EIT Mechanics of Materials 4

Question 1

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?

Accepted Answer

986 kN

Answer

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

Question 2

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

Accepted Answer

Zero normal stress, maximum shear stress

Answer

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

Question 3

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

Accepted Answer

Plane sections remain plane and the material is linearly elastic

Answer

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

Question 4

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

Accepted Answer

955 N·m

Answer

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

Question 5

Plane stress condition assumes which stress components are zero?

Accepted Answer

σ_z, τ_xz, and τ_yz

Answer

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

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