00 Cm2. 3/8" @ S = 11.80 Cm. 1/2" @ S = 21.50 Cm. 5/8" @ S = 33.30 Cm.
TERCIO SUPERIOR
"As"reparticin = 0.002xbxt 100.0 cm Asr. = 6.00 Cm2.30.0 cm
b =t =
b =t =
b =t =
Cara Anterior Asr / 3 = 2.00 Cm2.
As = 2.00 Cm2. 3/8" @ S = 35.50 Cm. 1/2" @ S = 64.50 Cm. 5/8" @ S = 100.00 Cm.
Cara Posterior 2xAsr / 3 = 4.00 Cm2.
As = 4.00 Cm2. 3/8" @ S = 17.80 Cm. 1/2" @ S = 32.30 Cm. 5/8" @ S = 50.00 Cm.
CHEQUEO DE LA SECCION C - C
ALERO CON RELLENO SOBRECARGADO
EMPUJE DE TIERRAh = (h1+h2+h3) h = 4.480 m.B = B1+B2+B3+B4 B = 4.300 m.E = 0.5xWrxh^2xC E = 8.894 Ton.
Ev = 2.076 Ton.Eh = ExCos(/2) Eh = 8.648 Ton.Punto de Aplicacin de Ehdh = h/3 dh = 1.493 m.
FUERZAS VERTICALES ESTABILIZADORASPi(Ton.) Xi(m.) Mi(Ton-m.)
P1 = B2x(h1+h2)xWc/2 P1 1.433 1.000 1.433P2 = B3x(h1+h2)xWc P2 2.866 1.250 3.582P3 = Bxh3xWc P3 5.160 2.150 11.094W1 = B4xh4xWr/2 W1 0.000 3.333 0.000W2 = B4x(h1+h2)Wr W2 27.239 2.850 77.631
Ev 2.076 4.300 8.927TOTAL 38.774 102.667
Xv = SUMA Mi/SUMA Pi Xv = 2.648 m.z = Ehxdh/SUMA Pi z = 0.333 m.e = B/2-(Xv-z) e = -0.165 m.
"e" debe ser menor que B/6 = 0.717 m.
CHEQUEOS
a) Compresiones y Tracciones
p2 = SUMA Pix(1+6xABS(e)/B)/(Bxa) a = 1.0 p2 = 11.093 Ton/m2.Comparar con Qa = 9.230 Ton/m2.p debe ser menor
p1 = SUMA Pix(1-6xABS(e)/B)/(Bxa) a = 1.0 p1 = 6.941 Ton/m2.
Chequeo al Volteo
FSV = SUMA Mi/(Ehxdh) Debe ser mayor FSV = 8.0o igual que 1.5
Chequeo al Deslizamiento
FSD = SUMA PixF1/Eh Debe ser mayor FSD = 1.9o igual que 1.5
Ev = ExSen(/2)
DISEO DE LA ZAPATA ANTERIOR ( Pie )
0.500h4
0.800 0.600 2.900
L1 L2 L3
6.941 Ton/m211.093 10.321 9.741 p1p2 p3 p4
Pp = h4xWc Pp = 1.200 Ton./m2/mM = -PpxL1^2/2+p3xL1^2/2+(p2-p3)xL1^2/6 M = 3.001 Ton.-mV = -PpxL1+p3xL1+ (p2-p3)xL1/2 V = 7.605 Ton.
ESPESOR POR MOMENTO FLECTOR
d = RAIZ(2xMix10^5/(Fcxkxjxb)) b = 100 Cm. d = 0.155 m.d debe ser menor que h4 = 0.500 m.
ESPESOR POR CORTE
Vu = 7.605 Ton.Vumax = 2.10xbxRAIZ(f'c) Vumax = Vu/ = 8.947 Ton.d = Vumax/(2.10xbxRAIZ(f'c)) d = 0.029 m.
d debe ser menor que h4 = 0.500 m.
DISEO POR FLEXION
REFUERZO PRINCIPAL
As = Mix10^5/(Fsxjxd) d = 0.450 m. As = 4.47 Cm2.Cuanta MnimaPmin = 0.0018xbxd b = 1.000 m. Asmin = 8.10 Cm2.
