﻿ Plate Formulas

# Plate Formulas

Plate formulas may be used to determine the deflection, shear and bending moment in a plate based on the applied loading and boundary conditions.

## Reference Documents:

1. Anisotropic Plates, Lekhnitskii, Gordon & Breach
2. Formulas for Stress and Strain, Roark & Young, McGraw-Hill
3. Formulas for Stress, Strain, and Structural Matrices, Pilkey, John Wiley & Sons.
4. Moments and Reactions of Rectangular Plates, Engineering Monograph #27, Moody, U.S. Department of the Interior (Available from NTIS).
5. Rectangular Concrete Tanks, Portland Cement Association
6. Theory of Plates and Shells, Timoshenko & Woinowsky, McGraw-Hill

## Common Plate Formulas:

 PIN-SUPPORTED PLATE WITH UNIFORM LOAD Legend: q = pressure E = modulus of elasticity t = thickness d = deflection M = moment / unit width V = Shear / unit width Y / X 1.00 1.25 1.50 1.75 2.00 3.00 4.00 ¥ C1 0.04436 0.06581 0.08350 0.09919 0.11060 0.13358 0.13998 0.14219 C2 0.04789 0.06610 0.08116 0.09287 0.10168 0.11886 0.12346 0.12500 C3 0.04789 0.05026 0.04984 0.04825 0.04635 0.04063 0.03841 0.00000 C4 0.41842 0.46035 0.48359 0.49562 0.50128 0.50263 0.49969 0.50000 C5 0.41843 0.36509 0.31771 0.27817 0.24587 0.16492 0.12326 0.00000