Statics, Dynamics & Mechanics of Materials Flashcards

Which stress state describes pure shear on an element rotated 45° from the principal planes?

Answer: Zero normal stress with maximum shear stress

At 45° from principal planes, normal stresses are zero and shear stress is at its maximum value τ_max = (σ₁–σ₂)/2.

The centroid of a triangle with base b and height h is located at what distance from its base?

Answer: h/3

The centroid of a triangle is at h/3 from the base (or 2h/3 from the apex), a standard result in statics.

A vehicle travels around a circular curve of radius 100 m at 20 m/s. What is its centripetal acceleration?

Answer: 4.0 m/s²

Centripetal acceleration aₙ = v²/r = (20)²/100 = 400/100 = 4.0 m/s².

Thermal stress in a fully restrained bar with temperature increase ΔT, coefficient α, and modulus E is:

Answer: EαΔT (compression)

When a bar is fully restrained and temperature rises, it wants to expand but cannot, creating compressive thermal stress σ = –EαΔT.

The parallel-axis theorem states that I = Ī + Ad², where d is the distance between:

Answer: The centroidal axis and any parallel axis

The parallel-axis theorem transfers moment of inertia from the centroidal axis Ī to any parallel axis at distance d: I = Ī + Ad².

In dynamics, the coefficient of restitution e = 1 describes a:

Answer: Perfectly elastic collision

e = 1 means the relative velocity of separation equals the relative velocity of approach — a perfectly elastic collision with no kinetic energy loss.

The flexure formula σ = Mc/I applies when:

Answer: The beam material is homogeneous, linearly elastic, and symmetric about the bending axis

The flexure formula assumes homogeneous, linearly elastic material with a symmetric cross-section and plane sections remaining plane (small deformation).