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EM 319 - Formula Sheet for 2nd Midterm

EM 319 - Formula Sheet for 2nd Midterm - Midterm#2 Formula...

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Midterm #2 Formula sheet Beam bending: Shear forces and bending moments – normal and shear stresses Shown are the positive moments and shears: ) ( ) ( ) ( ) ( x V dx x dM x q dx x dV = = = i i i A y A y where y at axis Neutral : , d A Q circle rect A V Ib VQ Ad I I circle d I rect bh I I My * 2 4 3 , ) ( 3 4 , .) ( 2 3 , , ) ( 64 , .) ( 12 , = = = = = + = = = = α α α τ π σ Plane Stress (Stress transformations - Mohr’s circle) c ys xs p s xy y x s y x xy p c p p xy y x y x c R shear plane in Maximum R stresses incipal R σ σ σ π θ θ τ σ σ θ τ σ σ τ θ σ σ τ σ σ σ σ σ = = = = = = ± = + = + = 4 , 2 2 tan , 2 2 tan , Pr 2 2 max 2 , 1 2 2 θ τ θ σ σ τ θ τ θ σ σ σ σ σ σ 2 cos 2 sin 2 , 2 sin 2 cos 2 2 , 1 1 1 1 xy y x y x xy y x y x y x + = ± ± + = } 2 , 2 { ) ( : 2 1 max σ σ τ Max Plane of Out shear plane of out Max = 2 , , : , xy xy y y x x replacing equations previous the all use strains For γ τ ε σ ε σ (+)

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