DISEÑO DE CIMENTACIONES
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Transcript of DISEÑO DE CIMENTACIONES
DISEO DE UNA ZAPATA AISLADADisear la zapata mostrada en la fig: Si la Columna de 70 x 50 lleva 10 fierros de 1" y transmite las cargas PD = 180 tn y PL = 100 tn . La capacidad portante admisible del suelo es qa = 2.5 kg/cm2 ; ademas fy = 4200kg/cm2 , fy = 280 kg/cm2 en la columna y fc = 210 kg/cm2 en la zapata
DATOS:Zapata 210 kg/cm Columna f ' c = 280 kg/cm 50 cm b= 70 cm t= f'c=S/C = PD = PL =
Otros 550 kg/m 180 Tn 100 Tn
Acero f y = 4200 kg/cm
Df = K2 = qa = db = Lv =
Suelo 1.4 1700 2.50 2.54 150
m kg/m kg/cm cm cm
1.- DIMENSIONAMIENTO DE LA ZAPATAClculo del peralte de la zapata ) (hc
MD,ML PD, PL
Ld =
0.08.db.F y f'c
Reemplazo los valores que tenemos: Ld = 58.89 cm ht Tomar Ld = 58.89 cm DfLv
(Del problema se emplean varillas de 1") b ( 1") = 2.54 cm (recubrimiento) r.e. = 7.50 cm hc = 68.93 cm hc = 70.00 cm hc = Ld + r.e + b Tomar ht = Df - hc ht = 70.00 cm Clculo de la presin neta del suelo ( qm )
hc T
B
qm ! qa Kht Kchc-s/cClculo del rea de la zapata ( Az )
qm = 2.16 kg/cm
t T
P qm (t1-t2) T= Az 2 (t1-t2) S! Az 2 Azap !
Azap = 129,629.63 cm 370.00 T = cm 350.00 B = cm
Donde: P = Carga de servicio Lv = Volados iguales sin excentricidad
2.- DETERMINACIN DE LA REACCIN AMPLIFICADA ( qmu )Donde: Pu = Carga Ultima
Pu Wnu ! Azap
=
1.4 x 180000 + 1.7 x 100000 350 x 370
=
3.26
kg/cm2
3.- VERIFICACION POR CORTE ( = 0.85 )Por Flexin:
Lv !
Tt 2 Vdu=(WnuxB)(L v-d)
Vc=0.53 f'cbd Vc u VduPor Punzonamiento :
Lv = 150.00 r.e = 7.50 b ( 3/4") = 1.91 d = 60.59 Vdu = 101,975.73 = 0.85
cm cm cm cm kg
(Suponiendo varillas 3/4") ( d = hc - b - r.e. ) (Coef. De reduccion por corte)
Vc = 162,875.03 kg Vc = 138,443.78 kg Vc > Vdu OK!
Vu=Pu-Wnu x mnVu = 374,938.21 kg bo = 2 x ( t + d ) + 2 x ( b + d )= bo = 482.36 cm 2m +2n (perimetro de los planos de falla) * f 'c^.5 * bo * d = 1.06 * f 'c^.5 * bo * d
4 Vc=0.272+ f ' cbo d F c Dmayor , F e 2 p Vc=1.06 f ' c bo d c Dmenor Vue Vc; =0.85
F
!
c
n = b+d
Vc = 0.27 * 2 + 4 F c Vc = 555,426.41 kg Vc= 472,112.45 kg Vc = Vc= Vc > Vdu OK! Fc = lado mayor columna ( t ) Fc = 1.4 lado menor columna ( b ) m=t+d n=t+b bo = 2*m + 2*n Vu = vc OK !