Escoger el mayor As = 8.10 Cm2.S = 100xAv/As Usar 3/8" @ S = 8.80 Cm.
1/2" @ S = 15.90 Cm. 5/8" @ S = 24.70 Cm. 3/4" @ S = 35.10 Cm. 1" @ S = 63.00 Cm.
ACERO DE REPARTICION TRANSVERSAL
As = 0.0015xbxd d = 0.450 m. As = 6.75 Cm2.Usar 3/8" @ S = 10.50 Cm.
1/2" @ S = 19.10 Cm. 5/8" @ S = 29.60 Cm.
DISEO DE LA ZAPATA POSTERIOR ( Taln )
0.500h4
0.800 0.600 2.900
L1 L2 L3
6.941 Ton/m211.093 10.321 9.741 p2p1 p3 p4
h = h1+h2+h3 h = 3.980 m.p = Wrxh p = 9.393 Ton./m2Pp = h4xWc Pp = 1.200 Ton./m2/mM = -PpxL3^2/2-pxL3^2/2+p2xL3^2/2+(p4-p2)xL3^2/6 M = -11.432 Ton.-mV = -PpxL3-pxL3+p2xL3+ (p4-p2)xL3/2 V = -6.531 Ton.
ESPESOR POR MOMENTO FLECTOR
d = RAIZ(2xMix10^5/(Fcxkxjxb)) b = 100 Cm. d = 0.303 m.d debe ser menor que h4 = 0.500 m.
ESPESOR POR CORTE
Vu = -6.531 Ton.Vumax = 2.10xbxRAIZ(f'c) Vumax = Vu/ = -7.684 Ton.d = Vumax/(2.10xbxRAIZ(f'c)) d = -0.025 m.
d debe ser menor que h4 = 0.500 m.
DISEO POR FLEXION
REFUERZO PRINCIPAL
As = Mix10^5/(Fsxjxd) d = 0.450 m. As = 17.01 Cm2.Cuanta MnimaPmin = 0.0018xbxd b = 1.000 m. Asmin = 8.10 Cm2.
Escoger el mayor As = 17.01 Cm2.S = 100xAv/As Usar 3/8" @ S = 4.20 Cm.
1/2" @ S = 7.60 Cm. 5/8" @ S = 11.80 Cm. 3/4" @ S = 16.70 Cm. 1" @ S = 30.00 Cm.
ACERO DE REPARTICION TRANSVERSAL
As = 0.0015xbxd d = 0.450 m. As = 6.75 Cm2.Usar 3/8" @ S = 10.50 Cm.
1/2" @ S = 19.10 Cm. 5/8" @ S = 29.60 Cm. 3/4" @ S = 42.10 Cm.
DISEO DE LAS ALAS DEL ESTRIBO
ELEVACION 1.0H = 3.980 2.5
2.985 1.99 ha
L = 5.97
PLANTA
45
PERFIL DE PRUEBA PARA EL MEDIO (H = 2.985m)
h4 0.9800 W1
W2P2
1.485 h1Ev E
h = 3.485P1 /2
Eh
1.500 h2dh
B -BP3
0.500 h3 C - C
0.600 0.250 0.250 2.450
B1 B2 B3 B43.550
B
q1=P/A(1- 6e/b)q2=P/A(1+ 6e/b)
DATOS
CONCRETO f'c = 210.00 Kg/cm2ACERO fy = 4,200.00 Kg/cm2ANGULO DE FRICCION INTERNA DEL RELLENO = 27.00 ANGULO SOBRE LA HORIZ. DEL TALUD DEL MATERIAL = 33.69 PESO ESPECIFICO DEL MATERIAL DE RELLENO Wr = 2.360 Ton/m3PESO ESPECIFICO DEL CONCRETO Wc = 2.400 Ton/m3RESISTENCIA ULTIMA DEL TERRENO Qa = 9.230 Ton/m2FRICCION ALBAILERIA SOBRE ALBAILERIA F1 = 0.70FRICCION ALBAILERIA SOBRE ARCILLA HUMEDA F2i = 0.421
hm=
FRICCION ALBAILERIA SOBRE ARCILLA HUMEDA F2d 0.413
A = 0.928X = 0.891
Y = RAIZ(A^2-X^2) Y = 0.259C = Ax(A-Y)/(A+Y) C = 0.523
RELACIONES CONCRETO ACERO.
