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Unformatted text preview: Moment-curvature equation (Second order) EI d2 V (x) = M ( x) dx2 Load-deﬂection equation (Fourth order) EI d4 V (x) = P (x) dx4 Pressure vessels For a cylinder, Axial Stress Hoop stress For a sphere, σs = Pr 2t Pr 2t Pr σh = t σa = Principal stresses σ1,2 = Maximum shear stress τM ax = σx − σy 2
2 2 + τxy σx + σy ± 2 σx − σy 2 2 2 + τxy Euler buckling load (Pinned-Pinned) PCR = π 2 EI L2 1st buckling mode 2nd buckling mode πx L 2πx V (x) = C sin L V (x) = C sin General buckling load (arbitrary supports) PCR = π 2 EI L2 e 1 ...
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