Post on 07-Apr-2018
8/3/2019 trab_pontes_rusch
1/50
Braslia, 26 de outubro de 2011
PONTESMEMRIA DE CLCULO - LAJES
GRUPO 6
ALUNOS
Li Chong Lee Bacelar de Castro
Alexandre de Oliveira Urzedo - 094436
Andr Luiz do Carmo Gomes - 093990
Denison Carlos de Paula Cardoso - 083465
Tiago Felipe Taffner Bezerra - 094014
PROFESSOR
8/3/2019 trab_pontes_rusch
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Planilha de clculo de carregamento
Definio do modelo estrutural - MTODO DE RUSCH
TABELA
Dados
Encontrando o valor de lmbda ()
ly
lx
lx 8.00 m
ly 10.00 m
1.25h (laje) 0.35 m
b 0.30 me (revest) 0.05 m
bw 1.00 m
g (peso prprio) 10.00 kN/m
a (dist. eixo veic) 2.00 m
g concreto 25.00 kN/mg revestimento 25.00 kN/m
fck 40.00 mPa
fyk 50.00 kN/cm
RO 0.23 (taxa mecnica de armadura longitudinal)
Clculo do carregamento
LAJE
kN/m
kN/m
kN/m
kN/m
Carga Total da Laje 10.00
Carga Adotada (p) 10.00
Cargas Permanentes
- Peso prprio da laje 8.75
- Peso do revestimento 1.25
8.00
10.
00
84.2
l = = 1.25
y
x
mesmosentido de
trfego
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Verificao
Carregamento esttico para laje com 1 engaste (Tabela Nr. 84.2)
Kxm 0.045
Kym 0.039
Kem 0.098
Mg0xm 28.80 kN.m/m
Mg0ym 24.96 kN.m/m
Mg0em 62.72 kN.m/m
Carga mvel
TP-12
Q 40.00 kN
q 4.00 kN/m
t 47.45 cm t=0,2.b+e.2+h
l 1.25j 1.34 j = 1,4-0,007.lx
lx/a 4.00
t/a 0.24
Momentos de clculo
Para laje com 1 apoio (Tabela Nr. 84.2)
Mq=j .(Q.ML+q1.Mp+q2.Mp')
M 0.610P 0.200P' 0.860
M 0.498
P 0.070P' 1.050
M 1.140P 0.450P' 2.500
Momento de projeto
y
Mqy = 32.70
Mg=K.g.lx
x
Mqx = 38.38
kN.m/m
e
Mqy = 76.92 kN.m/m
kN.m/m
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Md=1,4.Mg+1,4.j .Mq
Mg (kgf.m/m) Mq (kgf.m/m)x 2,880.00 3838.00 11,232.09 kgf.m/my 2,496.00 3270.00 9,628.92 kgf.m/me 6,272.00 7692.00 23,210.99 kgf.m/m
Clculo As
Quadro de Ao
LAJE Md KMD KX KZ As (calc) As Mnx 11232.09 0.0555 0.085 0.966 11.89 8.05y 9628.92 0.0476 0.072 0.971 10.14 8.05e 23210.99 0.1146 0.182 0.927 25.60 8.05
Kmd= Msd/bw.d.fcd
Kx= 1,25-1,917(0,425-kmd)
Kz=1-0,40kx
As=Msd/Kz.d.fydAsmin=( r /100).bw.h
Momento de Fissurao
CASO l 2B 1.25 4.26
Verificao das fissuras
Comparao do Maior Momento Positivo com o Momento de fissurao
mx,y,e = 23210.99 kN.cm/m
= 4.26fct = 0.35 kN/cm
Ic = 357292 cm4
yt = 17.5 cm
Clculo do Momento de Fissurao (mr)
mr = 30441.28 kN.cm/m
Comparao
como mr > mx,y,e no h fissuras.
