platea de cimentacion.xlsx
TRANSCRIPT
DISEÑO DE LA PLATEA DE CIMENTACIÓN
Y
X
5.95 m 3.00 m 2.70 m
1. Datos :
f´c= 210 kg/cm2 Columnas fy= 4200 kg/cm2 b = 40.00 m
1.80 kg/cm2 h = 30.00 mKo= 5000 tn/m3
C1 C2 C3 37.00 tn 51.00 tn 30.00 tn 8.80 tn 14.00 tn 7.70 tn 1.50 tn 0.90 tn 0.20 tn 0.45 tn 0.24 tn 0.10 tn 0.10 tn 0.20 tn 0.20 tn 0.10 tn 0.10 tn 0.10 tn
C4 C5 C6 30.00 tn/m 51.00 tn/m 37.00 tn
σt =
PD= PD= PD=PL= PL= PL=
MDX= MDX= MDX=MLX= MLX= MLX=MDY= MDY= MDY=MLY= MLY= MLY=
PD= PD= PD=
C3C2C1
C9C8C7
C4
C10
C15C14C13 C16
C21C20C19 C22
A B C D
G H I J
M N Ñ O
R S T U
7.70 tn/m 14.00 tn/m 8.80 tn 0.20 tn/m 0.90 tn/m 1.50 tn 0.10 tn/m 0.24 tn/m 0.45 tn 0.20 tn/m 0.20 tn/m 0.10 tn 0.10 tn/m 0.10 tn/m 0.10 tn
C7 C8 C9 21.00 tn 51.0 tn 14.00 tn 5.54 tn 18.0 tn 3.72 tn 2.00 tn 1.0 tn/m 0.50 tn 0.85 tn 0.4 tn/m 0.10 tn 1.41 tn 0.1 tn/m 1.14 tn 0.32 tn 0.1 tn/m 0.28 tn
C10 C11 C12 14.00 tn 51.0 tn 21.00 tn 3.72 tn 18.0 tn 5.54 tn 0.50 tn 1.0 tn 2.00 tn 0.10 tn 0.4 tn 0.85 tn 1.14 tn 0.1 tn 1.41 tn 0.28 tn 0.1 tn 0.32 tn
2. Cálculo del espesor de la platea:
780.02 tn 220.96 tn 1000.98 tn
1092.03 tn 1467.66 tn 375.63 tn
2.1. Verificación por punzonamiento :
Vc =
Verificación de la columna central C8
n
mm=40+dn=30+d
Pu = 101966.00 Kg
Vu= 101966.00 Kg
2*(40+d)+2*(30+d)140+4d
Igualando tenemos:
PL= PL= PL=MDX= MDX= MDX=MLX= MLX= MLX=MDY= MDY= MDY=MLY= MLY= MLY=
PD= PD= PD=PL= PL= PL=
MDX= MDX= MDX=MLX= MLX= MLX=MDY= MDY= MDY=MLY= MLY= MLY=
PD= PD= PD=PL= PL= PL=
MDX= MDX= MDX=MLX= MLX= MLX=MDY= MDY= MDY=MLY= MLY= MLY=
QDS=QLS= QS=QDU= QU=QLU=
Vu ≤ ØVc , donde :
b0 = b0 =
d/2
d/2
d/2d/2
dbcf o **'*1.1
101966.00dAsumido = 26.20 cm Ojo ver que los valores sean Aproximados
= 102238.6338 OKVerificación de la columna lateral C2
n
mn=30+d/2m=40+d
2*(30+d/2)+2*(40+d)140+3d
Pu = 95200 KgVu = 95200 Kg
95200 = 1.1*(210)^(1/2)*(140+3d)*ddAsumido = 27.10 cm Ojo ver que los valores sean Aproximados
= 95598.9313 OKVerificación de la columna de esquina (C1):
n
mn = 30 + d/2m = 40 + d/2
140 + 2dPu = 66760 KgVu = 66760 Kg
66760 = 1.1*(210)^(1/2)*(140+2d)*ddAsumido = 21.00 cm Ojo ver que los valores sean Aproximados
= 67954.41298 OK
Finalmente el espesor de la platea será :t = 8.27 cm
Asumiendo t (cm) = 65.00 cm d (cm) = 55.14
PRESIONES DEL SUELO EN LOS PUNTOS A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W.
