Max 1 and min 2 max in plane shearing stress maxin

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Unformatted text preview: gitudinal stress • Hoop stress: ∑ Fz = 0 = σ 1(2t Δx ) − p(2r Δx ) pr σ1 = t • Longitudinal stress: * ∑ F x = 0 = σ 2 (2 π rt ) − p (π r 2 ) σ 1dA p dA σ 1dA σ 2 dA p dA pr 2t σ 1 = 2σ σ 2 = 2 * Assume t/(2r) very small 14 7 D’ τ max E’ • Pts A & B correspond to hoop = σ 2 stress, σ 1 , and longitudinal stress, σ 2 . • σmax = σ1 and σmin= σ2 • Max in-plane shearing stress: τ max(in − plane) = σ 2 / 2 = pr 4t • Max out-of-plane shearing stress: τmax(out of plane) = σ2 = pr/(2t) 15 7.10 Transformation of Plane Strain • Plane strain - deformations of material take place in parallel planes and are the same in each of the planes. • Plane strain occurs in a plate subjected along its edges to a uniformly distributed load and restrained from expanding or contracting laterally by smooth, rigid and fixed supports • Components of strains are: εx ε y γ xy (ε z = γ zx = γ zy = 0) 16 8 Conventions • ε +ve when elongated • γ xy +ve when angle...
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This note was uploaded on 06/28/2013 for the course MEC 2001 taught by Professor Tansoonhuat during the Spring '10 term at Nanyang Technological University.

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