52928895-Strength-of-Materials-Formula-Sheet.pdf - Clarkson...

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Clarkson University – ES222, Strength of Materials Final Exam – Formula Sheet Axial Loading Normal Stress: P A σ = Splice joint: ave F A τ = Single shear: ave F A τ = Double shear: 2 ave F A τ = Bearing stress: b P td σ = 2 cos , sin cos o o P P A A σ θ τ θ θ = = Factor of Safety = F.S. = ultimate load allowable load Stress and Strain – Axial Loading Normal strain: L δ ε = Normal stress: E σ ε = Shear stress: G τ γ = Elongation: PL AE δ = Rods in series: i i i i i PL A E δ = Thermal elongation: ( ) T T L δ α = Thermal strain: ( ) T T ε α = Poisson’s ratio: lateral strain axial strain ν = − Generalized Hooke’s Law: y x z x E E E νσ σ νσ ε = y x z y E E E σ νσ νσ ε = − + y x z z E E E νσ νσ σ ε = − + , , xy yz xz xy yz xz G G G τ τ τ γ γ γ = = = Units : k = 10 3 M = 10 6 G = 10 9 Pa = N/m 2 psi = lb/in 2 ksi = 10 3 lb/in 2 Coordinates of the Centroid : i i i i i x A x A = i i i i i y A y A = Parallel Axis Theorem : 2 ' x x I I Ad = + , where d is the distance from the x –axis to the x
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