Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

224 CHAPTER 7 Bending of Thin Plates

Fig.7.5

(a) Plate subjected to bending and twisting; (b) tangential and normal moments on an arbitrary plane.

Fig.7.6

Complementary shear stresses due to twisting momentsMxy.

or

Mt=

(Mx−My)

2

sin2α+Mxycos2α (7.11)

(compareEqs.(7.10)and(7.11)withEqs.(1.8)and(1.9)).WeobservefromEq.(7.11)thatthereare
twovaluesofα,differingby90◦andgivenby

tan2α=−

2 Mxy

Mx−My