Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. 98-Civ-B1 Advanced Structural Analysis, National Examinations, May 2013 — 3 hours, closed book (an approved Sharp or Casio calculator is permitted). Nine questions are printed. The candidate must answer Question 1 and Question 2, then two of Questions 3–5 and two of Questions 6–9 — six questions constitute a complete paper (8 + 12 + 2 × 16 + 2 × 24 = 100 marks). Marks are shown in the left margin of the paper. All nine questions are solved below, because the set is intended as a study resource rather than as a three-hour sitting.
Reference texts.
Sign conventions used throughout. Slope-deflection end moments $M_{ij}$ are the moments the joint applies to the member, clockwise positive; joint rotations $\theta$ are clockwise positive; the chord rotation $\psi_{ij}=\Delta/L$ is positive when the member chord rotates clockwise. Bending moment diagrams are plotted with sagging positive, so that the sagging moment at end $i$ of member $ij$ is $+M_{ij}$ and at end $j$ it is $-M_{ji}$. All members are inextensible unless stated otherwise, so axial deformation contributes nothing to the compatibility equations.
