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This calculator computes the maximum displacement and stress of a clamped (fixed) rectangular plate under a uniformly distributed load.

Inputs
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
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 = 0.3
Output:   Unit of displacement w =

Displacement

where values of c1 are listed in the following table.

 Max(Lx/Ly, Ly/Lx) 1 1.2 1.4 1.6 1.8 2 c1 0.0138 0.0188 0.0226 0.0251 0.0267 0.0277 0.0284

Hence, wmax = 0.00539062500001 mm 0.00539 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-square curve-fitting.

Stress

where values of c2 are listed in the following table.

 Max(Lx/Ly, Ly/Lx) 1 1.2 1.4 1.6 1.8 2 c2 0.3078 0.3834 0.4356 0.468 0.4872 0.4974 0.5000

Hence, max = 0.192375 MPa 0.192 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.