Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

520 CHAPTER 17 Torsion of Beams

Fig.17.14

Determination of points of zero warping.

and

A 3 =312.5−

1

2

×8.04× 50 =111.5mm^2

Finally,

A 34 =111.5+

1

2

× 25 s 3 (iii)

SubstitutingforA 12 ,A 23 ,andA 34 fromEqs.(i)to(iii)inEq.(17.21),wehave

2 A′R=

1

200

⎡

⎣

∫^25

0

25 ×1.15s 1 ds 1 +

∫^50

0

2 (312.5−4.02s 2 )2.5ds 2 +

∫^25

0

2 (111.5+12.5s 3 )1.5ds 3

⎤

⎦ (iv)

EvaluationofEq.(iv)gives

2 A′R=424mm^2

Wenowexamineeachwallofthesectioninturntodeterminepointsofzerowarping.Supposethatin
thewall12apointofzerowarpingoccursatavalueofs 1 equaltos1,0.Then

2 ×

1

2

× 25 s1,0= 424