Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
04-BS-6: Mechanics of Materials — National Exams, December 2017. Closed-book, 3 hours; any FIVE of the eight questions constitute a complete paper (all eight are answered below as a complete study resource). Aid sheet permitted; geometric properties of W-shape sections were supplied as an appendix (not required for any of the eight questions solved here).
Reference texts: Hibbeler, Mechanics of Materials, 10th ed. (axial loading, shear/moment diagrams, beam deflection by integration, stress transformation & Mohr's circle, combined loadings, torsion, column buckling, unsymmetric-section flexure).