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7/28/2019 Losa Alivianada Bidireccional
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1.1 .- Tableros entre columnas y vigas
Tableros S L
N m m
1 5.80 6.20 0.94
2 5.80 6.50 0.89
3 5.80 6.50 0.89
4 6.20 6.20 1.00
5 6.20 6.50 0.95
6 5.60 6.20 0.90
7 5.60 6.50 0.86
8 5.60 6.50 0.86
m >= 0,5 Losas armadas en dos direccionesm
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2.- Mayorizacin de cargas
qm= 604 Kg/cm2
qv= 500 Kg/cm2
qm= PPL
qu= 1,4D + 1,7L
qu= 1,4*(0,604)+1,7(0,5)
qu= 1.70 Ton/m
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Tablero Apoyo o Coef. qu Mu
N S L m=s/L caso Tramo Momentos (Ton/m) (ton)
A 0.0268 1.528A-B 0.0406 2.315
B 0.0538 3.068
B 0.0410 2.672
B-C 0.0310 2.020
C 0.0410 2.672
C 0.0570 3.030
C-D 0.0430 2.286
D 0.0280 1.489
A 0.0210 1.369A-B 0.0310 2.020
B 0.0410 2.672
C 0.0445 2.900
C-D 0.0335 2.183
D 0.0225 1.466
A 0.0280 1.489
A-B 0.0430 2.286
B 0.0570 3.030
B 0.0508 2.701
B-C 0.0380 2.020
C 0.0508 2.701
C 0.0598 3.179
C-D 0.0450 2.392
D 0.0296 1.574
1 0.0250 1.426
1;2 0.0370 2.110
2 0.0490 2.794
2 0.0410 2.6722;3 0.0310 2.020
3 0.0410 2.672
3 0.0490 2.605
3;4 0.0370 1.967
4 0.0250 1.329
1 0.0210 1.369
1;2 0.0310 2.020
DETERMINACION DE MOMENTOS Y CORTES
Faja VI
4 6.20 6.20 1.00 II 1.70
6.20 6.20 1.00 II
Faja V
1 5.80 6.20 0.94 III
1.702
3 5.60 6.20 0.90 III
1.705 5.60 6.50 0.86 II
8 5.60 6.50 0.86 III
Faja IV
3 5.60 6.20
Faja II
2 6.20 6.20 1.00 II 1.70
Faja III
7 6.20 6.50 0.95 II 1.70
0.90 III
4 6.20 6.20 1.00 II
6 5.60 6.20 0.90 III
6.20 0.94 III
1.70
Dimensiones Identificacin
Faja I
1 5.80
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2 0.0410 2.672
3 0.0410 2.672
3;4 0.0310 2.020
4 0.0210 1.369
1 0.0250 1.3291;2 0.0370 1.967
2 0.0490 2.605
2 0.0410 2.180
2;3 0.0310 1.648
3 0.0410 2.180
3 0.0490 2.605
3;4 0.0370 1.967
4 0.0250 1.329
Mu= coef*qu*s^2
Vs= qu*s/3
VL= qu*s/3*((3-m^2/2)
8 5.60 6.50 0.86 III
5.60 6.50 0.86 II
Faja VIII
6 5.60 6.20 0.90 III
1.707
Faja VII
5 6.20 6.50 0.95 II 1.70
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Vs VL 1 0.0490
0.94 0.0538
0.9 0.0570
nota: Borde continuo porque tiene tablero arriba y abajo
1 0.0210
0.95 0.0225
0.9 0.0240
0.9 0.0280
0.86 0.0296
0.8 0.0320
3.504 3.504
3.504 3.504
3.482 3.278
3.1653.456
3.456 3.165
3.572 3.165
3.572 3.165
3.504 3.504
3.662 3.504
Interpolacin
3.482
3.504
3.456
3.278
3.504
3.165
Corte
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3.1653.572
