EIT Statics, Dynamics & Mechanics of Materials 5

Question 1

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

Accepted Answer

Zero normal stress with maximum shear stress

Answer

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

Question 2

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

Accepted Answer

h/3

Answer

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

Question 3

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

Accepted Answer

4.0 m/s²

Answer

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

Question 4

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

Accepted Answer

EαΔT (compression)

Answer

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

Question 5

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

Accepted Answer

The centroidal axis and any parallel axis

Answer

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

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