A couple is defined as two parallel forces that have the same magnitude, but opposite directions, and are separated by a perpendicular distance d, Fig. 4-25. Since the resultant force is zero, the only effect of a couple is to produce an actual rotation, or if no movement is possible, there is a tendency of rotation in a specified direction. For example, imagine that you are driving a car with both hands on the steering wheel and you are making a turn. One hand will push up on the wheel while the other hand pulls down, which causes the steering wheel to rotate. The moment produced by a couple is called a couple moment. We can determine its value by finding the sum of the moments of both couple forces about any arbitrary point. For example, in Fig. 4-26, position vectors Ta and rg are directed from point O to points A and B lying on the line of action of -F and F. The couple moment determined about O is therefore -F Fig. 4-25 -F м — Гр XF + гдх -F %3 (гр — г.)xF However rg = ra + r or r = rg – rA, so that Гв TA M = r x F (4–13) - 2 ft 3 ft- 50 lb 1 ft 30° 50 lb 80 lb 13 3 ft 80 lb -X- Probs. 4–79/80/81
A couple is defined as two parallel forces that have the same magnitude, but opposite directions, and are separated by a perpendicular distance d, Fig. 4-25. Since the resultant force is zero, the only effect of a couple is to produce an actual rotation, or if no movement is possible, there is a tendency of rotation in a specified direction. For example, imagine that you are driving a car with both hands on the steering wheel and you are making a turn. One hand will push up on the wheel while the other hand pulls down, which causes the steering wheel to rotate. The moment produced by a couple is called a couple moment. We can determine its value by finding the sum of the moments of both couple forces about any arbitrary point. For example, in Fig. 4-26, position vectors Ta and rg are directed from point O to points A and B lying on the line of action of -F and F. The couple moment determined about O is therefore -F Fig. 4-25 -F м — Гр XF + гдх -F %3 (гр — г.)xF However rg = ra + r or r = rg – rA, so that Гв TA M = r x F (4–13) - 2 ft 3 ft- 50 lb 1 ft 30° 50 lb 80 lb 13 3 ft 80 lb -X- Probs. 4–79/80/81
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
Related questions
Question
Two couples act on the frame. If d = 4 ft, determine
the resultant couple moment. Compute the result by
resolving each force into x and y components and (a) finding
the moment of each couple (Eq. 4–13) and (b) summing the
moments of all the force components about point A.
Transcribed Image Text:A couple is defined as two parallel forces that have the same magnitude,
but opposite directions, and are separated by a perpendicular distance d,
Fig. 4-25. Since the resultant force is zero, the only effect of a couple is to
produce an actual rotation, or if no movement is possible, there is a
tendency of rotation in a specified direction. For example, imagine that
you are driving a car with both hands on the steering wheel and you are
making a turn. One hand will push up on the wheel while the other hand
pulls down, which causes the steering wheel to rotate.
The moment produced by a couple is called a couple moment. We can
determine its value by finding the sum of the moments of both couple
forces about any arbitrary point. For example, in Fig. 4-26, position vectors
Ta and rg are directed from point O to points A and B lying on the line of
action of -F and F. The couple moment determined about O is therefore
-F
Fig. 4-25
-F
м — Гр XF + гдх -F %3 (гр — г.)xF
However rg = ra + r or r = rg – rA, so that
Гв
TA
M = r x F
(4–13)
Transcribed Image Text:- 2 ft 3 ft-
50 lb
1 ft
30°
50 lb
80 lb
13
3 ft
80 lb
-X-
Probs. 4–79/80/81
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