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GATE strength of materials: 5 practice questions

By the PrepMatic team · Updated 9 Oct 2026 · 4 min read

Strength of materials, called mechanics of materials in the GATE ME syllabus and solid mechanics in CE, is shared by two big papers, and it is also an option in Engineering Sciences (XE3). The questions are numerical and use a small set of formulas for axial, bending and torsional stress, principal stresses and buckling. Units are the usual trap: N, mm and MPa mix easily. The five original questions below cover each area once.

What GATE tests in strength of materials

The ME paper lists mechanics of materials in its Applied Mechanics and Design section, and CE lists solid mechanics under Structural Engineering. The syllabi were revised for 2027, so confirm your list on the official syllabus page. The standard content is stress and strain, elastic constants, composite bars and thermal stress, bending moment and shear force diagrams, bending and shear stress in beams, deflection, torsion, Mohr's circle, thin-walled vessels, columns and failure theories. The real paper also has MSQ and NAT questions; all five below are MCQ.

Practice questions

Question 1

A steel bar (E = 200 GPa) has two segments in series. Segment AB is 1 m long with a cross-section of 400 mm². Segment BC is 1.5 m long with a cross-section of 300 mm². The bar is loaded by an axial tensile force of 30 kN. The total elongation is:

• A. 0.75 mm
• B. 0.94 mm
• C. 1.125 mm
• D. 1.25 mm

Question 2

A simply supported beam of span 6 m carries a uniformly distributed load of 10 kN/m over the whole span, including self-weight. The section is rectangular, 100 mm wide and 300 mm deep. The maximum bending stress is:

• A. 7.5 MPa
• B. 15 MPa
• C. 22.5 MPa
• D. 30 MPa

Question 3

A solid circular shaft of diameter 50 mm transmits 10 kW at 300 rpm. The maximum shear stress in the shaft is closest to:

• A. 6.5 MPa
• B. 13.0 MPa
• C. 26.0 MPa
• D. 52.0 MPa

Question 4

At a point in a stressed body, σx = 80 MPa, σy = 20 MPa and τxy = 40 MPa. The maximum in-plane shear stress is:

• A. 50 MPa
• B. 40 MPa
• C. 30 MPa
• D. 100 MPa

Question 5

Two columns have the same length, material and cross-section. One has both ends fixed and the other has one end fixed and the other free. The ratio of their Euler buckling loads (fixed-fixed to fixed-free) is:

• A. 4
• B. 8
• C. 16
• D. 32

Answers and explanations

1. C. For bars in series under the same force, δ = (P / E) × (L1 / A1 + L2 / A2). Here P / E = 30 × 10³ / (200 × 10⁹) = 1.5 × 10⁻⁷ m². L1 / A1 = 1 / (400 × 10⁻⁶) = 2500 m⁻¹, and L2 / A2 = 1.5 / (300 × 10⁻⁶) = 5000 m⁻¹. So δ = 1.5 × 10⁻⁷ × 7500 = 1.125 × 10⁻³ m = 1.125 mm.
2. D. The maximum moment is wL²/8 = 10 × 36 / 8 = 45 kN·m. The section modulus is Z = b d² / 6 = 100 × 300² / 6 = 1.5 × 10⁶ mm³. The stress is σ = M / Z = 45 × 10⁶ N·mm / 1.5 × 10⁶ mm³ = 30 MPa.
3. B. The angular speed is ω = 2π × 300 / 60 = 31.42 rad/s, so the torque is T = P / ω = 10 000 / 31.42 = 318.3 N·m. For a solid shaft, τ = 16 T / (π d³) = 16 × 318.3 / (π × 0.05³) = 5093 / (3.927 × 10⁻⁴) = 1.297 × 10⁷ Pa = 13.0 MPa.
4. A. The maximum in-plane shear stress is τmax = √[((σx − σy) / 2)² + τxy²] = √(30² + 40²) = 50 MPa. The principal stresses are 50 ± 50 = 100 MPa and 0, which is a quick check, because the radius of Mohr's circle equals τmax.
5. C. The critical load is proportional to 1 / Le², where Le is the effective length. Fixed-fixed has Le = 0.5 L and fixed-free has Le = 2 L. The ratio is (2 L / 0.5 L)² = 4² = 16.

How to prepare strength of materials

• Fix a unit system before you start. Use N, mm and MPa, or kN and m, and never mix them mid-problem. Check that the final unit matches the question.
• Memorise the standard formulas as pairs: σ = P/A and δ = PL/AE; σ = M y / I; τ = T r / J; beam deflections under a point load and a UDL; Euler's critical load π² E I / Le².
• Draw the shear force and bending moment diagrams for every beam, using dM/dx = V to locate the maximum moment.
• Master Mohr's circle. It gives the principal stresses, the maximum shear stress and the plane angles. Practise sign conventions on at least ten problems.
• Learn the elastic constants and their relations, E = 2G(1 + ν) and E = 3K(1 − 2ν), then add thermal stress, failure theories (Tresca, von Mises) and thin cylinders, which give quick questions.

This subject feeds into structural analysis for civil aspirants, and mechanical aspirants can pair it with thermodynamics and fluid mechanics. The GATE mechanical preparation guide and GATE civil preparation guide give the subject order for each paper.

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