E = 2170000 Tn/m2t = 0.65 m
Ko = 5000 tn/m3
= 1.1*√210*(140+4d)*d
b0 = b0 =
b0=
d/2d/2
d/2
d/2
x Ko
b Ks λ 1.75/λ1.62 1265.53 0.28 6.192.97 1258.45 0.28 6.203.10 1258.08 0.28 6.201.75 1264.33 0.28 6.202.98 1258.42 0.28 6.204.48 1255.59 0.28 6.212.85 1258.79 0.28 6.202.85 1258.79 0.28 6.204.48 1255.59 0.28 6.212.98 1258.42 0.28 6.20
Direccion X L = 5.95 m < 6.20 m
Direccion Y L = 3.50 m < 6.21 m
▲ Se puede utilizar el Metodo Rigido Convencional
Y
ex
ey
X
5.95 3.00 2.70
3. Ubicación de la Resultante :
A B C D E F G
Direccion X
Direccion Y
En ambos casos se cumple que L< 1.75 / λ
Y´
x Ko
C3C2C1
C9C8C7
C4
C10
C15C14C13 C16
C21C20C19 C22
L M N Ñ O P Q
V W X Y Z á b
g h i j k l m
q r s t u v w
B'' C'' D'' E'' F'' G'' H''
M'' N'' Ñ'' O'' P'' Q'' R''2.975 2.975 1.5 1.5 1.35 1.35
Momentos de inercia :
1439.53 m46869.61 m4
X´= 10.30 m0.00 m
Y´= 4.612-0.103
Mx = -102.674
My = 0.000
Con : , encontramos la ecuación :
IX = IY =
eX (m) =
ey (m) =
q = 10.624 ± 0.000 X ± -0.071 Y
PUNTO Q/A (Tn/m2) X (m) 0.000 X Y -± 0.071 Y q (Tn/m2)
A 10.624 -10.30 0.000 4.58 -0.327 10.297B 10.624 -7.32 0.000 4.58 -0.327 10.297C 10.624 -4.35 0.000 4.58 -0.327 10.297D 10.624 -2.85 0.000 4.58 -0.327 10.297E 10.624 -1.35 0.000 4.58 -0.327 10.297F 10.624 0.00 0.000 4.58 -0.327 10.297G 10.624 1.35 0.000 4.58 -0.327 10.297H 10.624 2.85 0.000 4.58 -0.327 10.297I 10.624 4.35 0.000 4.58 -0.327 10.297J 10.624 7.32 0.000 4.58 -0.327 10.297K 10.624 10.30 0.000 4.58 -0.327 10.297L 10.624 -10.30 0.000 2.97 -0.211 10.412M 10.624 -7.32 0.000 2.97 -0.211 10.412N 10.624 -4.35 0.000 2.97 -0.211 10.412Ñ 10.624 -2.85 0.000 2.97 -0.211 10.412O 10.624 -1.35 0.000 2.97 -0.211 10.412P 10.624 0.00 0.000 2.97 -0.211 10.412Q 10.624 1.35 0.000 2.97 -0.211 10.412R 10.624 2.85 0.000 2.97 -0.211 10.412S 10.624 4.35 0.000 2.97 -0.211 10.412T 10.624 7.32 0.000 2.97 -0.211 10.412U 10.624 10.30 0.000 2.97 -0.211 10.412V 10.624 -10.30 0.000 1.35 -0.096 10.527W 10.624 -7.32 0.000 1.35 -0.096 10.527X 10.624 -4.35 0.000 1.35 -0.096 10.527Y 10.624 -2.85 0.000 1.35 -0.096 10.527Z 10.624 -1.35 0.000 1.35 -0.096 10.527a 10.624 0.00 0.000 1.35 -0.096 10.527b 10.624 1.35 0.000 1.35 -0.096 10.527c 10.624 2.85 0.000 1.35 -0.096 10.527d 10.624 4.35 0.000 1.35 -0.096 10.527e 10.624 7.32 0.000 1.35 -0.096 10.527f 10.624 10.30 0.000 1.35 -0.096 10.527g 10.624 -10.30 0.000 0.00 0.000 10.624h 10.624 -7.32 0.000 0.00 0.000 10.624i 10.624 -4.35 0.000 0.00 0.000 10.624j 10.624 -2.85 0.000 0.00 0.000 10.624k 10.624 -1.35 0.000 0.00 0.000 10.624l 10.624 0.00 0.000 0.00 0.000 10.624
m 10.624 1.35 0.000 0.00 0.000 10.624n 10.624 2.85 0.000 0.00 0.000 10.624ñ 10.624 4.35 0.000 0.00 0.000 10.624o 10.624 7.32 0.000 0.00 0.000 10.624p 10.624 10.30 0.000 0.00 0.000 10.624q 10.624 -10.30 0.000 -1.35 0.096 10.720r 10.624 -7.32 0.000 -1.35 0.096 10.720s 10.624 -4.35 0.000 -1.35 0.096 10.720t 10.624 -2.85 0.000 -1.35 0.096 10.720
u 10.624 -1.35 0.000 -1.35 0.096 10.720v 10.624 0.00 0.000 -1.35 0.096 10.720w 10.624 1.35 0.000 -1.35 0.096 10.720x 10.624 2.85 0.000 -1.35 0.096 10.720y 10.624 4.35 0.000 -1.35 0.096 10.720z 10.624 7.32 0.000 -1.35 0.096 10.720