Flechas
Flecha Imediata
= 4.26b = 350.00 cm
Mq
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p = 1.0000E-04 kN/cm
lx = 800.00 cm
Ec = 3010.49 kN/cm
I= Ic = 357292.00 cm4
Clculo de ai
ai = 0.05 cm
Flecha Diferida
f = 2.00 acima de 70 meses
Clculo de af
af = 0.10 cm
Flecha Total
at = 0.15 cm
Flecha Limite
alim = 3.20 cm
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As Adotado Bitola Espa. As Real11.89
10.14
25.60
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8/3/2019 trab_pontes_rusch
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Planilha de clculo de carregamento
Definio do modelo estrutural - MTODO DE RUSCH
TABELA
Dados
Encontrando o valor de lmbda ()
ly
lx
lx 8.00 m
ly 10.00 m
1.25h (laje) 0.35 m
b 0.40 m
e (revest) 0.05 m
bw 1.00 mg (peso prprio) 10.00 kN/m
a (dist. eixo veic) 2.00 m
g concreto 25.00 kN/mg revestimento 25.00 kN/m
fck 40.00 mPa
fyk 50.00 kN/cm
RO 0.23 (taxa mecnica de armadura longitudinal)
Clculo do carregamento
LAJE
kN/m
kN/m
kN/m
kN/m
Verificao
Carregamento esttico para laje com 1 engaste (Tabela Nr. 84.2)
Kxm 0.045
Kym 0.039
Kem 0.098
Mg0xm 28.80 kN.m/m
Mg0ym 24.96 kN.m/m
Mg0em 62.72 kN.m/m
=
Cargas Permanentes- Peso prprio da laje 8.75
l =
8.00
10.
00
84.2
1.25
Mg=K.g.lx
- Peso do revestimento 1.25
10.00
Carga Adotada (p) 10.00Carga Total da Laje
y
x
mesmosentido de
trfego
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Planilha de clculo de carregamento
Para laje com 1 apoio (Tabela Nr. 84.2)
Mq=j .(Q.ML+q1.Mp+q2.Mp')
M 0.610
P 0.200
P' 0.860
M 0.498
P 0.070
P' 1.050
M 1.140
P 0.450
P' 2.500
Momento de projeto
Md=1,4.Mg+1,4.j .Mq
Mg (kgf.m/m) Mq (kgf.m/m)
x 2,880.00 4797.00 13,031.17 kgf.m/my 2,496.00 4087.00 11,161.61 kgf.m/m
e 6,272.00 9615.00 26,818.54 kgf.m/m
Clculo As
Quadro de Ao
LAJE Md KMD KX KZ As (calc) As Mn As Ad
x 13031.17 0.0644 0.099 0.960 13.88 8.05 13
y 11161.61 0.0551 0.084 0.966 11.81 8.05 11
e 26818.54 0.1324 0.213 0.915 29.96 8.05 29
Kmd= Msd/bw.d.fcd
Kx= 1,25-1,917(0,425-kmd)
Kz=1-0,40kx
As=Msd/Kz.d.fyd
Asmin=( r /100).bw.h
Momento de Fissurao
CASO l 2B 1.25 4.26
Verificao das fissuras
Comparao do Maior Momento Positivo com o Momento de fissurao
m x y e = 26818 54 kN cm/m
e
Mqy = 96.15 kN.m/m
Mq
y
Mqy = 40.87 kN.m/m
x
Mqx = 47.97 kN.m/m
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Planilha de clculo de carregamento
= 4.26b = 350.00 cmp = 1.0000E-04 kN/cm
lx = 800.00 cm
Ec = 3010.49 kN/cm
I= Ic = 357292.00 cm4
Clculo de ai
ai = 0.05 cm
Flecha Diferida
f = 2.00 acima de 70 meses
Clculo de af
af = 0.10 cm
Flecha Total
at = 0.15 cm
Flecha Limite
alim = 3.20 cm
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Planilha de clculo de carregamento
Definio do modelo estrutural - MTODO DE RUSCH
TABELA
Dados
Encontrando o valor de lmbda ()
ly
lx
lx 8.00 m
ly 10.00 m
1.25h (laje) 0.35 m
b 0.50 m
e (revest) 0.05 m
bw 1.00 m
g (peso prprio) 10.00 kN/m
a (dist. eixo veic) 2.00 m
g concreto 25.00 kN/mg revestimento 25.00 kN/m
fck 40.00 mPa
fyk 50.00 kN/cmRO 0.23 (taxa mecnica de armadura longitudinal)
Clculo do carregamento
LAJE
kN/m
Cargas Permanentes- Peso prprio da laje 8.75
8.00
10.
