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GATE structural analysis: 5 practice questions with answers
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Structural analysis sits inside the Structural Engineering section of the GATE CE paper, alongside mechanics, solid mechanics, RCC and steel design. It is a procedure-heavy subject where the method (count unknowns, choose a technique, apply it without sign errors) decides the marks. The five original questions below practise determinacy, moment distribution, influence lines, deflection and arches.
What GATE tests in structural analysis
Structural analysis is part of the Structural Engineering section in the GATE 2027 CE syllabus, and the lists were revised, so confirm yours on the official syllabus page. The standard content is determinate and indeterminate structures, beams, trusses, frames and arches, deflections, influence lines and moving loads, the force method, displacement methods (slope-deflection and moment distribution) and an introduction to matrix methods. The real paper also has MSQ and NAT questions; all five below are MCQ.
Practice questions
Question 1
A single-bay, single-storey plane portal frame has both column bases fixed, rigid beam-to-column joints, and an internal hinge at the middle of the beam. The degree of static indeterminacy is:
- A. 1
- B. 2
- C. 3
- D. 4
Question 2
A continuous beam ABC has uniform flexural rigidity EI and equal spans AB and BC. End A is fixed and end C is a simple pin support. A moment of 100 kN·m is applied at joint B. The moment developed at the fixed end A is:
- A. 57.1 kN·m
- B. 42.9 kN·m
- C. 33.3 kN·m
- D. 28.6 kN·m
Question 3
A simply supported beam of span 12 m carries a uniformly distributed live load of 20 kN/m that can occupy any length of the span. The maximum shear force at a section 3 m from the left support is:
- A. 67.5 kN
- B. 90 kN
- C. 112.5 kN
- D. 135 kN
Question 4
A cantilever of length 2 m has EI = 10⁴ kN·m². It carries a point load of 15 kN at the free end. The deflection at the free end is:
- A. 1 mm
- B. 2 mm
- C. 4 mm
- D. 8 mm
Question 5
A three-hinged parabolic arch has a span of 20 m and a rise of 4 m, with both supports at the same level. A concentrated load of 40 kN acts at the crown hinge. The horizontal thrust at each support is:
- A. 25 kN
- B. 100 kN
- C. 200 kN
- D. 50 kN
Answers and explanations
- B. A plane portal frame with both bases fixed has 6 reactions against 3 equilibrium equations, so it is indeterminate to degree 3. The internal hinge supplies one extra condition, zero bending moment at that point, so the degree falls to 3 − 1 = 2. Two more releases, such as hinges at both bases, would give the determinate three-hinged frame.
- D. At joint B the member stiffnesses are 4EI / L for AB (far end fixed) and 3EI / L for BC (far end pinned). The distribution factor for AB is 4 / (4 + 3) = 4/7, so AB takes 4/7 × 100 = 57.1 kN·m at B. The carry-over factor to a fixed far end is 1/2, so the moment at A is 57.1 / 2 = 28.6 kN·m. Option A is the moment at the B end of AB.
- A. The influence line for shear at a section a = 3 m from the left support of a span L = 12 m has an ordinate of +(L − a) / L = 0.75 just to the right of the section, falling to zero at the right support. Maximum positive shear comes from loading the whole length to the right of the section: 20 × (1/2 × 9 × 0.75) = 20 × 3.375 = 67.5 kN. The largest negative shear is only 7.5 kN.
- C. For a cantilever with an end load, the tip deflection is P L³ / (3 E I) = 15 × 2³ / (3 × 10⁴) = 120 / 30 000 = 0.004 m = 4 mm.
- D. Each vertical reaction is 40 / 2 = 20 kN. Taking moments about the crown hinge for the left half, the bending moment must be zero there: 20 × 10 − H × 4 = 0, so H = 200 / 4 = 50 kN. In general H = W L / (4 h) = 40 × 20 / 16 = 50 kN.
How to prepare structural analysis
- Start every problem by counting. Classify the structure by static and kinematic indeterminacy, then pick the method: equilibrium for determinate structures, the force or an energy method for low indeterminacy, and slope-deflection or moment distribution for continuous beams and frames.
- Memorise the stiffness and carry-over factors (4EI/L and 3EI/L, carry-over 1/2) and the fixed-end moments for point loads and UDLs. They drive a large share of the numerical questions.
- Learn influence lines by shape. Draw the influence line for a reaction, shear or moment first, then place the loading to get the maximum.
- Keep a standard-deflection sheet for cantilevers and simply supported beams, plus the moment-area and conjugate-beam ideas for slopes.
- For trusses and arches, practise the method of joints and sections, zero-force members, and the zero-moment-at-hinge condition for three-hinged arches. Fix one sign convention and keep to it.
Structural analysis rests on strength of materials for stress and deflection formulas, and the soil side of civil engineering is in geotechnical engineering. The GATE civil preparation guide lays out all eight CE sections.
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