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2

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ψ α

H Hsinψ

Hcosψ

Hsinψ Hsinψ

∆Hi ∆H i δbHi

δ=P L3

12EI L P

δbHi

δbHi = ∆H isinψ =Hsinψl3

12EI sinψ =H l3sin2ψ

12EI

Hcosψ

Hcosψcosα

Hcosψsinα ∆Ho

∆Ho

δbHo

δbHo = ∆H osinαcosψ =Hcosψsinαl3

12EI sinαcosψ =Hl3cos2ψsin2α

12EI

Hcosψcosα

δaH

δaH =Hcosψcosαl

AE cosψcosα =Hlcos2ψcos2α

AE

krkθ

EA E I

11 =δH11

lcos ψcos α

=σ1tl(1 + sin ψ)

lcos ψl2

12kθsin2ψ+ cos2ψsin2α+cos2ψcos2α

kr

E1=σ1

11

ψ α

E1=cos ψ

t(1 + sin ψ)l2

12kθsin2ψ+ cos2ψsin2α+cos2ψcos2α

kr

ψ= 90◦−θ

2θ

E2

σ2

δV1δV2

δaV 1δbV 1i

δbV 1o

δV1=δaV 1+δbV 1i+δbV 1o

=V l sin2ψcos2α

AE +V l3cos2ψ

12EI +V l3sin2ψsin2α

12EI

V=σ2tl cos ψcos α

δaV 2

δbV 2o

2V

δV2=δaV 2+δbV 2o

=2V l cos2α

AE +2V l3sin2α

12EI

V A I AE EI

δV22 =δV1+δV2

=σ2tl cos ψcos αl2

12kθcos2ψ+ sin2ψsin2α+ 2 sin2α+cos2α

krsin2ψ+ 2

δbHi2δbH o2

δH21 =δbHi2+δbH o2

=−V l3sin ψcos ψ

12EI +V l3sin ψcos ψsin2α

12EI

=−V l3sin ψcos ψcos2α

12EI

kθ

EI

21 =δH21

lcos ψcos α

=−V l sin ψcos α

12kθ

ν21

ν21 =sin ψ(1 + sin ψ) cos2αl2

12kθl2

12kθcos2ψ+ sin2ψsin2α+ 2 sin2α+cos2α

krsin2ψ+ 2

ψ= 90◦−θ

2θ

E1ν21 =E2ν12 =

sin ψcos ψcos2αl2l2

12kθsin2ψ+ cos2ψsin2α+cos2ψcos2α

kr−1

12kθtl2

12kθcos2ψ+ sin2ψsin2α+ 2 sin2α+cos2α

krsin2ψ+ 2

E1E2ν12

ν21

˜

E1=cos ψ

(1 + sin ψ)λsin2ψ+ cos2ψsin2α+ cos2ψcos2α

˜

E2=1 + sin ψ

cos ψλcos2ψ+ sin2ψsin2α+ 2 sin2α+ cos2αsin2ψ+ 2

˜ν12 =sin ψcos2ψcos2αλ

(1 + sin ψ)λsin2ψ+ cos2ψsin2α+ cos2ψcos2α

˜ν21 =sin ψ(1 + sin ψ) cos2αλ

λcos2ψ+ sin2ψsin2α+ 2 sin2α+ cos2αsin2ψ+ 2

λ(= l2

12

kr

kθ

0.4 2.8

λ4

3l

d2

krkθ

l d

λ˜

E1=E1t

kr

˜

E2=E2t

kr

˜ν12 =ν12

˜ν21 =ν21

α= 0

E1=cos ψ

t(1 + sin ψ)l2

12kθ

sin2ψ+cos2ψ

kr

λ˜

E1˜

E2

θ α

λ=l2kr

12kθ

˜

E1=E1t

kr

˜

E2=E2t

kr

l t

λ ν12 ν21

˜ν12 =ν12 ˜ν21 =ν21 θ

α λ =l2kr

12kθ

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