n = 2.1x10^6/(15000xRAIZ(f'c)) n = 10Fc = 0.4xf'c Fc = 84 Kg/cm2Fs = 0.4xfy Fs = 1,680 Kg/cm2r = Fs/Fc r = 20k = n/(n+r) k = 0.3333j = 1-k/3 j = 0.8889
DISEO DE LA PANTALLA
SOPORTARA SOLO EL EMPUJE DEL SUELO
PRESION DEL SUELOh = (h1+h2) h = 2.985 m.B = B2+B3 B = 0.500 m.E = 0.5xWrxh^2xC E = 5.499 Ton.
Ev = 3.050 Ton.Eh = 4.575 Ton.
Punto de Aplicacin de Ehdh = h/3 dh = 0.995 m.
ESPESOR POR MOMENTO FLECTOR
Pi(Ton.) Xi(m.) Mi(Ton-m.)Eh 4.575 0.995 4.552
TOTAL 4.575 4.552
d = RAIZ(2xMix10^5/(Fcxkxjxb)) b = 100 Cm. d = 0.191 m."d" debe ser menor que B2+B3 = 0.500 m.
ESPESOR POR CORTE
Vu = Eh Vu = 4.575 Ton.Vumax = 2.10xbxRAIZ(f'c) Vumax = Vu/ = 5.382 Ton.d = Vumax/(2.10x100xRAIZ(f'c)) d = 0.018 m.
"d" debe ser menor que B2+B3 = 0.500 m.
DISEO POR FLEXION
REFUERZO PRINCIPAL
As = Mix10^5/(Fsxjxd) d = 0.450 m. As = 6.77 Cm2.Cuanta MnimaAsmin = 0.0018xbxd b = 1.000 m. Asmin = 8.10 Cm2.
Escoger el mayor As = 8.10 Cm2.S = 100xAv/As Usar 3/8" @ S = 8.80 Cm.
1/2" @ S = 15.90 Cm. 5/8" @ S = 24.70 Cm. 3/4" @ S = 35.10 Cm. 1" @ S = 61.70 Cm.
C = Cos x Cos - Cos2 - Cos2 Cos + Cos2 - Cos2
A = Cos X = Cos
Ev = ExSenEh = ExCos
AREA DE ACERO PARA DISTINTOS VALORES DE "d" y "Y".
B3 Y d dh Eh M As Asmin 1" 3/4" 5/8"0.250 0.000 0.200 0.000 0.000 0.000 0.00 3.60 138.90 78.90 55.60
0.500 0.242 0.167 0.128 0.021 0.06 4.35 114.80 65.20 45.901.000 0.284 0.333 0.513 0.171 0.40 5.11 97.90 55.60 39.201.500 0.326 0.500 1.155 0.578 1.19 5.86 85.30 48.50 34.10
Y dh 2.000 0.368 0.667 2.054 1.369 2.50 6.62 75.60 42.90 30.202.500 0.409 0.833 3.209 2.674 4.37 7.37 67.90 38.50 27.10
2.985 H d 3.000 0.451 1.000 4.621 4.621 6.86 8.12 61.60 35.00 24.603.500 0.493 1.167 6.290 7.339 9.97 8.88 56.30 32.00 22.504.000 0.535 1.333 8.216 10.954 13.71 9.63 51.90 20.70 14.602.985 0.450 0.995 4.575 4.552 6.77 8.10 61.70 41.90 29.50
0.500B2+B3
d = YxB2/H+B3-.05dh = y/3
REFUERZO VERTICAL POR MONTAJE EN CARA ANTERIOR
"As"montaje = (0.0018xbxd)/2 b = 100 m "As"mont. = 4.05 Cm2.
As = 4.05 Cm2. 3/8" @ S = 17.50 Cm. 1/2" @ S = 31.90 Cm. 5/8" @ S = 49.40 Cm.
REFUERZO HORIZONTAL POR REPARTICION
TERCIO INFERIOR
"As"reparticin = 0.002xbxt 100.0 cm Asr. = 10.00 Cm2.50.0 cm
Cara Anterior Asr / 3 = 3.33 Cm2.
