DISEO DE PUENTE LOSA
L 5.00 mCamion D HL-93
C 0.40 mf'c 210 kg/cm2fy 4200 kg/cm2
Ancho cal 6.00 me.asfalto 5.00 cm
Diseo de la losa1. PREDIMENCIONAMIENTO
L
6. METRADO DE CARGASA) carga uniformemente distribuida
p.p de losa 1.125 Tn/mp del asfalto 0.11 Tn/m
D 1.235 Tn/m
B) S/C vehicular
SOBRECARGA VEHICULAR :
0.8 W 0.8 W 0.2
4,27 a 9,15 m. 4.3 m.
S / C Vehicular : HL93Neumatico delantero ( P' ) = 3.57 Tn
Neumatico posteriores ( P ) = 14.78 Tn
7. CALCULO DEL MOMENTO FLECTORA) momento por carga muerta
MD=DL^2/8MD 4.501575 Tn-m
A) momento por S/C vehicular*por camion de diseo
dist.ejes. = 4.3 m. 4.3
14.78 Tn 14.78 Tn
A
RA
X 5.40 -
X + 4.30 1.10
Ld.= 5.40
X < 1.10
5.40 RA = 96.07 29.56 X
RA = 17.79 5.474 X
M x. = RA * X
M x. = 17.79 X - 5.474
Derivando respecto a X
( d M x / d X ) = 0
17.79 10.95 X = 0
X = 1.63 m.
M 14.4549768519
ML 5.67 Tn - m.
*por eje tandem1.20 m.
11.20 Tn 11.20 Tn
A
RAX + 1.20 4.20
X 5.40 X5.40
0 < = X 4.20
S.( MB ) = 0
5.40 * RA = 107.52 22.40
RA = 19.91 4.148
Mx = RA * X
Derivando respecto a X
( d M x / d X ) = 019.911 8.296 X = 0
X = 2.40 m.Remplazando en ecuacin ( 3 ) el valor de X :
M = 23.89 Tn - m. ( por via de circulacin )
ML 9.37 Tn - m.
*por sobre carga
W =
A UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU
RA
L / 2 L / 2
Ld. = 5.40 m.
ML = W ( L) / 8
M= 3.54 Tn - m.
M= 1.18 Tn - m.
ML 10.55 Tn - m.
*por impactoMI = I.dise. * ML ; I.dise. = 0.330
MI = 3.092 Tn - m
MS= 18.140 Tn - m
MOMENTO FACTORIZADO : ( POR ROTURA )
MU = n( 1.25MD +1.75ML + 1.75MI )nD 1.05nR 1.05nI 1.05n 1.157625
MU = 34.14 Tn - m
8. CALCULO DE LA FUERZA CORTANTE a-) POR CARGA MUERTA :
Z = 0.20WD = 1.24 Tn / m.
A UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU
RA VDL ' = 5.00 m.
Ld. = 5.40 m.
VD = WD * ( L ' ) / 2 3.09 Tn
a-) CAMION DE DISEO:
dist.ejes. = 4.3 m. 4.3Z = 0.20
14.78 Tn 14.78 Tn
A
RA
X 5.40 -
X + 4.30 1.10
Ld.= 5.40
5.40 RA = 96.07 29.56 X
RA = 17.79 5.474 X
VL 6.55 Tn
POR EJE TANDEM :
Z = 0.20 1.20
11.20 Tn 11.20 Tn
A
RA5.20
5.40
SMB = 0RA = 19.08 Tn.
RA/E = VL = 7.48 Tn.
CORTANTE POR VIGA : ( VL)
VL 6.55 Tn.
POR SOBRECARGA DISTRIBUIDA :
Z = 0.20
W =
A UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU
RAVL
5.20 m.Ld. = 5.40 m.