448,939.43381,598.52
Kg Kg
d/2 b d/2 t m = t+d T
b m = 130.59 n = 110.59 Vu = 1.1 x f'c x b x d o Vu = 448,939.43 kg vc = 381,598.52 kg
4.- CALCULO DEL REFUERZO LONGITUDINAL ( = 0.90 )Direccin Mayor: (Wnu x B)L v 2 Mu= 2 Mu As= a Fy(d- ) 2 As.Fy a! 0.85f'c b As mn = 0.0018 * B * d As > As mn OK !! Lv = Mu = B= d= a= As = a= 150.0012,831,081.08 350.00
cm ree = 7.50 kg-cm b ( 3/4") = 1.91
cm (Valor Asumido) Ab ( 3/4" ) = 2.85 # Varilla ( n ) = 20 Espaciam = 17.53
60.59 3.89 57.88 3.89
cm2 cm cm cm2
B
As = 57.88 cm2 Ab # Varilla ( n ) = As Ab Espaciam = B - 2*r.e - b n -1
20 3/4" @ 17.53 cm Ab ( 3/4" ) = 2.85 # Varilla ( n ) = 15 Espaciam = 23.79 15 3/4" @ 23.79 cmOK !!
As mn = 44.1 As >
cm2 As mn
Direccin Menor: As tranv = As * T B As mn = 0.0018 * B * d As > As mn OK !! Ab # Varilla ( n ) = As Ab As transv = 61.19 cm2 Espaciam = B - 2*r.e - b n -1
T= B= d= a=
370 350 cm 60.59 cm2 5.01 cm
b ( 3/4")
ree = 7.50 cm2 = 1.91 cm
(Valor Asumido) Ab ( 3/4" ) = 2.85 cm2 # Varilla ( n ) = 21 Espaciam = 17.65 21 3/4" @ 17.65 cm Ab ( 3/4" ) = 2.85 # Varilla ( n ) = 16 Espaciam = 23.54 16 3/4" @ 23.54 cm As mnOK !!
Asmin = 46.62 cm2 As transv Longitud de desarrollo en Traccion ( Ld ) ld = b * fy * EFKP 3.54 * f 'c^.5 * C + Kr b Lv1 = Lv - r.e.e < Lv1 >
La Zapata es rectangular se debe compartir el Refuerzo adecuadamente de la siguiente manera: Asc = 2 * Astrv (F + 1 ) F = Lado mayor Zapata Lado menor Zapata Ab # Varilla ( n ) = As Ab Espaciam = B - 2*r.e.e - b n -1 Espaciamiento del Refuerzo Asc = 61.19 cm2 45 cm > 17.65 3xh 210 cmOK !!
F= K= P= E=
1.00 0.80 1.00 1.00
b (3/4") = 1.91 r.e.e = 7.50 fy = 4200 f'c = 210
C = 8.50 ktr = 02.5
q = ( C+kt r )/ b q= 10.41q >= 2.5 ,PONER 2.5 !! q < 2.5 ,PONER q !!
Longitud de desarrollo en traccin Lv1 = 142.50 cm Ld = 50.04 cm Ld < Lv1
OK !!
5.- VERIFICACION DE LA CONEXIN COLUMNA - ZAPATA ( = 0.70 )Para la seccin A colum = 70*50 = 3500 cm ( COLUMNA ) * 0.85 * f 'c * As1 A colum = b *t Pu < ( * 0.85 * f 'c * A1) Ab As mn = 0.005 * A1 # Varilla = As1 Ab As col. > As mn OK !! cm2 # Varilla ( n ) = 6
Pu = 422000 kg A1 = 3500 cm2 * 0.85 * f 'c * A1 = 583100 kg Pu < * 0.85 * f 'c * A1 As mn = 17.50 cm2 Ab ( 3/4" ) = 2.85 cm2 USAR : As1 = 17.50 cm2 OK !! As col > As min
OK !!
Para la seccin A zapata = 350*370 = 129500 cm ( ZAPATA ) Pu < x 0.85 x f 'c x A2/A1 x A1 Pu = 422000 kg A1 = 3500 cm2 A2 = 129500 cm2 874650 kgOK !!