A'' 10.624 10.30 0.000 -1.35 0.096 10.720B'' 10.624 -10.30 0.000 -3.10 0.221 10.845C'' 10.624 -7.32 0.000 -3.10 0.221 10.845D'' 10.624 -4.35 0.000 -3.10 0.221 10.845E'' 10.624 -2.85 0.000 -3.10 0.221 10.845F'' 10.624 -1.35 0.000 -3.10 0.221 10.845G'' 10.624 0.00 0.000 -3.10 0.221 10.845H'' 10.624 1.35 0.000 -3.10 0.221 10.845I'' 10.624 2.85 0.000 -3.10 0.221 10.845J'' 10.624 4.35 0.000 -3.10 0.221 10.845K'' 10.624 7.32 0.000 -3.10 0.221 10.845L'' 10.624 10.30 0.000 -3.10 0.221 10.845M'' 10.624 -10.30 0.000 -4.85 0.346 10.970N'' 10.624 -7.32 0.000 -4.85 0.346 10.970Ñ'' 10.624 -4.35 0.000 -4.85 0.346 10.970O'' 10.624 -2.85 0.000 -4.85 0.346 10.970P'' 10.624 -1.35 0.000 -4.85 0.346 10.970Q'' 10.624 0.00 0.000 -4.85 0.346 10.970R'' 10.624 1.35 0.000 -4.85 0.346 10.970S'' 10.624 2.85 0.000 -4.85 0.346 10.970T'' 10.624 4.35 0.000 -4.85 0.346 10.970U'' 10.624 7.32 0.000 -4.85 0.346 10.970V'' 10.624 10.30 0.000 -4.85 0.346 10.970
- Las presiones admisibles del suelo en todos los puntos son menores que el valor qadm(neta) =
3.23 m
2.70 m
3.50 m
3.00 m 5.95 m
C13 C14 C15 18.40 tn 49.90 tn 11.00 tn 5.00 tn 17.74 tn 3.00 tn 1.96 tn 0.90 tn 0.40 tn 0.85 tn 0.36 tn 0.15 tn 1.45 tn 0.10 tn 0.20 tn 0.32 tn 0.05 tn 0.10 tn
C16 C17 C18 11.00 tn/m 49.90 tn/m 18.40 tn
PD= PD= PD=PL= PL= PL=
MDX= MDX= MDX=MLX= MLX= MLX=MDY= MDY= MDY=MLY= MLY= MLY=
PD= PD= PD=
C6C5
C10 C12C11
C16 C18C17
C22 C24C23
E F
K L
P Q
V W
3.00 tn/m 17.74 tn/m 5.00 tn 0.40 tn/m 0.90 tn/m 1.96 tn 0.15 tn/m 0.36 tn/m 0.85 tn 0.20 tn/m 0.10 tn/m 1.45 tn 0.10 tn/m 0.05 tn/m 0.32 tn
C19 C20 C21 34.00 tn 47.6 tn 25.11 tn 8.00 tn 13.0 tn 6.00 tn 1.50 tn 0.9 tn/m 0.30 tn 0.45 tn 0.2 tn/m 0.10 tn 0.16 tn 0.2 tn/m 0.15 tn 0.10 tn 0.1 tn/m 0.05 tn
C22 C23 C24 25.11 tn 47.6 tn 34.00 tn 6.00 tn 13.0 tn 8.00 tn 0.30 tn 0.9 tn 1.50 tn 0.10 tn 0.2 tn 0.45 tn 0.15 tn 0.2 tn 0.16 tn 0.05 tn 0.1 tn 0.10 tn
PL= PL= PL=MDX= MDX= MDX=MLX= MLX= MLX=MDY= MDY= MDY=MLY= MLY= MLY=
PD= PD= PD=PL= PL= PL=
MDX= MDX= MDX=MLX= MLX= MLX=MDY= MDY= MDY=MLY= MLY= MLY=
PD= PD= PD=PL= PL= PL=
MDX= MDX= MDX=MLX= MLX= MLX=MDY= MDY= MDY=MLY= MLY= MLY=
3.23 m
2.70 m
3.50 m
3.00 5.95
H I J K
X ´C6C5
C10 C12C11
C16 C18C17
C22 C24C23
1.615R S T U
1.615c d e f
1.35
n ñ o p
1.35
x y z A''
1.75
I'' J'' K'' L''
1.75
S'' T'' U'' V''1.5 1.5 2.975 2.975
Verificación
27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!
27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!27.900 OK!
27.90 Tn/m2
4. Acero en la platea :
FRANJAS DE DISEÑO :
FRANJA V FRANJA VI FRANJA VII FRANJA VIII FRANJA IX FRANJA X
FRANJA I 1.62 m
FRANJA II 2.97 m
FRANJA III 3.10 m
FRANJA IV 1.75 m
2.98 m 4.48 m 2.85 m 2.85 m 4.48 m 2.98 m
FRANJA b b1 PUNTOSq
Q1 (Tn) Q2 (Tn) Q3 (Tn) Q4 (Tn) Q5 (Tn) Q6 (Tn)Carga q´ (tn/m2) F Q1´ Q2´ Q3´ Q4´ Q5´ Q6´
