고체역학 (Gere) — Stresses in Beams (Advanced Topics): Problem 6.2-8

6.2-8 A plastic-lined steel pipe has the cross-sectional shape shown in the figure. The steel pipe has an outer diameter \( d_3 = 100 \text{ mm} \) and an inner diameter \( d_2 = 94 \text{ mm} \). The plastic liner has an inner diameter \( d_1 = 82 \text{ mm} \). The modulus of elasticity of the steel is 75 times the modulus of the plastic. (a) Determine the allowable bending moment \( M_{\text{allow}} \) if the allowable stress in the steel is \( 35 \text{ MPa} \) and in the plastic is \( 600 \text{ kPa} \). (b) If pipe and liner diameters remain unchanged, what new value of allowable stress for the steel pipe will result in the steel pipe and plastic liner reaching their allowable stress values under the same maximum moment (i.e., a balanced design)? What is the new maximum moment?