6.5 Cables: Concentrated Loads

Transcription

1 6.5 ables: oncentrated Loads

2 6.5 ables: oncentrated Loads Procedures and Strategies, page 1 of 3 Procedures and Strategies for Solving Problems Involving ables With oncentrated Loads 1. Pass sections through the cable at points where something about the cable geometry is known. For example, consider the following situations: 4 m a) The location of a load point is known. Pass a section through the cable close to the point, draw a free-body diagram of either the portion of the cable to the left or to the right of the section, and write M = 0 about the point. This gives an equation involving the reaction components at one of the supports. Then writing three equilibrium equations for a free body of the entire cable will allow you to solve simultaneously for all reaction components x y Fx = 0 F y = 0 M = 0 4 m 3 kn x Three equations involving x, y, x, and y. T 3 kn 1.6 kn y Section M = 0 quation involving x and y only 3 kn 1.6 kn y x

3 6.5 ables: oncentrated Loads Procedures and Strategies, page 2 of 3 b) The horizontal and vertical distances between two adjacent load points are known. onsider a free body of the cable segment between the load points (o not include the load points in the free body.) and sum moments about either end to obtain an equation relating the x and y components of the tension in the cable segment. Next pass a section through the segment, and consider a free body of either the part of the cable to the left or right of the section. Write Fx = 0 and Fy = 0. These equations, together with three equilibrium equations for a free body of the entire cable, will allow you to solve for the support reactions. T x 1.5 m T y T y T x 1.5 m 3 kn 1.6 kn Section Point on just to left of Point on just to right of M = 0 quation involving T x and T y only. y x T y 3 kn T x Fx = 0 F y = 0 Two equations involving x, y, T x, and T y.

4 6.5 ables: oncentrated Loads Procedures and Strategies, page 3 of 3 2. Once the support-reaction components are known, you can determine the elevation of any load point by passing a section through the cable Now known near the load point, considering a free-body diagram of the part of the cable on either side of the section, and then writing M = 0 about the section. The unknown elevation will occur as a moment arm in this equation and can thus be found. x y y T M = 0 quation involving y.

5 6.5 ables: oncentrated Loads Problem Statement for xample 1 1. For the cable system shown, determine the reactions at support and the distance y. 4 m 2.5 m y 1.4 kn

6 6.5 ables: oncentrated Loads Problem Statement for xample 2 2. The horizontal force P is applied to end of the cable as shown. etermine the value of P and the distance d required to keep the cable system in the configuration shown. lso determine the total length of the cable. 4 m d 1 15 m P 3.5 kn

7 6.5 ables: oncentrated Loads Problem Statement for xample 3 3. The cable supports the 150 N and 500 N loads shown. etermine the distance x and the tension in each segment of the cable. 4 m 150 N 6 m 500 N x

8 6.5 ables: oncentrated Loads Problem Statement for xample 4 4. For the cable system shown, determine the distance y for which segment will be horizontal. lso determine y. y y kn 0.25 m 0.5 m

9 6.5 ables: oncentrated Loads Problem Statement for xample 5 5. For the cable system shown, determine the value of the forces P and P necessary to maintain the given configuration. P 5 m 200 N 7 m P 4 m 4 m

10 6.5 ables: oncentrated Loads Problem Statement for xample 6 6. For the cable system shown, determine distance y and the tension in each segment. 1.5 ft 3.5 ft y 50 lb 80 lb 2 ft 3.5 ft 5 ft

11 6.5 ables: oncentrated Loads Problem Statement for xample 7 7. The cable supports the four forces shown. etermine the maximum tension in the cable. 18 ft 18 ft 18 ft 18 ft 18 ft 15 ft 35 ft F 2 kip 2 kip 2 kip 2 kip

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