Mechanics of Materials Flashcards

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?

Answer: 120 MPa tension

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

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

Answer: The maximum in-plane shear stress

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

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

Answer: The bending moment changes sign (crosses zero)

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

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

Answer: Both A and B are equivalent definitions

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

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

Answer: It determines whether Euler or inelastic buckling governs

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

The angle of twist θ of a circular shaft subjected to torque T over length L is given by:

Answer: θ = TL/(GJ)

The angle of twist formula is θ = TL/(GJ), where G is the shear modulus and J is the polar moment of inertia.

A rectangular bar (20 mm × 40 mm) is subjected to a bending moment of 500 N·m about the strong axis. What is the maximum bending stress?

Answer: 93.75 MPa

S = bh²/6 = 0.02 × 0.04²/6 = 5.33×10⁻⁶ m³; σ = M/S = 500/5.33×10⁻⁶ ≈ 93.75 MPa.