Mechanics of Materials Flashcards

A hollow circular shaft has outer diameter 60 mm and inner diameter 40 mm. What is the polar moment of inertia J?

Answer: approximately 1.02 × 10⁻⁶ m⁴

J = π(do⁴ − di⁴)/32 = π(0.06⁴ − 0.04⁴)/32 ≈ 1.02 × 10⁻⁶ m⁴.

A steel rod (E = 200 GPa) of 20 mm diameter and 2 m length is subjected to a tensile load of 50 kN. What is the elongation?

Answer: 1.59 mm

δ = PL/(AE) = 50000 × 2 / (π/4 × 0.02² × 200×10⁹) ≈ 1.59 mm.

A beam with a rectangular cross-section (width b, height h) is subjected to bending. Where does the maximum shear stress occur?

Answer: At the neutral axis

For a rectangular section, the shear stress distribution is parabolic, peaking at the neutral axis where τ_max = 3V/(2A).

Which failure theory is most appropriate for ductile materials under static multiaxial loading?

Answer: Von Mises (distortion energy) theory

The von Mises (distortion energy) criterion best predicts yielding in ductile materials under multiaxial stress states.

A column with both ends pinned has a length of 3 m and a cross-sectional area moment of inertia I = 8 × 10⁻⁶ m⁴. If E = 200 GPa, what is the Euler critical buckling load?

Answer: approximately 1,754 kN

P_cr = π²EI/L² = π² × 200×10⁹ × 8×10⁻⁶ / 3² ≈ 1,754 kN.

A thin-walled pressure vessel (sphere) has radius 0.5 m, wall thickness 10 mm, and internal pressure 2 MPa. What is the hoop stress?

Answer: 50 MPa

For a spherical vessel, σ = pr/(2t) = 2×10⁶ × 0.5 / (2 × 0.01) = 50 MPa.

A material has yield strength Sy = 250 MPa and ultimate strength Su = 400 MPa. The percent elongation at fracture is 35%. This material is best classified as:

Answer: Ductile

A percent elongation greater than 5% (here 35%) and a clearly defined yield point indicate a ductile material.