EIT Mechanics of Materials 2

Question 1

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

Accepted Answer

1.81 × 10⁻⁶ m⁴

Answer

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

Question 2

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

Accepted Answer

PL

Answer

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

Question 3

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

Accepted Answer

Maximum Shear Stress (Tresca) Theory

Answer

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

Question 4

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?

Accepted Answer

1.0 mm

Answer

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

Question 5

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

Accepted Answer

At midspan

Answer

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

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