Solved Example & Practice Problems: Couple (in Mechanics)

Solved Examples for Understanding

Example 3.4.1 

Determine the moment of couple acting on the right square plate shown in Fig. 3.4.2.

Solution: 

Couple due to vertical forces,

Example 3.4.2 

A lug wrench is used to tighten a square head bolt. If 250 N force is applied to wrench as shown in Fig. 3.4.3. Determine the magnitude F of the equal force exerted on the four contact points on the 25 mm bolt head so that their external effect on the bolt is equivalent to that of the two 250 N forces. Assume that the forces are perpendicular to the flats of the bolt head.

Solution: 

The four forces on the bolt head will be as shown in Fig. 3.4.3 (a). The two 250 N forces applied on the wrench are equivalent to a couple producing a moment which must be equal to the moment produced by the four forces which are equivalent to two couples.

Example 3.4.3 

A plate ABCD in the shape of a parallelogram is acted upon by two couples, as shown in the Fig. 3.4.4. Determine the angle ẞ if the resultant couple is 1.8 Nm clockwise.

Solution: 

The moment of couple about any point in the plane is same.

Taking moment about B,

Example for Practice

Q.1

Determine the moment of the couple shown in Fig. 3.4.5.

[Ans. : 266.51 Nm ]