A2/A1 =
2
x 0.85 x f 'c x A2/A1 x A1 =
Pgina 1 de 5
DISEO DE ZAPATA COMBINADADisear la zapata combinada que soportara las columnas mostradas en la figura. La capacidad portante del suelo es qa = 2 kg/cm2Considere fy = 4200 kg/cm2 y f'c = 210 kg/cm2 para la cimentacion . F'c = 280 kg/cm2 en las columnas. COL: C1 C2 SECCION 50 X 50 40 X 50 b x t REF. 9 3/4" 9 3/4" Acero PD 20 40 tn PL 15 24 tn 2 b1 b2
PL1 S/C = 500 kg/m
PL2
1
Km
h t = 101.00
t1
t2
hc = 54.00
4.55
m
1.40
Df = 1.60 Km = 1800 qa = 2.00
m Otros kg/m3 S/C = 500 kg/m kg/cm2 d(eje-eje)= 4.3 m
Columna f ' c = 210 kg/cm
f'c= fy =
Zapata 175 kg/cm 4200 kg/cm
Clculo del peralte de la zapata (hc ) ld = 0.08 * b * Fy raiz(f 'c) ld >= 0.004 * b * fy
1.- DIMENSIONAMIENTO DE LA ZAPATA ( Az = S*T )b ( 3/4" ) = 0.08 x b x fy / f c = .004*b*fy = Tomar ld = r.e = hc= ht= Tomar ht = 1.91 49 32 49 7.50 59.00 101.00 101.00 cm cm cm cm cm cm cm cm
OK !! Longitud de desarrollo en compresin
hc = ld + r.e + b hm = Df - hc
Clculo de la presin neta del suelo ( qm ) qm = qa - Km*hm - c*hc - s/c
qm =
1.63
kg/cm
Clculo del rea de la zapata ( Az ) Ps1 = P1D + P1L Ps2 = P2D + P2L Rs = P1s + P2s 20 +IMo = 0 Rs * Xo = P1s* t1/2 + P2s * 455 Xo = ?? 0 Xo 455.00 Rs = Lz / 2 e = Lz / 2 - Xo Lz / 6 e < Lz/6 q1,2 = Rs * 1 6 * e Lz Lz P1s = P2s = Rs = Xo = Lz = Lz / 2 = e= Lz / 6= 35 64 99 301.21 625.00 312.50 11.29 104 Tn Tn Tn cm cm cm cm cm 99 Tn 170.00 cm P1s = 35 Tn P2s = 64 Tn
20
30
30
Pgina 2 de 5
L = 2 x Xo B =(P1s +P2s) qn x L
602 L= cm B= 101 cm tomamos B = 85 cm
Como S/C = 500 kg/cm, Verificamos las presiones del suelo - ADICIONAL ( q 1,2 ) Ps1 = P1D + 50%P1L Ps2 = P2D + P2L R1s = P1s + P2s +IMo = 0 R1s * Xo = P1s* t1/2 + P2s * 455 Xo = ?? 0 Xo 455.00 e = Xo1 - Xo q = Ps + Mc = Ps + Ps x e Az I Az I P1s = P2s = R1s = Xo1 = 27.5 64 91.5 324.26 Tn Tn Tn cm R1s = 91.5 Tn I = ( B x L^3 )/12 I= 1454767.917 cm4 170.00 cm 20
P1s =
27.5 Tn
P2s =
64 Tn
20
30
30
e=
23.05
cm
AUMENTAMOS EL ANCHO B q= 44.56 kg/cm2 q < qm cumple " OK " q > qm no cumple "AUMENTAMOS EL ANCHO B" Aumentamos el Ancho hc = 150 cm Un nuevo calculo Ps = 91500 kg q = 1.41 kg/cm2 e = 23.05 cm B = 265 cm I = 74531250 cm4
OK !!
Ps1 = P1D + P1L Ps2 = P2D + 50%P2L R2s = P1s + P2s +IMo = 0 R2s * Xo = P1s* t1/2 + P2s * 455 Xo = ?? 0 20
P1s =
35 Tn
P2s =
52 Tn
20
30
30
Xo 470.00 1.40 87 Tn m
Lz / 2 e2 = Lz / 2 - Xo Lz / 6 e2 < Lz/6 q1,2 = R2s * 1 6 * e2 L B L
P1s = P2s = R2s = Xo =
35 52 87 288.97
Tn Tn Tn cm e=
R2s =
12.24
cm
I = ( B x L^3 )/12 I= 74531250
cm4
q > qm no cumple "AUMENTAMOS EL ANCHO B" q < qm cumple " OK "
q=
1.62
kg/cm2
OK !!
