Mechanics of Materials Flashcards

What is the SI unit of stress?

Answer: Pascal (Pa)

Stress is force per unit area; in SI units, 1 Pa = 1 N/m², which is the standard unit for stress.

Hooke's Law states that stress is proportional to strain within the elastic limit. The constant of proportionality is called the:

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.

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?

Answer: 200 MPa

Stress σ = P/A = 100,000 N / 500 mm² = 200 N/mm² = 200 MPa.

Poisson's ratio (ν) is defined as the ratio of:

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.

Beyond the elastic limit of a material, what occurs when the load is removed?

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.

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?

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.

The factor of safety in structural design is defined as the ratio of:

Answer: Ultimate (failure) stress to allowable (working) stress

Factor of safety = ultimate stress / allowable stress (or failure load / working load), ensuring adequate reserve strength.