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### Flat Rectangular Loaded Plate Stress and Strain Formula and Calculator

Flat Rectangular Plate; one edge fixed, opposite edge free, remaining edges simply supported Uniform loading over entire plate Stress and Deflection Equation and Calculator.

Per. Roarks Formulas for Stress and Strain Formulas for flat plates with straight boundaries and constant thickness

Rectangular plate; one edge fixed, opposite edge free, remaining edges simply supported Uniform loading over entire plate

 Rectangular plate; one edge fixed, opposite edge free, remaining edges simply supported Uniform loading over entire plate

Stress Maximum at center of fixed edge:

 and R = γ1qb

Stress Maximum at center of free edge:

 and R = γ2qb

Symbols used:
q = Applied Load or Force to Flat Area of Plate (N/m2, lbs/2)
v = Poisson’s ratio (assumed to be 0.2)
t = plate thickness, (m, in)
a = plate length, (m, in)
b = plate width, (m, in)
σ max = maximum stress, (N/m2, lbs/in2)
R = Reaction force per unit length (N/m, lbs/in) normal to the plate surface exerted by the boundary support on the edge of the plate.
β1 = From Table A
β2 = From Table A
γ1 From Table A
γ2 From Table A

Table A

 a/b 0.25 0.5 0.75 1 1.5 2 3 β1 0.044 0.176 0.38 0.665 1.282 1.804 2.45 β2 0.048 0.19 0.386 0.565 0.73 0.688 0.434 γ1 0.183 0.368 0.541 0.701 0.919 1.018 1.055 γ2 0.131 0.295 0.526 0.832 1.491 1.979 2.401

Reference:

Roarks Formulas for Stress and Strain, 7th Edition