 Plate Calculator Formula Home Plate Theory Classical Plate Eqn. Sign Convention Plate Calculators Calculator List Plate Case Study Material Data Elastic Moduli Resources Bibliography  Login   Home Membership Magazines Forum Search Member Calculators  Materials  Design  Processes  Units  Formulas  Math This calculator computes the displacement of a free on one edge, simply-supported on three edges, rectangular plate under a uniformly distributed load. Inputs
 Uniform Loading p = Pa kPa MPa GPa psi ksi lbf/ft^2 kgf/cm^2 atm bar mmHg inHg ftH2O
Geometry:
 Width Lx = km m cm mm micron mi yd ft in mil Length Ly = Thickness h = km m cm mm micron mi yd ft in mil Boundary Free edge along x axis Free edge along y axis
Material
 Young's modulus E = Pa kPa MPa GPa psi ksi lbf/ft^2 kgf/cm^2 atm bar mmHg inHg ftH2O Poisson's ratio =
Output:
 Unit of displacement w = km m cm mm micron mi yd ft in mil Unit of stress = Pa kPa MPa GPa psi ksi lbf/ft^2 kgf/cm^2 atm bar mmHg inHg ftH2O

Displacement  Notice that the maximum displacement is expressed in terms of the length of the simply-supported edges that are adjacent to the free edge and the values of c1 are listed in the following table.

 LFree Edge/LSS Edge 0.5 0.667 1 1.5 2 4 c1 0.08 0.106 0.14 0.16 0.165 0.167

Hence, wmax = 0.054689395931 mm 0.0547 mm

The formula is valid for most commonly used metal materials that have Poission's ratios around 0.3. In fact, the Poisson's ratio has a very limited effect on the displacement and the above calculation normally gives a very good approximation for most practical cases. The coefficient c1 is calculated by the polynomial least-squares curve-fitting. Stress  Again, notice that the maximum stress is expressed in terms of the length of the simply-supported edges that are adjacent to the free edge and the values of c2 are listed in the following table.

 LFree Edge/LSS Edge 0.5 0.667 1 1.5 2 4 c2 0.36 0.45 0.67 0.77 0.79 0.8

Hence, max = 0.40770096664 MPa 0.408 MPa

The formula is valid for most commonly used metal materials that have Poission's ratios around 0.3. The coefficient c2 is calculated by the polynomial least-square curve-fitting. Home  Membership  About Us  Privacy  Disclaimer  Contact  Advertise Copyright © 2020 eFunda, Inc.