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11. Method of Members

• Sometimes we must deal with structures that do not have simple two-force beams, in this case we must use the method of members.

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• These structures are commonly called frames, referring to the fact that they have at least one member that has more than two forces. We can see some examples of these members in the picture below,

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• In basic terms we are just making good use of free body diagrams, and quite often solving parametric equations. Consider how we could isolate the free body diagrams in the figures below.

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• If we were to assume that beams in a truss have a mass, then we would have to use the method of members to solve the problem.

• A sample problem is given to illustrate the method, ([Hibbeler, 1992], prob. 6-60, pg. )

Problem 11.1 For the structure to the right, find the reaction forces in all of the joints. You can use any methods (or combination) that you find suitable.

Problem 11.2 Determine the reactions at A and B.

• Sometimes these problems are made easier with Mathcad,

11.1 Problems
Problem 11.3 In the figure below, determine the force exerted by pin B. The method of members will be most useful.

Problem 11.4 What are the reactions on each of the members (clearly indicate the results on FBDs)?

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Answer 11.4 Ax=150N, Ay=150N, Bx=0, By=50N, Cx=150N, Cy=0, Dx=0, Dy=150N

Problem 11.5 Calculate the x- and y-components of the force at D which member AD exerts on member DE. The deflection of the spring in the equilibrium state shown is 2.5 inches. The mass of the members and friction are negligible.

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Answer 11.5 70.7N in both

Problem 11.6 The three member frame below is exposed to a load of L=60lb. The beams that the frame is made from weight 8lb/ft. Find the reaction at the base, and find the reaction at each joint and in each member.

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Answer 11.6

Problem 11.7 For the structure below, find the reaction forces in pins B and E.

Problem 11.8 Find the forces acting on DCBA at pin D,

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Answer 11.8 35.4 kip <135°

Problem 11.9 We work for a maker of hand tools, and today we are evaluating a new design for vice grip pliers. In the configuration pictured we want a gripping force of 50 lb. between the jaws. How much force P must be applied at the handles to achieve this?

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Answer 11.9 P = 12.9 lb

11.2 References
11.1 Hibbeler, R.C., Engineering Mechanics: Statics and Dynamics, 6th edition, MacMillan Publishing Co., New York, USA, 1992.

11.3 Summary
• A simple way to differentiate between the different methods is,

• You are encouraged to mix and match methods in any way that will simplify a solution. For example, in a couple of cases a problem that is being solved by the method of sections could easily use the method of joints in a couple of places.

11.4 REFERENCES
11.2 Soustas-Little, R.W. and Inman, D.J., Engineering Mechanics Statics, Prentice-Hall, 1997.