00
84.2
l = = 1.25
y
x
mesmosentido de
trfego
8/3/2019 trab_pontes_rusch
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kN/m
kN/m
kN/m
Verificao
Carregamento esttico para laje com 1 engaste (Tabela Nr. 84.2)
Kxm 0.045
Kym 0.039
Kem 0.098
Mg0xm 28.80 kN.m/m
Mg0ym 24.96 kN.m/m
Mg0em 62.72 kN.m/m
Carga mvel
TP-45
Q 50.00 kN
q 5.00 kN/m
t 48.16 cm t=0,2.b+e.2+h
l 1.25j 1.34 j = 1,4-0,007.lx
lx/a 4.00 m
t/a 0.24 m
Momentos de clculo
Para laje com 1 apoio (Tabela Nr. 84.2)
Mq=j .(Q.ML+q1.Mp+q2.Mp')
M 0.610P 0.200P' 0.860
M 0.498P 0.070P' 1.050
y
Mqy = 40.87 kN.m/m
kN.m/m
Carga Total da Laje 10.00
Carga Adotada (p) 10.00
Mg=K.g.lx
x
Mqx = 47.97
- Peso do revestimento 1.25
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M 1.140P 0.450P' 2.500
Momento de projeto
Md=1,4.Mg+1,4. j .Mq
Mg (kgf.m/m) Mq (kgf.m/m)
x 2,880.00 4797.00 13,031.17 kgf.m/m
y 2,496.00 4087.00 11,161.61 kgf.m/m
e 6,272.00 9615.00 26,818.54 kgf.m/m
Clculo As
Quadro de Ao
LAJE Md KMD KX KZ As (calc) As Mnx 13031.17 0.0644 0.099 0.960 13.88 8.05
y 11161.61 0.0551 0.084 0.966 11.81 8.05
e 26818.54 0.1324 0.213 0.915 29.96 8.05
Kmd= Msd/bw.d.fcd
Kx= 1,25-1,917(0,425-kmd)
Kz=1-0,40kx
As=Msd/Kz.d.fyd
Asmin=( r /100).bw.h
Momento de Fissurao
CASO l 2B 1.25 4.26
Verificao das fissuras
Comparao do Maior Momento Positivo com o Momento de fissurao
mx,y,e = 26818.54 kN.cm/m
= 4.26fct = 0.35 kN/cm
Ic = 357292 cm4
yt = 17.5 cm
Clculo do Momento de Fissurao (mr)
mr = 30441.28 kN.cm/m
Comparao
Mq
e
Mqy = 96.15 kN.m/m
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como mr > mx,y,e no h fissuras.
Flechas
Flecha Imediata
= 4.26b = 350.00 cmp = 1.0000E-04 kN/cm
lx = 800.00 cm
Ec = 3010.49 kN/cm
I= Ic = 357292.00 cm4
Clculo de ai
ai = 0.05 cm
Flecha Diferida
f = 2.00 acima de 70 meses
Clculo de af
af = 0.10 cm
Flecha Total
at = 0.15 cm
Flecha Limite
alim = 3.20 cm
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As Adotado Bitola Espa. As Real13.88
11.81
29.96
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Planilha de clculo de carregamento
Definio do modelo estrutural - MTODO DE RUSCH
TABELA
Dados
Encontrando o valor de lmbda ()
ly
lx
lx
8.00 mly 13.00 m
1.63h (laje) 0.35 m
b 0.30 m
e (revest) 0.05 m
bw 1.00 m
g (peso prprio) 10.00 kN/m
a (dist. eixo veic) 2.00 m
g concreto 25.00 kN/mg revestimento 25.00 kN/m
fck 40.00 mPafyk 50.00 kN/cm
RO 0.23 (taxa mecnica de armadura longitudinal)
Clculo do carregamento
LAJECargas Permanentes
8.00
13.
