6.6 Cables: Uniform Loads

Transcription

1 6.6 Cables: Uniform Loads

2 6.6 Cables: Uniform Loads Procedures and Strategies, page 1 of 3 Procedures and Strategies for Solving Problems Involving Cables With Uniform Loads 1. Draw a free-body diagram of the entire cable and write three equilibrium equations involving the four reaction components at the supports. 2 m 2. Obtain a fourth equation by using additional information given in the problem, such as the following: a) The location of the low point of the cable is specified. In this case, pass a section through the low point, consider a free body of the portion of the cable on one side of the section, and write M = 0 about the low point. 6 m Section through low point y w kn/m x 2 m To 6 m w

3 6.6 Cables: Uniform Loads Procedures and Strategies, page 2 of 3 b) The tension in the cable is known at a support. In this case, draw a free-body diagram of a short piece of cable at the support, and write Fx = 0 and F y = 0. c) The slope of the cable at a support is known. In this case, proceed as in case b). 3. Once the support reactions are known, you can solve for all other quantities such as cable tensions or the sag by considering free-body diagrams of the supports or of portions of the cable found by passing a section through the cable and isolating the portion on one side. T known, unknown, so one additional unknown and two additional equations. w kn/m y x T y known (slope = tan ), T unknown, so one additional unknown and two additional equations. T x

4 6.6 Cables: Uniform Loads Procedures and Strategies, page 3 of 3 Notes: a) You can solve most uniform-load cable problems by using free bodies and equilibrium equations only. You do not need to use the equation for the cable shape, y = wx 2 /(2To) (1) y Cable unless the cable length, s, is part of the problem, in which case you must use Eq. 1 together with the equation for calculating s. w ds = [(dx) 2 + (dy) 2 ] (2) In using Eq. 1, take into account that the origin of the xy-coordinate system is at the low point of the parabola, but the low point and hence the origin need not by part of the cable, since the cable coincides with only a part of the parabola. b) You can find the maximum tension in the cable by calculating the tension at the point where the slope is a maximum. c) In some problems you can save some work by using the fact that the horizontal component, To, of the cable tension is constant throughout the cable. Parabolic Curve y = wx 2 2T o x

5 6.6 Cables: Uniform Loads Problem Statement for Example 1 1. Each cable of the center span of the suspension bridge supports a uniform load of 10 kip/ft along the horizontal. If the span is 3,800 ft and the sag 400 ft, determine the maximum and minimum tensions in the cable ft 400 ft

6 6.6 Cables: Uniform Loads Problem Statement for Example 2 2. length of oil pipeline weighing 3200 lb is supported by a system of cables as shown. Determine a) the distance h to the lowest point C on the cable and b) the maximum tension in the cable. 8 ft h C 30 ft 50 ft

7 6.6 Cables: Uniform Loads Problem Statement for Example 3 3. n 18-lb washer load of wet beach-towels is hung on a clothesline to dry. Each beach towel is 72-in. long, and the clothesline is tied to supports located 75 in. above the ground. If the breaking strength of the clothesline is 280 lb, determine if the clothesline can be tightened enough to keep the middle towel from touching the ground. 28 ft 75 in 75 in

8 6.6 Cables: Uniform Loads Problem Statement for Example 4 4. Chains and C are attached to a roller support at as shown. The chains support beams that have mass per length of 0.5 kg/m. Determine the maximum tension in each chain and the sag s in chain C. 80 m 60 m 3 m s C 0.5 kg/m 0.5 kg/m

9 6.6 Cables: Uniform Loads Problem Statement for Example 5 5. Cable supports a uniformly distributed mass of 0.2 kg/m. The slope of the cable at is known to be 40. Determine the maximum tension in the cable and the length of the cable m 0.2 kg/m 3 m

10 6.6 Cables: Uniform Loads Problem Statement for Example 6 6. Determine the largest uniform load, w lb/ft, that the cable can support if it will fail at a tension of 3,000 lb. lso determine the location of the low point C of the cable. 4 ft 6 ft C w lb/ft 48 ft

11 6.6 Cables: Uniform Loads Problem Statement for Example 7 7. The cable system shown supports a uniformly distributed mass of 5 kg/m along the horizontal. Determine the tension at and the length of portion of the cable. ssume that the pulleys are frictionless. 100 kg 4 m 5 kg/m 20 m

12 6.6 Cables: Uniform Loads Problem Statement for Example 8 8. The chain supports a horizontal, uniform beam of mass per length 22 kg/m. If the maximum allowable tension in the chain is 7 kn, determine distances d and d of the supports above the low point C of the chain. lso determine the length of the chain. 30 m y 16 m d d C x 22 kg/m

13 6.6 Cables: Uniform Loads Problem Statement for Example m length of rope has a uniformly distributed mass of 0.1 kg/m and has one end fixed and the other end attached to a cart as shown. Determine the distance d and the sag h when the cable and cart are in equilibrium under the force supplied by the 10-kg load. d C h 10 kg

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