Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

472 CHAPTER 15 Bending of Open and Closed, Thin-walled Beams

Fig. P.15.1

P.15.2 Athin-walled,cantileverbeamofunsymmetricalcrosssectionsupportsshearloadsatitsfreeendasshown
inFig.P.15.2.Calculatethevalueofdirectstressattheextremityofthelowerflange(pointA)atasectionhalfway
alongthebeamifthepositionoftheshearloadsissuchthatnotwistingofthebeamoccurs.

Ans. 194.7N/mm^2 (tension).

Fig. P.15.2

P.15.3 Abeam,simplysupportedateachend,hasathin-walledcrosssectionshowninFig.P.15.3.Ifauniformly
distributedloadingofintensityw/unitlengthactsonthebeamintheplaneofthelower,horizontalflange,calculate
themaximumdirectstressduetobendingofthebeamandshowdiagrammaticallythedistributionofthestressat
thesectionwherethemaximumoccurs.
Thethicknesstistobetakenassmallincomparisonwiththeothercross-sectionaldimensionsincalculating
thesectionpropertiesIxx,Iyy,andIxy.

Ans. σz,max=σz,3= 13 wl^2 / 384 a^2 t, σz,1=wl^2 / 96 a^2 t, σz,2=−wl^2 / 48 a^2 t.

P.15.4 Athin-walledcantileverwithwallsofconstantthicknessthasthecrosssectionshowninFig.P.15.4.Itis
loadedbyaverticalforceWatthetipandahorizontalforce2Watthemidsection,bothforcesactingthroughthe
shearcenter.Determineandsketchthedistributionofdirectstress,accordingtothebasictheoryofbending,along
thelengthofthebeamforthepoints1and2ofthecrosssection.