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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 = γ_{1}w 
Stress and Reaction Force at center of free edge:
and  R = γ_{2}w 
Symbols used:
w = Applied Line Load or Force to Flat Area of Plate (lbs/in^{2})
v = Poisson’s ratio (assumed to be 0.2)
t = plate thickness, ( in)
a = plate length, ( in)
b = plate width, (in)
σ = stress, (lbs/in^{2})
R = Reaction force per unit length (lbs/in) normal to the plate surface exerted by the boundary support on the edge of the plate.
β_{1,2} = Constant From Table A
γ_{1,2} = Constant From Table A
Table A
a/b

0.25

0.50

0.75

1.0

1.5

2.0

3.0

β_{1}

0.000

0.024

0.188

0.570

1.726

2.899

4.508

β_{2}

0.321

0.780

1.204

1.554

1.868

1.747

1.120

γ_{1}

0.000

0.028

0.160

0.371

0.774

1.004

1.119

γ_{2}

1.236

2.381

3.458

4.510

6.416

7.772

9.031

Reference:
Roarks Formulas for Stress and Strain, 7th Edition
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