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### Plate line load Applied Stress and Deflection Equation and Calculator

Flat Rectangular Plate; one edge fixed, opposite edge free, remaining edges simply supported loading distributed line load w lb/in along free edge Stress and Deflection Equation and Calculator.

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

Rectangular plate; one edge fixed, opposite edge free, remaining edges simply supported loading distributed line load w lb/in along free edge.

 Rectangular plate; one edge fixed, opposite edge free, remaining edges simply supported. Uniformly decreasing from fixed edge to zero at 2/3 b. Stress and Reaction Force at center of fixed edge: and R = γ1w

Stress and Reaction Force at center of free edge: and R = γ2w

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

Table A

 a/b 0.25 0.5 0.75 1 1.5 2 3 β1 0 0.024 0.188 0.57 1.726 2.899 4.508 β2 0.321 0.78 1.204 1.554 1.868 1.747 1.12 γ1 0 0.028 0.16 0.371 0.774 1.004 1.119 γ2 1.236 2.381 3.458 4.51 6.416 7.772 9.031

Reference:

Roarks Formulas for Stress and Strain, 7th Edition 