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This calculator computes the maximum stress of a free on one edge, clamped on three edges rectangular plate under a uniformly distributed load.

Inputs
Loading: 
 Uniform Load p =    
 Geometry: 
 Width Lx =    
 Length Ly =  
 Thickness h =    
Boundary  Free edge along x axis
 Free edge along y axis
 Material
 Young's modulus E =    
 Poisson's ratio nu =  
Output: 
 Unit of displacement w =  
 Unit of stress =  

 
 
Displacement

where the maximum displacement is expressed in terms of the length of the clamped edges that are adjacent to the free edge and the values of c1 are listed in the following table.

LFree Edge/LCC Edge 0.25 0.5 0.75 1.0 1.5 2.0 3.0
c1  0.0272  0.0800  0.117  0.140  0.160  0.165  0.166

Hence, wmax = 0.054689395931 mm ~ 0.0547 mm

The formula is valid for most materials that have a Poisson's ratio around 0.3. However, the Poisson's ratio has a very limited effect on the displacement and the above calculation normally gives a very good approximation in most practical cases. The coefficient c1 is calculated by polynomial least-square curve-fitting.  

Stress

Notice that the maximum stress is expressed in terms of the length of the clamped edges that are adjacent to the free edge and the values of c2 are listed in the following table.

LFree Edge/LCC Edge 0.25 0.5 0.75 1.0 1.5 2.0 3.0
c2  0.020  0.081  0.173  0.321  0.727  1.226  2.105

Hence, max = 0.202474389384 MPa ~ 0.202 MPa

The formula is valid for materials that have a Poisson's ratio around 0.3. The coefficient c2 is calculated by polynomial least-square curve-fitting.  

Glossary