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1、MOMENT OF A COUPLE,Todays Objectives: Students will be able to a) define a couple, and, b) determine the moment of a couple.,In-Class activities: Check Homework Reading Review Applications Moment of a Couple Concept Review Group Problem Solving Attention Review,MOMENT OF A COUPLE,A couple is defined
2、 as two parallel forces with the same magnitude but opposite in direction separated by a perpendicular distance d.,The moment of a couple is defined as MO = F d (using a scalar analysis) or as MO = r F (using a vector analysis). Here r is any position vector from the line of action of F to the line
3、of action of F.,MOMENT OF A COUPLE (continued),The net external effect of a couple is that the net force equals zero and the magnitude of the net moment equals F d,Moments due to couples can be added using the same rules as adding any vectors.,Since the moment of a couple depends only on the distanc
4、e between the forces, the moment of a couple is a free vector. It can be moved anywhere on the body and have the same external effect on the body.,EXAMPLE - SCALAR APPROACH,Given: Two couples act on the beam and d equals 8 ft. Find: The resultant couple,1) Resolve the forces in x and y directions so
5、 they can be treated as couples. 2) Determine the net moment due to the two couples.,The x and y components of the top 60 lb force are: (4/5)(60 lb) = 48 lb vertically up (3/5)(60 lb) = 36 lb to the left Similarly for the top 40 lb force: (40 lb) (sin 30) up (40 lb) (cos 30) to the left,EXAMPLE - SC
6、ALAR APPROACH,EXAMPLE VECTOR APPROACH,Given: A force couple acting on the rod. Find: The couple moment acting on the rod in Cartesian vector notation.,1) Use M = r F to find the couple moment. 2) Set r = rAB and F = 14 i 8 j 6 k N . 3) Calculate the cross product to find M.,rAB = 0.8 i + 1.5 j 1 k m
7、 F = 14 i 8 j 6 k N,EXAMPLE VECTOR APPROACH,CONCEPT Review,1. F1 and F2 form a couple. The moment of the couple is given by _ . A) r1 F1 B) r2 F1 C) F2 r1 D) r2 F2,2. If three couples act on a body, the overall result is that A) the net force is not equal to 0. B) the net force and net moment are eq
8、ual to 0. C) the net moment equals 0 but the net force is not necessarily equal to 0. D) the net force equals 0 but the net moment is not necessarily equal to 0 .,GROUP PROBLEM SOLVING SCALAR APPROACH,Given: Two couples act on the beam. The resultant couple is zero. Find: The magnitudes of the force
9、s P and F and the distance d.,1) Resolve the 300 N force in x and y directions. 2) Determine the net moment. 3) Equate the net moment to zero to find d.,GROUP PROBLEM SOLVING SCALAR APPROACH,From the definition of a couple: P = 500 N and F = 300 N.,Resolve the 300 N force into vertical and horizonta
10、l components. The vertical component is (300 cos 30) N and the horizontal component is (300 sin 30) N.,Now solve this equation for d. d = (1000 + 60 sin 30) / (300 cos 30) = 3.96 m,GROUP PROBLEM SOLVING VECTOR APPROACH,Given: F = 25 k N and - F = - 25 k N Find: The couple moment acting on the pipe a
11、ssembly using Cartesian vector notation.,1) Use M = r F to find the couple moment. 2) Set r = rAB and F = 25 k N . 3) Calculate the cross product to find M.,rAB = - 350 i 200 j mm = - 0.35 i 0.2 j m F = 25 k N,=,GROUP PROBLEM SOLVING VECTOR APPROACH,ATTENTION Review,1. A couple is applied to the beam as shown. Its moment equals _ Nm. A) 50 B) 60 C) 80 D) 100,2. You can determine the couple moment as M = r F If F = -20 k lb, then r is A) rBC B) rAB C) rCB D) rAC,3,4,5,1m,2m,50 N,End of the Lecture,Let Learning Continue,
