Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

Problems 477

Ans. (a)3wlIxy/8Ixx; (b)wl^4 /8EIxx.

Fig. P.15.14

P.15.15Auniformbeamofarbitrary,unsymmetricalcrosssectionandlength2lisbuilt-inatoneendandsimply
supportedintheverticaldirectionatapointhalfwayalongitslength.Thissupport,however,allowsthebeamto
deflectfreelyinthehorizontalxdirection(Fig.P.15.15).
ForaverticalloadWappliedatthefreeendofthebeam,calculateanddrawthebendingmomentdiagram,
puttingintheprincipalvalues.

Ans. MC=0,MB=Wl,MA=−Wl/2.Lineardistribution.

Fig. P.15.15

P.15.16ThebeamsectionofP.15.4issubjectedtoatemperatureriseof4T 0 initsupperflange12,atemperature
riseof2T 0 inbothverticalwebs,andatemperatureriseofT 0 initslowerflange34.Determinethechangesinaxial
forceandinthebendingmomentsaboutthexandyaxes.Young’smodulusforthematerialofthebeamisE,and
itscoefficientoflinearexpansionisα.

Ans. NT= 9 EαdtT 0 ,MxT= 3 Eαd^2 tT 0 /2,MyT= 3 Eαd^2 tT 0 /4.