00
58.2
l = = 1.63
y
x
mesmosentido de
trfego
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kN/m
kN/m
kN/m
kN/m
Verificao
Carregamento esttico para laje com 1 engaste (Tabela Nr. 58.2)
Kxm 0.125
Kym 0.021
Kem 0.125
kyr 0.034
Mg0xm 80.00 kN.m/m
Mg0ym 13.44 kN.m/m
Mg0ye 80.00 kN.m/mMg yr 21.76 kN.m/m
Carga mvel
TP-12
Q 40.00 kN
q 4.00 kN/m
t 47.45 cm t=0,2.b+e.2+h
l 1.63j 1.34 j = 1,4-0,007.lx
lx/a 4.00 m
t/a 0.24 m
Momentos de clculo
Para laje com 1 apoio engastado (Tabela Nr. 58.2)
Mq=j .(Q.ML+q1.Mp+q2.Mp')
M 0.850P 2.200P' 2.850
kN.m/m
Carga Total da Laje 10.00
Carga Adotada (p) 10.00
Mg=K.g.lx
x
Mqx = 72.63
- Peso prprio da laje 8.75
- Peso do revestimento 1.25
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M 0.530P 0.370P' 1.030
M 1.200
P 1.400P' 3.400
M 0.498P 0.070P' 1.050
Momento de projeto
Md=1,4.Mg+1,4. j .Mq
Mg (kgf.m/m) Mq (kgf.m/m)x 8,000.00 7263.00 24,825.39 kgf.m/m
y 1,344.00 3591.00 8,618.32 kgf.m/m
e 8,000.00 9005.00 28,093.38 kgf.m/m
r 2,176.00 3270.00 9,180.92 kgf.m/m
Clculo As
Quadro de Ao
LAJE Md KMD KX KZ As (calc) As Mn
x 24825.39 0.1226 0.196 0.922 27.52 8.05
y 8618.32 0.0426 0.065 0.974 9.05 8.05
e 28093.38 0.1387 0.224 0.910 31.56 8.05
r 9180.92 0.0453 0.069 0.972 9.66 8.05
Kmd= Msd/bw.d.fcd
Kx= 1,25-1,917(0,425-kmd)
Kz=1-0,40kx
As=Msd/Kz.d.fyd
Asmin=( r /100).bw.h
Momento de Fissurao
CASO l 4B 1.65 2.92
Verificao das fissuras
Comparao do Maior Momento Positivo com o Momento de fissurao
r
Mqy = 32.70 kN.m/m
Mq
y
Mqy = 35.91 kN.m/m
e
Mqy = 90.05 kN.m/m
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mx,y,e = 28093.38 kN.cm/m
= 2.92fct = 0.35 kN/cm
Ic = 357292 cm4
yt = 17.5 cm
Clculo do Momento de Fissurao (mr)
mr = 20865.85 kN.cm/m
Comparao
como mr > mx,y,e no h fissuras.
Flechas
Flecha Imediata
= 2.92b = 350.00 cmp = 1.0000E-04 kN/cm
lx = 800.00 cm
Ec = 3010.49 kN/cm
I= Ic = 357292.00 cm4
Clculo de ai
ai = 0.03 cm
Flecha Diferida
f = 2.00 acima de 70 meses
Clculo de af
af = 0.06 cm
Flecha Total
at = 0.09 cm
Flecha Limite
alim = 0.40 cm
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As Adotado Bitola Espa. As Real27.52
9.05
31.56
9.66
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Planilha de clculo de carregamento
Definio do modelo estrutural - MTODO DE RUSCH
TABELA
Dados
Encontrando o valor de lmbda ()
ly
lx
lx
8.00 mly 13.00 m
1.63h (laje) 0.35 m
b 0.40 m
e (revest) 0.05 m
bw 1.00 m
g (peso prprio) 10.00 kN/m
a (dist. eixo veic) 2.00 m
g concreto 25.00 kN/mg revestimento 25.00 kN/m
fck 40.00 mPafyk 50.00 kN/cm
RO 0.23 (taxa mecnica de armadura longitudinal)
Clculo do carregamento
LAJECargas Permanentes
8.00
13.
00
58.2
l = = 1.63
y
x
mesmosentido de
trfego
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kN/m
kN/m
kN/m
kN/m
Verificao
Carregamento esttico para laje com 1 engaste (Tabela Nr. 58.2)
Kxm 0.125
Kym 0.021
Kye 0.125
Kyr 0.034
Mg0xm 80.00 kN.m/m
Mg0ym 13.44 kN.m/m
Mg0ye 80.00 kN.m/mMg yr 21.76 kN.m/m
Carga mvel
TP-30
Q 50.00 kN
q 5.00 kN/m
t 47.83 cm t=0,2.b+e.2+h
l 1.63j 1.34 j = 1,4-0,007.lx
lx/a 4.00 m
t/a 0.24 m
Momentos de clculo
Para laje com 1 apoio engastado (Tabela Nr. 58.2)
Mq=j .(Q.ML+q1.Mp+q2.Mp')
M 0.850P 2.200P' 2.850
y
kN.m/m
Carga Total da Laje 10.00
Carga Adotada (p) 10.00
Mg=K.g.lx
x
Mqx = 90.79
- Peso prprio da laje 8.75
- Peso do revestimento 1.25
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M 0.530P 0.370P' 1.030
M 1.200P 1.400
P' 3.400
M 0.498P 0.070P' 1.050
Momento de projeto
Md=1,4.Mg+1,4. j .Mq
Mg (kgf.m/m) Mq (kgf.m/m)
x 8,000.00 9079.00 28,232.20 kgf.m/my 1,344.00 4489.00 10,302.96 kgf.m/m
e 8,000.00 11256.00 32,316.26 kgf.m/m
r 2,176.00 4087.00 10,713.61 kgf.m/m
Clculo As
Quadro de Ao
LAJE Md KMD KX KZ As (calc) As Mn
x 28232.20 0.1394 0.226 0.910 31.71 8.05
y 10302.96 0.0509 0.077 0.969 10.87 8.05e 32316.26 0.1596 0.262 0.895 36.91 8.05
r 10713.61 0.0529 0.081 0.968 11.31 8.05
Kmd= Msd/bw.d.fcd
Kx= 1,25-1,917(0,425-kmd)
Kz=1-0,40kx
As=Msd/Kz.d.fyd
Asmin=( r /100).bw.h
Momento de Fissurao
CASO l 4B 1.65 2.92
Verificao das fissuras
Comparao do Maior Momento Positivo com o Momento de fissurao
Mq
r
Mqy = 40.87 kN.m/m
Mqy = 44.89 kN.m/m
e
Mqy = 112.56 kN.m/m
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mx,y,e = 32316.26 kN.cm/m
= 2.92fct = 0.35 kN/cm
Ic = 357292 cm4
yt = 17.5 cm
Clculo do Momento de Fissurao (mr)
mr = 20865.85 kN.cm/m
Comparao
como mr > mx,y,e no h fissuras.