2.- DISEO EN SENTIDO LONGITUDINALClculo de la presin neta por unidad de longitud( qm )
P1s =
35 Tn
P2s =
64 Tn
cm3 qm qn = P1s + P2s Az qn = 6205.729 kg/m Por unidad de Longitud qm = qm1*B 0.2 ( No amplificada ) qm = 6205.73 kg/m m 4.50 m 140.00 m
Por Unidad de LONGITUD
Pgina 3 de 5
V 1241.15 kg
55311.98 kg
+ -
+
1.6297
m
+ -8688.022 kg
-33758.85 kg kg - m -27385.1
M
+
+124.12 kg - m
+6081.62 kg - m
Encontramos el diagrama de fuerzas cortantes verificamos el corte por Flexion: 67050.27 d = -ree + hc 1.50 x Vu = d = 141.00 cm Vu = Vmax - qn x ( b2/2 + d ) = 44700.18 kg Aporte del Concreto : Vc = 0.53 x f ' c x b x d = 0.85 x Vc = 222678.8 kg Aumentamos el Peralte a h = 150 cm. 44700.18 kg 261975.02 kg OK !! d= h- ree d= 141 cm
kg
ya que : F = ( 1.4 x D + 1.7 x L )/( D + L ) F= 1.5
Vu < 0 x Vc
Cumple !!
Vu = Vmax - qn x ( b2/2 + d ) = Aporte del Concreto :
Vc = 0.53 x f ' c x b x d = 0.85 x Vc = 222678.8 kg
261975.02 kg Vu < 0 x Vc Cumple !! Vu < O x Vc CUMPLE !!
VERIFICACION POR CORTE ( = 0.85 )COLUMNA EXTERIOR : 31075.81 kg Vu = 1.50 x ( Pu - qnu x m x n ) = Vu = 31075.8055 kg El aporte del Concreto : Fc = 1 bo = ( b + ,5*d ) + 2x( t + d ) = 422 cm COLUMNA INTERIOR : Vu = 1.50 x ( Pu - qnu x m x n ) = Vu = 75697.49 kg El aporte del Concreto : Fc = 75697.49 1.25 kg
bo = ( b + 0,5*d ) + 2x( t + d ) = 493 cm
Vc = 0.27 x 2 + 4 x f 'c x bo x d Fc Vc = 1396870.76 kg Vc = 1187340.14 kg Vc = 1.10 x f 'c x bo x d = Vc = 948492.49 kg Vc = 806218.62 kg CUMPLE !! Vu < Vc 948492.5 kg
Vc = 0.27 x 2 + 4 x f 'c x bo x d Fc Vc = 1412870 kg Vc = 1200939 kg Vc = 1.10 x f 'c x bo x d = Vc = 1106949 kg Vc = 940906.8 kg CUMPLE !! Vu < Vc 1E+06 kg
Pgina 4 de 5
4.- CALCULO DEL REFUERZO EN EL TRAMO CENTRALX x qn - P1 = 0 X= P1 qn Calculo de As : X = 5.64 mMu =
qn x X^2 2
_
P1 x X
Mu = -91699.11
kg - m
Mu =
91699.11 r .e .e = 8 cm
kg - m db = 1.91c
As = Mu / ( * fy * ( d - a/2 )) a = As * fy / ( 0.85 * f 'c * B )
As mn = 0.0018 * B * d As > As mn OK !! Ab # Varilla ( n ) = As Ab Espaciam = B - 2*r.e - b n -1
B= d= a= As = a=
265 cm2 141 cm2 2.77 cm 26.06 cm2 2.78 cm
As = 26.06 cm2