tn/m2 promed. modific. (Tn) (Tn) (Tn) (Tn) (Tn) (Tn)I 20.60 1.62 (A+K)/2 10.30 61.2 88.74 45.354 45.354 88.74 61.2 366.58 11.02 0.94 57.44 83.29 42.57 42.57 83.29 57.44II 20.60 2.97 (V+f)/2 10.53 34.26 100.018 20.5 20.5 100.018 34.26 476.28 7.80 1.54 52.71 153.89 31.54 31.54 153.89 52.71III 20.60 3.10 (q+A'')/2 10.72 38.818 101.966 25.924 25.924 101.966 38.818 509.00 7.97 1.53 59.26 155.66 39.58 39.58 155.66 59.26IV 20.60 1.75 (M''+V'')/2 10.97 66.76 95.2 55.09 55.09 95.2 66.76 414.78 11.51 0.96 63.79 90.96 52.64 52.64 90.96 63.79V 9.43 2.98 (A+M'')/2 10.63 66.76 38.818 34.26 61.2 0.00 0.00 249.67 8.90 1.24 82.91 48.21 42.55 76.01 0.00 0.00VI 9.43 4.48 (C+Ñ'')/2 10.63 95.2 101.966 100.018 69.7 0.00 0.00 407.80 9.66 1.11 105.82 113.34 111.17 77.47 0.00 0.00VII 9.43 2.85 (E+P'')/2 10.63 55.09 25.924 20.5 45.354 0.00 0.00 216.32 8.05 1.47 81.14 38.18 30.19 66.80 0.00 0.00VIII 9.43 2.85 (G+R'')/2 10.63 55.09 25.924 20.5 45.354 0.00 0.00 216.32 8.05 1.47 81.14 38.18 30.19 66.80 0.00 0.00IX 9.43 4.48 (I+T'')/2 10.63 95.2 101.966 100.018 69.7 0.00 0.00 407.80 9.66 1.11 105.82 113.34 111.17 77.47 0.00 0.00X 9.43 2.98 (K+V'')/2 10.63 66.76 38.818 34.26 61.2 0.00 0.00 249.67 8.90 1.24 82.91 48.21 42.55 76.01 0.00 0.00
DIAGRAMA DE MOMENTO FLECTOR
1.- Diseño de la Franja I :
57.44 83.29 42.57 42.57 83.29 57.44 5.95 m 3.00 m 2.70 m 3.00 m 5.95 m
20 cm 20 cm q*b1=
17.80 tn/m
26.21 6.66 5.4 6.66 26.3
52.4 53.59 13.32 13.32 52.59 52.6
Apoyos A, B,E,F Apoyos C,D
Mu= 5359000.00 kg - cm fy= 4200 kg/cm2 Mu= 1332000.00 kg - cm fy= 4200 kg/cm2d= 55.135 cm Asumiendo 3/4" f'c= 210 kg/cm2 d= 55.135 cm Asumiendo 3/4" f'c= 210 kg/cm2a= 11.027 cm a= 11.027 cmø= 0.9 ver norma E.060 - RNE ø= 0.9 ver norma E.060 - RNEb= 161.5 cm b= 161.5 cmh= 65 cm h= 65 cm
Iteraciones IteracionesAs (cm²) a (cm) As (cm²) a (cm)28.5708 4.1626 7.1014 1.034626.7224 3.8933 6.4518 0.940026.6548 3.8834 6.4462 0.939226.6523 3.8831 6.4461 0.939226.6522 3.8830 6.4461 0.9392
Por lo tanto: Por lo tanto:a= 3.88 0.17 m a= 0.94 0.28 m
As= 26.65 cm² As= 6.45 cm²As(min)= 16.03 cm² As(min)= 16.03 cm²
S= 17.27 cm S= 28.72 cm
Verificacion de la cuantia Verificacion de la cuantiaℓ= 0.0030 ℓmin ℓmin ≤ ℓ ≤ ≤ ℓ ≤ ℓmax ℓ= 0.0007 ℓmin ℓmin ≤ ℓ ≤ ≤ ℓ ≤ ℓmaxℓb= 0.0212 0.0018 0.0018 0.0030 0.0030 0.016 ok ℓb= 0.0212 0.0018 0.0018 0.0007 0.0007 0.016 okℓmin= 0.0018 ℓmin= 0.0018ℓmax= 0.016 ℓmax= 0.016
CLAROS AB,EF CLAROS BC,CD,DE
Mu= 2630000.00 kg - cm fy= 4200 kg/cm2 Mu= 666000.00 kg - cm fy= 4200 kg/cm2d= 55.135 cm Asumiendo 3/4" f'c= 210 kg/cm2 d= 55.135 cm Asumiendo 3/4" f'c= 210 kg/cm2a= 11.027 cm a= 11.027 cmø= 0.9 ver norma E.060 - RNE ø= 0.9 ver norma E.060 - RNEb= 161.5 cm b= 161.5 cmh= 65 cm h= 65 cm
Iteraciones IteracionesAs (cm²) a (cm) As (cm²) a (cm)14.0215 2.0428 3.5507 0.517312.8575 1.8733 3.2107 0.467812.8374 1.8703 3.2092 0.467612.8371 1.8703 3.2092 0.467612.8371 1.8703 3.2092 0.4676
Por lo tanto: Por lo tanto:a= 1.87 0.28 m a= 0.47 0.28 m
As= 12.84 cm² As= 3.21 cm²As(min)= 16.03 cm² As(min)= 16.03 cm²
S= 28.72 cm S= 28.72 cm
Verificacion de la cuantia Verificacion de la cuantiaℓ= 0.0014 ℓmin ℓmin ≤ ℓ ≤ ≤ ℓ ≤ ℓmax ℓ= 0.0004 ℓmin ℓmin ≤ ℓ ≤ ≤ ℓ ≤ ℓmaxℓb= 0.0212 0.0018 0.0018 0.0014 0.0014 0.016 ok ℓb= 0.0212 0.0018 0.0018 0.0004 0.0004 0.016 okℓmin= 0.0018 ℓmin= 0.0018ℓmax= 0.016 ℓmax= 0.016
DIAGRAMA DE MOMENTO FLECTOR
1.- Diseño de la Franja II :
52.71 153.89 31.54 31.54 153.89 52.71 5.95 m 3.00 m 2.70 m 3.00 m 5.95 m
20 cm 20 cm q*b1=
23.12 tn/m
