Corrugated Wood Composite Panels For Structural Decking

4 4 4∂∆ ∂∆ ∂∆x 4 2 2 y 4( xy , ) ( xy , ) ( xy , )D + 2 H + D = q( x, y)∂x ∂x ∂y ∂ywhere qxy ( , ) can be any loading function and ∆ ( x, y)is the deflection normal to the(9)plate or the solution for the differential equation.D x,Dy, and H are the flexuralrigidities, which can, theoretically, be estimated from the following equations [Troitsky,1976].Dx=w2DS3Et−ν212(1 )EIw(10)cy= (11)H = D12 + 2Dxy(12)where, S is the arc length of one half of a wavelength, calculated as,⎛1−cos( θ ) ⎞S = w+ 2h⎜ ⎟⎝ sin( θ ) ⎠and Dxyis the torsional rigidity, approximated as,(13)D12is estimated as,3S GtDxy=w2 12(14)D12DDx y=νD + Dxy(15)Bending moments, ( Mxx, Myy, and Mxy), shear forces, ( V xand Vy), and reactionforces, ( R andxR ), can expressed in terms of the deflection, ∆ ( x, y), or the solution toythe plate bending equation (9).2 2∂∆( x, y) ∂∆( x, y)Mxx( x, y)=−Dx−D2 12 2∂x∂y(16)28