(Valor Asumido) Ab ( 3/4" ) = 2.85 cm2 # Varilla ( n ) = 9 Espaciam = 31 cm 9 3/4" @ 31 cm Ab ( 3/4" ) = 2.85 cm2 # Varilla ( n ) = 24 Espaciam = 11 cm 24 3/4" @ 11 cm
As mn = 67.26 cm2 As >
As mn
5.- CALCULO DEL REFUERZO POR DEBAJO DE LA COLUMNA INTERIORqn x ( L )^2 2
Mu =
Mu =
6081.61 1.91 m
kg - m 1.4 6081.61 r .e .e = 8 cmc
L= Calculo de As :
14 5/8"@ 22cm kg - m db = 1.91
Mu =
As = Mu / ( * fy * ( d - a/2 )) a = As * fy / ( 0.85 * f 'c * B )
As mn = 0.0018 * B * d As > As mn OK !! Ab # Varilla ( n ) = As Ab Espaciam = B - 2*r.e - b n -1
B= d= a= As = a=
265 141 0.18 1.71 0.18
cm2 cm2 cm2 cm2 cm
As = 1.71 cm2
(Valor Asumido) Ab ( 3/4" ) = 2.85 cm2 # Varilla ( n ) = 1 Espaciam = #DIV/0! cm 1 3/4" @ #DIV/0! cm Ab ( 3/4" ) = 2.85 cm2 # Varilla ( n ) = 25 Espaciam = 10 cm 25 3/4" @ 10 cmASUMIR As mn !!
As mn = 71.55 cm2 As >
As mn
Disear en sentido transversal a cada columna le corresponde una porcion de Zapata
d/2
d/2
d/2
1.205
1.91
ZAPATA EXTERIOR
ZAPATA INTERIOR
Pgina 5 de 5
qn =
Pu Az
qn =
1.68
kg/cm2
qn =
Pu Az qnu x B x (L^2) 2 191 141 0.64 4.34 0.64 cm cm2 cm cm2 cm cm2
qn = 1.91 kg/cm2
Mu = B= d= a= As = a=
qnu x B x (L^2) 2
Mu = 1169724 1.59 cm2
Mu = B= d= a= As = a=
Mu = 2E+06 r .e .e = 8 cm (Valor Asumido) db = 1.59 cm2
120.5 cm2 r .e .e = 8 cm db = 141 cm2 0.52 (Valor Asumido) cm 2.20 cm2 0.52 cm cm2
As = 2.2
As mn = 32.54 cm2
Ab ( 3/4" ) = 2.85 cm2 # Varilla ( n ) = 11 Espaciam = 10.00 cm 11 3/4" @ 10 cm
As = 4.34
As mn = 51.57
cm2
Ab ( 3/4" ) = # Varilla ( n ) = Espaciam = 18 3/4" @
2.85 cm2 18 10.00 cm 10 cm
6.- VERIFICACION DE LA CONEXIN ZAPATA - COLUMNA( = 0.70 )Para la seccin A columna = 50*50 = 2500 cm ( COLUMNA ) c * 0.85 * f 'c * As1 A colum = b *t Pu < ( * 0.85 * f 'c * A1) As mn = 0.005 * A1 # Varilla = As1 Ab As col. > As mn OK !! Pu = 53500 kg A1 = 2500 cm2 * 0.85 * f 'c * A1 = 312375 kg Pu < * 0.85 * f 'c * A1CUMPLE !!
As mn = 12.50 cm2 As col > As minOK !!
Para la seccin B columna = 40*50 = 2000 cm ( COLUMNA ) * 0.85 * f 'c * As1 A colum = b *t Pu < ( * 0.85 * f 'c * A1) As mn = 0.005 * A1 # Varilla = As1 Ab As col. > As mn OK !! Pu = 96800 kg A1 = 2000 cm2 c * 0.85 * f 'c * A1 = 249900 kg Pu < * 0.85 * f 'c * A1CUMPLE !!
As mn = 10.00 cm2 As col > As minOK !!
