NCEES Mechanics of Materials 4

Question 1

A steel bolt (E = 200 GPa, α = 12 × 10⁻⁶ /°C) is constrained between two rigid walls. If temperature drops by 50°C, what thermal stress develops?

Accepted Answer

120 MPa tension

Answer

σ = EαΔT = 200×10⁹ × 12×10⁻⁶ × 50 = 120 MPa; a temperature drop in a constrained member induces tension.

Question 2

On Mohr's circle for a 2D stress state, the radius of the circle represents:

Accepted Answer

The maximum in-plane shear stress

Answer

The radius of Mohr's circle equals τ_max (in-plane) = √[(σx−σy)²/4 + τxy²].

Question 3

A simply supported beam with overhang can have an inflection point where:

Accepted Answer

The bending moment changes sign (crosses zero)

Answer

An inflection point is where the bending moment equals zero and changes sign, meaning curvature reverses.

Question 4

The shear flow q in a thin-walled open cross-section is defined as:

Accepted Answer

Both A and B are equivalent definitions

Answer

Shear flow q = VQ/I has units of force/length and also equals the product of shear stress and wall thickness (q = τt).

Question 5

What is the significance of the slenderness ratio (KL/r) in column design?

Accepted Answer

It determines whether Euler or inelastic buckling governs

Answer

A high slenderness ratio (KL/r) indicates elastic (Euler) buckling; a low ratio indicates inelastic (Johnson) buckling governs.

NCEES Practice Test