trab_pontes_rusch

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


2/50

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


3/50

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


4/50

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


5/50

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


6/50


7/50


8/50

As Adotado Bitola Espa. As Real11.89

10.14

25.60


9/50


10/50



TABELA

Dados


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



fck 40.00 mPa

fyk 50.00 kN/cm



LAJE

kN/m

kN/m

kN/m

kN/m

Verificao


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


10.00

Carga Adotada (p) 10.00Carga Total da Laje

y

x

mesmosentido de

trfego


11/50




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



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


12/50


= 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


Clculo de af

af = 0.10 cm

Flecha Total

at = 0.15 cm

Flecha Limite

alim = 3.20 cm


13/50



TABELA

Dados


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




fck 40.00 mPa

fyk 50.00 kN/cmRO 0.23 (taxa mecnica de armadura longitudinal)


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


14/50

kN/m

kN/m

kN/m

Verificao


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



M 0.610P 0.200P' 0.860

M 0.498P 0.070P' 1.050

y

Mqy = 40.87 kN.m/m

kN.m/m



Mg=K.g.lx

x

Mqx = 47.97



15/50

M 1.140P 0.450P' 2.500

Momento de projeto

Md=1,4.Mg+1,4. j .Mq


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


Momento de Fissurao

CASO l 2B 1.25 4.26



mx,y,e = 26818.54 kN.cm/m

= 4.26fct = 0.35 kN/cm

Ic = 357292 cm4

yt = 17.5 cm


mr = 30441.28 kN.cm/m

Comparao

Mq

e

Mqy = 96.15 kN.m/m


16/50


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


Clculo de af

af = 0.10 cm

Flecha Total

at = 0.15 cm

Flecha Limite

alim = 3.20 cm


17/50


18/50


19/50


11.81

29.96


20/50


21/50



TABELA

Dados


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




fck 40.00 mPafyk 50.00 kN/cm



LAJECargas Permanentes

8.00

13.

00

58.2

l = = 1.63

y

x

mesmosentido de

trfego


22/50

kN/m

kN/m

kN/m

kN/m

Verificao


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)


M 0.850P 2.200P' 2.850

kN.m/m



Mg=K.g.lx

x

Mqx = 72.63




23/50

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


Momento de Fissurao

CASO l 4B 1.65 2.92



r

Mqy = 32.70 kN.m/m

Mq

y

Mqy = 35.91 kN.m/m

e

Mqy = 90.05 kN.m/m


24/50

mx,y,e = 28093.38 kN.cm/m

= 2.92fct = 0.35 kN/cm

Ic = 357292 cm4

yt = 17.5 cm


mr = 20865.85 kN.cm/m

Comparao


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


Clculo de af

af = 0.06 cm

Flecha Total

at = 0.09 cm

Flecha Limite

alim = 0.40 cm


25/50


26/50


27/50


9.05

31.56

9.66


28/50


29/50



TABELA

Dados


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








8.00

13.

00

58.2

l = = 1.63

y

x

mesmosentido de

trfego


30/50

kN/m

kN/m

kN/m

kN/m

Verificao


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



M 0.850P 2.200P' 2.850

y

kN.m/m



Mg=K.g.lx

x

Mqx = 90.79




31/50

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


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


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


Momento de Fissurao

CASO l 4B 1.65 2.92



Mq

r

Mqy = 40.87 kN.m/m

Mqy = 44.89 kN.m/m

e

Mqy = 112.56 kN.m/m


32/50

mx,y,e = 32316.26 kN.cm/m

= 2.92fct = 0.35 kN/cm

Ic = 357292 cm4

yt = 17.5 cm


mr = 20865.85 kN.cm/m

Comparao


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


Clculo de af

af = 0.06 cm

Flecha Total

at = 0.09 cm

Flecha Limite

alim = 0.40 cm


33/50


34/50


35/50


10.8736.91

11.31


36/50


37/50



TABELA

Dados


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








8.00

13.

00

58.2

l = = 1.63

y

x

mesmosentido de

trfego


38/50

kN/m

kN/m

kN/m

kN/m

Verificao


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



M 0.850P 2.200P' 2.850

y

kN.m/m



Mg=K.g.lx

x

Mqx = 90.79




39/50

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


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


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


Momento de Fissurao

CASO l 4B 1.65 2.92



r

Mqy = 40.87 kN.m/m

Mq

Mqy = 44.89 kN.m/m

e

Mqy = 112.56 kN.m/m


40/50

mx,y,e = 32316.26 kN.cm/m

= 2.92fct = 0.35 kN/cm

Ic = 357292 cm4

yt = 17.5 cm


mr = 20865.85 kN.cm/m

Comparao


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


Clculo de af

af = 0.06 cm

Flecha Total

at = 0.09 cm

Flecha Limite

alim = 0.40 cm


41/50


42/50


43/50


10.8736.91

11.31


44/50


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


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


47/50

l mx+ mx- my+ my-


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


48/50

l mx+ mx- my+ my-


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


49/50

l mx+ mx- my+ my-


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


50/50

l mx+ mx- my+ my-


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

trab_pontes_rusch

Documents

Transcript of trab_pontes_rusch