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

Second moment of area about the centroidal x-axis

Answer

Section modulus in torsion

Answer

Modulus of rigidity of the material

Question 2

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

Accepted Answer

πD⁴/32

Answer

πD⁴/64

Answer

πD³/16

Answer

πD⁴/16

Question 3

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

Accepted Answer

Pcr = π²EI/(KL)²

Answer

Pcr = π²EI/L²

Answer

Pcr = EI/L²

Answer

Pcr = πEI/(KL)²

Question 4

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

Accepted Answer

1.0

Answer

0.5

Answer

0.7

Answer

2.0

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/EJ

Answer

φ = GJ/TL

Answer

φ = TJ/GL

Question 6

When a structural member carries both an axial compressive load P and a bending moment M simultaneously, the critical total compressive stress is found by:

Accepted Answer

Adding P/A and My/I (principle of superposition)

Answer

Multiplying P/A by My/I

Answer

Subtracting My/I from P/A

Answer

Using only the larger of P/A or My/I

Question 7

The slenderness ratio of a column is defined as:

Accepted Answer

Effective length (KL) divided by radius of gyration (r)

Answer

Actual length divided by cross-sectional area

Answer

Axial load divided by Euler critical load

Answer

Cross-sectional area divided by moment of inertia