WORLD FOR CIVIL

Statics & Strength of Materials

Problems Assignment - Frames 2

Draw a complete free body diagram as a part of the solution for each problem.

1. Determine the reaction at supports A and B of the beam in the diagram shown. Neglect the weight of the beam. (Ax = 938 lb., Ay = 728 lb., B = 814 lb.)

2. A 700 lb. weight is carried by a boom-and-cable arrangement, as shown in the diagram. Determine the force in the cable and the reactions at point A. (Ax = 404 lb., Ay = 296 lb., C = 572 lb.)

3. A brace is hinged at one end to a vertical wall and at the other end to a beam 14ft long. The beam weighs 250 lb. and is also hinged to a vertical wall as shown. The beam carries load of 500 lb. at the free end. What will be the compressive force in the brace, and what will be the values of the vertical and horizontal components of the reaction at hinge A? (Ax = 596 lb., Ay = 45 lb., B = 994 lb.)

4. A gate has a weight of 200 lb., which may be considered as uniformly distributed, see the diagram shown. A small boy weighing 95 lb. climbs up on the gate at the point B. What will be the reactions on the hinges? (Upper hinge horizontal force only = 318 lb., lower hinge horizontal force = 318 lb., vertical force = 295 lb.)

5. In an irrigation project, it was found necessary to cross low ground or else swing the canal to the left by cutting into the solid rock. It was decided to run the canal as a flume and support it on a number of frames as shown in the diagram. The two members rest in sockets in solid rock at points A and B. These sockets may be considered as hinges. What will be the vertical and horizontal components of the reactions at A and B? The weight of the water in the flume supported by each frame is estimated as 18,200 lb. (This is a somewhat more complicated problem then the others in this problem set, and it may be skipped. Or contact your instructor for hints.) (Ax = 6389 lb., Ay = 5093 lb., Bx = 6389 lb., By = 13, 107 lb.)

6. An Ocean liner has an arrangement for supporting lifeboats and for lowering them over the side as shown in the diagram. There is a socket at A and a smooth hole through the deck rail at B. If the boat and its load weigh 2,000 lb., what are the reactions at A and B? Two identical davits support each lifeboat. (Ay = 1000 lb., Ax = 1250 lb., Bx = 1250 lb.)

Answers: 1) Ax = 938 lb., Ay = 728 lb., B = 814 lb.; 2) Ax = 404 lb., Ay = 296 lb., C = 572 lb.; 3) Ax = 596 lb., Ay = 45 lb., B = 994 lb.; 4) Upper hinge horizontal force only = 318 lb., lower hinge horizontal force = 318 lb., vertical force = 295 lb.; 5) Ax = 6389 lb., Ay = 5093 lb., Bx = 6389 lb., By = 13, 107 lb.; 6) Ay = 1000 lb., Ax = 1250 lb., Bx = 1250 lb.