BME Advanced Mechanics 5

Question 1

Which theory of failure predicts that fracture occurs when the maximum principal stress reaches the uniaxial tensile strength, making it most suitable for:

Accepted Answer

Brittle materials like ceramics and cast iron

Answer

The maximum normal stress (Rankine) criterion applies to brittle materials because they fracture with minimal plastic deformation when the principal stress reaches the tensile strength.

Question 2

For a thick-walled cylinder under internal pressure p_i with inner radius a and outer radius b, the hoop stress is maximum at:

Accepted Answer

The inner surface (r = a)

Answer

By the Lamé equations, hoop stress decreases radially outward and is highest at the inner wall r = a.

Question 3

In torsion of non-circular cross-sections, Prandtl's stress function φ satisfies which governing equation?

Accepted Answer

∇²φ = −2Gθ (Poisson's equation)

Answer

Prandtl's stress function satisfies the Poisson equation ∇²φ = −2Gθ within the cross-section, with φ = 0 on the boundary.

Question 4

The Airy stress function approach in 2D elasticity ensures equilibrium automatically. The compatibility condition requires the Airy function φ to satisfy:

Accepted Answer

∇⁴φ = 0

Answer

The Airy stress function must satisfy the biharmonic equation ∇⁴φ = 0 in the absence of body forces to ensure strain compatibility.

Question 5

A shaft is subjected to combined bending moment M and torque T. The von Mises equivalent stress for design is:

Accepted Answer

√(σ² + 3τ²)

Answer

The von Mises criterion gives σ_eq = √(σ² + 3τ²) for combined normal stress σ and shear stress τ in a shaft.

BME - Bachelor of Mechanical Engineering Practice Test

BME - Bachelor of Mechanical Engineering Practice Test

BME Advanced Mechanics 5