De

Now -— = D is a constant and termed the flexural stiffness

de e

It is now possible to write the stress equations in terms of the applied moments,

73. General equation for slope and deflection

Consider now Fig. 7.4 which shows the forces and moments per unit length acting on a small element of the plate subtending an angle Sep at the centre. Thus Mxy and MYz are the moments per unit length in the two planes as described above and q is the shearing force per unit length in the direction OY.

Fig. 7.4. Small element of circular plate showing applied moments and forces per unit length.

For equilibrium of moments in the radial XY plane, taking moments about the outside edge, (.Mxy + SMXy){x + 8x)8<p - MXYx84> - 2Myz8x sin ±50 + Qx8<j>8x = 0 which, neglecting squares of small quantities, reduces to

In the limit, therefore, dMXr

Substituting eqns. (7.8) and (7.9), and simplifying d2e \ do e _ q dx2 x dx x2 D This may be re-written in the form d

x dx

0 0

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