Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

494 CHAPTER 16 Shear of Beams

centerofasectionproduceszerotwist.Itfollowsthatdθ/dzinEq.(16.22)iszerosothat

0 =

∮

qs

Gt

ds

or

0 =

∮

1

Gt

(qb+qs,0)ds

whichgives

qs,0=−

∮

(qb/Gt)ds

∮

ds/Gt

(16.27)

IfGt=constant,thenEq.(16.27)simplifiesto

qs,0=−

∮

qbds

∮

ds

(16.28)

ThecoordinateηSisfoundinasimilarmannerbyapplyingSxthroughS.

Example 16.3
Athin-walledclosedsectionbeamhasthesinglysymmetricalcrosssectionshowninFig.16.13.Each
wallofthesectionisflatandhasthesamethicknesstandshearmodulusG.Calculatethedistanceof
theshearcenterfrompoint4.

Theshearcenterclearlyliesonthehorizontalaxisofsymmetrysothatitisonlynecessarytoapply
ashearloadSythroughSandtodetermineξS.Ifwetakethexreferenceaxistocoincidewiththeaxis

Fig.16.13

Closed section beam of Example 16.3.