NCEES Mechanics of Materials 3

Question 1

A cantilever beam of length L with a point load P at the free end has a maximum bending moment of:

Accepted Answer

PL at the fixed end

Answer

For a cantilever with tip load P, the maximum moment M = PL occurs at the fixed support.

Question 2

Two bars made of different materials are connected in parallel (same strain) under an axial load. How is the load shared?

Accepted Answer

Proportional to each bar's axial stiffness (AE/L)

Answer

In a parallel assembly with equal deformation, load is distributed proportional to each member's stiffness k = AE/L.

Question 3

A simply supported beam of span 6 m carries a uniformly distributed load of 10 kN/m. What is the maximum bending moment?

Accepted Answer

45 kN·m

Answer

M_max = wL²/8 = 10 × 6² / 8 = 45 kN·m, occurring at mid-span.

Question 4

The modulus of resilience for a material is best defined as:

Accepted Answer

The strain energy per unit volume at the yield point

Answer

Modulus of resilience = Sy²/(2E), representing the energy stored per unit volume at yielding.

Question 5

A solid circular shaft of diameter 50 mm transmits a torque of 2 kN·m. What is the maximum shear stress?

Accepted Answer

approximately 81.5 MPa

Answer

τ = Tc/J = 2000 × 0.025 / (π × 0.05⁴/32) = 2000 × 0.025 / 6.136×10⁻⁷ ≈ 81.5 MPa.

NCEES Practice Test