Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Examination, May 2018, 07-Str-A4 Advanced Structural Analysis — 3 hours, CLOSED BOOK (an approved Casio or Sharp calculator is permitted). Nine questions: #1 and #2 are compulsory (8 and 12 marks), then TWO of #3, #4, #5 (16 marks each) and TWO of #6, #7, #8, #9 (24 marks each); six questions constitute a complete paper (100 marks). All nine are solved here, because the set is a study resource rather than a timed sitting.
Reference texts.
Sign convention used throughout. Member end moments $M_{ij}$ are counter-clockwise positive on the member end, which is the convention that matches the standard 6-degree-of-freedom element stiffness matrix and the counter-clockwise-positive joint rotations that Question 9 asks for. With that convention the fixed-end moment of a downward uniform load is $M^{F}_{ij}=+wL^{2}/12$ at the near end, the chord rotation is $\psi_{ij}=\left[(\mathbf{D}_{j}-\mathbf{D}_{i})\cdot\mathbf{e}_{2}\right]/L$ with $\mathbf{e}_{2}$ the member axis turned $+90^{\circ}$, and the ordinary sagging moments plotted on the diagrams are $M_{\text{sag}}(i)=-M_{ij}$ and $M_{\text{sag}}(j)=+M_{ji}$. Where a step of the working is quicker in the clockwise-positive (Hibbeler) form the sign is stated explicitly.
