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 =     Pa kPa MPa GPa psi ksi lbf/ft^2 kgf/cm^2 atm bar mmHg inHg ftH2O
Geometry:	Width Lx =     km m cm mm micron mi yd ft in mil  Length Ly =    Thickness h =     km m cm mm micron mi yd ft in mil Boundary   Free edge along x axis   Free edge along y axis
Material:	Young's modulus E =     Pa kPa MPa GPa psi ksi lbf/ft^2 kgf/cm^2 atm bar mmHg inHg ftH2O  Poisson's ratio =
Output:	Unit of displacement w =   km m cm mm micron mi yd ft in mil  Unit of stress =   Pa kPa MPa GPa psi ksi lbf/ft^2 kgf/cm^2 atm bar mmHg inHg ftH2O

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.

LSS Edge/LFree 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, w_max = 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.  

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.

LSS Edge/LFree 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.