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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.

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