Detalle de refuerzos en la Zapata Combinada verificamos primero el espaciamiento maximo Espaciamiento del Refuerzo > 45 cm OK !! 450 3xh= 450 cm
d/2 24 3/4"@ 11cm
d/2
d/2
18 3/4"@ 10cm
11 3/4"@ 10cm Longitud de desarrollo en Traccion ( Ld ) ld = b * fy * EFKP < 3.54 * f 'c^.5 * C + Kr b Lv1 = Lv - r.e.e Lv1 Ld = 71 cm
25 3/4"@ 10cm
Ld1 = 46 cm
La Zapata es rectangular se debe compartir el Refuerzo adecuadamente de la siguiente manera: Asc = 2 * Astrv (F + 1 ) F = Lado mayor Zapata Lado menor Zapata # Varilla ( n ) = As Ab Espaciam = B - 2*r.e.e - b n -1 Calculo del refuerzo minimo : As mn = 71.55 cm2 Ab ( 3/4" ) = # Varilla ( n ) = Espaciam = 25 3/4" @ 2.85 cm2 25 10.00 cm 10 cm b (3/4") = 1.91 F = 1.00 b (5/8") = 1.59 K = 0.80 r.e.e = 7.50 P = 1.00 fy = 4200 E = 1.30 f'c = 175 E = 1.00 Longitud de desarrollo en traccin
C = 6.50 ktr = 0
2.5
q=
q = ( C+kt r )/ b 8.41
q >= 2.5 ,PONER 2.5 !! q < 2.5 ,PONER q !!
Lv1 = 132.50 Ld < Lv1 Ld = 71.26 cm Refuerzo montaje en forma de Garrido 3/8" para refuerzo principal =< 3/4" 1/2" para refuerzo principal > 3/4" con espaciamiento maximo de 45 cm.
OK !!
0.2
Pgina 1 de 4
DISEO DE ZAPATA CONECTADA
Disear la zapata conectada que soportara las columnas mostradas en la figura . La capacidad portante admisible del suelo es qa = 2.0 kg/cm2 . Considere Fy = 4200 kg/cm2 , f'c = 175 kg/cm2 para la cimentacion
DATOS:Zapata f ' c = 175 kg/cm Columna f ' c = 210 kg/cm b1 = 50 cm t1 = 50 cm b2 = 40 cm t2 = 50 cm COL 1 2 fy= Df = Km = Kc = qa = db = Acero 4200 Suelo 1.60 1800 2400 2.00 1.91 PD (tn) 50 40 kg/cm m kg/m kg/m kg/cm cm PL (tn) 30 24 S/C = 500 kg/m
Lc = 550 cm db = 1.91 cm
SECCION REFUERZO 50 X 50 9 3/4" 40 X 50 9 3/4"
1.- DIMENSIONAMIENTO DE LA ZAPATA Y VIGA DE CIMENTACIONZAPATA EXTERIOR:
Ld =
0.08xdbxfy
f 'c
Ld = 0.08x1,91x4200/(175^(1/2)) = Ld = 49 cm
48.5
cm
hc = Ld + r.ee + b hm = Df - hc
ld >= 0.004 * b * fy
Ld >= 0.004x1.91x4200 = Ld = 32 cm
32.09 cm
Clculo del peralte de la zapata (hc ) hc = 59 cm hc = Ld + 10 = ht = Df - hc = ht = 101 cm
Clculo de la presin neta del suelo ( qm ) qn = qa - Km*hm - gc*hc - s/c qn = 2.4-(1800xE^-06)x(101)-(2400xE^06)x(59)-(500xE^04) = qn = CALCULO DE P'2 : Tanteo 1.63 kg/cm2
e =
57 cm
P'2 = P'2 = Az = Ps qn
P1xe 9249.49 kg
=
