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

Inputs
Loading:   Uniform loading p =  
 Geometry: 
 Width Lx =    
 Length Ly =  
 Thickness h =    
 Material
 Young's modulus E =    
 Poisson's ratio nu =   0.3
Output:   Unit of displacement w =  

 
 
Displacement

where values of c1 are listed in the following table.

Max(Lx/Ly, Ly/Lx) 1.0 1.2 1.4 1.6 1.8 2.0
c1  0.0138  0.0188  0.0226  0.0251  0.0267  0.0277  0.0284

Hence, wmax = 0.00539062500001 mm ~ 0.00539 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.  

Stress

where values of c2 are listed in the following table.

Max(Lx/Ly, Ly/Lx) 1.0 1.2 1.4 1.6 1.8 2.0
c2  0.3078  0.3834  0.4356  0.4680  0.4872  0.4974  0.5000

Hence, max = 0.192375 MPa ~ 0.192 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.  

Glossary