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This calculator computes the displacement of a free on one edge, simply-supported on three edges, rectangular plate under a uniformly distributed load.

Inputs
Loading: 
 Uniform Loading 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

Notice that the maximum displacement is expressed in terms of the length of the simply-supported edges that are adjacent to the free edge and the values of c1 are listed in the following table.

LFree Edge/LSS Edge 0.5 0.667 1.0 1.5 2.0 4.0
c1  0.080  0.106  0.140  0.160  0.165  0.167

Hence, wmax = 0.054689395931 mm ~ 0.0547 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-squares curve-fitting.  

Stress

Again, notice that the maximum stress is expressed in terms of the length of the simply-supported edges that are adjacent to the free edge and the values of c2 are listed in the following table.

LFree Edge/LSS Edge 0.5 0.667 1.0 1.5 2.0 4.0
c2  0.36  0.45  0.67  0.77  0.79  0.80

Hence, max = 0.40770096664 MPa ~ 0.408 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.  

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