( PD + PL ) x
e
Lc - eAz =
=
( 50 + 30 ) x 1000 x 57 550 - 57
= =
9249.49
P1 + P' 2 qn b = 166
= 54868.437 cm P'1 = P'2 =
cm2
A = 2 x( b )^2 = nuevo e = + b -t 2 2
54868.44 e = 58
=
A = 2 x( b )^2 = 54980
9431 54980 b = 166 b= 165 t= 330
0 tomamos
+
t=2b
Tomamos b = 165 cm
-----> A = 165 x 330
e = 57 cm
Pgina 2 de 4
ZAPATA EXTERIOR:
Ld =
0.08xdbxfy
f 'c
Ld = 0.08x1.91x4200/(175^(1/2)) = Ld = 49 cm
49 cm
hc = Ld + r.ee + b hm = Df - hc
ld >= 0.004 * b * fy
Ld >= 0.004x1.91x4200 = Ld = 32 cm
32 cm
Clculo del peralte de la zapata (hc ) hc = 60 cm hc = Ld + 10 = ht = Df - hc = ht = 100 cm
Clculo de la presin neta del suelo ( qm ) qn = qa - Km*hm - gc*hc - s/c qn = 2.4-(1700xE^-06)x(120)-(2400xE-06)x(60)-(500xE-04) = qn = CALCULO DE P'2 : Tanteo 2.00 kg/cm2
e =
71 cm
P'2 = P'2 = Az = Ps qn
P1xe 9486.00 kg
=
( PD + PL ) x
e
Lc - eAz =
=
( 40 + 24 ) x 1000 x 50 550 - 50
=
= 9486
P2 + P' 2 qn b = 192
=
36743 usamos b = 2 P'1 = P'2 =
cm2 155 cm
A = ( b )^2 = nuevo e = + b -t 2 2
36743.00 e = 71
=
A = 2 x( b )^2 = 44743
9486 44743 b = 150
0
b= 150 + VIGAS DE CIMENTACION h= b= Lc 7 = P1 31 x Lc 550 7
A2 = ( 150 x 150 ) =
0
+
h = 79 cm b = 47 cm
SECCION 50 x 80
DISEO DE LA VIGA DE CONEXIN Wv = b x h x Kc = 9.6 kg/m Mu = P' 2 x L + Wv x ( L^2 )/2= 7250000 Mu = 7250000 kg-cm b ( 3/4") = 1.91 ree = 7.50 B = 50 cm d = 79.00 cm2 a = 5.00 cm2 (Valor Asumido) Ab ( 1" ) = 2.54 cm2 As = 25.07 cm2 a = 14.16 cm # Varilla ( n ) = 11 Espaciam = 3 cm As = 26.67 cm2 11 1" @ 3 cm
As = Mu / ( * fy * ( d - a/2 )) a = As x fy / ( 0.85 x f 'c x b ) As mn = 0.8 x (f ' c ^0.5) x B * d/ fy As > As mn OK !! # Varilla ( n ) = As Ab Espaciam = B - 2*r.e - b n -1
As mn = 9.95
cm2 As > Asmin
11
1" @OK !!
3 cm
Pgina 3 de 4
VERIFICACION POR CORTE Vu = P' 2 + Wv x L L Vu = 21982 KG Vu < Vc
APORTE DEL CONCRETO Vc = 0.53 x (f ' c ^0.5) x b x d =OK !!
23540 kg
DISEO DE LA ZAPATA EXTERIOR
ZAPATA EXTERIOR qn = Pu Az qnu x B x (L^2) 2 150 cm2 41 cm2 5.00 #DIV/0! #DIV/0! qn = #DIV/0! kg/cm2
ZAPATA INTERIOR qn = Pu Az #DIV/0!
Mu = B= d= a= As = a=
Mu =
#DIV/0!
Mu = L= B= d= a= As = a=
cm2 cm2 cm
r .e .e = 7.5 cm db = 1.59 cm2 (Valor Asumido)
qnu x B x (L^2) #DIV/0! kg 2 100 cm r .e .e = 8 cm 250 cm2 51 5 cm ( Valor Asumido ) #DIV/0! 2 cm cm #DIV/0!
