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:
δ=PLAEdelta equals the fraction with numerator cap P cap L and denominator cap A cap E end-fraction 2. Torsion (Circular Shafts)
σ=Eϵwhere E is Young′s Modulussigma equals cap E epsilon space where cap E is Young prime s Modulus Mechanics of Materials - Formulas and Problems:...
τ=TcJtau equals the fraction with numerator cap T c and denominator cap J end-fraction Measured in radians.
The most basic concepts involve forces applied along the longitudinal axis of a member. The internal force per unit area. τ=VQIttau equals the fraction with numerator cap V
ϵ=δLepsilon equals the fraction with numerator delta and denominator cap L end-fraction For materials in the elastic region.
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 The internal force per unit area
Bending moments cause internal stresses that vary linearly from the neutral axis.