Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

17.2 Torsion of Open Section Beams 519

Fig.17.13

Warping distribution in channel section of Example 17.3.

restrainedwarpingofanopensectionbeam.Thus,wecanseethat

2 A′R=

∫

sect∫^2 AR,Otds

secttds

(17.21)

in whichAR,Ois the area swept out by a generator rotating about the center of twist from some
convenientorigin,andA′RisthevalueofAR,Oatthepointofzerowarping.Asanillustration,weshall
applythemethodtothebeamsectionofExample17.3.
Supposethatthepositionofthecenteroftwist(i.e.,theshearcenter)hasalreadybeencalculated,
andsupposealsothatwechoosetheoriginforstobeatthepoint1.Then,inFig.17.14,
∫

sect

tds= 2 ×1.5× 25 +2.5× 50 =200mm^2

Inthewall12,

A 12 =

1

2

× 25 s 1 (AR,Oforthewall12) (i)

fromwhich

A 2 =

1

2

× 25 × 25 =312.5mm^2

Also,

A 23 =312.5−

1

2

×8.04s 2 (ii)