07-Str-A1, May 2014: worked solutions

Paper format. National Examinations, May 2014 — 07-Str-A1 Elementary Structural Analysis. Three hours, CLOSED BOOK, an approved Sharp or Casio calculator permitted. Six questions constitute a complete paper: answer ALL of Questions 1 to 4, ONE of Questions 5 or 6, and ONE of Questions 7 or 8. Marks are shown in the left margin (7 + 18 + 15 + 18 + 20 + 22 = 100). All eight questions are solved below, because the alternatives test different topics and the whole set is the more useful study resource.

Reference texts.

R. C. Hibbeler, Structural Analysis, 10th ed. — Ch. 2 (determinacy and stability), Ch. 3–5 (trusses, internal loadings, frames), Ch. 6 (influence lines), Ch. 8–9 (deflections, virtual work), Ch. 11–12 (slope-deflection, moment distribution).
A. Kassimali, Structural Analysis, 6th ed. — Ch. 3 (equilibrium and determinacy), Ch. 4 (plane trusses), Ch. 5 (beams and frames), Ch. 7 (deflections by virtual work), Ch. 8–9 (influence lines), Ch. 16–17 (slope-deflection, moment distribution).
K. Leet, C.-M. Uang and A. Gilbert, Fundamentals of Structural Analysis, 5th ed. — a parallel treatment of the same syllabus.
C. H. Norris, J. B. Wilbur and S. Utku, Elementary Structural Analysis, 4th ed. — the classical text after which this exam code is named.
Canadian design context: CSA S16 Design of Steel Structures, CSA A23.3 Design of Concrete Structures and the National Building Code of Canada. This is a pure analysis paper, so no code clause is needed to answer it, but every result below is in the SI units those documents use.

Sign conventions used throughout. For a beam, or for one member of a frame, shear is positive when the resultant of the forces on the left of (or below) a section acts upward, and bending moment is positive when it sags the member — that is, when it puts the underside of a beam, or the inside face of a frame member, in tension. Truss forces are quoted as T for tension and C for compression. In every figure applied loads are red, reactions are blue, and an internal hinge is a red circle.

07-Str-A1: May 2014