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

Torsion refers to the twisting of a structural member when loaded by couples (torques). Maximum at the outer surface (

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 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. Torsion refers to the twisting of a structural

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 ( Pure Bending τ=TcJtau equals the fraction with numerator

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.

δ=(80,000)(2)(400×10-6)(200×109)delta equals the fraction with numerator open paren 80 comma 000 close paren open paren 2 close paren and denominator open paren 400 cross 10 to the negative 6 power close paren open paren 200 cross 10 to the nineth power close paren end-fraction

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: