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### Uniform Loading over 1/3 of plate Stress and Deflection Equation and Calculator

Flat Rectangular Plate, Three Edges Fixed, One Edge (a) Simply Supported Uniform Loading over 1/3 of plate from fixed edge Stress and Deflection Equation and Calculator.

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

Flat Rectangular plate, Three Edges Fixed, One Edge Uniform Loading over 1/3 of Plate

Rectangular plate;
Three Edges Fixed |
Uniform Loading over
1/3 of plate from fixed edge |

At x = 0, z = 0

Stress

Reaction Force

Stress at x = 0, z = 0.2b

and |

At x = 0, z = b

Reaction Force

At x = ± a/2, z = 0.2b

Stress

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_{1,2,3,4} = Constant From Table A

γ_{1,2,3} = Constant From Table A

Table A

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

β _{1} |
0.020 |
0.068 |
0.108 |
0.148 |
0.194 |
0.213 |
0.222 |

β _{2} |
0.005 |
0.026 |
0.044 |
0.050 |
0.047 |
0.041 |
0.037 |

β _{3} |
0.013 |
0.028 |
0.031 |
0.026 |
0.016 |
0.011 |
0.008 |

β _{4} |
0.026 |
0.063 |
0.079 |
0.079 |
0.068 |
0.056 |
0.037 |

γ _{1} |
0.114 |
0.210 |
0.261 |
0.290 |
0.312 |
0.316 |
0.316 |

γ _{2} |
0.000 |
0.000 |
0.004 |
0.011 |
0.020 |
0.021 |
0.020 |

γ _{3} |
0.111 |
0.170 |
0.190 |
0.185 |
0.176 |
0.175 |
0.190 |

Reference:

Roarks Formulas for Stress and Strain, 7th Edition

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