BCE Mechanics of Materials 1 — Questions and Answers
Question 1: What is the SI unit of stress?
- Newton (N)
- Pascal (Pa) (Correct answer)
- Joule (J)
- Watt (W)
Correct answer: Pascal (Pa)
Stress is force per unit area; in SI units, 1 Pa = 1 N/m², which is the standard unit for stress.
Question 2: Hooke's Law states that stress is proportional to strain within the elastic limit. The constant of proportionality is called the:
- Poisson's ratio
- Shear modulus
- Modulus of elasticity (Young's modulus) (Correct answer)
- Bulk modulus
Correct answer: Modulus of elasticity (Young's modulus)
Young's modulus E is the proportionality constant in Hooke's Law (σ = Eε) relating normal stress to normal strain in the elastic range.
Question 3: A steel rod with a cross-sectional area of 500 mm² is subjected to an axial tensile load of 100 kN. What is the tensile stress?
- 100 MPa
- 200 MPa (Correct answer)
- 50 MPa
- 400 MPa
Correct answer: 200 MPa
Stress σ = P/A = 100,000 N / 500 mm² = 200 N/mm² = 200 MPa.
Question 4: Poisson's ratio (ν) is defined as the ratio of:
- Longitudinal strain to lateral strain
- Lateral strain to longitudinal strain (Correct answer)
- Shear stress to shear strain
- Volumetric strain to linear strain
Correct answer: Lateral strain to longitudinal strain
Poisson's ratio ν = –(lateral strain / longitudinal strain); the negative sign accounts for the opposite sense of the strains.
Question 5: Beyond the elastic limit of a material, what occurs when the load is removed?
- The material returns fully to its original dimensions
- Permanent (plastic) deformation remains (Correct answer)
- The material fractures immediately
- Necking begins at the midpoint
Correct answer: Permanent (plastic) deformation remains
The elastic limit is the maximum stress below which a material fully recovers; beyond it, permanent plastic deformation is retained after unloading.
Question 6: A steel bar (E = 200 GPa) of length 2 m and cross-sectional area 200 mm² carries an axial tensile load of 40 kN. What is the elongation?
- 1 mm
- 2 mm (Correct answer)
- 0.5 mm
- 4 mm
Correct answer: 2 mm
δ = PL/(AE) = (40,000 N × 2,000 mm) / (200 mm² × 200,000 N/mm²) = 80,000,000 / 40,000,000 = 2 mm.
Question 7: The factor of safety in structural design is defined as the ratio of:
- Working stress to ultimate stress
- Ultimate (failure) stress to allowable (working) stress (Correct answer)
- Yield stress to elastic limit
- Elastic limit to working stress
Correct answer: Ultimate (failure) stress to allowable (working) stress
Factor of safety = ultimate stress / allowable stress (or failure load / working load), ensuring adequate reserve strength.
BCE Mechanics of Materials 1
What is the SI unit of stress?