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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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