Flechas
Flecha Imediata
= 2.92b = 350.00 cmp = 1.0000E-04 kN/cm
lx = 800.00 cm
Ec = 3010.49 kN/cm
I= Ic = 357292.00 cm4
Clculo de ai
ai = 0.03 cm
Flecha Diferida
f = 2.00 acima de 70 meses
Clculo de af
af = 0.06 cm
Flecha Total
at = 0.09 cm
Flecha Limite
alim = 0.40 cm
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As Adotado Bitola Espa. As Real31.71
10.8736.91
11.31
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Planilha de clculo de carregamento
Definio do modelo estrutural - MTODO DE RUSCH
TABELA
Dados
Encontrando o valor de lmbda ()
ly
lx
lx
8.00 mly 13.00 m
1.63h (laje) 0.35 m
b 0.50 m
e (revest) 0.05 m
bw 1.00 m
g (peso prprio) 10.00 kN/m
a (dist. eixo veic) 2.00 m
g concreto 25.00 kN/mg revestimento 25.00 kN/m
fck 40.00 mPafyk 50.00 kN/cm
RO 0.23 (taxa mecnica de armadura longitudinal)
Clculo do carregamento
LAJECargas Permanentes
8.00
13.
00
58.2
l = = 1.63
y
x
mesmosentido de
trfego
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kN/m
kN/m
kN/m
kN/m
Verificao
Carregamento esttico para laje com 1 engaste (Tabela Nr. 58.2)
Kxm 0.125
Kym 0.021
Kye 0.125
Kyr 0.034
Mg0xm 80.00 kN.m/m
Mg0ym 13.44 kN.m/m
Mg0ye 80.00 kN.m/mMg0yr 21.76 kN.m/m
Carga mvel
TP-45
Q 50.00 kN
q 5.00 kN/m
t 48.16 cm t=0,2.b+e.2+h
l 1.63j 1.34 j = 1,4-0,007.lx
lx/a 4.00 m
t/a 0.24 m
Momentos de clculo
Para laje com 1 apoio engastado (Tabela Nr. 58.2)
Mq=j .(Q.ML+q1.Mp+q2.Mp')
M 0.850P 2.200P' 2.850
y
kN.m/m
Carga Total da Laje 10.00
Carga Adotada (p) 10.00
Mg=K.g.lx
x
Mqx = 90.79
- Peso prprio da laje 8.75
- Peso do revestimento 1.25
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M 0.530P 0.370P' 1.030
M 1.200P 1.400
P' 3.400
M 0.498P 0.070P' 1.050
Momento de projeto
Md=1,4.Mg+1,4. j .Mq
Mg (kgf.m/m) Mq (kgf.m/m)
x 8,000.00 9079.00 28,232.20 kgf.m/my 1,344.00 4489.00 10,302.96 kgf.m/m
e 8,000.00 11256.00 32,316.26 kgf.m/m
r 2,176.00 4087.00 10,713.61 kgf.m/m
Clculo As
Quadro de Ao
LAJE Md KMD KX KZ As (calc) As Mn
x 28232.20 0.1394 0.226 0.910 31.71 8.05
y 10302.96 0.0509 0.077 0.969 10.87 8.05e 32316.26 0.1596 0.262 0.895 36.91 8.05
r 10713.61 0.0529 0.081 0.968 11.31 8.05
Kmd= Msd/bw.d.fcd
Kx= 1,25-1,917(0,425-kmd)
Kz=1-0,40kx
As=Msd/Kz.d.fyd
Asmin=( r /100).bw.h
Momento de Fissurao
CASO l 4B 1.65 2.92
Verificao das fissuras
Comparao do Maior Momento Positivo com o Momento de fissurao
r
Mqy = 40.87 kN.m/m
Mq
Mqy = 44.89 kN.m/m
e
Mqy = 112.56 kN.m/m
8/3/2019 trab_pontes_rusch
40/50
mx,y,e = 32316.26 kN.cm/m
= 2.92fct = 0.35 kN/cm
Ic = 357292 cm4
yt = 17.5 cm
Clculo do Momento de Fissurao (mr)
mr = 20865.85 kN.cm/m
Comparao
como mr > mx,y,e no h fissuras.
