Equation Sheet Final Test

# Equation Sheet Final Test - Failure theories Maximum Normal...

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Failure theories: Maximum Normal Stress Criterion: 1 1 2 2 , , , t c t c S S S S (at failure) Maximum Shear Stress (Tresca) Criterion: 1 2 1 2 ,, Y Y Y S S S (at failure) Maximum Distortion Energy (Von-Mises) Criterion 2 2 2 1 1 2 2 Y S   (at failure) Principal Stresses (plane stress)   2 2 1,2 1 4 22 xy x y xy  Fatigue: Goodman Equation ,0 1 m am au SS     S m = mean stress S a = stress amplitude S u = ultimate stress m = material property Virtual work of a uniaxial bar: Internal virtual work of a beam: Rayleigh Ritz Method: Strain energy and Complementary strain energy: Linear Thermoelastic Bar: Linear Thermoelastic Beam: ( ) 0 o z z V F w L dV          2 2 2 2 0 L o o o i o xx o yy o dw d v d u d d d W E A w I v I u dz dz dz dz dz dz dz   1 ( ) ( ) N o j j j u z a f z 1 ( ) ( ) N o j j j u z a f z  2 1 2 T z z z V U E E dV

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Equation Sheet Final Test - Failure theories Maximum Normal...

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