SMB = 0
RA = [(( Ld-Z)*W - ( Z *W )] / 2
RA = 2.43 Tn
V 0.81 Tn
VL 7.35 Tn
POR IMPACTO : ( VI )
VI = I.dise. * VL ; I dise. = 0.330
VI = 2.16 Tn
CORTE FACTORIZADO : ( Por Servicio)
VU = n (1.25VD+1.75VL+1.75-+VI)
VU = 23.74 Tn
9 DISEO DE LA SECCION:
POR FLEXION :MU 34.14
d = h - recubrim. h =recubrimi =
d = 39.00 cm.W= 0.128 Kg / cm = 0.006 m
As 25.05 cm^2
min = 0.002 cuantia balanceada
Asmin 7.02 cm^2
b = 0.022 cuantia balanceada
Amax 63.18 cm^2
ESPACIAMIENTO :
As 25.05 cm^2
PROVANDO 1 "Ab 5.07
S= 20.22 cm1@1 20 Cm
Asmin 7.02 cm^2
PROVANDO 1/2 "Ab 1.27
S= 18.05 cm1@1/2 18.00 Cm
Acero de reparticion y temperatura
1750/S
S= 24.38 cm1@5/8 24.00 Cm
As 2.28 cm^2
PROVANDO 3/8 "Ab 0.71
S= 31.32 cm1@3/8 31.00 Cm
1@1/2 18 1@3/8
1@5/8 22.51@1 20
POR CORTE :
Vu 23.74 Tn
corte resistente del concreto Vc=0.53*(f'c)^0.5*b*d
Vc 29.95 Tn
Vc 2546.06 Tn > 23.74
10. VERIFICACION POR SERVICIOa) Peralte Requerido
M's= 18.140 Tn
fc= 94.50fs= 1700.00n= 9.20K= 0.34J= 0.89
dmin= 35.76 cm
=( / ))2 (
45
d= 39.73 >
a) Agrietamineto
A 210.8 cm
fs 2054.079558818 < 2100se toma el menor valor de estos
fs 2054.07955882 Kg/cm2
Z 21273.7638798 Kg/cm
a) Verficacion por fatiga
9.00 m 4.30 m.
14.78 14.78 Tn 3.57 Tn
A
RA
X 5.40 -
X + 4.30 1.10
Ld.= 5.40
5.40 RA = 83.739 18.35 X
RA = 15.51 3.398 X
=(2 )/(# )
M x. = RA * X
M x. = 15.51 X - 3.398
Derivando respecto a X
( d M x / d X ) = 0
15.51 6.80 X = 0
X = 2.28 m.
M 17.691543347
ML 6.94 Tn - m.
MI 2.29 Tn - m.
Ms' = MD + ML + MI
Ms' = 13.73 Tn - m.
Esfuerzo mximo:
fsmax= 1554.41 kg/cm2
Esfuerzo mnimo:
fsmin= 509.73 kg/cm2
Esfuerzo admisible:
fs1=1470 + 551.2*(r/h)
fs1= 1635.36 kg/cm2
fsadm= 1467.15 kg/cm2
1044.68
a) Verficacion por vibraciones
L= 5.80 mEc= 2173706.51
WD= 1.24 Tn/mg= 9.80 m/seg2I= 0.04404375 m4
f= 28.57 >
10. CALCULO DE L CONTRAFECHA
a) Evacuacion de aguas:
evac.aguas= 1.45 cm
b) Deformacion maxima:
maxs = cp + sc
Deformacion por carga muerta:
As(-)= 7.02 cm2As(+)= 25.05 cm2
momento de inercia de la seccion llena
Ig= 759375.00 cm4
momento de iagrietamiento
fr= 28.98
Mcr= 9.78 Tn-m
momento de inercia de la seccion agrietada:
As= 25.05 cm2As'= 7.02 cm2
d= 39.73 cmd'= 5.27 cm
n= 9.00
(2n-1)*As'= 119.34n*As= 225.49
=2/( ^2) (( ) )3 /
r=nAs +(2n-1)As'= 344.83p=nAs*d +(2n-1)As'*d'= 9587.51
C= 10.82
momento de inercia de la seccion agrietada:
Icr=bc^3/3+nAs(d-c)^2+(2n-1)As'(c-d)^2
Icr= 234359.14 cm4
MOENTO DE INERCIA EFECTIVO
Ms= 18.140
Ie= 31.67 cm4
c) Deformacion instantanea:
icp = 0.20 cm
c) Deformacion instantanea:
1.83
dcp = 0.36
c) Deformacion por S/C vehicular:
5.84 Tn 5.84 Tnl= 1.20
A
RA
2.1 1.20 2.10
Ld.= 5.40
=
((1+ / ^2))=/ 2 ( -1)
= )^3 +[1(/ )^3(/ ]
P'= 5.84P'1= 14.49P'2= 23.91
cl = 40.85 /EI
EI= 68836523084.6238
cl = 0.59 cm
c) Deformacion por S/C distribuida:
W =
A UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU
RA
Ld. = 5.40 m.
