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

Inputs
Loading:	triangular 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
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

where values of c₁ are listed in the following table.

Lx/Ly	0.6	0.8	1.0	1.2	1.4	1.6	1.8	2.0
c1	0.0016	0.0047	0.0074	0.0097	0.0113	0.0126	0.0133	0.0136

Hence, w_max = 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.  

where values of c₂ are listed in the following table.

Lx/Ly	0.6	0.8	1.0	1.2	1.4	1.6	1.8	2.0
c2	0.1304	0.1436	0.1686	0.1800	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.