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### Loading Uniformly Decreasing to 1/3b Stress and Deflection Equation and Calculator.

Flat Rectangular Plate, Three Edges Fixed, One Edge (a) Free Loading Uniformly decreasing from fixed edge to zero at 1/3 b Stress and Reaction Loading Equation and Calculator.

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

Rectangular plate;
Three Edges Fixed One Edge Free |
Loading Uniformly decreasing from fixed edge to zero at 1/3 b |

At x = 0, z = 0

Stress and Reaction Force

Reaction Force

Stress and Reaction Force at x = 0, z = b

Reaction Force

Where used:

E = Modulus of Elasticity (lbs/in^{2})

q = Total load or force to Plate (lbs/in^{2})

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

t = plate thickness, (in)

a = plate length, (in)

b = plate width, (in)

σ_{b} = stress, (lbs/in^{2})

R = Reaction Force (lbs/in)

β_{1,2} = Constant From Table A

γ_{1,2} = Constant From Table A

Table A

a/b |
.25 |
0.50 |
0.75 |
1.0 |
1.5 |
2.0 |
3.0 |

β _{1} |
0.014 |
0.035 |
0.047 |
0.061 |
0.075 |
0.080 |
0.082 |

β _{2} |
0.010 |
0.024 |
0.031 |
0.030 |
0.025 |
0.020 |
0.013 |

γ _{1} |
0.088 |
0.130 |
0.146 |
0.155 |
0.161 |
0.162 |
0.162 |

γ _{2} |
0.046 |
0.069 |
0.079 |
0.077 |
0.074 |
0.074 |
0.082 |

Reference:

Roarks Formulas for Stress and Strain, 7th Edition

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