Mechanics of Materials Flashcards

A cantilever beam of length L with a point load P at the free end has a maximum bending moment of:

Answer: PL at the fixed end

For a cantilever with tip load P, the maximum moment M = PL occurs at the fixed support.

Two bars made of different materials are connected in parallel (same strain) under an axial load. How is the load shared?

Answer: Proportional to each bar's axial stiffness (AE/L)

In a parallel assembly with equal deformation, load is distributed proportional to each member's stiffness k = AE/L.

A simply supported beam of span 6 m carries a uniformly distributed load of 10 kN/m. What is the maximum bending moment?

Answer: 45 kN·m

M_max = wL²/8 = 10 × 6² / 8 = 45 kN·m, occurring at mid-span.

The modulus of resilience for a material is best defined as:

Answer: The strain energy per unit volume at the yield point

Modulus of resilience = Sy²/(2E), representing the energy stored per unit volume at yielding.

A solid circular shaft of diameter 50 mm transmits a torque of 2 kN·m. What is the maximum shear stress?

Answer: approximately 81.5 MPa

τ = Tc/J = 2000 × 0.025 / (π × 0.05⁴/32) = 2000 × 0.025 / 6.136×10⁻⁷ ≈ 81.5 MPa.

Plane stress conditions are characterized by:

Answer: All stress components on one plane being zero (σ_z = τ_xz = τ_yz = 0)

In plane stress, stresses normal to one face (typically z) vanish: σ_z = τ_xz = τ_yz = 0.

For a statically indeterminate axial member problem, which additional condition is needed beyond equilibrium?

Answer: Compatibility (geometric constraint on deformation)

Indeterminate problems require a compatibility equation relating deformations to ensure geometric consistency.