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.

Preview: Flat Rectangular Plate Stress and Deflection Calculator

Uniform Loading over the Entire 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)
y_max = 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

Reference:

Roarks Formulas for Stress and Strain, 7th Edition