고체역학 (Gere) — Stresses in Beams (Advanced Topics): Problem 6.4-15

6.4-15 A built-up I-section steel beam with channels attached to the flanges (see figure part a) is simply supported at the ends. Two equal and oppositely directed bending moments \( M_0 \) act at the ends of the beam, so the beam is in pure bending. The moments act in plane \( mm \), which is oriented at an angle \( \alpha \) to the \( x-y \) plane. (a) Determine the orientation of the neutral axis and calculate the maximum tensile stress \( \sigma_{\max} \) due to the moments \( M_0 \). (b) Repeat part (a) if the channels now have their flanges pointing away from the beam flange, as shown in the figure part b. Data for the beam are IPN 160 section with UPN 100 sections attached to the flanges, \( M_0 = 5 \text{ kN}\cdot\text{m} \), and \( \alpha = 40^\circ \). See Tables F-2 and F-3 of Appendix F for the dimensions and properties of the IPN and UPN shapes.