Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

306 CHAPTER 9 Thin Plates

whichgives

σz=σtcos^2 α

or,substitutingforσtfromEq.(9.15),

σz=

τ

tanα

(9.17)

or,forthisparticularbeam,fromEq.(9.14)

σz=

W

tdtanα

(9.18)

Sinceτandσtare constant through the depth of the beam, it follows thatσzis constant through the
depthofthebeam.
Thedirectloadsintheflangesarefoundbyconsideringalengthzofthebeam,asshowninFig.9.9.
Ontheplanemm,therearedirectandshearstressesσzandτactingintheweb,togetherwithdirectloads
FTandFBinthetopandbottomflanges,respectively.FTandFBareproducedbyacombinationof
thebendingmomentWzatthesectionplusthecompressiveaction(σz)ofthediagonaltension.Taking
momentsaboutthebottomflange,

Wz=FTd−

σztd^2

2

Hence,substitutingforσzfromEq.(9.18)andrearranging,

FT=

Wz

d

+

W

2tanα

(9.19)

Fig.9.9

Determination of flange forces.