As = 3.33 Cm2. 3/8" @ S = 21.30 Cm. 1/2" @ S = 38.70 Cm. 5/8" @ S = 60.00 Cm.
Cara Posterior 2xAsr / 3 = 6.67 Cm2.
As = 6.67 Cm2. 3/8" @ S = 10.70 Cm. 1/2" @ S = 19.40 Cm. 5/8" @ S = 30.00 Cm.
TERCIO MEDIO
"As"reparticin = 0.002xbxt 100.0 cm Asr. = 7.50 Cm2.37.5 cm
Cara Anterior Asr / 3 = 2.50 Cm2.
As = 2.50 Cm2. 3/8" @ S = 28.40 Cm. 1/2" @ S = 51.60 Cm. 5/8" @ S = 80.00 Cm.
Cara Posterior 2xAsr / 3 = 5.00 Cm2.
As = 5.00 Cm2. 3/8" @ S = 14.20 Cm. 1/2" @ S = 25.80 Cm. 5/8" @ S = 40.00 Cm.
TERCIO SUPERIOR
"As"reparticin = 0.002xbxt 100.0 cm Asr. = 5.00 Cm2.
b =t =
b =t =
b =
25.0 cmt =
Cara Anterior Asr / 3 = 1.67 Cm2.
As = 1.67 Cm2. 3/8" @ S = 42.60 Cm. 1/2" @ S = 77.40 Cm. 5/8" @ S = 120.00 Cm.
Cara Posterior 2xAsr / 3 = 3.33 Cm2.
As = 3.33 Cm2. 3/8" @ S = 21.30 Cm. 1/2" @ S = 38.70 Cm. 5/8" @ S = 60.00 Cm.
CHEQUEO DE LA SECCION C - C
ALERO CON RELLENO SOBRECARGADO
EMPUJE DE TIERRAh = (h1+h2+h3) h = 3.485 m.B = B1+B2+B3+B4 B = 3.550 m.E = 0.5xWrxh^2xC E = 7.495 Ton.
Ev = 1.750 Ton.Eh = 7.288 Ton.
Punto de Aplicacin de Ehdh = h/3 dh = 1.162 m.
FUERZAS VERTICALES ESTABILIZADORASPi(Ton.) Xi(m.) Mi(Ton-m.)
P1 = B2x(h1+h2)xWc/2 P1 0.896 0.767 0.687P2 = B3x(h1+h2)xWc P2 1.791 0.975 1.746P3 = Bxh3xWc P3 4.260 1.775 7.562W1 = B4xh4xWr/2 W1 2.833 2.733 7.744W2 = B4x(h1+h2)Wr W2 17.259 2.325 40.128
Ev 1.750 3.550 6.213TOTAL 28.789 64.080
Xv = SUMA Mi/SUMA Pi Xv = 2.226 m.z = Ehxdh/SUMA Pi z = 0.294 m.e = B/2-(Xv-z) e = -0.157 m.
"e" debe ser menor que B/6 = 0.592 m.
CHEQUEOS
a) Compresiones y Tracciones
p2 = SUMA Pix(1+6xABS(e)/B)/(Bxa) a = 1.0 p2 = 10.261 Ton/m2.Comparar con Qa = 9.230 Ton/m2.p debe ser menor
p1 = SUMA Pix(1-6xABS(e)/B)/(Bxa) a = 1.0 p1 = 5.958 Ton/m2.
Chequeo al Volteo
FSV = SUMA Mi/(Ehxdh) Debe ser mayor FSV = 7.6o igual que 1.5
Chequeo al Deslizamiento
FSD = SUMA PixF1/Eh Debe ser mayor FSD = 1.7o igual que 1.5
Ev = ExSen(/2)Eh = ExCos
DISEO DE LA ZAPATA ANTERIOR ( Pie )
0.500h4
0.600 0.500 2.450
L1 L2 L3
5.958 Ton/m210.261 9.534 8.928 p1p2 p3 p4
Pp = h4xWc Pp = 1.200 Ton./m2/mM = -PpxL1^2/2+p3xL1^2/2+(p2-p3)xL1^2/6 M = 1.544 Ton.-mV = -PpxL1+p3xL1+ (p2-p3)xL1/2 V = 5.218 Ton.