S/C = 0.16 cm
S/C = 0.05 cm
S/C vehculo= 0.20
= 3.88 cm deformacion maxima
contraflecha= 4.00 cm
11. VIGA SARDINEL
0.15
b=0.6 # h=
d=0.25 L=0.45
1.35
a) Metrado de cargas:*Carga Muerta:
P. propio: 2.36 Tn/mP. Guardera: 0.23 Tn/mP. Tubo: 0.08 Tn/mPiso Termin: 0.12 Tn/m
D= 2.79 Tn/m
*Carga Viva:s/c Peatonal: 0.43 Tn/ms/c Baranda: 0.15 Tn/m
L= 0.58 Tn/m
U= 1.4*D+1.7*L= 4.89 Tn/m
Momento al centro de la luz:
Mu= WL^2/8= 17.83 Tn-m
Momento por s/c vehicular:Fc=
Mu(s/c)= 0.1*Pm*L(1+I)*Fc I=Mu(s/c)= 9.29 Tn-m Pm=
L=
Por lo tanto: Mut= 27.12 Tn-m
Fuerza cortante en la cara de apoyo:
Mcl= 9.29 Tn-m P1= 6.88 Tn
0.2U=
A UUUUUUUUUUUUUUUUUUUUUUUUUUU
RA
L= 5.40 m.
RA= 19.83 Tn
Vu= 19.93 - 0.2*4.89= 18.86 Tn
b) Diseo del refuerzo:
b1) Clculo del momento ltimo:
Mu=Ma/0.9= 30.13 Tn-m
b2) Cuanta balanceada, mxima y Kumx:
b= 0.0216 mx= 0.0162
b3) Momento ltimo resistente Mur:
Mur= 27.39 Tn-m 4200. kg/cm2
fs=fy
As2=A's= 1.13 cm2 Finalmente:
As=As1+As2= 187.75 cm2
b7) Seleccin de los dimetros y numero de varillas:
As= 187.75 cm2Ab= 10.1 cm2
19 1 3/8" As= 191.9 cm2
A's= 1.13 cm21/2" Ab= 1.29 cm2
1 1 3/8 As= 1.29 cm2
Asmin= 28.51 cm21" Ab= 5.10 cm2
6 1" As= 30.60 cm2
1 3/8"
DISEO DE PUENTE LOSA
se elije el mayor valor de los "e" calculados
se elije el menor valor de los "L" calculados
factor de amplificacion
un carril cargadodos carriles cargados
calculado para un solo carril
Wcada uno.
3.57 Tn
B
RB
X
- X
( 1)
X^2
B
RBX
X
X
( por via de circulacin )
0.97 Tn / m.
B
RB
( por via de circulacin )
(general )
BRB
1.24 Tn
B
RB
X
( 1)
B
RB
- X
0.97 Tn / m.
UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU B
RB
( calculado anteriormente )
0.45 m.0.06 m
diametro de varilla
diametro de varilla
ok
diametro de varilla
diametro de varilla
S< 22.5
22.50
Tn
5.27
35.76
B
RB
X
( 1)
- X
X^2
1467.15
6 ciclos
< 18.14
BRB
0.97 Tn / m.
B
RB
deformacion maxima
1.35 m0.70 m
0.64 m5.40 m
1.750.337.39
5.40 m
4.89 Tn/m
Kumx= 49.5301
Mu= 30.13 Tn-m
OK
Hoja1