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This calculator computes the maximum displacement and stress of a clamped (fixed) rectangular plate under a triangular 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 = 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 values of c1 are listed in the following table.

 Lx/Ly 0.6 0.8 1 1.2 1.4 1.6 1.8 2 c1 0.0016 0.0047 0.0074 0.0097 0.0113 0.0126 0.0133 0.0136

Hence, wmax = 0.00289831912879 mm 0.00290 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 polynomial least-square curve-fitting.

Stress

where values of c2 are listed in the following table.

 Lx/Ly 0.6 0.8 1 1.2 1.4 1.6 1.8 2 c2 0.1304 0.1436 0.1686 0.18 0.1845 0.1874 0.1902 0.1908

Hence, max = 0.105699945887 MPa 0.106 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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