Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

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

Fig. P.15.5 Fig. P.15.6

P.15.7 Athin-walledcantileverhasaconstantcrosssectionofuniformthicknesswiththedimensionsshownin
Fig.P.15.7.Itissubjectedtoasystemofpointloadsactingintheplanesofthewallsofthesectioninthedirections
shown.
Calculatethedirectstressesaccordingtothebasictheoryofbendingatthepoints1,2,and3ofthecrosssection
atthebuilt-inendandhalfwayalongthebeam.Illustrateyouranswerbymeansofasuitablesketch.
Thethicknessistobetakenassmallincomparisonwiththeothercross-sectionaldimensionsincalculating
thesectionpropertiesIxx,Ixy,andsoon.

Ans. Atbuilt-inend,σz,1=−11.4N/mm^2 ,σz,2=−18.9N/mm^2 ,σz,3=39.1N/mm^2

Halfway,σz,1=−20.3N/mm^2 ,σz,2=−1.1N/mm^2 ,σz,3=15.4N/mm^2.

Fig. P.15.7

P.15.8 Auniformthin-walledbeamhastheopencrosssectionshowninFig.P.15.8.Thewallthicknesstisconstant.
CalculatethepositionoftheneutralaxisandthemaximumdirectstressforabendingmomentMx=3.5Nmapplied
aboutthehorizontalaxisCx.Taker=5mm,t=0.64mm.