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

Inputs
Loading:   triangular load p =  
 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 table.

Lx/Ly 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
c1  0.0016  0.0047  0.0074  0.0097  0.0113  0.0126  0.0133  0.0136

Hence, wmax = 0.00289831912879 mm ~ 0.00290 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 polynomial least-square curve-fitting.  

Stress

where values of c2 are listed in the following table.

Lx/Ly 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
c2  0.1304  0.1436  0.1686  0.1800  0.1845  0.1874  0.1902  0.1908

Hence, max = 0.105699945887 MPa ~ 0.106 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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