BCE Mechanics of Materials 3

Question 1

In the torsion formula τ = Tr/J, what does J represent?

Accepted Answer

Polar moment of inertia of the cross-section

Answer

J is the polar moment of inertia (second moment of area about the longitudinal axis), which governs resistance to torsion.

Question 2

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

Accepted Answer

πD⁴/32

Answer

J = πD⁴/32 for a solid circular shaft; note that the planar I = πD⁴/64 and J = 2I.

Question 3

Euler's formula for the critical buckling load of a column is:

Accepted Answer

Pcr = π²EI/(KL)²

Answer

Euler's critical load Pcr = π²EI/(KL)², where KL is the effective length accounting for end conditions and I is the minimum second moment of area.

Question 4

For a column with both ends pinned (pin-pin), the effective length factor K is:

Accepted Answer

1.0

Answer

A pin-pin column buckles in a single half-sine wave so its effective length equals its actual length, giving K = 1.0.

Question 5

The angle of twist φ (in radians) of a shaft of length L under torque T is given by:

Accepted Answer

φ = TL/GJ

Answer

φ = TL/(GJ), where G is the shear modulus (modulus of rigidity), L is the shaft length, and J is the polar moment of inertia.

BCE - Bachelor of Civil Engineering Practice Test