fatores2a 10

1
8 2 1 qL M + = 8 2 2 qL M = [ ] [ ] ) 3 ( 12 12 ) 3 ( 12 12 2 2 2 2 2 2 2 1 a L c b a L qc M b L c ab L qc M + = + + = [ ] 2 2 1 ) ( 4 8 c L b a L qbc M + + = [ ] 2 2 2 ) ( 4 8 c L a b L qac M + = 30 20 2 2 2 1 qL M qL M = + = 15 2 1 qL M + = 120 7 2 2 qL M = 8 8 2 1 PL M PL M = + = 16 3 1 PL M + = 16 3 2 PL M = 2 2 2 2 2 1 L b Pa M L Pab M = + = ) ( 2 2 1 b L L Pab M + + = ) ( 2 2 2 a L L Pab M + = ) 3 2 ( ) 3 2 ( 2 1 L a L Ma M L b L Mb M + = + = ) 3 1 ( 2 2 2 1 L b M M = ) 3 1 ( 2 2 2 2 L a M M = ) ( 1 2 t t t = Δ t h EI M t h EI M Δ = Δ = α α 2 1 . t h EI M Δ = α 2 3 1 t h EI M Δ + = α 2 3 2 L Ta T L Tb T + = + = 2 1 T T + = 1 T T + = 2 L Pa N L Pb N + = + = 2 1 L Pa N L Pb N + = + = 2 1 L Pa N L Pb N + = + = 2 1 12 12 2 2 2 1 qL M qL M = + = θ θ L EI M 3 + = M ρ ρ 2 3 L EI M = M θ θ θ L EI M L EI M 2 4 21 11 + = + = 11 M 21 M ρ × + = = 2 21 11 6 L EI M M 11 M 21 M ρ θ ϕ ϕ L GJ T T = = 12 22 Δ Δ = = L EA N N 12 22 θ θ θ s M 1 AS M s M 2 AS M θ θ L EI M L EI M S S 2 2 2 1 = + = θ θ L EI M L EI M AS AS 6 6 + = + =

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Page 1: Fatores2a 10

8

2

1qLM +=

8

2

2qLM −=

[ ]

[ ])3(1212

)3(1212

2222

2221

aLcbaL

qcM

bLcabL

qcM

−+−=

−++= [ ]221 )(4

8cLba

LqbcM −++= [ ]2

22 )(48

cLabL

qacM −+−=

30

202

2

2

1

qLM

qLM

−=

+=

15

2

1qLM +=

1207 2

2qLM −=

8

8

2

1

PLM

PLM

−=

+=

163

1PLM +=

163

2PLM −=

2

2

2

2

2

1

LbPaM

LPabM

−=

+=)(

2 21 bLL

PabM ++= )(2 22 aL

LPabM +−=

)32(

)32(

2

1

La

LMaM

Lb

LMbM

−+=

−+=

)31(2 2

2

1 LbMM −= )31(

2 2

2

2 LaMM −=

)( 12 ttt −=Δt

hEIM

thEIM

Δ=

Δ−=

α

α

2

1 .

th

EIM Δ−= α2

31 t

hEIM Δ+= α2

32

LTaT

LTbT

+=

+=

2

1

TT +=1 TT +=2

LPaN

LPbN

+=

+=

2

1

LPaN

LPbN

+=

+=

2

1

LPaN

LPbN

+=

+=

2

1

12

122

2

2

1

qLM

qLM

−=

+=θθ

LEIM 3

+=M

ρ ρ2

3LEIM =

M

θ

θ

θ

LEIM

LEIM

2

4

21

11

+=

+=11M 21M

ρ×+== 221116LEIMM

11M21Mρ

θ

ϕϕ

LGJTT =−= 1222

Δ

Δ=−=L

EANN 1222

θ

θ θ

sM 1

ASM

sM 2

ASM

θ

θ

LEIM

LEIM

S

S

2

2

2

1

−=

+=

θ

θ

LEIM

LEIM

AS

AS

6

6

+=

+=