This calculator computes the maximum displacement and stress of a simply-supported 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 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

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

w_max = 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.  

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.