
The magnitude of the couple (M) and direction of its axis after replacing two couples in to single equivalent couple.

Answer to Problem 3.79P
The magnitude of the couple (M) and direction of its axis
Explanation of Solution
Given information:
The two vertical forces
The inclined force acting at point B
The inclined force acting at point C
The force acting at the point E
The force acting at the point D
The height between point C and F (CF) is 120 mm.
The height between point F and A (FA) is 120 mm.
The horizontal distance between point E and D (ED) is 192 mm.
The height between point E and B (EB) is 144 mm.
The distance between point C and D (CD) is 160 mm.
Calculation:
Replace the couple in the ABCD plane with two couple’s P and Q.
Draw the couple ABCD by replacing with two couple’s P and Q as in Figure (1).
Calculate the distance CG using the Pythagoras theorem:
Substitute 160 mm for CD and 120 mm for CF.
Calculate the force (P) acting at the point B using the formula:
Substitute 50 N for
Calculate the force (Q) acting at the point C using the formula:
Substitute 50 N for
Calculate the angle
Substitute 144 mm for EB and 192 mm for ED.
Calculate the couple vector
Substitute 40 N for P, 120 mm for CF, 120 mm for FA, 30 N for Q, and 160 mm for CD.
Write the couple vector
Substitute
Calculate the couple vector
Substitute 12.5 N for
Write the couple vector
Calculate the position vector of BC
Substitute 160 mm for CD, 144 mm for EB, and 192 mm for ED.
Calculate the couple vector
Substitute
Calculate magnitude of the couple (M) using the relation:
Substitute
Calculate the direction of axis along x direction
Substitute
Calculate the direction of axis along y direction
Substitute
Calculate the direction of axis along z direction
Substitute
Thus, the magnitude of the couple (M) and direction of its axis
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Chapter 3 Solutions
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