Mechanics of Materials Flashcards

The modulus of resilience of a material is defined as:

Answer: The strain energy per unit volume stored up to the proportional limit

Modulus of resilience = σ_y²/(2E), representing elastic strain energy stored per unit volume up to yielding.

A thin-walled pressure vessel (sphere) has radius r and wall thickness t. The hoop stress is:

Answer: pr/(2t)

For a spherical pressure vessel, hoop stress = pr/(2t) due to biaxial symmetry (both principal stresses are equal).

Which of the following boundary conditions applies to a pin support in beam analysis?

Answer: Deflection = 0, moment = 0

A pin (simple support) prevents translation (δ = 0) but allows rotation, so bending moment M = 0 there.

Shear flow q in a thin-walled open section beam is defined as:

Answer: Both A and B are equivalent definitions

Shear flow q = VQ/I (from shear formula) and also equals τ × t (shear stress × wall thickness), so both are correct.

A 200 mm long, 10 mm diameter aluminum rod (α = 23 × 10⁻⁶/°C, E = 70 GPa) is fixed at both ends. If the temperature rises 50°C, what is the thermal stress?

Answer: 80.5 MPa

σ = αEΔT = 23×10⁻⁶ × 70×10⁹ × 50 = 80.5 MPa (compressive) in a fully restrained member.

On a Mohr's circle, the radius represents:

Answer: The maximum in-plane shear stress

The radius of Mohr's circle equals the maximum in-plane shear stress τ_max = (σ₁ − σ₂)/2.

For a beam in pure bending, the neutral axis is located at:

Answer: The centroid of the cross-section

In pure bending, the neutral axis passes through the centroid of the cross-section where normal stress is zero.