# Formula - Formula Sheet avg = N A Lf Lo =-Lo =-Lo avg = V A...

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Formula Sheet σ avg N A = τ avg V A = σ ij F j A i --------- A i 0 lim = ε L f L o L o ----------------- = ε δ L o ----- = ε u B u A x B x A ------------------ = γ π 2 α = ε xx x d d u x ( ) = ε xx σ xx ν σ yy σ zz + ( ) [ ] E = γ xy τ xy G = G E 2 1 ν + ( ) -------------------- = σ xx ε xx νε yy + [ ] E 1 ν 2 ( ) ------------------- = ε zz ν 1 ν ----------- ε xx ε yy + ( ) = x d d u N EA ------- = u 2 u 1 N x 2 x 1 ( ) EA -------------------------- = δ N L EA -------- = σ xx N A ---- = x d d φ T GJ ------ = φ 2 φ 1 T x 2 x 1 ( ) GJ -------------------------- = τ x θ T ρ J ------- = M z EI zz x 2 2 d d v = σ xx M z y I zz ---------- = τ xs V y Q z I zz t --------------- = σ xx M y z I yy ---------- = τ xs V z Q y I yy t -------------- = V y V = x d d V p = x d d M z V = V 2 V 1 p x d x 1 x 2 + = M 2 M 1 V x d x 1 x 2 + = σ nn σ xx θ 2 cos σ yy θ 2 sin 2 τ xy θ θ cos sin + + = τ nt σ xx θ θ sin cos σ yy θ θ cos sin τ xy θ 2 cos θ 2 sin ( ) + + = 2 θ p tan 2 τ xy σ xx σ yy ( ) ---------------------------- = σ 1 2 , σ xx σ yy + ( ) 2 ---------------------------- σ xx σ yy 2 ----------------------- 2 τ xy 2 + ± = τ max max σ 1 σ 2 2 ----------------- σ 2 σ 3 2 -----------------
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