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ce204_equation_sheet

# ce204_equation_sheet - 1D stress components = max = P A =...

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1D stress components σ = P A , σ = My I , τ = V Q It , τ = Tr J τ max = 3 V 2 A rectangle , τ max = 4 V 3 A solid circle , τ max = 2 V A thin tube shear stress distribution in a rectangle τ = 3 V 2 A 1 y c 2 where y is measured from the neutral axis and c is the half height of the beam ( c = h/ 2) Axial Torsion Beams Δ = PL EA φ = TL GJ 1 ρ = κ = d 2 v dx 2 = M EI dM dx = V dV dx = w Axial Torsion Δ = L 0 P ( x ) EA dx φ = L 0 T ( x ) GJ dx Thermal strain for an axial rod: ε = α Δ T , where α is the coeﬃcient of thermal expansion and Δ T is the change in temperature from a reference temperature. Q x = y dA , Q y = x dA ¯ y = Q x A , ¯ x = Q y A I x = y 2 dA , I y = x 2 dA Solid circle: I x = I y = π r 4 4 , J = π r 4 2 Plane stress σ xx σ yy σ xy
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