EIT Mechanics of Materials 3

Question 1

The modulus of resilience of a material is defined as:

Accepted Answer

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

Answer

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

Question 2

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

Accepted Answer

pr/(2t)

Answer

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

Question 3

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

Accepted Answer

Deflection = 0, moment = 0

Answer

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

Question 4

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

Accepted Answer

Both A and B are equivalent definitions

Answer

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

Question 5

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?

Accepted Answer

80.5 MPa

Answer

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

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EIT Mechanics of Materials 3