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Solid Mech

# Solid Mech - Mech 2 Mechanics of Materials Formula and Data...

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Mech 2 Mechanics of Materials Formula and Data Sheet Some Engineering Material Properties: Property Steel Aluminum Brass Young’s Modulus, E 210 GPa (30 psi x 10 6 ) 70 GPa (10 psi x 10 6 ) 105 GPa (15 psi x 10 6 ) Shear Modulus, G 81 GPa (11.6 psi x 10 6 ) 26 GPa (3.7 psi x 10 6 ) 39 GPa (5.6 psi x 10 6 ) Poisson’s Ratio, ν 0.30 0.33 0.35 Thermal Expansion, α 11x10 -6 /ºC (6x10 -6 º/F) 22x10 -6 /ºC (12x10 -6 º/F) 20x10 -6 /ºC (11x10 -6 º/F) Density, ρ 7850 kg/m 3 (0.28 lb/in 3 ) 2720 kg/m 3 (0.10 lb/in 3 ) 8410 kg/m 3 (0.30 lb/in 3 ) Elastic relationships: T E E E z y x x Δ α + σ ν σ ν σ = ε G τ = γ ) 2(1 E G ν + = ) 2 - 3(1 E K ν = Pinned Trusses: m + r < 2j (mechanism) m + r = 2j (determinate) m + r > 2j (redundant) Thin-Walled Pressure Vessels: 0 t 2 R p t R p : Cylinder r a σ = σ = σ θ 0 t 2 R p : Sphere r a σ = σ = σ θ Shaft Torsion: Beam Bending: Parallel Axis Theorem: L G J T r φ = = τ R E I M Y = = σ 2 0 d A I I(d) + = Power Transmission: c J f 2 π P max τ = watts (metric units) c J rpm 10 15.87 P max -6 τ × = h.p. (lb.in units) Beam Formulas: x d M d V = x d V d w = EI M dx y d 2 2 = Moments of Area for Common Shapes: Shape Cross-section A I x I y J = I x + I y solid circle

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Solid Mech - Mech 2 Mechanics of Materials Formula and Data...

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