1_-CABLES-AND-ARCHES.pptx

engineering

1. CABLES and ARCHES STRUCTURAL THEORY CIV 0314 - 4

2. Methods of Analysis for Statically Determinate Cables and Arches a. Cables Subjected to Concentrated Load b. Cables Subjected to Uniform Distributed Loads c. Three-Hinged Arch

3. CABLES are often used in engineering structures for support and to transmit loads from one member to another. When used to support suspension roofs, bridges, and trolley wheels, cables form the main load-carrying element in the structure.

4. Brooklyn Bridge Akashi-Kaikyo Bridge

5. Cables are perfectly flexible, resistance to shear and bending is small and may be neglected. Cables’ Assumptions 01 02 03 By means of cable flexibility, the force acting in the cable is always tangent to the cable at the point along its length. Cables are inextensible, its length is constant for both before and after the load is applied.

6. CABLES SUBJECTED TO CONCENTRATED LOADS When a cable of negligible weight supports several concentrated loads, the cable takes the form of several straight-line segments, each of which is subjected to constant tensile force.

7. Determine the value of h and the tension in each segment of the cable shown. Sample Problem No. 1

8. Solution:

9. at Point C:

10. at Point B:

11. SOLVING FOR h:

12. Sample Problem No. 2 Cable ABCD supports the 120-kg uniform beam. Determine the maximum tension in this cable and the sag at point B.

13. Consider the beam SOLUTION: Solving for CF Solving for BE

14. Solving for D = CD

15. Solving for A = AB

16. SOLVING FOR y B

17. Sample Problem No. 3 The cable supports the loading shown. Determine the magnitude of the horizontal force P so that x = 6m. 2 m 2 m 8 m 5 m 400 N

18. Solution: Joint B: TAB 400 lb TBC 2   2   2 2 8 8

19. Joint C: P TBC   2   5 2 8 6

20. CABLES SUBJECTED TO UNIFORMLY DISTRIBUTED LOADS Cables subjected to uniformly distributed loads are called parabolic cables . If a cable supports vertical load only, the horizontal component () of the cable tension is constant at all sections along the axis of the cable. The maximum tension occurs at supports where the cable slop is largest.

21. CABLES SUBJECTED TO UNIFORMLY DISTRIBUTED LOADS Tension at any point on the cable Equation of the parabola Slope at any point on the cable Maximum tension in the cable

22. Sample Problem No. 4 The cable is subjected to a uniform loading of w = 60 kN/m. Determine the maximum and minimum tension in cable.

23. Solution:

24. Sample Problem No. 5 The cable in the figure supports a girder which weighs 850 N/m. Determine the tension in the cable at points A , B , and C . 100 m 40 m 20 m

25. Equation of the cable: 40 m 100 m 20 m

26. At point C, x = x’ At point A, x = 100 - x’ 40 m 100 m 20 m

27. Slope equation: At point A, x = -58.58 40 m 100 m 20 m

28. At point B, x = 0 At point C, x = 41.42 20 m 100 m 40 m

29. The suspension bridge in the figure is constructed using the two stiffening trusses that are pin connected at their ends C and supported by a pin at A and a rocker at B . Determine the minimum and maximum tensions and the uniform load in the cable IH . The cable has a parabolic shape, and the bridge is subjected to the single load of 50 kN. Sample Problem No. 6

30. Arches Arches can be used to reduce the bending moments in long-span structures. Essentially, an arch acts as an inverted cable, so it receives its load mainly in compression although, because of its rigidity, it must also resist some bending and shear depending upon how it is loaded and shaped. Arches are used for buildings where large clear spans are required such as gymnasiums, churches, warehouse, & conventional halls.

31. A three-hinged arch is subjected to two concentrated loads, as shown in the figure. Determine the support reactions of the arch. Sample Problem No. 7

32. Consider the whole arch: Consider the segment CE:

33. Solving for Ex and Ey: Solving for Ax and Ay:

34. The three-hinged tied arch is subjected to the loading shown in the figure. Determine the force in members CH and CB. The dashed member GF of the truss is intended to carry no force. Sample Problem No. 8

35. Support Reactions:

36. Free body diagram of the left part of the arch:

37. Isolate joint G: Isolate joint C:

38. Sample Problem No. 9 Determine the magnitudes of the resultant forces at pin A,B and C of the three hinged-arched roof truss.

39. Solution:

40. Solution:

41. Solution:

42. Solution:

43. “Dreams are the trusses of our ambitions, the beams of our determination, and the cables that lift us to new heights. Keep building, keep rising.” Corocotchia , R.B.D, Gallarte, A.C., Licayan , J.Z., Venturina, R.A.V.