3.572 3.165
3.456 3.165
3.662 3.504
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CALCULO DEL ACERO DE REFUERZO
fc= 210 Kg/cm2
fy= 3500 Kg/cm2
d(asumido)= 17.30 cm
Ru= 57.370 Kg/cm2
Apoyo o
Tramo
A 1.528 30 0.06482 0.09907 0.10566
A-B 2.315 110 0.01768 0.04093 0.04197
B 3.068 30 0.06482 0.19889 0.23014
B-C 2.020 110 0.01768 0.03571 0.03650
C 3.030 30 0.06482 0.19644 0.22678C-D 2.286 110 0.01768 0.04041 0.04143
D 1.489 30 0.06482 0.09649 0.10272
A 1.369 30 0.06482 0.08871 0.09391
A-B 2.020 110 0.01768 0.03571 0.03650
B 2.672 30 0.06482 0.17320 0.19582
C 2.900 30 0.06482 0.18798 0.21534
C-D 2.183 110 0.01768 0.03859 0.03952
D 1.466 30 0.06482 0.09505 0.10107
A 1.489 30 0.06482 0.09649 0.10272
A-B 2.286 110 0.01768 0.04041 0.04143
B 3.030 30 0.06482 0.19644 0.22678
B-C 2.020 110 0.01768 0.03572 0.03650
C 3.179 30 0.06482 0.20608 0.24010
C-D 2.392 110 0.01768 0.04229 0.04341
D 1.574 30 0.06482 0.10201 0.10902
1 1.426 30 0.06482 0.09242 0.09810
1;2 2.110 110 0.01768 0.03730 0.03816
2 2.794 30 0.06482 0.18114 0.20624
2;3 2.020 110 0.01768 0.03571 0.036503 2.672 30 0.06482 0.17320 0.19582
3;4 1.967 110 0.01768 0.03478 0.03552
4 1.329 30 0.06482 0.08616 0.09105
1 1.369 30 0.06482 0.08871 0.09391
1;2 2.020 110 0.01768 0.03571 0.03650
2 2.672 30 0.06482 0.17320 0.19582
Faja
Faja
Faja
Faja
Diseo ductil
k
Faja
Faja
Mu b k w
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3 2.672 30 0.06482 0.17320 0.19582
3;4 2.020 110 0.01768 0.03571 0.03650
4 1.369 30 0.06482 0.08871 0.09391
1 1.329 30 0.06482 0.08616 0.09105
1;2 1.967 110 0.01768 0.03478 0.03552
2 2.605 30 0.06482 0.16887 0.190212;3 1.648 110 0.01768 0.02914 0.02966
3 2.605 30 0.06482 0.16887 0.19021
3;4 1.967 110 0.01768 0.03478 0.03552
4 1.329 30 0.06482 0.08616 0.09105
Faja
Faja
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As/m As/n varillas varillas As/N varillas
3.290 1.645 114 @ 10cm 1.097
4.792 2.396 212 @ 10cm 1.597
7.166 3.583 214 @ 10cm 2.389
4.168 2.084 212 @ 10cm 1.389
7.062 3.531 214 @ 10cm 2.3544.730 2.365 212 @ 10cm 1.577
3.199 1.599 114 @ 10cm 1.066
2.924 1.462 114 @ 10cm 0.975
4.168 2.084 212 @ 10cm 1.389
6.098 3.049 214 @ 10cm 2.033
6.706 3.353 214 @ 10cm 2.235
4.512 2.256 212 @ 10cm 1.504
3.147 1.574 114 @ 10cm 1.049
3.199 1.599 114 @ 10cm 1.066
4.730 2.365 212 @ 10cm 1.577
7.062 3.531 214 @ 10cm 2.354
4.168 2.084 212 @ 10cm 1.389
7.477 3.738 214 @ 10cm 2.492
4.956 2.478 212 @ 10cm 1.652
