δ=PLAEdelta equals the fraction with numerator cap P cap L and denominator cap A cap E end-fraction 2. Torsion (Circular Shafts)
σmax=McIsigma sub m a x end-sub equals the fraction with numerator cap M c and denominator cap I end-fraction 4. Transverse Shear Internal shear forces ( ) result in shear stresses across the cross-section. Mechanics of Materials - Formulas and Problems:...
σ=−MyIsigma equals negative the fraction with numerator cap M y and denominator cap I end-fraction (Where is the distance from the neutral axis and is the moment of inertia). Occurs at the furthest fiber ( δ=PLAEdelta equals the fraction with numerator cap P
ϵ=δLepsilon equals the fraction with numerator delta and denominator cap L end-fraction For materials in the elastic region. Practice Problem: Axial Loading A steel rod (
Ï„=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=160,00080,000,000=0.002 m or 2 mmdelta equals the fraction with numerator 160 comma 000 and denominator 80 comma 000 comma 000 end-fraction equals 0.002 m or 2 mm Practice Problem: Bending Stress A rectangular beam ( ) experiences a maximum bending moment of . Determine the maximum bending stress. Solution: Find : Find : Apply Formula: Result: