Design Of Continuous Beams 30_8.pptx

beamand column design

1. Design Of Continuous Beams Dr Sandip A Vasanwala ‹#›

2. Design of Continuous beam The design process of continuous beam is quite similar to that of simply-supported beam except that hogging moments at supports have to be designed for in continuous beam. For beam in building structures, sagging moment in the mid-span is usually resisted by flanged section while hogging moments in the supports are resisted by rectangular section ‹#›

3. Bending moment coefficients (Table 12, IS:456-2000) ‹#›

4. Shear force coefficients (Table 13, IS:456-2000) ‹#›

5. Design example Design 3 span continuous beam of typical interior idealize plane frame of a building The frames are spaced 5.5m apart and 140mm thick continuous slab is cast monolithically with beam. Thickness of floor finish is 40mm Size of column is 400mm x 400mm The beam has three equal span length of 6.1m (Effective Span) The floor has to support imposed load of 5 kN/m 2 at the service state. The unit weight of finishing material is 20 kN/m 3 M20 grade of concrete and HYSD steel of grade Fe415 to be used ‹#›

6. Design constants for M20 concrete and Fe415 grade steel are : f ck = 20 Mpa , f y = 415 Mpa , x u,max = 0.4791d M u,lim = 0.1388 x f ck x b x d 2 P t,lim = 0.961% ‹#›

7. Factored dead load from the slab and floor per meter run of beam is W us = 1.5 x (0.14 x 25 + 0.04 x 20) x 5.5 = 35.48 kN/m Factored live load from the slab is given by W ul = 1.5 x (5.0 x 5.5) = 41.25 kN/m Factored dead load of the web beam: (It is assumed as 5% of total of both loads) W uw = 0.05 x (W us + W ul ) = 0.05 x (35.48 + 41.25) = 3.84 kN/m Load calculations ‹#›

8. Total factored dead load per meter run of beam: W ud = W us + W uw = 39.32 kN/m Total factored load per meter run of beam: W u = W ud + W ul = 80.57 kN/m Note : The continuous beam sections at supports are generally doubly reinforced. Thus the depth of beam may be determined by considering it to be a doubly reinforced beam with about 60 to 65 % of design moment being resisted as a singly reinforced balance section Load calculations ‹#›

9. (a) : Elastic analysis with total w u on all span Here due to geometric symmetry the one cycle of MDM will be enough to obtain the results Maximum +ve and –ve BM, and reaction coefficients will be as follows All span carrying dead load simultaneously Pattern live load causing the worst effect Analysis : for comparison, the moment have been obtained by following methods 0.1 0.1 0.4 0.5 0.6 0.6 0.5 0.4 0.08 0.025 0.08 0.45 0.45 0.117 0.117 0.58 0.62 0.62 0.58 0.101 0.075 0.101 ‹#›

10. Span moments : End span M1 = 0.08 x w u x l 2 = 0.08 x 80.57 x 6.1 2 = 239.94 kN.m Interior span M2 = 0.025 x w u x l 2 = 0.025 x 80.57 x 6.1 2 = 74.95 kN.m Support moment: Interior support M3 = -0.1 x w u x l 2 = -0.1 x 80.57 x 6.1 2 = -299.80 kN.m ‹#›

11. (b) Elastic analysis with pattern loading In this method the maximum moments are obtained by superimposing the contributions of live and dead load acting seperately Total moments Span moments : End span M1 = 0.101 x w ul x l 2 + 0.08 x w ud x l 2 = 272.07 kN.m Interior span M2 = 0.075 x w ul x l 2 + 0.025 x w ud x l 2 = 151.70 kN.m Support moments: Interior support M3 = -0.117 x w ul x l 2 – 0.1 x w ud x l 2 = -325.89 kN.m ‹#›

12. [c] code specified coefficients (IS 456 table 12) Span moments: Support moments: ‹#›

13. The pattern loading method is more realistic and is consider to be more accurate. For this problem the moment obtained by code specified coefficient will be used. Consider b = 300 mm for singly reinforced section design and for a moment of 0.6 x 316.86 kN.m 0.6 x (316.86 x 10 6 ) = 0.1388 x f ck x b x d 2 = 0.1388 x 20 x 300 x d 2 d = 477.62 mm   consider 25mm # bars for reinforcement at nominal cover of 30mm D = 477.62 + 30 + (25 / 2) = 520.12mm So taking depth = 530mm and effective depth = 487.50mm ‹#›

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15. Design moments   ‹#›

16. Design for support moment   ‹#›

17.   Design for support moment ‹#›

18. Design for span moment   ‹#›

19. Design for span moment   ‹#›

20. Design for span moment   ‹#›

21. Design for span moment   ‹#›

22. Design for span moment   ‹#›

23. Check for serviceability requirement of deflection   ‹#›

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25. Curtailment of reinforcement   ‹#›

26. Check for development length   ‹#›

27. Check for development length   ‹#›

28. Design for shear force: End support   ‹#›

29. Design for shear force: End support   ‹#›

30. Design for shear force: Interior support   ‹#›

31.   Design for shear force: Interior support ‹#›

32. Simplified detailing scheme of reinforcement for a continuous beam ‹#›