Solved Example & Practice Problems: Moment of Force about a Line in Space

Moment of Force about a Line in Space

Solved Examples for Understanding

Example 3.12.1 

Find the resultant moment of the force system in Fig. 3.12.2 acting on a rectangular plate about a) X-axis b) Y axis c) Z-axis.

Solution: 

When forces are all parallel to one of the axis, moment about coordinate axis can be obtained by looking towards the origin along that axis and calculating moment. Treat anticlockwise moment positive.

⸫ Mx = 100 × 5 + 50 × 2.5 – 300 × 5 = 1875 Nm

 (Negative sign means clockwise moment)

My = 0 as all forces are parallel to Y-axis.

Mz = 200 × 4 – 50 × 4 + 300 × 8 = 3000 Nm

Example 3.12.2 

Determine the moment of force F shown in Fig. 3.12.3 about the line OA.

Solution : 

The required coordinates are A (6, 3, 0), B (4, − 1, 4), C (− 1, 6, 1)

The unit vector along OA is

Example 3.12.3 

A force acts at point C(1, 1, 1). Determine the C(1,1,1). moment of the force about line passing through A (2, 1, 2) and B(4,3,2)

Solution: 

Example 3.12.4 

If the magnitude of moment of about the line AB is 1000 Nm, determine the magnitude of . Refer Fig. 3.12.4.

Solution : 

Example 3.12.5 

Find the moment of the 10 kN force about an axis going between points D and C

Moment of F = 10 kN about line DC is

The co-ordinates of required points are

A (1, 0, 0), B (0, 2, 1), C (0, 2, 0) and D (1, 2, 1)

Examples for Practice

Q.1

Determine the moment of the force F shown in Fig. 3.12.6 about the line AB.

 [Ans.: 1.872-Nm]

Q.2

Determine the resultant moment of the force system shown in Fig. 3.12.7 about i) X-axis ii) Y-axis iii) Z-axis.

 [Ans. : MX = 2400 Nm, MY = 0, MZ = 7000 Nm]