Usar 1ФN°6@ Usar 1ФN°6@
USANDO ФN° 6 USANDO ФN° 6
Usar 1ФN°6@ Usar 1ФN°6@
USANDO ФN° 6 USANDO ФN° 6
A B C D E F
23.12 tn/m
34.10 8.67 7.02 8.67 34.21
68.2 68.20 17.34 17.34 68.43 68.43
Apoyos G, H,K,L Apoyos I,J
Mu= 6843000.00 kg - cm fy= 4200 kg/cm2 Mu= 1734000.00 kg - cm fy= 4200 kg/cm2d= 55.135 cm Asumiendo 3/4" f'c= 210 kg/cm2 d= 55.135 cm Asumiendo 3/4" f'c= 210 kg/cm2a= 11.027 cm a= 11.027 cmø= 0.9 ver norma E.060 - RNE ø= 0.9 ver norma E.060 - RNEb= 296.50 m cm b= 296.5 cmh= 65 cm h= 65 cm
Iteraciones IteracionesAs (cm²) a (cm) As (cm²) a (cm)36.4825 2.8952 9.2446 0.733633.7196 2.6759 8.3759 0.664726.3532 2.0913 8.3706 0.664326.2108 2.0800 8.3706 0.664326.2081 2.0798 8.3706 0.6643
Por lo tanto: Por lo tanto:a= 2.08 0.28 m a= 0.66 0.28 m
As= 26.21 cm² As= 8.37 cm²As(min)= 29.43 cm² As(min)= 29.43 cm²
S= 28.72 cm S= 28.72 cm
Verificacion de la cuantia Verificacion de la cuantiaℓ= 0.0016 ℓmin ℓmin ≤ ℓ ≤ ≤ ℓ ≤ ℓmax ℓ= 0.0005 ℓmin ℓmin ≤ ℓ ≤ ≤ ℓ ≤ ℓmaxℓb= 0.0212 0.0018 0.0018 0.0016 0.0016 0.016 ok ℓb= 0.0212 0.0018 0.0018 0.0005 0.0005 0.016 okℓmin= 0.0018 ℓmin= 0.0018ℓmax= 0.016 ℓmax= 0.016
CLAROS GH,KL CLAROS HI,IJ,JK
Mu= 3421000.00 kg - cm fy= 4200 kg/cm2 Mu= 867000.00 kg - cm fy= 4200 kg/cm2d= 55.135 cm Asumiendo 3/4" f'c= 210 kg/cm2 d= 55.135 cm Asumiendo 3/4" f'c= 210 kg/cm2a= 11.027 cm a= 11.027 cmø= 0.9 ver norma E.060 - RNE ø= 0.9 ver norma E.060 - RNEb= 296.5 cm b= 296.5 cmh= 65 cm h= 65 cm
Iteraciones IteracionesAs (cm²) a (cm) As (cm²) a (cm)18.2386 1.4474 4.6223 0.366816.6331 1.3200 4.1739 0.331216.6136 1.3184 4.1726 0.331116.6134 1.3184 4.1726 0.331116.6134 1.3184 4.1726 0.3311
Por lo tanto: Por lo tanto:a= 1.32 0.28 m a= 0.33 0.28 m
As= 16.61 cm² As= 4.17 cm²As(min)= 29.43 cm² As(min)= 29.43 cm²
S= 28.72 cm S= 28.72 cm
Verificacion de la cuantia Verificacion de la cuantiaℓ= 0.0010 ℓmin ℓmin ≤ ℓ ≤ ≤ ℓ ≤ ℓmax ℓ= 0.0003 ℓmin ℓmin ≤ ℓ ≤ ≤ ℓ ≤ ℓmaxℓb= 0.0212 0.0018 0.0018 0.0010 0.0010 0.016 ok ℓb= 0.0212 0.0018 0.0018 0.0003 0.0003 0.016 okℓmin= 0.0018 ℓmin= 0.0018ℓmax= 0.016 ℓmax= 0.016
DIAGRAMA DE MOMENTO FLECTOR
1.- Diseño de la Franja III :
59.26 155.66 39.58 39.58 155.66 59.26 5.95 m 3.00 m 2.70 m 3.00 m 5.95 m
20 cm 20 cm q*b1=
24.71 tn/m
36.39 9.25 7.49 9.25 36.51
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G H I J K L
M N Ñ O P Q
72.77 72.77 18.50 18.5 73 73
Apoyos M,N,P,Q Apoyos Ñ,O
Mu= 7300000.00 kg - cm fy= 4200 kg/cm2 Mu= 1850000.00 kg - cm fy= 4200 kg/cm2d= 55.135 cm Asumiendo 3/4" f'c= 210 kg/cm2 d= 55.135 cm Asumiendo 3/4" f'c= 210 kg/cm2a= 11.027 cm a= 11.027 cmø= 0.9 ver norma E.060 - RNE ø= 0.9 ver norma E.060 - RNEb= 310 cm b= 310 cmh= 65 cm h= 65 cm
Iteraciones IteracionesAs (cm²) a (cm) As (cm²) a (cm)38.9190 2.9540 9.8630 0.748635.9912 2.7318 8.9374 0.678435.9168 2.7261 8.9317 0.677935.9150 2.7260 8.9316 0.677935.9149 2.7260 8.9316 0.6779
Por lo tanto: Por lo tanto:a= 2.73 0.24 m a= 0.68 0.28 m
As= 35.91 cm² As= 8.93 cm²As(min)= 30.77 cm² As(min)= 30.77 cm²
S= 24.60 cm S= 28.72 cm
Verificacion de la cuantia Verificacion de la cuantiaℓ= 0.0021 ℓmin ℓmin ≤ ℓ ≤ ≤ ℓ ≤ ℓmax ℓ= 0.0005 ℓmin ℓmin ≤ ℓ ≤ ≤ ℓ ≤ ℓmaxℓb= 0.0212 0.0018 0.0018 0.0021 0.0021 0.016 ok ℓb= 0.0212 0.0018 0.0018 0.0005 0.0005 0.016 okℓmin= 0.0018 ℓmin= 0.0018ℓmax= 0.016 ℓmax= 0.016
