Mechanics of Materials Formula Sheet, Summaries of Engineering

Download Mechanics of Materials Formula Sheet and more Summaries Engineering in PDF only on Docsity! Stress (W = γ.V || P = F/A || F = μN) Normal Stress: σavg = N/A || σmax = R/A Shear Stress: τavg = V/A || τmax = R/(2A) Factor of Safety: F.S = Ffail/Fallow = σfail/σallow = τfail/τallow || A = N/σallow = V/τallow Load Factors: R= 1.2D + 1.6L + 0.5S || Resistance Factor: Φ = 0.9N Strain Normal Strain: εavg = ΔL/L0 Shear Strain: γ = π/2 - θ Mechanical Properties of Materials Hooke's Law for Normal: σ = Eε Percent Elongation: [(Lf - L0)/L0)]100 || Percent Reduction in Area: [(A0 - Af)/A0]100 Strain Energy: ΔU = [(1/2)ΔF]εΔz = [(1/2)σΔxΔy]εΔz = (1/2)σεΔV Strain Energy Density: u = ΔU/ΔV = (1/2)σε Elastic Strain Energy Density: u = (1/2)σ2/E Modulus of Resilience: ur = (1/2)σplεpl = (1/2)σ2pl/E Longitudinal Strain: εlong = δ/L || Lateral Strain: εlat = δ'/r Poisson's Ratio: v = -(εlat/εlong) Hooke's Law for Shear: τ = Gγ ; G = E/2(1+v) Axial Load Relative Displacement (Elastic): δ = ∫[N(x)/(E(x)A(x))]dx (Load and Area varies) || δ = NL/EA (Load and Area constant) Thermal Stress: δ = αΔTL Torsion Shear Stress: τ = Tc/J Polar Moment of Inertia: J = (π/2)c4 (Solid Shaft) || J = (π/2)(c4o - c4i) (Hollow Shaft) Power: P = T.w Angle of Twist: Φ = ∫[T(x)/(J(x)G(x))]dx (Variable) || Φ = TL/JG (Constant) Bending σ = Mc/I Ix = Ix' + Ady2 || Iy = Iy' + Adx2 y' = (ΣyA)/ΣA n = E1/E2 Transverse Shear Transverse Shear: τ = VQ/It Shear Flow: q = VQ/I ; q = F/s Q = ΣyA