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

Inputs
Loading: 
 Triangular Load p =    
Loading shape  Constant along x, triangular along y
 Constant along y, triangular along x
 Geometry: 
 Width Lx =    
 Length Ly =  
 Thickness h =    
 Material
 Young's modulus E =    
 Poisson's ratio nu =   0.3
Output: 
 Unit of displacement w =  
 Unit of stress =  

 
 
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.