Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

140 CHAPTER 5 Energy Methods

Fig.5.19

Deflection of a bent rod.

First,considerthedisplacementinthedirectionparalleltothexaxis.FromEqs.(5.21),

(^) x=

∫

L

M 0 M 1

EI

ds+

∫

L

T 0 T 1

GJ

ds

Usingatabularprocedure,

M 0 M 1 T 0 T 1

︷ ︸︸ ︷ ︷ ︸︸ ︷︷ ︸︸ ︷ ︷ ︸︸ ︷

Plane xy xz yz xy xz yz xy xz yz xy xz yz

CD 0 0 0 y 0000 0 00 0

CB 0 0 −wz^2 /2 0 z 000 0 l 00

BA −wlx 00 ll 000 wl^2 /200 0

Hence,

(^) x=
∫l
0

−

wl^2 x

EI

dx

or

(^) x=−
wl^4
2 EI