Mechanics of Materials Flashcards

A hollow circular shaft has outer diameter 80 mm and inner diameter 50 mm. What is its polar moment of inertia (J)?

Answer: 1.81 × 10⁻⁶ m⁴

J = π/32 × (D⁴ - d⁴) = π/32 × (0.08⁴ - 0.05⁴) ≈ 1.81 × 10⁻⁶ m⁴.

A cantilever beam of length L carries a point load P at its free end. What is the maximum bending moment?

Answer: PL

The maximum bending moment in a cantilever with tip load P occurs at the fixed end and equals PL.

Which failure theory is most conservative for a ductile material under biaxial stress?

Answer: Maximum Shear Stress (Tresca) Theory

The Tresca criterion is more conservative than Von Mises because its yield surface is inscribed within the Von Mises ellipse.

A steel bar (E = 200 GPa) of cross-sectional area 500 mm² and length 2 m is subjected to an axial load of 100 kN. What is the axial deformation?

Answer: 1.0 mm

δ = PL/(AE) = (100,000 × 2)/(500×10⁻⁶ × 200×10⁹) = 0.001 m = 1.0 mm.

For a simply supported beam with a uniformly distributed load w over its full length L, where does the maximum deflection occur?

Answer: At midspan

By symmetry, the maximum deflection of a simply supported beam under UDL occurs at midspan (x = L/2).

Poisson's ratio (ν) for an incompressible material is:

Answer: 0.5

An incompressible material has zero volumetric strain, which requires ν = 0.5.

A 10 mm diameter rod is loaded in tension with 20 kN. What is the average normal stress?

Answer: 255 MPa

A = π(0.01)²/4 = 7.854×10⁻⁵ m²; σ = 20,000/7.854×10⁻⁵ ≈ 255 MPa.