Advanced Mechanics Flashcards

A thin-walled pressure vessel with radius r and wall thickness t is subjected to internal pressure p. What is the hoop stress?

Answer: pr/t

Hoop (circumferential) stress in a thin-walled cylinder is σ_h = pr/t, twice the longitudinal stress.

In Euler-Bernoulli beam theory, which assumption is NOT made?

Answer: Large deflections are permitted

Euler-Bernoulli beam theory assumes small deflections; large-deflection problems require nonlinear analysis.

Which failure criterion is most appropriate for ductile metals under multiaxial loading?

Answer: von Mises (distortion energy) criterion

The von Mises criterion accurately predicts yielding in ductile metals by considering all stress components through the distortion energy.

A simply supported beam of length L carries a uniform distributed load w. The maximum bending moment occurs at:

Answer: x = L/2

For a uniformly loaded simply supported beam, the bending moment is parabolic and peaks at mid-span with M_max = wL²/8.

The polar moment of inertia J for a solid circular shaft of diameter d is:

Answer: πd⁴/32

J = πd⁴/32 for a solid circle; this quantity is used in the torsion formula τ = Tr/J.

Which of the following best describes the shear center of a cross-section?

Answer: The point through which a transverse load must act to produce no twisting

The shear center is the unique point where a transverse load causes pure bending without twisting of the beam.

Castigliano's second theorem states that the partial derivative of strain energy U with respect to a force P equals:

Answer: The deflection at the point and in the direction of P

Castigliano's second theorem: δ = ∂U/∂P, giving the displacement at the load's point of application in the direction of the load.