Mechanics of Materials Flashcards

A steel column (E = 200 GPa, I = 8 × 10⁻⁶ m⁴) is 4 m long and pin-pin supported. What is the Euler critical load?

Answer: 986 kN

P_cr = π²EI/L² = π²×200×10⁹×8×10⁻⁶/4² ≈ 986 kN for a pin-pin column (K=1).

Which stress state exists at the neutral axis of a beam subjected to transverse loading?

Answer: Zero normal stress, maximum shear stress

At the neutral axis, bending normal stress is zero while transverse shear stress is maximum.

The flexure formula σ = Mc/I applies only when:

Answer: Plane sections remain plane and the material is linearly elastic

The flexure formula assumes linear elastic behavior and the Bernoulli-Euler hypothesis that plane sections remain plane.

A shaft transmits 50 kW at 500 rpm. What is the torque?

Answer: 955 N·m

T = P/ω = 50,000/(2π×500/60) = 50,000/52.36 ≈ 955 N·m.

Plane stress condition assumes which stress components are zero?

Answer: σ_z, τ_xz, and τ_yz

In plane stress, all out-of-plane stress components (σ_z, τ_xz, τ_yz) are zero while in-plane components may exist.

The stiffness of a helical coil spring with n active coils, wire diameter d, coil radius R, and shear modulus G is:

Answer: k = Gd⁴/(64nR³)

Spring stiffness k = Gd⁴/(64nR³), derived from torsional deflection of the coil wire.

Under combined axial and bending loads, the maximum stress in a cross-section is:

Answer: σ_max = P/A + Mc/I

By superposition, normal stresses from axial load (P/A) and bending (Mc/I) add algebraically at the extreme fiber.