Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

5.3Application to Deflection Problems 121

Fig.5.7

Deflection of a simply supported beam by the method of complementary energy.

and

∂C

∂PC,f

=

∫

L

dθ

∂M

∂PC,f

− (^) C=0(iii)
Assumingalinearlyelasticbeam,Eqs.(ii)and(iii)become
(^) B=

1

EI

∫L

0

M

∂M

∂PB,f

dz (iv)

(^) C=

1

EI

∫L

0

M

∂M

∂PC,f

dz (v)

FromAtoB,

M=

(

3

4

PB,f+

1

2

PC,f+

wL

2

)

z−

wz^2

2

sothat

∂M

∂PB,f

=

3

4

z,

∂M

∂PC,f

=

1

2

z

FromBtoC,

M=

(

3

4

PB,f+

1

2

PC,f+

wL

2

)

z−

wz^2

2

−PB,f

(

z−

L

4

)

giving

∂M

∂PB,f

=

1

4

(L−z),

∂M

∂PC,f

=

1

2

z