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This calculator computes the maximum displacement and stress of a simply-supported rectangular plate under a triangular load.

Inputs
 Triangular Load p =     Pa kPa MPa GPa psi ksi lbf/ft^2 kgf/cm^2 atm bar mmHg inHg ftH2O Loading shape  Constant along x, triangular along y Constant along y, triangular along x
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 tables.

 Triangular loading along the LONGER side Max(Lx/Ly, Ly/Lx) 1.0 1.5 2.0 2.5 3.0 3.5 4.0 c1 0.022 0.043 0.060 0.070 0.078 0.086 0.091 Triangular loading along the SHORTER side Max(Lx/Ly, Ly/Lx) 1.0 1.5 2.0 2.5 3.0 3.5 4.0 c1 0.022 0.042 0.056 0.063 0.067 0.069 0.070

wmax = 0.00852949134199 mm 0.00853 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 based on the above tables.

Stress

where values of c2 are listed in the following tables.

 Triangular loading along the LONGER side Max(Lx/Ly, Ly/Lx) 1.0 1.5 2.0 2.5 3.0 3.5 4.0 c2 0.16 0.26 0.34 0.38 0.43 0.47 0.49 Triangular loading along the SHORTER side Max(Lx/Ly, Ly/Lx) 1.0 1.5 2.0 2.5 3.0 3.5 4.0 c2 0.16 0.26 0.32 0.35 0.37 0.38 0.38

max = 0.0998511904762 MPa 0.0999 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 based on the above tables.