Flechas
Flecha Imediata
= 2.92b = 350.00 cmp = 1.0000E-04 kN/cm
lx = 800.00 cm
Ec = 3010.49 kN/cm
I= Ic = 357292.00 cm4
Clculo de ai
ai = 0.03 cm
Flecha Diferida
f = 2.00 acima de 70 meses
Clculo de af
af = 0.06 cm
Flecha Total
at = 0.09 cm
Flecha Limite
alim = 0.40 cm
8/3/2019 trab_pontes_rusch
41/50
8/3/2019 trab_pontes_rusch
42/50
8/3/2019 trab_pontes_rusch
43/50
As Adotado Bitola Espa. As Real31.71
10.8736.91
11.31
8/3/2019 trab_pontes_rusch
44/50
8/3/2019 trab_pontes_rusch
45/50
1 2A 2B 3 4A 4B
1.00 4.76 1.00 3.26 1.00 3.26 1.00 2.46 1.00 2.25 1.00 2.251.05 5.26 1.05 3.68 1.05 3.48 1.05 2.72 1.05 2.60 1.05 2.351.10 5.74 1.10 4.11 1.10 3.70 1.10 2.96 1.10 2.97 1.10 2.451.15 6.20 1.15 4.55 1.15 3.89 1.15 3.18 1.15 3.35 1.15 2.531.20 6.64 1.20 5.00 1.20 4.09 1.20 3.40 1.20 3.74 1.20 2.611.25 7.08 1.25 5.44 1.25 4.26 1.25 3.61 1.25 4.14 1.25 2.681.30 7.49 1.30 5.88 1.30 4.43 1.30 3.80 1.30 4.56 1.30 2.741.35 7.90 1.35 6.32 1.35 4.58 1.35 3.99 1.35 5.01 1.35 2.771.40 8.29 1.40 6.74 1.40 4.72 1.40 4.15 1.40 5.41 1.40 2.801.45 8.67 1.45 7.15 1.45 4.87 1.45 4.31 1.45 5.83 1.45 2.851.50 9.03 1.50 7.55 1.50 5.01 1.50 4.46 1.50 6.25 1.50 2.891.55 9.39 1.55 7.95 1.55 5.09 1.55 4.61 1.55 6.66 1.55 2.911.60 9.71 1.60 8.32 1.60 5.18 1.60 4.73 1.60 7.06 1.60 2.921.65 10.04 1.65 8.68 1.65 5.22 1.65 4.86 1.65 7.46 1.65 2.921.70 10.34 1.70 9.03 1.70 5.26 1.70 4.97 1.70 7.84 1.70 2.931.75 10.62 1.75 9.36 1.75 5.36 1.75 5.06 1.75 8.21 1.75 2.931.80 10.91 1.80 9.69 1.80 5.46 1.80 5.16 1.80 8.58 1.80 2.941.85 11.16 1.85 10.00 1.85 5.53 1.85 5.25 1.85 8.93 1.85 2.941.90 11.41 1.90 10.29 1.90 5.60 1.90 5.33 1.90 9.25 1.90 2.951.95 11.65 1.95 10.58 1.95 5.68 1.95 5.41 1.95 9.58 1.95 2.952.00 11.89 2.00 10.87 2.00 5.76 2.00 5.49 2.00 9.90 2.00 2.96
15.63 15.63 6.50 6.50 15.63 3.13
Tabela de coeficientes para clculo de flechas elsticas em lajes retangulares comcarregamento uniformemente distribuido
CASO
l
8/3/2019 trab_pontes_rusch
46/50
l mx+ mx- my+ my-1.00 27.20 27.20
1.05 24.50 27.501.10 22.40 27.90
1.15 20.70 28.40
1.20 19.10 29.10
1.25 17.80 29.90
1.30 16.80 30.90
1.35 15.80 31.80
1.40 15.00 32.80
1.45 14.30 33.80
1.50 13.70 34.70
