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### Flat Rectangular Plate with All Edges Simply Supported Equations and Calculator

Flat Rectangular Plate with All Edges Simply Supported Stress and Deflection with straight boundaries and constant thickness Equation and Calculator

NOTATION: The notation applies with the following modifications: a and b refer to plate dimensions, and when used as subscripts for stress, they refer to the stresses in directions parallel to the sides a and b, respectively. s is a bending stress which is positive when tensile on the bottom and compressive on the top if loadings are considered vertically downward. R is the reaction force per unit length normal to the plate surface exerted by the boundary support on the edge of the plate.

Stress at Center

Deflection at Center

Reaction Force at Center of Long Sides

Symbols used:
q = Load per unit area (N/m2, lbs/in2)
v = Poisson’s ratio (assumed to be 0.3)
E = Young’s modulus, (N/m2, lbs/in2)
t = plate thickness, (m, in)
a = plate length, (m, in)
b = plate width, (m, in)
σ max = maximum stress, (N/m2, lbs/in2)
ymax = maximum deflection, (m, in)
R = Reaction force (N/m, lbs/in)
β = Constant derived from table a/b
α = Constant derived from table a/b
γ = Constant derived from table a/b

 a/b 1 1.2 1.4 1.6 1.8 2 3 4 5 ∞ β 0.2874 0.3762 0.453 0.5172 0.5688 0.6102 0.7134 0.741 0.7476 0.7500 α 0.0444 0.0616 0.077 0.0906 0.1017 0.111 0.1335 0.14 0.1417 0.1421 γ 0.42 0.455 0.478 0.491 0.499 0.503 0.505 0.502 0.501 0.500

Reference:

Roarks Formulas for Stress and Strain, 7th Edition