CLAROS MN,PQ CLAROS NÑ,ÑO,OP
Mu= 3651000.00 kg - cm fy= 4200 kg/cm2 Mu= 925000.00 kg - cm fy= 4200 kg/cm2d= 55.135 cm Asumiendo 3/4" f'c= 210 kg/cm2 d= 55.135 cm Asumiendo 3/4" f'c= 210 kg/cm2a= 11.027 cm a= 11.027 cmø= 0.9 ver norma E.060 - RNE ø= 0.9 ver norma E.060 - RNEb= 310 cm b= 310 cmh= 65 cm h= 65 cm
Iteraciones IteracionesAs (cm²) a (cm) As (cm²) a (cm)19.4648 1.4774 4.9315 0.374317.7562 1.3477 4.4535 0.338017.7351 1.3461 4.4520 0.337917.7348 1.3461 4.4520 0.337917.7348 1.3461 4.4520 0.3379
Por lo tanto: Por lo tanto:a= 1.35 0.28 m a= 0.34 0.28 m
As= 17.73 cm² As= 4.45 cm²As(min)= 30.77 cm² As(min)= 30.77 cm²
S= 28.72 cm S= 28.72 cm
Verificacion de la cuantia Verificacion de la cuantiaℓ= 0.0010 ℓmin ℓmin ≤ ℓ ≤ ≤ ℓ ≤ ℓmax ℓ= 0.0003 ℓmin ℓmin ≤ ℓ ≤ ≤ ℓ ≤ ℓmaxℓb= 0.0212 0.0018 0.0018 0.0010 0.0010 0.016 ok ℓb= 0.0212 0.0018 0.0018 0.0003 0.0003 0.016 okℓmin= 0.0018 ℓmin= 0.0018ℓmax= 0.016 ℓmax= 0.016
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DIAGRAMA DE MOMENTO FLECTOR
1.- Diseño de la Franja IV :
63.79 90.96 52.64 52.64 90.96 63.79 5.95 m 3.00 m 2.70 m 3.00 m 5.95 m
20 cm 20 cm q*b1=
20.13 tn/m
29.61 7.53 6.1 7.53 29.71
59.23 59.23 15.06 15.06 59.43 59.43
Apoyos R,S,V,W Apoyos T,U
Mu= 5943000.00 kg - cm fy= 4200 kg/cm2 Mu= 1506000.00 kg - cm fy= 4200 kg/cm2d= 55.135 cm Asumiendo 3/4" f'c= 210 kg/cm2 d= 55.135 cm Asumiendo 3/4" f'c= 210 kg/cm2a= 11.027 cm a= 11.027 cmø= 0.9 ver norma E.060 - RNE ø= 0.9 ver norma E.060 - RNEb= 175 cm b= 175 cmh= 65 cm h= 65 cm
Iteraciones IteracionesAs (cm²) a (cm) As (cm²) a (cm)31.6843 4.2601 8.0290 1.079529.6618 3.9881 7.2976 0.981229.5859 3.9779 7.2910 0.980329.5831 3.9776 7.2909 0.980329.5830 3.9775 7.2909 0.9803
Por lo tanto: Por lo tanto:a= 3.98 0.16 m a= 0.98 0.28 m
As= 29.58 cm² As= 7.29 cm²As(min)= 17.37 cm² As(min)= 17.37 cm²
S= 16.86 cm S= 28.72 cm
Verificacion de la cuantia Verificacion de la cuantiaℓ= 0.0031 ℓmin ℓmin ≤ ℓ ≤ ≤ ℓ ≤ ℓmax ℓ= 0.0008 ℓmin ℓmin ≤ ℓ ≤ ≤ ℓ ≤ ℓmaxℓb= 0.0212 0.0018 0.0018 0.0031 0.0031 0.016 ok ℓb= 0.0212 0.0018 0.0018 0.0008 0.0008 0.016 okℓmin= 0.0018 ℓmin= 0.0018ℓmax= 0.016 ℓmax= 0.016
CLAROS RS,VW CLAROS ST,TU,UV
Mu= 2971000.00 kg - cm fy= 4200 kg/cm2 Mu= 753000.00 kg - cm fy= 4200 kg/cm2d= 55.135 cm Asumiendo 3/4" f'c= 210 kg/cm2 d= 55.135 cm Asumiendo 3/4" f'c= 210 kg/cm2a= 11.027 cm a= 11.027 cmø= 0.9 ver norma E.060 - RNE ø= 0.9 ver norma E.060 - RNEb= 175 cm b= 175 cmh= 65 cm h= 65 cm
Iteraciones IteracionesAs (cm²) a (cm) As (cm²) a (cm)15.8395 2.1297 4.0145 0.539814.5363 1.9545 3.6308 0.488214.5128 1.9513 3.6291 0.488014.5123 1.9512 3.6291 0.487914.5123 1.9512 3.6291 0.4879
Por lo tanto: Por lo tanto:a= 1.95 0.28 m a= 0.49 0.28 m
As= 14.51 cm² As= 3.63 cm²As(min)= 17.37 cm² As(min)= 17.37 cm²
S= 28.72 cm S= 28.72 cm
Verificacion de la cuantia Verificacion de la cuantiaℓ= 0.0015 ℓmin ℓmin ≤ ℓ ≤ ≤ ℓ ≤ ℓmax ℓ= 0.0004 ℓmin ℓmin ≤ ℓ ≤ ≤ ℓ ≤ ℓmaxℓb= 0.0212 0.0018 0.0018 0.0015 0.0015 0.016 ok ℓb= 0.0212 0.0018 0.0018 0.0004 0.0004 0.016 okℓmin= 0.0018 ℓmin= 0.0018ℓmax= 0.016 ℓmax= 0.016