3.395 1.697 114 @ 10cm 1.132
3.055 1.527 114 @ 10cm 1.018
4.357 2.179 114 @ 10cm 1.452
6.422 3.211 214 @ 10cm 2.141
4.168 2.084 114 @ 10cm 1.3896.098 3.049 214 @ 10cm 2.033
4.056 2.028 212 @ 10cm 1.352
2.835 1.418 212 @ 10cm 0.945
2.924 1.462 114 @ 10cm 0.975
4.168 2.084 114 @ 10cm 1.389
6.098 3.049 212 @ 10cm 2.033
112 @ 10cm
V
VI
212 @ 10cm
212 @ 10cm
212 @ 10cm
212 @ 10cm
IV
214 @ 10cm
214 @ 10cm
214 @ 10cm
I
II
III
Faja central Franja Lateral
214 @ 10cm
214 @ 10cm
212 @ 10cm
212 @ 10cm
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6.098 3.049 214 @ 10cm 2.033
4.168 2.084 114 @ 10cm 1.389
2.924 1.462 212 @ 10cm 0.975
2.835 1.418 114 @ 10cm 0.945
4.056 2.028 212 @ 10cm 1.352
5.923 2.962 214 @ 10cm 1.9743.386 1.693 114 @ 10cm 1.129
5.923 2.962 214 @ 10cm 1.974
4.056 2.028 114 @ 10cm 1.352
2.835 1.418 212 @ 10cm 0.945
112 @ 10cm
112 @ 10cm
II
III
214 @ 10cm
214 @ 10cm
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CHEQUEO A LA FLEXION Y CORTE
FLEXIN
Momento Crtico Mu = 3.179Ton/m
Corte Crtico Vu = 3.66Ton
hmin= 25 cm
fc= 210 Kg/cm2fy= 3500 Kg/cm2
Ru= 57.370 Kg/cm2
dn= 17.55 cm
dex= 22.30 cm
dex >> dn
22.3 cm ok 17.55 cm
Mn= 20*22,30 2*57,370
Mn= 603451.47 Kg-cm
Mn= 5.71 Ton-m
Mn= 0,9*6,03
Mn= 5.14 Ton-m
Mu vs Mn
3.179Ton-m
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CHEQUEO DE DEFLEXIONES (Tramo corto)
Momento Crtico Mu(+)= 2.392Ton-m
qm= 604 Kg/cm2
qv= 500 Kg/cm2
ppl= 0.60 Ton/m2 520833.333
L= 6.50 m 213333.333
bw= 20.00 m 2500
b= 100 cm 1600
hmin= 25 cm 287.11
hf= 5 cm
fc= 210 Kg/cm2
fy= 3500 Kg/cm2
Y= 16.94 cm
Ig= 49097 cm4
c= 0.021
L= 5.60m
Mv= 0.329Ton-m
Mm= 0.398Ton-m
Ec= 218820 Kg/cm2
Ie= 44188 cm4
(v)= 0.135 cm
(m)= 0.109 cm
(s)= 0.176 cm
(LP)= 0.528cm
T= 0.663 cm
adm= 1.354cm
adm VS T
1.354cm >> 0.663 cm
ok
= ^2
=0,5*0,021*5,60^2
= ^2
=0,60*0,021*5,60^2
= 15100
= 15100 240
= 0,9
= 0,9 66667
()=3
32
()=3 (0,792 10) 4 3 0
32 218820 72542
()=1
16
()=
1 1,123 100000 430
16 218820 72542
= +%
= 0,137+(0,50)*(0,145)
=
= 3 0,123
=
= 0,094 0,368
=
480
=430
480
=
()
()
=
()
()
Ig=(
()
)-((b*h)-(b-bw)*(h-hf))
Ig=(
()
)-((110*30)-(110-30)*(30-5)) 18,85
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CHEQUEO DE DEFLEXIONES (Tramo Largo)
Momento Crtico Mu(+)= 2.392Ton-m
qm= 604 Kg/cm2
qv= 500 Kg/cm2
ppl= 0.60 Ton/m2 520833.333L= 6.50 m 213333.333
bw= 20.00 m 2500
b= 100 cm 1600
hmin= 25 cm 287.11
hf= 5 cm
fc= 210 Kg/cm2
fy= 3500 Kg/cm2
Y= 16.94 cm
Ig= 49097 cm4
c= 0.031