ESPESOR POR MOMENTO FLECTOR
d = RAIZ(2xMix10^5/(Fcxkxjxb)) b = 100 Cm. d = 0.111 m.d debe ser menor que h4 = 0.500 m.
ESPESOR POR CORTE
Vu = 5.218 Ton.Vumax = 2.10xbxRAIZ(f'c) Vumax = Vu/ = 6.139 Ton.d = Vumax/(2.10xbxRAIZ(f'c)) d = 0.020 m.
d debe ser menor que h4 = 0.500 m.
DISEO POR FLEXION
REFUERZO PRINCIPAL
As = Mix10^5/(Fsxjxd) d = 0.450 m. As = 2.30 Cm2.Cuanta MnimaPmin = 0.0018xbxd b = 1.000 m. Asmin = 8.10 Cm2.
Escoger el mayor As = 8.10 Cm2.S = 100xAv/As Usar 3/8" @ S = 8.80 Cm.
1/2" @ S = 15.90 Cm. 5/8" @ S = 24.70 Cm. 3/4" @ S = 35.10 Cm. 1" @ S = 63.00 Cm.
ACERO DE REPARTICION TRANSVERSAL
As = 0.0015xbxd d = 0.450 m. As = 6.75 Cm2.Usar 3/8" @ S = 10.50 Cm.
1/2" @ S = 19.10 Cm. 5/8" @ S = 29.60 Cm.
DISEO DE LA ZAPATA POSTERIOR ( Taln )
0.500h4
0.600 0.500 2.450
L1 L2 L3
5.958 Ton/m210.261 9.534 8.928 p2p1 p3 p4
h = h1+h2+h3 h = 2.985 m.p = Wrxh p = 7.045 Ton./m2Pp = h4xWc Pp = 1.200 Ton./m2/mM = -PpxL3^2/2-pxL3^2/2+p2xL3^2/2+(p4-p2)xL3^2/6 M = -3.893 Ton.-mV = -PpxL3-pxL3+p2xL3+ (p4-p2)xL3/2 V = -1.965 Ton.
ESPESOR POR MOMENTO FLECTOR
d = RAIZ(2xMix10^5/(Fcxkxjxb)) b = 100 Cm. d = 0.177 m.d debe ser menor que h4 = 0.500 m.
ESPESOR POR CORTE
Vu = -1.965 Ton.Vumax = 2.10xbxRAIZ(f'c) Vumax = Vu/ = -2.312 Ton.d = Vumax/(2.10xbxRAIZ(f'c)) d = -0.008 m.
d debe ser menor que h4 = 0.500 m.
DISEO POR FLEXION
REFUERZO PRINCIPAL
As = Mix10^5/(Fsxjxd) d = 0.450 m. As = 5.79 Cm2.Cuanta MnimaPmin = 0.0018xbxd b = 1.000 m. Asmin = 8.10 Cm2.
Escoger el mayor As = 8.10 Cm2.S = 100xAv/As Usar 3/8" @ S = 8.80 Cm.
1/2" @ S = 15.90 Cm. 5/8" @ S = 24.70 Cm. 3/4" @ S = 35.10 Cm. 1" @ S = 63.00 Cm.
ACERO DE REPARTICION TRANSVERSAL
As = 0.0015xbxd d = 0.450 m. As = 6.75 Cm2.Usar 3/8" @ S = 10.50 Cm.
1/2" @ S = 19.10 Cm. 5/8" @ S = 29.60 Cm. 3/4" @ S = 42.10 Cm.