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R S T U V W
Franja Nº q`modif (tn/m2)
I11.02
11.02
II7.80
7.80
III7.97
7.97
IV11.51
11.51
V8.90
8.90
VI9.66
9.66
VII8.05
8.05
VIII8.05
9.66
IX 9.669.66
X8.908.90
5.- Verficación de la fuerza cortante en la platea :
Con la fórmula :, que es la fuerza cortante actuante
b (cm) = 100.00d (cm) = 55.14f´c (kg/cm2) = 210.00
Ø = 0.85
También :
ØVc = 35994.14 kg
Es decir : ØVc = 35.99 Tn
Franja Nº q´ (tn/m2) L (m) Vu (Tn)
I
11.02 5.95 32.78
11.02 3.00 16.53
11.02 2.70 14.88
11.02 3.00 16.5311.02 5.95 32.78
II
7.80 5.95 23.20
7.80 3.00 11.707.80 2.70 10.537.80 3.00 11.70
7.80 5.95 23.20
III
7.97 5.95 23.71
7.97 3.00 11.96
7.97 2.70 10.76
7.97 3.00 11.96
7.97 5.95 23.71
IV
11.51 5.95 34.23
11.51 3.00 17.26
11.51 2.70 15.53
11.51 3.00 17.26
11.51 5.95 34.23
V
8.90 3.23 14.37
8.90 2.70 12.01
8.90 3.50 15.57
VI9.66 3.23 15.61
9.66 2.70 13.05
9.66 3.50 16.91
VII
8.05 3.23 13.00
8.05 2.70 10.87
8.05 3.50 14.09
VIII
8.05 3.23 13.008.05 2.70 10.87
8.05 3.50 14.09
IX9.66 3.23 15.619.66 2.70 13.059.66 3.50 16.91
X8.90 3.23 14.378.90 2.70 12.018.90 3.50 15.57
Luego : Vu max = 34.23 < Ø Vc = 35.99 (OK !!!)
2´**0.1L
qVu
dbcfØØVc **´*53.0*
4. Acero en la platea :
FRANJAS DE DISEÑO :
FRANJA V FRANJA VI FRANJA VII FRANJA VIII FRANJA IX FRANJA X
FRANJA I 1.62 m
FRANJA II 2.97 m
FRANJA III 3.10 m
FRANJA IV 1.75 m
2.98 m 4.48 m 2.85 m 2.85 m 4.48 m 2.98 m
FRANJA b b1 PUNTOSq
Q1 (Tn) Q2 (Tn) Q3 (Tn) Q4 (Tn) Q5 (Tn) Q6 (Tn)Carga q´ (tn/m2) F Q1´ Q2´ Q3´ Q4´ Q5´ Q6´
tn/m2 promed. (tn) modific. (Tn) (Tn) (Tn) (Tn) (Tn) (Tn)I 20.60 1.62 (A+K)/2 10.30 61.2 88.74 45.354 45.354 88.74 61.2 366.58 11.02 0.94 57.44 83.29 42.57 42.57 83.29 57.44II 20.60 2.97 (V+f)/2 10.53 34.26 100.018 20.5 20.5 100.018 34.26 476.28 7.80 1.54 52.71 153.89 31.54 31.54 153.89 52.71III 20.60 3.10 (q+A'')/2 10.72 38.818 101.966 25.924 25.924 101.966 38.818 509.00 7.97 1.53 59.26 155.66 39.58 39.58 155.66 59.26IV 20.60 1.75 (M''+V'')/2 10.97 66.76 95.2 55.09 55.09 95.2 66.76 414.78 11.51 0.96 63.79 90.96 52.64 52.64 90.96 63.79V 9.43 2.98 (A+M'')/2 10.63 66.76 38.818 34.26 61.2 0.00 0.00 249.67 8.90 1.24 82.91 48.21 42.55 76.01 0.00 0.00VI 9.43 4.48 (C+Ñ'')/2 10.63 95.2 101.966 100.018 69.7 0.00 0.00 407.80 9.66 1.11 105.82 113.34 111.17 77.47 0.00 0.00VII 9.43 2.85 (E+P'')/2 10.63 55.09 25.924 20.5 45.354 0.00 0.00 216.32 8.05 1.47 81.14 38.18 30.19 66.80 0.00 0.00VIII 9.43 2.85 (G+R'')/2 10.63 55.09 25.924 20.5 45.354 0.00 0.00 216.32 8.05 1.47 81.14 38.18 30.19 66.80 0.00 0.00IX 9.43 4.48 (I+T'')/2 10.63 95.2 101.966 100.018 69.7 0.00 0.00 407.80 9.66 1.11 105.82 113.34 111.17 77.47 0.00 0.00X 9.43 2.98 (K+V'')/2 10.63 66.76 38.818 34.26 61.2 0.00 0.00 249.67 8.90 1.24 82.91 48.21 42.55 76.01 0.00 0.00
DIAGRAMA DE MOMENTO FLECTOR
1.- Diseño de la Franjas V y X:
82.91 48.21 42.55 76.01 3.23 m 2.70 m 3.50 m
15 cm 15 cmq*b1=
26.48 tn/m
10.81 8.05 12.95
26.03 26.03 26.74 26.74
Apoyos A, G,M,N CLAROS AG,GM,MR
