ce204_equation_sheet

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

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1D stress components σ = P A = My I = VQ It = Tr J τ max = 3 V 2 A rectangle max = 4 V 3 A solid circle max = 2 V A thin tube shear stress distribution in a rectangle τ = 3 V 2 A ± 1 y c 2 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 R L 0 P ( x ) dx φ = R 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 = Z ydA, Q y = Z xdA ¯ y = Q x A , ¯ x = Q y A I x = Z y 2 dA , I y = Z 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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This note was uploaded on 10/01/2010 for the course CE 204 taught by Professor Denatale during the Fall '05 term at Cal Poly.

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