DISEO DE LAS ALAS DEL ESTRIBO
ELEVACION 1.0H = 3.980 2.0
ha = 1.99
L = 5.97
PLANTA
45
PERFIL DE PRUEBA PARA EL FINAL (H = 1.99m)
h4 1.00 W1
W2P2 p2
p10.490 h1
Ev E
h = 2.490P1 /2
Eh
1.500 h2dh
B -BP3
0.500 h3 C - C
0.400 0.200 0.200 2.000
B1 B2 B3 B42.800
B
q1=P/A(1- 6e/b)q2=P/A(1+ 6e/b)
DATOS
CONCRETO f'c = 210.00 Kg/cm2ACERO fy = 4,200.00 Kg/cm2ANGULO DE FRICCION INTERNA DEL RELLENO = 27.00 ANGULO SOBRE LA HORIZ. DEL TALUD DEL MATERIAL = 33.69 PESO ESPECIFICO DEL MATERIAL DE RELLENO Wr = 2.360 Ton/m3PESO ESPECIFICO DEL CONCRETO Wc = 2.400 Ton/m3RESISTENCIA ULTIMA DEL TERRENO Qa = 9.230 Ton/m2FRICCION ALBAILERIA SOBRE ALBAILERIA F1 = 0.70FRICCION ALBAILERIA SOBRE ARCILLA HUMEDA F2i = 0.421
FRICCION ALBAILERIA SOBRE ARCILLA HUMEDA F2d 0.413
A = 0.894X = 0.891
Y = RAIZ(A^2-X^2) Y = 0.073C = Ax(A-Y)/(A+Y) C = 0.759
RELACIONES CONCRETO ACERO.
n = 2.1x10^6/(15000xRAIZ(f'c)) n = 10Fc = 0.4xf'c Fc = 84 Kg/cm2Fs = 0.4xfy Fs = 1,680 Kg/cm2r = Fs/Fc r = 20k = n/(n+r) k = 0.3333j = 1-k/3 j = 0.8889
DISEO DE LA PANTALLA
SOPORTARA SOLO EL EMPUJE DEL SUELO
PRESION DEL SUELOh = (h1+h2) h = 1.990 m.B = B2+B3 B = 0.400 m.E = 0.5xWrxh^2xC E = 3.547 Ton.
Ev = 1.967 Ton.Eh = 2.951 Ton.
Punto de Aplicacin de Ehdh = h/3 dh = 0.663 m.
ESPESOR POR MOMENTO FLECTOR
Pi(Ton.) Xi(m.) Mi(Ton-m.)Eh 2.951 0.663 1.957
TOTAL 2.951 1.957
d = RAIZ(2xMix10^5/(Fcxkxjxb)) b = 100 Cm. d = 0.125 m."d" debe ser menor que B2+B3 = 0.400 m.
ESPESOR POR CORTE
Vu = Eh Vu = 2.951 Ton.Vumax = 2.10xbxRAIZ(f'c) Vumax = Vu/ = 3.472 Ton.d = Vumax/(2.10x100xRAIZ(f'c)) d = 0.011 m.
"d" debe ser menor que B2+B3 = 0.400 m.
DISEO POR FLEXION
REFUERZO PRINCIPAL
As = Mix10^5/(Fsxjxd) d = 0.350 m. As = 3.74 Cm2.Cuanta MnimaAsmin = 0.0018xbxd b = 1.000 m. Asmin = 6.30 Cm2.
Escoger el mayor As = 6.30 Cm2.S = 100xAv/As Usar 3/8" @ S = 11.30 Cm.
1/2" @ S = 20.50 Cm. 5/8" @ S = 31.70 Cm. 3/4" @ S = 45.10 Cm. 1" @ S = 79.40 Cm.
C = Cos x Cos - Cos2 - Cos2 Cos + Cos2 - Cos2
A = Cos X = Cos
Ev = ExSenEh = ExCos
AREA DE ACERO PARA DISTINTOS VALORES DE "d" y "Y".
B3 Y d dh Eh M As Asmin 1" 3/4" 5/8"0.200 0.000 0.150 0.000 0.000 0.000 0.00 2.70 185.20 105.20 74.10
0.500 0.200 0.167 0.186 0.031 0.10 3.60 138.70 78.80 55.501.000 0.251 0.333 0.745 0.248 0.66 4.51 110.90 63.00 44.401.500 0.301 0.500 1.677 0.838 1.87 5.41 92.40 52.50 36.90
Y dh 2.000 0.351 0.667 2.981 1.987 3.79 6.32 79.10 45.00 31.702.500 0.401 0.833 4.658 3.881 6.48 7.22 69.20 39.30 27.70
1.990 H d 1.990 0.350 0.663 2.951 1.958 3.75 6.30 79.40 45.10 31.70
0.400B2+B3
d = YxB2/H+B3-.05dh = y/3
REFUERZO VERTICAL POR MONTAJE EN CARA ANTERIOR
"As"montaje = (0.0018xbxd)/2 b = 100 m "As"mont. = 3.15 Cm2.
