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4/28/2015 Secant Formula 1 of 62 Real engineers actually laugh at jokes about mathematicians.

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Presentation on theme: "4/28/2015 Secant Formula 1 of 62 Real engineers actually laugh at jokes about mathematicians."— Presentation transcript:

1 4/28/2015 Secant Formula 1 of 62 Real engineers actually laugh at jokes about mathematicians.

2 4/28/2015 Secant Formula 2 of 62

3 4/28/2015 Secant Formula 3 of 62

4 4/28/2015 Secant Formula 4 of 62

5 4/28/2015 Secant Formula 5 of 62 Ideal pin-ended compression members

6 4/28/2015 Secant Formula 6 of 62

7 4/28/2015 Secant Formula 7 of 62

8 4/28/2015 Secant Formula 8 of 62

9 4/28/2015 Secant Formula 9 of 62

10 4/28/2015 Secant Formula 10 of 62

11 4/28/2015 Secant Formula 11 of 62

12 4/28/2015 Secant Formula 12 of 62 EI

13 4/28/2015 Secant Formula 13 of 62

14 4/28/2015 Secant Formula 14 of 62

15 4/28/2015 Secant Formula 15 of 62

16 4/28/2015 Secant Formula 16 of 62

17 4/28/2015 Secant Formula 17 of 62 (with )

18 4/28/2015 Secant Formula 18 of 62

19 4/28/2015 Secant Formula 19 of 62

20 4/28/2015 Secant Formula 20 of 62

21 4/28/2015 Secant Formula 21 of 62

22 4/28/2015 Secant Formula 22 of 62

23 4/28/2015 Secant Formula 23 of 62

24 4/28/2015 Secant Formula 24 of 62

25 4/28/2015 Secant Formula 25 of 62

26 4/28/2015 Secant Formula 26 of 62

27 4/28/2015 Secant Formula 27 of 62

28 4/28/2015 Secant Formula 28 of 62

29 4/28/2015 Secant Formula 29 of 62 Remember: 2 plus 2 is four, but adding a safety factor we will call it 5.

30 4/28/2015 Secant Formula 30 of 62

31 4/28/2015 Secant Formula 31 of 62

32 4/28/2015 Secant Formula 32 of 62

33 4/28/2015 Secant Formula 33 of 62 Did they know that?

34 4/28/2015 Secant Formula 34 of 62

35 4/28/2015 Secant Formula 35 of 62

36 4/28/2015 Secant Formula 36 of

37 4/28/2015 Secant Formula 37 of 62

38 4/28/2015 Secant Formula 38 of 62

39 4/28/2015 Secant Formula 39 of 62

40 4/28/2015 Secant Formula 40 of 62

41 4/28/2015 Secant Formula 41 of 62 Oops: Collapse of the Second Narrows Bridge, Vancouver

42 4/28/2015 Secant Formula 42 of 62

43 4/28/2015 Secant Formula 43 of 62

44 4/28/2015 Secant Formula 44 of 62 4

45 4/28/2015 Secant Formula 45 of 62

46 4/28/2015 Secant Formula 46 of 62

47 4/28/2015 Secant Formula 47 of 62

48 4/28/2015 Secant Formula 48 of 62

49 4/28/2015 Secant Formula 49 of 62

50 4/28/2015 Secant Formula 50 of 62

51 4/28/2015 Secant Formula 51 of 62

52 4/28/2015 Secant Formula 52 of 62

53 4/28/2015 Secant Formula 53 of 62

54 4/28/2015 Secant Formula 54 of 62

55 4/28/2015 Secant Formula 55 of 62 Pre-stressed Concrete Stage 1 Tendons and reinforcement are positioned in the beam mould. Stage 2 Tendons are stressed to about 70% of their ultimate strength. Stage 3 Concrete is cast into the beam mould and allowed to cure to the required initial strength. Stage 4 When the concrete has cured the stressing force is released and the tendons anchor themselves in the concrete.

56 4/28/2015 Secant Formula 56 of 62 Prestressed Concrete

57 4/28/2015 Secant Formula 57 of 62 Post-tensioned Beams Stage 1 Cable ducts and reinforcement are positioned in the beam mould. The ducts are usually raised towards the neutral axis at the ends to reduce the eccentricity of the stressing force. Stage 2 Concrete is cast into the beam mould and allowed to cure to the required initial strength. Stage 3 Tendons are threaded through the cable ducts and tensioned to about 70% of their ultimate strength. Stage 4 Wedges are inserted into the end anchorages and the tensioning force on the tendons is released. Grout is then pumped into the ducts to protect the tendons.

58 4/28/2015 Secant Formula 58 of 62 Post-tensioned Beams

59 4/28/2015 Secant Formula 59 of 62 When the tensioning force is released and the tendons are anchored to the concrete a series of effects result in a loss of stress in the tendons. The effects are : relaxation of the steel tendons elastic deformation of the concrete shrinkage and creep of the concrete slip or movement of the tendons at the anchorages during anchoring other causes in special circumstances, such as when steam curing is used with pre-tensioning. Total losses in prestress can amount to about 30% of the initial tensioning stress. Loss of Prestress

60 4/28/2015 Secant Formula 60 of 62 Arrgggh, it’s over!

61 4/28/2015 Secant Formula 61 of 62 Burj Dubai Tower 800 metres (2,640 feet) tall Upward-spiral design Exterior cladding system Built of glass, aluminium, concrete, steel Designed by Skidmore, Owings & Merrill, Chicago Total floor space of 500,000 sq m (5.35 million sq ft)

62 4/28/2015 Secant Formula 62 of 62 Solution to Problem 3:


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