1.55 13.20 35.40
1.60 12.70 36.10
1.65 12.30 36.70
1.70 11.90 37.30
1.75 11.50 37.90
1.80 11.30 38.50
1.85 11.00 38.901.90 10.80 39.40
1.95 10.60 39.80
2.00 10.40 40.30
3
1.00 31.40 11.90 41.20
1.05 29.20 11.30 43.20
1.10 27.30 10.90 45.10
1.15 25.80 10.50 47.10
1.20 24.50 10.20 48.80
1.25 23.40 9.90 50.30
1.30 22.40 9.70 51.80
1.35 21.60 9.40 53.20
1.40 21.00 9.30 54.30
1.45 20.30 9.10 55.001.50 19.80 9.00 55.60
1.55 19.40 8.90 56.20
1.60 19.00 8.80 56.80
1.65 18.60 8.00 57.30
1.70 18.30 8.60 57.80
1.75 18.00 8.50 58.20
1.80 17.80 8.40 58.60
1.85 17.50 8.30 58.80
1.90 17.40 8.30 59.00
1.95 17.20 8.30 59.10
2.00 17.10 8.30 59.20
3
Tabela de Czerny para clculo dos momentos em lajes retangulares comgargas uniformemente distribudas.
CASO1
CASO2A
8/3/2019 trab_pontes_rusch
47/50
l mx+ mx- my+ my-
Tabela de Czerny para clculo dos momentos em lajes retangulares comgargas uniformemente distribudas.
1.00 41.20 29.40 11.901.05 36.50 29.00 11.30
1.10 31.90 28.80 10.90
1.15 28.30 28.80 10.40
1.20 25.90 28.90 10.10
1.25 23.40 29.20 9.80
1.30 21.70 29.70 9.60
1.35 20.10 30.20 9.30
1.40 18.80 30.80 9.20
1.45 17.50 31.60 9.00
1.50 16.60 32.30 8.90
1.55 15.70 33.00 8.80
1.60 15.00 33.60 8.70
1.65 14.30 34.30 8.60
1.70 13.80 34.90 8.50
1.75 13.20 35.60 8.50
1.80 12.80 36.20 8.401.85 12.30 36.90 8.40
1.90 12.00 37.50 8.30
1.95 11.60 38.20 8.30
2.00 11.40 38.80 8.20
3
1.00 42.70 14.30 40.20 14.30
1.05 38.00 13.30 41.00 13.80
1.10 35.10 12.70 42.00 13.60
1.15 32.20 12.00 42.90 13.30
1.20 30.00 11.50 44.00 13.10
1.25 28.00 11.10 45.60 12.90
1.30 26.50 10.70 47.60 12.80
1.35 25.20 10.30 49.60 12.70
1.40 24.10 10.00 51.00 12.60
1.45 23.10 9.80 52.10 12.50
1.50 22.20 9.60 53.00 12.40
1.55 21.60 9.40 54.10 12.30
1.60 21.00 9.20 54.80 12.30
1.65 24.00 9.10 55.60 12.20
1.70 19.90 8.90 56.30 12.20
1.75 19.50 8.80 57.00 12.20
1.80 19.10 8.70 57.70 12.20
1.85 18.70 8.60 58.30 12.20
1.90 18.40 8.50 59.00 12.20
1.95 18.10 8.40 59.60 12.20
2.00 17.90 8.40 60.20 12.20
3
CASO3
CASO2
B
8/3/2019 trab_pontes_rusch
48/50
l mx+ mx- my+ my-
Tabela de Czerny para clculo dos momentos em lajes retangulares comgargas uniformemente distribudas.
