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### Uniform Force Over Entire Plate Beam Stress and Deflection Equations and Calculator

Flat Rectangular Uniform over entire plate plus uniform tension or compression P lb/linear in applied to short edges Stress and deflection Equation and Calculator.

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

Stress Maximum (Equations for σ_{a} and σ_{b} are stresses due to bending only;):

Stress Maximum Including Direct Stress and σ_{a}

+ P/t |

Where α β_{x} and β_{y} depend on ratios a / b and P / P_{E} where:

Deflection:

Symbols used:

E = Modulus of Elasticity (N/m^{2}, lbs/^{2})

q = Applied Load or Force to Flat Area of Plate (N/m^{2}, lbs/^{2})

P = Tension or Compression to Short Edges (N/m, Lbs/in)

v = Poisson’s ratio (assumed to be 0.3)

t = plate thickness, (m, in)

a = plate length, (m, in)

b = plate width, (m, in)

σ _{max} = maximum stress, (N/m^{2}, lbs/in^{2})

y_{max} = Maximum deflection (m, in)

α = From Table A

β_{x} = From Table A

β_{y} = From Table A

Table A (Click on Table to enlarge in Pop-up Window)

Reference:

Roarks Formulas for Stress and Strain, 7th Edition