5.2 Rigid Bodies and Two-Dimensional Force Systems

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Berniece Cain
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1 5.2 Rigid odies and Two-Dimensional Force Systems

2 5.2 Rigid odies and Two-Dimensional Force Systems Procedures and Strategies, page 1 of 1 Procedures and Strategies for Solving Problems Involving Equilibrium of a Rigid ody in a Two-Dimensional Force System P 1. Draw a free-body diagram by showing all external forces: a) applied loads and couple moments b) weight of the body if the weight or mass is given c) reactions from the supports. If a constraint prevents motion in a certain direction, then show a reaction force acting in that direction on the free-body diagram. If a constraint prevents rotation about a certain axis, then show a reaction couple-moment on the free-body diagram. 2. Introduce sufficient dimensions on the diagram to allow for calculating the moments of forces. x y P 3. Write three equations of equilibrium. Notes: a) In writing moment equilibrium equations, remember that a couple moment can be considered to act anywhere on the free-body diagram. b) Do not show internal forces on a free-body diagram because they occur in equal and opposite sense and thus will cancel out. x P c) t most, three equations of equilibrium are independent. If you find that you have more unknowns than independent equations, then look for an error in your free-body diagram you may have made a mistake in representing the reaction forces from the supports. Do not write an additional equilibrium equation by, for example, summing moments about a new point. Such an equation will not be independent of the equilibrium equations that you have already written. x M y P

3 5.2 Rigid odies and Two-Dimensional Force Systems Problem Statement for Example 1 1. Determine the reactions at and. The weight of the rod is negligible. 3 ft 40 lb 3 ft 30 30

4 5.2 Rigid odies and Two-Dimensional Force Systems Problem Statement for Example 2 2. Determine the reactions at and. The weight of the rod is negligible. 5 ft 3 kip 4 ft 4 ft

5 5.2 Rigid odies and Two-Dimensional Force Systems Problem Statement for Example 3 3. Determine the reactions at supports and. 4 ft 400 lb 30 5 ft

6 5.2 Rigid odies and Two-Dimensional Force Systems Problem Statement for Example 4 4. The automobile shown is being pushed up the incline at a constant velocity by a force, P, from a tow truck. The 2,600-lb weight of the car acts at the center of gravity, O, and the friction forces acting on the wheels are negligible. Determine the force P and the forces from the ground acting on the individual tires. 20 in. O P 12 in in. 15 in.

7 5.2 Rigid odies and Two-Dimensional Force Systems Problem Statement for Example 5 5. Plate D is supported by cord E and a pin at. Determine the tension in the cord and the horizontal and vertical reactions at. The weight of the plate is negligible. E 4 kn D 20 2 m 5 kn m 3 m

8 5.2 Rigid odies and Two-Dimensional Force Systems Problem Statement for Example 6 6. Member has the shape of a quarter circle centered at O. Determine the reactions at each of the roller supports. O 3 ft lb 45

9 5.2 Rigid odies and Two-Dimensional Force Systems Problem Statement for Example 7 7. The end of pole D is buried deep in the ground. The tension in cable E is 2 kip and in cable F is 3 kip. Determine the reactions at. 2 ft D 6 kip 2 ft 5 ft E F 8 ft 12 ft

10 5.2 Rigid odies and Two-Dimensional Force Systems Problem Statement for Example 8 8. smooth slot has been cut in the plate shown, and a pin,, fixed to a support behind the plate, fits in the slot. Determine the forces acting on the plate at the supports and and from pin. 4 lb ft D ft 1.5 ft 2 lb 3 ft 2 ft

11 5.2 Rigid odies and Two-Dimensional Force Systems Problem Statement for Example 9 9. Pin is rigidly attached to the plate and can slide freely in the slot cut in member D. Determine the reaction force at the pin support at and the force transmitted at. 100 mm D mm E 12 N m

12 5.2 Rigid odies and Two-Dimensional Force Systems Problem Statement for Example Member D is supported by a pin at and a cord attached at and D. The cord passes over a frictionless pulley at. Determine the reaction at and the tension in the cord. 3 kn m D 2 m 2 m 3 m 5 kn

13 5.2 Rigid odies and Two-Dimensional Force Systems Problem Statement for Example The rigid bar is supported by two rollers attached to its ends at and. If the bar is in equilibrium in the position shown, determine the inclination,, of the inclined plane. 7 in. 20 lb 25 3 in.

14 5.2 Rigid odies and Two-Dimensional Force Systems Problem Statement for Example The uniform square plate of mass 10 kg is supported by a vertical cord at. Determine the tension in the cord and the forces from the walls if the walls are smooth at the contact points and. D 20

11.1 Virtual Work Procedures and Strategies, page 1 of 2

11.1 Virtual Work Procedures and Strategies, page 1 of 2 11.1 Virtual Work 11.1 Virtual Work rocedures and Strategies, page 1 of 2 rocedures and Strategies for Solving roblems Involving Virtual Work 1. Identify a single coordinate, q, that will completely define