Chapter 2 Review of Forces and Moments - Brown University

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2D Mickey Mouse problem 2 Mickey mouse of weight W M stands on a balcony of weight W B as shown. The weight of strut CB may be neglected. This time we need to deal with a structure that has two parts connected by a joint (the strut BC is connected to the floor AB through a pin joint). In cases like this you have a choice of (a) treating the two parts together as a single system; or (b) considering the strut and floor as two separate systems. As an exercise, we will draw free body diagrams for both here. 2L/3 L/3 Romeo, Romeo, wherefore art thou j Romeo? i A Pin joint B Pin joint 60 o C Pin joint 2L/3 L/3 A free body diagram for the balcony and strut together is shown on the right. Note again the convention used to denote the reactions: the first label denotes the location of the force, the second denotes the direction. Both A and C are pin joints, and therefore exert both horizontal and vertical forces. R Ax R Ay W B W M L/ 3 A B R cx C The picture shows free body diagrams for both components. Note the convention we’ve introduced to deal with the reaction force acting at B – it’s important to use a systematic way to deal with forces exerted by one component in a system on another, or you can get hopelessly confused. The recommended procedure is 1. Label the components with numbers – here the balcony is (1) and the strut is (2) 2. Denote reaction forces acting between components with the following convention. In the symbol R (1/ 2) Bx , the superscript (1/2) denotes that the variable signifies the force exerted by component (1) on component (2) (it’s easy to remember that (1/2) is 1 on 2). The subscript Bx denotes that the force acts at B, and it acts in the positive x direction. 3. The forces (1/ 2) (1/ 2) R Bx , R By exerted by component (1) on component (2) are drawn in the positive x and y directions on the free body diagram for component (2). 4. The forces exerted by component (2) on component (1) are equal and opposite to (1/ 2) R Bx , (1/ 2) R By . They are therefore drawn in the negative x and y directions on the free body diagram for component (1). You need to think of the reaction force components as acting in two directions at the same time. This is confusing, but that’s the way life is. R cy 2L/3 L/3 R Ax Ay A R (1) B R (1/2) Bx W B W M R (1/2) By R (1/2) Bx R (1/2) By (2) R cx L/ 3 C R cy
2.4.4 Reaction Forces and Moments associated with various types of joint Clamped, or welded joints No relative motion or rotation is possible. Reaction forces: No relative motion is possible in any direction. Three components of reaction force must be present to prevent motion in all three directions. Reaction moments: No relative rotation is possible about any axis. Three components of moment must be present to prevent relative rotation. The figure shows reaction forces acting on the two connected components. The forces and moments are labeled according to the conventions described in the preceding section. 2D versions of the clamped joint are shown below A A A j R Ax M Az i R (1/2) Ay R (1/2) Ax M (1/2) Az (2) R Ay (1) A M (1/2) Az R (1/2) Ax R (1/2) Ay Pinned joint. A pinned joint is like a door hinge, or the joint of your elbow. It allows rotation about one axis, but prevents all other relative motion. Reaction forces: No relative motion is possible at the joint. There must be 3 components of reaction force acting to prevent motion. Reaction moments: Relative rotation is possible about one axis (perpendicular to the hinge) but is prevented about axes perpendicular to the hinge. There must be two components of moment acting at the joint.
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Chapter 2 Review of Forces and Moments - Brown University

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