Mechanics Of Materials - Formulas And Problems:... -

σ=Eϵwhere E is Young′s Modulussigma equals cap E epsilon space where cap E is Young prime s Modulus

ϵ=δLepsilon equals the fraction with numerator delta and denominator cap L end-fraction For materials in the elastic region. Mechanics of Materials - Formulas and Problems:...

τ=VQIttau equals the fraction with numerator cap V cap Q and denominator cap I t end-fraction (Where is the first moment of area and is the thickness at the point of interest). Practice Problem: Axial Loading A steel rod ( ) is 2 meters long and has a cross-sectional area of . If it is subjected to a tensile load of , calculate the total elongation. Solution: Identify Givens: Apply Formula: Calculate: σ=Eϵwhere E is Young′s Modulussigma equals cap E

σ=PAsigma equals the fraction with numerator cap P and denominator cap A end-fraction The deformation per unit length. If it is subjected to a tensile load

τ=TcJtau equals the fraction with numerator cap T c and denominator cap J end-fraction Measured in radians.

δ=PLAEdelta equals the fraction with numerator cap P cap L and denominator cap A cap E end-fraction 2. Torsion (Circular Shafts)

ϕ=TLGJphi equals the fraction with numerator cap T cap L and denominator cap G cap J end-fraction (Note: is the polar moment of inertia; for solid shafts). 3. Pure Bending