Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

318 CHAPTER 9 Thin Plates

Fig.9.18

Determination of flange stress.

fromwhich

σcf=

Fc−^12 (σtcsinθcosθ+τm)twcc

Acf

(9.59)

whereFcistheforceinthecompressionflangeatWandAcfisthecross-sectionalareaofthecompression
flange.
Similarly,forthetensionflange,

σtf=

Ft+^12 (σttsinθcosθ+τm)twct

Atf

(9.60)

TheforcesFcandFtarefoundbyconsideringtheequilibriumofthebeamtotherightofWY(Fig.9.19).
Then,resolvingverticallyandnotingthatScr=τmtwd,

Sult=Fwsinθ+τmtwd+

∑

Wn (9.61)

ResolvinghorizontallyandnotingthatHcr=τmtw(b−cc−ct),

Fc−Ft=Fwcosθ−τmtw(b−cc−ct) (9.62)

TakingmomentsaboutO,wehave

Fc+Ft=

2

d

[

Sult

(

s+

b+cc−ct

2

)

+Mpt′−Mpc′

+Fwq−Mw−

∑

n

Wnzn

] (9.63)

whereW 1 toWnare external loads applied to the beam to the right of WY andMwis the bending
momentinthewebwhenithasbuckledandbecomeatensionfield,thatis,

Mw=

σmbbd^2

b