Page 167 - Aircraft Stuctures for Engineering Student

Problems 151

nv
mr6
4W sin - -
sin
Ans. A, = a b
m2
~bh~[($+$)~-~]
N,
P.5.8 A square plate of side a is simply supported along all four sides and is
subjected to a transverse uniformly distributed load of intensity qo. It is proposed
to determine the deflected shape of the plate by the Rayleigh-Ritz method employing
a 'guessed' form for the deflection of

in which the origin is taken at the centre of the plate.
Comment on the degree to which the boundary conditions are satisfied and find the
central deflection assuming Y = 0.3.
0.0389q0a4
Ans.
Et3
P.5.9 A rectangular plate a x b, simply supported along each edge, possesses a
small initial curvature in its unloaded state given by
7rx . 7ry
wo = All sin-sin-
a b
Determine, using the energy method, its final deflected shape when it is subjected to a
compressive load N, per unit length along the edges x = 0, x = a.