1.00 35.10 14.30 61.701.05 33.00 13.80 64.50
1.10 31.70 13.50 67.20
1.15 30.40 13.20 69.60
1.20 29.40 13.00 71.50
1.25 28.50 12.70 72.80
1.30 27.80 12.60 73.50
1.35 27.10 12.40 74.10
1.40 26.60 12.30 74.60
1.45 26.10 12.20 75.30
1.50 25.80 12.20 75.80
1.55 25.40 12.10 76.50
1.60 25.20 12.00 77.00
1.65 24.90 12.00 77.00
1.70 24.70 12.00 77.00
1.75 24.50 12.00 77.00
1.80 24.40 12.00 77.001.85 24.30 12.00 77.00
1.90 24.30 12.00 77.00
1.95 24.20 12.00 77.00
2.00 24.10 12.00 77.00
3
1.00 63.30 35.10 14.30
1.05 52.20 33.70 13.40
1.10 46.10 32.90 12.70
1.15 39.80 32.20 12.00
1.20 35.50 31.70 11.50
1.25 31.50 31.30 11.10
1.30 28.50 31.20 10.70
1.35 25.80 31.20 10.30
1.40 23.70 31.40 10.00
1.45 22.00 31.70 9.75
1.50 20.40 32.10 9.50
1.55 19.00 32.70 9.30
1.60 17.90 33.30 9.20
1.65 16.90 34.00 9.10
1.70 16.00 34.90 8.90
1.75 15.20 35.90 8.80
1.80 14.60 37.10 8.70
1.85 13.90 38.30 8.60
1.90 13.40 39.70 8.50
1.95 12.90 41.10 8.40
2.00 12.50 42.40 8.40
3
CASO4
A
CASO4B
8/3/2019 trab_pontes_rusch
49/50
l mx+ mx- my+ my-
Tabela de Czerny para clculo dos momentos em lajes retangulares comgargas uniformemente distribudas.
1.00 44.10 16.20 55.90 18.301.05 40.50 15.30 57.50 17.901.10 37.90 14.80 60.30 17.70
1.15 35.50 14.20 64.20 17.601.20 33.80 13.90 66.20 17.501.25 32.30 13.50 67.70 17.501.30 31.00 13.20 69.00 17.501.35 29.90 12.90 70.50 17.50
1.40 29.00 12.70 72.00 17.501.45 28.20 12.60 73.40 17.501.50 27.60 12.50 75.20 17.501.55 27.00 12.40 76.90 17.50
1.60 26.50 12.30 78.70 17.501.65 26.10 12.20 80.50 17.501.70 25.70 12.20 82.50 17.501.75 25.30 12.10 84.60 17.50
1.80 25.10 12.10 86.80 17.501.85 24.90 12.00 89.20 17.501.90 24.70 12.00 91.70 17.501.95 24.60 12.00 94.30 17.502.00 24.50 12.00 97.00 17.50
3
1.00 59.50 18.30 44.10 16.201.05 51.60 16.60 43.60 15.401.10 46.10 15.40 43.70 14.80
1.15 41.40 14.40 44.20 14.301.20 37.50 13.50 44.80 13.901.25 34.20 12.70 40.50 13.501.30 31.80 12.20 46.90 13.30
1.35 29.60 11.60 48.60 13.101.40 28.00 11.20 50.30 13.001.45 26.40 10.90 52.30 12.801.50 25.20 10.60 55.00 12.701.55 24.20 10.30 58.20 12.60
1.60 23.30 10.10 61.60 12.601.65 22.50 9.90 65.60 12.501.70 21.70 9.70 70.40 12.501.75 21.10 9.50 75.00 12.401.80 20.50 9.40 79.60 12.40
1.85 20.00 9.20 84.70 12.301.90 19.50 9.00 89.80 12.301.95 19.10 8.90 95.40 12.302.00 18.70 8.80 101.00 12.30
3
CASO5
A
CASO5
B
8/3/2019 trab_pontes_rusch
50/50
l mx+ mx- my+ my-
Tabela de Czerny para clculo dos momentos em lajes retangulares comgargas uniformemente distribudas.
1.00 56.80 19.40 56.80 19.401.05 50.60 18.20 58.20 18.80
1.10 46.10 17.10 60.30 18.40
1.15 42.40 16.30 62.60 18.10
1.20 39.40 15.50 65.80 17.90
1.25 37.00 14.90 69.40 17.70
1.30 34.80 14.50 73.60 17.60
1.35 33.30 14.00 78.40 17.50
1.40 31.90 13.70 83.40 17.50
1.45 30.60 13.40 89.40 17.50
1.50 29.60 13.20 93.50 17.50
1.55 28.80 13.00 96.10 17.50
1.60 28.10 12.80 98.10 17.50
1.65 27.50 12.70 99.90 17.50
1.70 26.90 12.50 101.30 17.50
1.75 26.40 12.40 102.40 17.50
1.80 26.00 12.30 103.30 17.501.85 25.70 12.20 104.00 17.50
1.90 25.40 12.10 104.60 17.50
1.95 25.20 12.00 104.90 17.50
2.00 25.00 12.00 105.00 17.50
3
CASO6