Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

15.1 Symmetrical Bending 429

Fig.15.6

Direct stress distribution in beam of Example 15.1.

The cross section of the beam is doubly symmetrical so that the centroid, C, of the section, and
thereforetheoriginofaxes,coincideswiththemidpointoftheweb.Furthermore,thebendingmoment
isappliedtothebeamsectioninaverticalplanesothatthexaxisbecomestheneutralaxisofthebeam
section;therefore,weneedtocalculatethesecondmomentofarea,Ixx,aboutthisaxis.

Ixx=

200 × 3003

12

−

175 × 2603

12

=193.7× 106 mm^4 (seeSection15.4)

FromEq.(15.9),thedistributionofdirectstress,σz,isgivenby

σz=−

100 × 106

193.7× 106

y=−0.52y (i)

Thedirectstress,therefore,varieslinearlythroughthedepthofthesectionfromavalue

−0.52×(+ 150 )=−78N/mm^2 (compression)

atthetopofthebeamto

−0.52×(− 150 )=+78N/mm^2 (tension)

atthebottomasshowninFig.15.5(b).