BME Advanced Mechanics 4

Question 1

The stress intensity factor K_I for a through-crack of half-length a in an infinite plate under remote stress σ is:

Accepted Answer

σ√(πa)

Answer

For a central through-crack in an infinite plate, K_I = σ√(πa), the fundamental result of linear elastic fracture mechanics.

Question 2

Which of the following correctly defines the term 'plane strain' condition?

Accepted Answer

Strain in one direction (usually z) is constrained to zero

Answer

Plane strain occurs in thick components where strain in the thickness direction (ε_z = 0) is constrained by the surrounding material.

Question 3

In the finite element method, the stiffness matrix [K] relates nodal forces to nodal displacements via [K]{u} = {F}. The stiffness matrix is always:

Accepted Answer

Symmetric and positive semi-definite before boundary conditions are applied

Answer

The global stiffness matrix is symmetric (from reciprocity) and positive semi-definite (singular until supports are applied to remove rigid body modes).

Question 4

A gear tooth experiences repeated bending stress that reverses each rotation. The appropriate design criterion is:

Accepted Answer

Endurance limit under fully reversed bending

Answer

Gear teeth undergo fully reversed (R = −1) cyclic bending, so the endurance limit (or corrected fatigue strength) governs design life.

Question 5

The principle of virtual work states that a body is in equilibrium if and only if:

Accepted Answer

Virtual work done by external forces equals virtual work done by internal forces for every admissible virtual displacement

Answer

The principle of virtual work (PVW) equates external and internal virtual work for any kinematically admissible virtual displacement, providing an equilibrium criterion.

BME - Bachelor of Mechanical Engineering Practice Test

BME - Bachelor of Mechanical Engineering Practice Test

BME Advanced Mechanics 4