L= 5.60m
Mv= 0.486Ton-m
= ^2
=0,5*0,021*5,60^2
=
()
()
=
()
()
Ig=(
()
)-((b*h)-(b-bw)*(h-hf))
Ig=(
()
)-((110*30)-(110-30)*(30-5)) 18,85
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Mm= 0.587Ton-m
Ec= 218820 Kg/cm2
Ie= 44188 cm4
(v)= 0.199 cm
(m)= 0.160 cm
(s)= 0.260 cm
= ^2
=0,60*0,021*5,60^2
= 15100
= 15100 240
= 0,9
= 0,9 66667
()=3
32
()=3 (0,792 10) 4 3 0
32 218820 72542
()=1
16
()=1 1,123 100000 430
16 218820 72542
=
+%
= 0,137+(0,50)*(0,145)
=
=
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(LP)= 0.780cm
T= 0.979 cm
adm= 1.354cm
adm VS T1.354cm >> 0.979 cm
ok
,
=
= 0,094 0,368
=
480
=430
480
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bw= 20cm
NEV= 2
fy= 3500 Kg/cm2
Y= 2.60 cm
AHT= 104 cm2
AEHT= 52.00 cm2 por cada varilla
fs= 2100 Kg/cm2
w= 0.129cm
wadm vs wcal
0.400 cm >> 0.129 cm
ok
CHEQUEO DE AGRIETAMIENTOS
= /2
= 2 0,6
AHT =2*bw*Y
AHT =2*30*2,6
=
=162
2
f = 0,6
f = 0,6 2800
=
= 1,2 1680 2,6 86,67
/100000
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f'c= 210 Kg/cm2 L= 6.50 m
fy= 3500 Kg/cm2
qm= 604 Kg/cm2
qv= 500 Kg/cm2
qu= 1,4D + 1,7L
qu= 1,4*(0,2)+1,7(0,6)
qu= 1.70 Ton/m
B1= 0.85
qu*= 1.695 Ton/m
1.- MOMENTO ULTIMO
Mu= 8.95 Ton/m
2.- CUANTIA BALANCEADA
0.04335 0.63157895
b= 0.027378947
b= 2.74 %
3.- "PREDISEO"
Tablas: = 0.027379 "reeplazar los datos segn mi diseo en tablas"
w= 0.45646
Ru= 57.370 Kg/cm2 DISEO DUCTIL
b d h h b*h h/b
cm cm cm cm cm2
20 29.45 36.45 40.00 800 2.00 *
25 26.34 33.34 35.00 875 1.40
30 24.04 31.04 35.00 1050 1.17
35 22.26 29.26 35.00 1225 1.00
40 20.82 27.82 30.00 1200 0.75
(*nota)
escojo b= 0.20 m
h= 0.40 m
0.40
m
0.20
m
7.- PESO PROPIO DE LA VIGA (PPV)
PPV= 0.192 Ton/m
qPPV= 1,2*PPV
qPPV= 0.23 Ton/m
Mppv= 1.01 Ton/m
MT= 9.97 Ton/m
9.- dn (necesario)
* Momento mayor Mu= 9.97 Ton/m en mi caso es momento negativo
b= 0.20 m
dn= 31.07 cm
10.- PREDIMENSIONAMIENTO
r= 4 TN 1.27
As=*b*dn 5 22mm 19.01 cm2 = 1
As= 17.01 cm2 ns= 2
n= 3
"ver en tablas para el acero"
Er= 20 cm
Er=2r+2+ns+n
11.- d(existente)
d(exiatente)= h - y
d(existente)= 30.95cm
12.- As (negativo)
As(min)= 2.05 cm2
As(min)= 2.49 cm2 2 12mm 2.26 cm2
13.- COMPROBACION
Cc=Ts
0,85F`c*a*b=As*fs
a= 16.68
a= B1*C
C= 19.62
s= 0.00173cm/cm
y= 0.00167cm/cm
s vs y
0.00173cm/cm > 0.00167cm/cm
fs=fy
Cc= 0,85*f`c*a*b
Cc= 59543 kg
Ts= As*fy
Ts= 59543 kg
Mn= Ts*(dex-a/2)
Mn= 13.463Ton-m
Mu Vs Mn
9.97Ton/m < 12.117Ton-m
diseo ductil
1,5 < h/b < 2,0
PREDISEO DE LA VIGA
b=,
(
+)
=
=