find the maximum torque - i-sectionan i-section

Question

Find the maximum torque - I-section:

An I-section 150 × 80 mm has flanges 6 mm thick and web 4 mm thick. Discover the maximum torque that may be safely applied if the shear stress is limited to 30 N/mm² and twist per metre length to 6^o. G = 80 GPa.

Solution

∑ h t ²  = 2 × 80 × 6²  + 150 × 4²  = 8160 mm³

T = τ_max . (1/3) (∑ h t 2 ) = 30 × (1 /3) × 8160 = 81, 600 N-mm

∑ h t₃  = 2 × 80 × 6³  + 150 × 4³  = 44,160 mm⁴

θ=        3Tl  / G (∑ h t³ )

 

⇒         6 × (π /180) =        3T × 1000 / (80 × 10³ × 44160)

∴          T = 123318 N-mm

∴ T = 44,160 N-mm (least value).