As = 3.15 Cm2. 3/8" @ S = 22.50 Cm. 1/2" @ S = 41.00 Cm. 5/8" @ S = 63.50 Cm.
REFUERZO HORIZONTAL POR REPARTICION
TERCIO INFERIOR
"As"reparticin = 0.002xbxt 100.0 cm Asr. = 8.00 Cm2.40.0 cm
Cara Anterior Asr / 3 = 2.67 Cm2.
As = 2.67 Cm2. 3/8" @ S = 26.60 Cm. 1/2" @ S = 48.40 Cm. 5/8" @ S = 75.00 Cm.
Cara Posterior 2xAsr / 3 = 5.33 Cm2.
As = 5.33 Cm2. 3/8" @ S = 13.30 Cm. 1/2" @ S = 24.20 Cm. 5/8" @ S = 37.50 Cm.
TERCIO MEDIO
"As"reparticin = 0.002xbxt 100.0 cm Asr. = 6.00 Cm2.30.0 cm
Cara Anterior Asr / 3 = 2.00 Cm2.
As = 2.00 Cm2. 3/8" @ S = 35.50 Cm. 1/2" @ S = 64.50 Cm. 5/8" @ S = 100.00 Cm.
Cara Posterior 2xAsr / 3 = 4.00 Cm2.
As = 4.00 Cm2. 3/8" @ S = 17.80 Cm. 1/2" @ S = 32.30 Cm. 5/8" @ S = 50.00 Cm.
TERCIO SUPERIOR
"As"reparticin = 0.002xbxt 100.0 cm Asr. = 4.00 Cm2.
b =t =
b =t =
b =
20.0 cmt =
Cara Anterior Asr / 3 = 1.33 Cm2.
As = 1.33 Cm2. 3/8" @ S = 53.30 Cm. 1/2" @ S = 96.80 Cm. 5/8" @ S = 150.00 Cm.
Cara Posterior 2xAsr / 3 = 2.67 Cm2.
As = 2.67 Cm2. 3/8" @ S = 26.60 Cm. 1/2" @ S = 48.40 Cm. 5/8" @ S = 75.00 Cm.
CHEQUEO DE LA SECCION C - C
ALERO CON RELLENO SOBRECARGADO
EMPUJE DE TIERRAh = (h1+h2+h3) h = 2.490 m.B = B1+B2+B3+B4 B = 2.800 m.E = 0.5xWrxh^2xC E = 5.553 Ton.
Ev = 3.080 Ton.Eh = 4.620 Ton.
Punto de Aplicacin de Ehdh = h/3 dh = 0.830 m.
FUERZAS VERTICALES ESTABILIZADORASPi(Ton.) Xi(m.) Mi(Ton-m.)
P1 = B2x(h1+h2)xWc/2 P1 0.478 0.533 0.255P2 = B3x(h1+h2)xWc P2 0.955 0.700 0.669P3 = Bxh3xWc P3 3.360 1.400 4.704W1 = B4xh4xWr/2 W1 2.360 2.133 5.035W2 = B4x(h1+h2)Wr W2 9.393 1.800 16.907
Ev 3.080 2.800 8.624TOTAL 19.626 36.194
Xv = SUMA Mi/SUMA Pi Xv = 1.844 m.z = Ehxdh/SUMA Pi z = 0.195 m.e = B/2-(Xv-z) e = -0.249 m.
"e" debe ser menor que B/6 = 0.467 m.
CHEQUEOS
a) Compresiones y Tracciones
p2 = SUMA Pix(1+6xABS(e)/B)/(Bxa) a = 1.0 p2 = 10.749 Ton/m2.Comparar con Qa = 9.230 Ton/m2.p debe ser menor
p1 = SUMA Pix(1-6xABS(e)/B)/(Bxa) a = 1.0 p1 = 3.269 Ton/m2.
Chequeo al Volteo
FSV = SUMA Mi/(Ehxdh) Debe ser mayor FSV = 9.4o igual que 1.5
Chequeo al Deslizamiento
FSD = SUMA PixF1/Eh Debe ser mayor FSD = 1.8o igual que 1.5
Ev = ExSenEh = ExCos
DISEO DE LA ZAPATA ANTERIOR ( Pie )
0.500h4
0.400 0.400 2.000
L1 L2 L3
3.269 Ton/m210.749 9.680 8.612 p1p2 p3 p4
Pp = h4xWc Pp = 1.200 Ton./m2/mM = -PpxL1^2/2+p3xL1^2/2+(p2-p3)xL1^2/6 M = 0.707 Ton.-mV = -PpxL1+p3xL1+ (p2-p3)xL1/2 V = 3.606 Ton.
ESPESOR POR MOMENTO FLECTOR
d = RAIZ(2xMix10^5/(Fcxkxjxb)) b = 100 Cm. d = 0.075 m.d debe ser menor que h4 = 0.500 m.
ESPESOR POR CORTE
Vu = 3.606 Ton.Vumax = 2.10xbxRAIZ(f'c) Vumax = Vu/ = 4.242 Ton.d = Vumax/(2.10xbxRAIZ(f'c)) d = 0.014 m.
d debe ser menor que h4 = 0.500 m.
DISEO POR FLEXION
REFUERZO PRINCIPAL
As = Mix10^5/(Fsxjxd) d = 0.450 m. As = 1.05 Cm2.Cuanta MnimaPmin = 0.0018xbxd b = 1.000 m. Asmin = 8.10 Cm2.
Escoger el mayor As = 8.10 Cm2.S = 100xAv/As Usar 3/8" @ S = 8.80 Cm.
1/2" @ S = 15.90 Cm. 5/8" @ S = 24.70 Cm. 3/4" @ S = 35.10 Cm. 1" @ S = 63.00 Cm.
ACERO DE REPARTICION TRANSVERSAL
As = 0.0015xbxd d = 0.450 m. As = 6.75 Cm2.Usar 3/8" @ S = 10.50 Cm.
1/2" @ S = 19.10 Cm. 5/8" @ S = 29.60 Cm.
DISEO DE LA ZAPATA POSTERIOR ( Taln )
0.500h4
0.400 0.400 2.000
L1 L2 L3
3.269 Ton/m210.749 9.680 8.612 p2p1 p3 p4
h = h1+h2+h3 h = 1.990 m.p = Wrxh p = 4.696 Ton./m2Pp = h4xWc Pp = 1.200 Ton./m2/mM = -PpxL3^2/2-pxL3^2/2+p2xL3^2/2+(p4-p2)xL3^2/6 M = -1.692 Ton.-mV = -PpxL3-pxL3+p2xL3+ (p4-p2)xL3/2 V = 0.089 Ton.
ESPESOR POR MOMENTO FLECTOR
d = RAIZ(2xMix10^5/(Fcxkxjxb)) b = 100 Cm. d = 0.117 m.d debe ser menor que h4 = 0.500 m.
ESPESOR POR CORTE
Vu = 0.089 Ton.Vumax = 2.10xbxRAIZ(f'c) Vumax = Vu/ = 0.105 Ton.d = Vumax/(2.10xbxRAIZ(f'c)) d = 0.000 m.
d debe ser menor que h4 = 0.500 m.
DISEO POR FLEXION
REFUERZO PRINCIPAL
As = Mix10^5/(Fsxjxd) d = 0.450 m. As = 2.52 Cm2.Cuanta MnimaPmin = 0.0018xbxd b = 1.000 m. Asmin = 8.10 Cm2.
Escoger el mayor As = 8.10 Cm2.S = 100xAv/As Usar 3/8" @ S = 8.80 Cm.
1/2" @ S = 15.90 Cm. 5/8" @ S = 24.70 Cm. 3/4" @ S = 35.10 Cm. 1" @ S = 63.00 Cm.
ACERO DE REPARTICION TRANSVERSAL
As = 0.0015xbxd d = 0.450 m. As = 6.75 Cm2.Usar 3/8" @ S = 10.50 Cm.
1/2" @ S = 19.10 Cm. 5/8" @ S = 29.60 Cm. 3/4" @ S = 42.10 Cm.
EstribosAlero InicioAlero MedioAlero Final