# Deflection of Rectangular Plate with 2 Simply Supported Edges

As shown in the figure provided, a Uniform load acts upon a rectangular plate with edges at Y = 0 and Y = b which are simply supported.

Using this form of the Plate Equation:

$$\frac{\partial^4 \omega}{\partial x^4} + 2\frac{\partial^4 \omega}{\partial x^2\partial y^2}+\frac{\partial^4\omega }{\partial y^4} = \frac{P}{D}$$

Where P is the Uniform Load and,

$$D = \frac{Et^3}{12(1-v^2)}$$

How do you determine an equation that describes the Deflection of the plate?

Also, how is load 'P' put into the equation?

• If the edges are supported as shown the deflections only change with $y$, not with $x$, so this is the same as a beam. – alephzero Apr 16 '19 at 12:39
• Do you need to derive the equation? If not there are many formulas available Roark's Formulas of Stress and Strain have lots of equations for plates. – ShadowMan Apr 16 '19 at 17:20
• See researchgate.net/publication/… for various solutions of plate problems. Will give you an idea how these equations are solved. – Biswajit Banerjee Apr 17 '19 at 0:42

Many codes adopt using effective width for design of strength and deflection of short, wide slabs. for example for a ratio of support b to span a of 1.6 $$(effective\ width)/a\quad is\ 1.519\ and\ E= E/(1-v^2)$$, (in pp:170 Roark’s Formulas for Stress and Strain by YOUNG and BUDYNAS 7th ed).