As = #DIV/0!cm2
Ab ( 5/8" ) = 1.98 cm2 # Varilla ( n ) = #DIV/0! Espaciam = #DIV/0! cm cm2 #DIV/0! cm
As mn = 13.5 ####
As = #DIV/0! 2 cm #Varilla n = 14 Espaciam. = 17.88 Asmin = 27 cm2 14 5/8" @ 18 cm
5/8" @
6.- VERIFICACION DE LA CONEXIN ZAPATA - COLUMNA( = 0.70 )Columna Exterior Para la seccin A columna = 50 x 50 = 2500 cm ( COLUMNA ) * 0.85 * f 'c * As1 A colum = b *t Pu < ( * 0.85 * f 'c * A1) As mn = 0.005 * A1 # Varilla = As1 Ab As col. > As mn OK !! c # Varilla ( n ) = 4
Pu = 121000 kg A1 = 2500 cm2 * 0.85 * f 'c * A1 = 312375 kg Pu < * 0.85 * f 'c * A1
OK !!
As mn = 12.50 cm2 Ab ( 3/4" ) = 2.85 cm2 USAR : As1 = 12.50 cm2 OK !! As col > As min Columna Interior Para la seccin B columna = 50 x 50 = 2500 cm ( COLUMNA ) Pu = 96800 c kg * 0.85 * f 'c * As1 A1 = 2000 cm2 A colum = b *t * 0.85 * f 'c * A1 = 249900 kg # Varilla ( n ) = 4 cm2 Pu < ( * 0.85 * f 'c * A1) Ab ( 3/4" ) = 2.85 Pu < * 0.85 * f 'c * A1 As mn = 0.005 * A1 USAR : As1 = 10.00 cm2 # Varilla = As1 OK !! Ab As mn = 10.00 cm2 OK !! As col. > As mn OK !! As col > As min
Longitud de desarrollo en Traccion ( Ld ) ld = b * fy * EFKP 3.54 * f 'c^.5 * C + Kr b Lv1 = Lv - r.e.e < Lv1
Pgina 4 de 4
La Zapata es rectangular se debe compartir el Refuerzo adecuadamente de la siguiente manera: Asc = 2 * Astrv (F + 1 ) F = Lado mayor Zapata Lado menor Zapata Ab # Varilla ( n ) = As Ab Espaciam = B - 2*r.e.e - b n -1 Espaciamiento del Refuerzo 45 cm As1 = > 3xh 0 cmOK !!
F= K= P= E=
1.00 0.80 1.00 1.00
b (5/8") = 1.59 r.e.e = 7.50 fy = 4200 f'c = 175
C = 8.50 ktr = 02.5
q = ( C+kt r )/ b q= 10.09
Longitud de desarrollo en traccin Lv1 = 38.13 cm Ld = 46 cm AUMENTAR EL T !! Ld < Lv1
q >= 2.5 ,PONER 2.5 !! q < 2.5 ,PONER q !!
6 1"@ 7cm
d/2 d/2
14 5/8"@ 22cm 12 5/8"@ 12cm
14 5/8"@ 18cm
DISEO DE LOSA DE CIMENTACIONS/C= 450
Km1=
1700
KS 0.9
Y' A 1 B 2 C 3 D 0.2
E Y 9.8 4 5 X G 6
F
4.5
H 4.5
7 I O 0.2 J 5.4 11.6 DATOSCOLUMNA
8
9 L K 5.4 0.6 0.6 X'
PD (ton) 45 60 60 60 100 70 60 70 60 585
PL (ton) 25 30 30 30 40 30 30 30 30 275
Pu 70 90 90 90 140 100 90 100 90 860
1 2 3 4 5 6 7 8 9
F'c = Fy =
210 4200 2400 1.4 1 450 1700
kg/cm kg/cm2
2
Kc=qa = Ks = S/C=
kg/m3 2 kg/cm 3 kg/cm 2 Kg/m kg/m3
Km1=
1.- CALCULO DEL ESPESOR DE LA PLACA METODO DE DISEO ASUMIENDO
t=
50
cm.
P=
4
3Ks Et3 P= 0.003242 m 5.401-1
E=15000*F'c
P= Lc= 5.4 Lc= 4.5
0.003240
m
-1
1.75 P
Se debe cumplir la siguiente condicin: 1.75/P