Strength of materials: board exam questions with solutions
On the REE exam under Engineering Sciences and Allied Subjects (ESAS). Try each question before you open its solution, then practise with fresh numbers below: 1 computed question type on this topic.
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Questions
1. A bar with a 400 mm² cross-section carries an axial tensile load of 20 kN. What is the normal stress?
- 20 MPa
- 50 MPa
- 500 MPa
- 8 MPa
Show the answer and solution
Answer: B. 50 MPa
σ = P/A = 20 000 N/400 mm² = 50 N/mm² = 50 MPa.
2. A steel rod 2 m long with a 100 mm² area carries 10 kN in tension. Find its elongation. (E = 200 GPa)
- 0.1 mm
- 10 mm
- 1.0 mm
- 0.5 mm
Show the answer and solution
Answer: C. 1.0 mm
δ = PL/(AE) = 10 000 × 2/(100×10⁻⁶ × 200×10⁹) = 0.001 m = 1.0 mm.
3. A simply supported beam with a 6 m span carries a 12 kN point load at midspan. What is the maximum bending moment?
- 18 kN·m
- 36 kN·m
- 72 kN·m
- 9 kN·m
Show the answer and solution
Answer: A. 18 kN·m
M_max = PL/4 = 12 × 6/4 = 18 kN·m.
4. A 3 m cantilever carries a uniform load of 5 kN/m over its full length. What is the maximum bending moment?
- 45.0 kN·m
- 15.0 kN·m
- 5.6 kN·m
- 22.5 kN·m
Show the answer and solution
Answer: D. 22.5 kN·m
M_max occurs at the fixed end: wL²/2 = 5 × 9/2 = 22.5 kN·m.
5. A thin-walled cylindrical tank of 1 m diameter and 10 mm wall thickness holds gas at 2 MPa. What is the hoop stress?
- 100 MPa
- 50 MPa
- 200 MPa
- 20 MPa
Show the answer and solution
Answer: A. 100 MPa
σ_h = pD/(2t) = 2 × 1000/(2 × 10) = 100 MPa. The longitudinal stress is half that, 50 MPa.
6. Hooke's law states that, within the proportional limit:
- Stress is proportional to strain squared
- Strain is independent of stress
- Stress is proportional to strain
- Stress is inversely proportional to strain
Show the answer and solution
Answer: C. Stress is proportional to strain
Up to the proportional limit, σ = Eε, where E is the modulus of elasticity.
7. A solid 50 mm steel shaft transmits 20 kW at 300 rpm. Find the maximum shear stress.
- 51.9 MPa
- 25.9 MPa
- 13.0 MPa
- 2.6 MPa
Show the answer and solution
Answer: B. 25.9 MPa
T = P/ω = 20 000/(2π × 300/60) = 636.6 N·m. τ = 16T/(πd³) = 16 × 636.6/(π × 0.05³) = 25.9 MPa.
8. A steel rail is fixed at both ends with no initial stress, and its temperature rises 30 °C. Find the thermal stress. (α = 11.7×10⁻⁶/°C, E = 200 GPa)
- 35.1 MPa
- 7.02 MPa
- 702 MPa
- 70.2 MPa
Show the answer and solution
Answer: D. 70.2 MPa
Expansion is fully blocked, so σ = EαΔT = 200×10⁹ × 11.7×10⁻⁶ × 30 = 70.2 MPa (compressive).
Worked examples with computed numbers
These numbers are fixed on this page; in practice they change every time.
9. A 16 mm diameter steel rod 4 m long carries a tensile load of 38 kN. With E = 200 GPa, how much does it stretch?
- 3780 mm
- 0.945 mm
- 3.78 mm
- 10.8 mm
Show the answer and solution
Answer: C. 3.78 mm
δ = PL/AE with A = π(16 mm)²/4 = 201.1 mm²: δ = 38000×4/(0.0002011×200×10⁹) = 3.78 mm.
Other topics in the same subjects
Physics: mechanics · Physics: waves, electricity and magnetism · General chemistry · Thermodynamics · Fluid mechanics · Engineering materials · Engineering economics · Engineering management · Computer fundamentals and programming · RA 7920 and ethics (electrical) · PEC Part 1: general requirements
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