NCEES Mechanics of Materials 2

Question 1

A hollow circular shaft has outer diameter 60 mm and inner diameter 40 mm. What is the polar moment of inertia J?

Accepted Answer

approximately 1.02 × 10⁻⁶ m⁴

Answer

J = π(do⁴ − di⁴)/32 = π(0.06⁴ − 0.04⁴)/32 ≈ 1.02 × 10⁻⁶ m⁴.

Question 2

A steel rod (E = 200 GPa) of 20 mm diameter and 2 m length is subjected to a tensile load of 50 kN. What is the elongation?

Accepted Answer

1.59 mm

Answer

δ = PL/(AE) = 50000 × 2 / (π/4 × 0.02² × 200×10⁹) ≈ 1.59 mm.

Question 3

A beam with a rectangular cross-section (width b, height h) is subjected to bending. Where does the maximum shear stress occur?

Accepted Answer

At the neutral axis

Answer

For a rectangular section, the shear stress distribution is parabolic, peaking at the neutral axis where τ_max = 3V/(2A).

Question 4

Which failure theory is most appropriate for ductile materials under static multiaxial loading?

Accepted Answer

Von Mises (distortion energy) theory

Answer

The von Mises (distortion energy) criterion best predicts yielding in ductile materials under multiaxial stress states.

Question 5

A column with both ends pinned has a length of 3 m and a cross-sectional area moment of inertia I = 8 × 10⁻⁶ m⁴. If E = 200 GPa, what is the Euler critical buckling load?

Accepted Answer

approximately 1,754 kN

Answer

P_cr = π²EI/L² = π² × 200×10⁹ × 8×10⁻⁶ / 3² ≈ 1,754 kN.

NCEES Practice Test

NCEES Practice Test

NCEES Mechanics of Materials 2