Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

228 CHAPTER 7 Bending of Thin Plates

Fig.7.9

Plate element subjected to bending, twisting, and transverse loads.

centroidofthefacesoftheelement.Fromtheprevioussections,

Mx=

∫t/^2

−t/ 2

σxzdzMy=

∫t/^2

−t/ 2

σyzdzMxy=(−Myx)=−

∫t/^2

−t/ 2

τxyzdz

Inasimilarfashion,

Qx=

∫t/^2

−t/ 2

τxzdzQy=

∫t/^2

−t/ 2

τyzdz (7.15)

ForequilibriumoftheelementparalleltoOzandassumingthattheweightoftheplateisincluded
inq

(

Qx+

∂Qx

∂x

δx

)

δy−Qxδy+

(

Qy+

∂Qy

∂y

δy

)

δx−Qyδx+qδxδy= 0

or,aftersimplification,

∂Qx

∂x

+

∂Qy

∂y

+q= 0 (7.16)