Mu= 2674000.00 kg - cm fy= 4200 kg/cm2 Mu= 1295000.00 kg - cm fy= 4200 kg/cm2d= 55.135 cm Asumiendo 3/4" f'c= 210 kg/cm2 d= 55.135 cm Asumiendo 3/4" f'c= 210 kg/cm2a= 11.027 cm a= 11.027 cmø= 0.9 ver norma E.060 - RNE ø= 0.9 ver norma E.060 - RNEb= 297.5 cm b= 297.5 cmh= 65 cm h= 65 cm
Iteraciones IteracionesAs (cm²) a (cm) As (cm²) a (cm)14.2561 1.1275 6.9041 0.546012.9630 1.0253 6.2446 0.493912.9509 1.0243 6.2417 0.493712.9508 1.0243 6.2416 0.493712.9508 1.0243 6.2416 0.4937
Por lo tanto: Por lo tanto:a= 1.02 0.28 m a= 0.49 0.28 m
As= 12.95 cm² As= 6.24 cm²As(min)= 29.52 cm² As(min)= 29.52 cm²
S= 28.72 cm S= 28.72 cm
Verificacion de la cuantia Verificacion de la cuantiaℓ= 0.0008 ℓmin ℓmin ≤ ℓ ≤ ≤ ℓ ≤ ℓmax ℓ= 0.0004 ℓmin ℓmin ≤ ℓ ≤ ≤ ℓ ≤ ℓmaxℓb= 0.0212 0.0018 0.0018 0.0008 0.0008 0.016 ok ℓb= 0.0212 0.0018 0.0018 0.0004 0.0004 0.016 okℓmin= 0.0018 ℓmin= 0.0018ℓmax= 0.016 ℓmax= 0.016
DIAGRAMA DE MOMENTO FLECTOR
1.- Diseño de la Franjas VIy IX:
105.82 113.34 111.17 77.47
3.23 m 2.70 m 3.50 m
15 cm 15 cm
q*b1=
43.25 tn/m
17.67 13.15 20.51
37.65 37.65 43.70 43.7
Apoyos B,H,N,S CLAROS AG,GM,MR
Mu= 4370000.00 kg - cm fy= 4200 kg/cm2 Mu= 2051000.00 kg - cm fy= 4200 kg/cm2d= 55.135 cm Asumiendo 3/4" f'c= 210 kg/cm2 d= 55.135 cm Asumiendo 3/4" f'c= 210 kg/cm2a= 11.027 cm a= 11.027 cmø= 0.9 ver norma E.060 - RNE ø= 0.9 ver norma E.060 - RNEb= 447.5 cm b= 447.5 cmh= 65 cm h= 65 cm
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A G M R
B H N S
Iteraciones IteracionesAs (cm²) a (cm) As (cm²) a (cm)23.2981 1.2250 10.9346 0.574921.2038 1.1149 9.8927 0.520221.1824 1.1138 9.8878 0.519921.1822 1.1138 9.8878 0.519921.1822 1.1138 9.8878 0.5199
Por lo tanto: Por lo tanto:a= 1.11 0.28 m a= 0.52 0.28 m
As= 21.18 cm² As= 9.89 cm²As(min)= 44.41 cm² As(min)= 44.41 cm²
S= 28.72 cm S= 28.72 cm
Verificacion de la cuantia Verificacion de la cuantiaℓ= 0.0009 ℓmin ℓmin ≤ ℓ ≤ ≤ ℓ ≤ ℓmax ℓ= 0.0004 ℓmin ℓmin ≤ ℓ ≤ ≤ ℓ ≤ ℓmaxℓb= 0.0212 0.0018 0.0018 0.0009 0.0009 0.016 ok ℓb= 0.0212 0.0018 0.0018 0.0004 0.0004 0.016 okℓmin= 0.0018 ℓmin= 0.0018ℓmax= 0.016 ℓmax= 0.016
DIAGRAMA DE MOMENTO FLECTOR
1.- Diseño de la Franjas VIIy VIII:
81.14 38.18 30.19 66.80 3.23 m 2.70 m 3.50 m
15 cm 15 cmq*b1=
22.94 tn/m
9.37 6.97 10.87
19.96 19.96 23.17 23.17
ApoyosC,I,Ñ,T CLAROS CI ,IÑ, ÑT
Mu= 2317000.00 kg - cm fy= 4200 kg/cm2 Mu= 1087000.00 kg - cm fy= 4200 kg/cm2d= 55.135 cm Asumiendo 3/4" f'c= 210 kg/cm2 d= 55.135 cm Asumiendo 3/4" f'c= 210 kg/cm2a= 11.027 cm a= 11.027 cmø= 0.9 ver norma E.060 - RNE ø= 0.9 ver norma E.060 - RNEb= 285 cm b= 285 cmh= 65 cm h= 65 cm
Iteraciones IteracionesAs (cm²) a (cm) As (cm²) a (cm)12.3528 1.0198 5.7952 0.478411.2213 0.9264 5.2384 0.432511.2117 0.9256 5.2362 0.432311.2116 0.9256 5.2362 0.432311.2116 0.9256 5.2362 0.4323
Por lo tanto: Por lo tanto:a= 0.93 0.28 m a= 0.43 0.28 m
As= 11.21 cm² As= 5.24 cm²As(min)= 28.28 cm² As(min)= 28.28 cm²
S= 28.72 cm S= 28.72 cm
Verificacion de la cuantia Verificacion de la cuantiaℓ= 0.0007 ℓmin ℓmin ≤ ℓ ≤ ≤ ℓ ≤ ℓmax ℓ= 0.0003 ℓmin ℓmin ≤ ℓ ≤ ≤ ℓ ≤ ℓmaxℓb= 0.0212 0.0018 0.0018 0.0007 0.0007 0.016 ok ℓb= 0.0212 0.0018 0.0018 0.0003 0.0003 0.016 okℓmin= 0.0018 ℓmin= 0.0018ℓmax= 0.016 ℓmax= 0.016
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C I Ñ T