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This calculator computes the maximum stress of a free on one edge, clamped on three edges rectangular plate under a uniformly distributed load.

Inputs
 Uniform Load 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

where the maximum displacement is expressed in terms of the length of the clamped edges that are adjacent to the free edge and the values of c1 are listed in the following table.

 LFree Edge/LCC Edge 0.25 0.5 0.75 1 1.5 2 3 c1 0.0272 0.08 0.117 0.14 0.16 0.165 0.166

Hence, wmax = 0.054689395931 mm 0.0547 mm

The formula is valid for most materials that have a Poisson's ratio around 0.3. However, the Poisson's ratio has a very limited effect on the displacement and the above calculation normally gives a very good approximation in most practical cases. The coefficient c1 is calculated by polynomial least-square curve-fitting.

Stress

Notice that the maximum stress is expressed in terms of the length of the clamped edges that are adjacent to the free edge and the values of c2 are listed in the following table.

 LFree Edge/LCC Edge 0.25 0.5 0.75 1 1.5 2 3 c2 0.02 0.081 0.173 0.321 0.727 1.226 2.105

Hence, max = 0.202474389384 MPa 0.202 MPa

The formula is valid for materials that have a Poisson's ratio around 0.3. The coefficient c2 is calculated by polynomial least-square curve-fitting.