07-Str-A4: May 2014

Paper format. 07-Str-A4 Advanced Structural Analysis, National Examination, May 2014 — 3 hours, closed book (approved Sharp or Casio calculator permitted). Nine questions over seven pages: Questions 1 and 2 are compulsory (8 and 12 marks), then any two of Questions 3, 4, 5 (16 marks each) and any two of Questions 6, 7, 8, 9 (24 marks each). Six questions constitute a complete paper and total 100 marks. Marks are printed in the left margin. All nine questions are solved here, because the set is a study resource rather than a three-hour sitting.

Reference texts.

• R. C. Hibbeler, Structural Analysis, 10th ed. — Ch. 9 (deflections by energy methods), Ch. 10 (force/flexibility method), Ch. 11–12 (slope-deflection and moment distribution).
• A. Kassimali, Structural Analysis, 6th ed. — Ch. 3 (determinacy and stability), Ch. 7 (deflections by work-energy), Ch. 16 (slope-deflection with sidesway).
• A. Ghali, A. M. Neville and T. G. Brown, Structural Analysis: A Unified Classical and Matrix Approach, 7th ed. — Ch. 3–4 (force and displacement methods), Ch. 5 (lack of fit and support movement).
• W. McGuire, R. H. Gallagher and R. D. Ziemian, Matrix Structural Analysis, 2nd ed. — Ch. 4–5 (member stiffness, assembly, kinematic constraints).

Throughout this paper end moments are quoted with the counter-clockwise-positive sign convention, the one that matches the standard six-degree-of-freedom stiffness element. In that convention the slope-deflection equation is

$$M_{ij}=\frac{2EI}{L}\bigl(2\theta_i+\theta_j-3\psi_{ij}\bigr)+\mathrm{FEM}_{ij}$$

the chord rotation is $\psi_{ij}=\bigl[(\mathbf{d}_j-\mathbf{d}_i)\cdot\mathbf{e}_2\bigr]/L$ with $\mathbf{e}_2$ the member axis turned $+90^\circ$, the fixed-end moment of a downward UDL is $\mathrm{FEM}_{i}=+wL^{2}/12$ and $\mathrm{FEM}_{j}=-wL^{2}/12$, and the ordinary sagging bending moment is recovered as $M_{\text{sag}}(i)=-M_{ij}$, $M_{\text{sag}}(j)=+M_{ji}$. Mixing this with the clockwise-positive convention of some textbooks is the single most common source of clean-looking but wrong answers on this paper.