Beam design

Basic of reinforced concrete designs and singly,doubly reinforced beam design according to bs 8110

1. Design in reinforced concrete Prepared by: M.N.M Azeem Iqrah B.Sc.Eng ( Hons ), C&G ( Gdip ) Skills College of Technology

2. I n t r o d uction Reinforced concrete is a composite material, consisting of steel reinforcing bars embedded in concrete. Concrete has high compressive strength but low tensile strength. Steel bars can resist high tensile stresses but will buckle when subjected to comparatively low compressive stresses.

3. I n t r o d uction Steel bars are used in the zones within a concrete member which will be subjected to tensile stresses. Reinforced concrete is an economical structural material which is both strong in compression and in tension. Concrete provides corrosion protection and fire resistance to the steel bars.

4. Basic of design Two limit states design for reinforced concrete in accordance to BS 8110. Ultimate limit state – considers the behaviour of the element at failure due to bending, shear and compression or tension. The serviceability limit state considers the behaviour of the member at working loads and is concerned with deflection and cracking.

5. Material properties - concrete The most important property is the compressive strength. The strength may vary due to operation such as transportation, compaction and curing. Compressive strength is determined by conducting compressive test on concrete specimens after 28 days of casting. Two types of specimen: (1) 100 mm cube (BS standard), and (2) 100 mm diameter by 200 mm long cylinder.

6. Characteristic compressive strength of concrete Characteristic strength of concrete is defined as the value below which no more than 5 percent of the test results fall.,

7. Characteristic compressive strength (f cu ) of concrete Chanakya Arya, 2009. Design of structural elements 3 rd edition, Spon Press. Cylinder strength Cube strength Concrete strength classes in the range of C20/25 and C50/60 can be designed using BS 8110.

8. Stress-strain curve for concrete Stress strain curve for concrete cylinder (Chanakya Arya, 2009. Design of structural elements 3 rd edition, Spon Press.) Idealized stress strain curve for concrete in the BS8110

9. Material properties of steel Idealized stress-strain curve for steel. An elastic region, Perfectly plastic region (strain hardening of steel is ignored) BS 8110, 1997

10. Durability (clause 3.1.5, BS 8110) Durability of concrete structures is achieved by: The minimum strength class of concrete The minimum cover to reinforcement The minimum cement content The maximum water/cement ratio The cement type or combination The maximum allowable surface crack width

11. Fire protection (clause 3.3.6, BS8110) Fire protection of reinforced concrete members is largely by specifying limits for: Nominal thickness of cover to the reinforcement, Minimum dimensions of members.

12. Concrete cover for fire resistance BS 8110, 1997

13. Minimum dimension for reinforced concrete members for fire resistance BS 8110, 1997

14. Beams (clause 3.4, BS8110) Beams in reinforced concrete structures can be defined according to: Cross-section Position of reinforcement Support conditions

15. Beam design In ultimate limit state, bending is critical for moderately loaded medium span beams. Shear is critical for heavily loaded short span beams. In service limit state, deflection will be considered. Therefore, every beam must be design against bending moment resistance, shear resistance and deflection.

16. Types of beam by cross section Rectangular section L - s e c t i on T - s e c t i on L- and T-section beams are produced due to monolithic construction between beam and slab. Part of slab contributes to the resistance of beam. • Under certain conditions, L- and T-beams are more economical than rectangular beams.

17. Types of beam by reinforcement position Singly reinforced Doubly reinforced Singly reinforced – reinforcement to resist tensile stress. Doubly reinforced – reinforcement to resist both tensile and compressive stress. Compressive reinforcement increases the moment capacity of the beam and can be used to reduce the depth of beams.

18. Notation for beam (clause 3.4.4.3, BS 8110) b h d d’ A S A ’ S

19. Design for bending M ≤ Mu Maximum moment on beam ≤ moment capacity of the section The moment capacity of the beam is affected by: The effective depth, d Amount of reinforcement, Strength of steel bars Strength of concrete

20. Singly reinforced beam

21. Moment capacity of singly reinforced beam F cc F st z Force equilibrium F st = F cc F cc = stress x area = Moment capacity of the section

22. Singly reinforced beam If Then the singly reinforced section is sufficient to resist moment. Otherwise, the designer have to increase the section size or design a doubly reinforced section

23. Doubly reinforced beam If The concrete will have insufficient strength in compression. Steel reinforcement can be provided in the compression zone to increase compressive force. Beams which contain tension and compression reinforcement are termed doubly reinforced.

24. Doubly reinforced beam M = F sc (d-d’) + F cc z

25. Example 3.2 Singly reinforced beam (Chanakya Arya, 2009) A simply supported rectangular beam of 7 m span carries characteristic dead (including self-weight of beam), gk and imposed, qk, loads of 12 kN/m and 8 kN/m respectively. Assuming the following material strengths, calculate the area of reinforcement required.

26. Example 3.2 Singly reinforced beam (Chanakya Arya, 2009) Compression reinforcement is not required

27. Example 3.2 Singly reinforced beam (Chanakya Arya, 2009) Provide 4H20, (As = 1260 mm 2 )

28. Cross section area for steel bars (mm 2 )

29. Example 3.7 Doubly reinforced beam (Chanakya Arya, 2009) The reinforced concrete beam has an effective span of 9m and carries uniformly distributed dead load (including self weight of beam) and imposed loads as shown in figure below. Design the bending reinforcement.

30. Example 3.7 Doubly reinforced beam (Chanakya Arya, 2009)

31. Example 3.7 Doubly reinforced beam (Chanakya Arya, 2009) Compression reinforcement is required

32. Example 3.7 Doubly reinforced beam (Chanakya Arya, 2009)

33. Failure mode of beam in beam The failure mode of beam in bending depends on the amount of reinforcement. under reinforced reinforced beam – the steel yields and failure will occur due to crushing of concrete. The beam will show considerable deflection and severe cracking thus provide warning sign before failure. over-reinforced – the steel does not yield and failure is due to crushing of concrete. There is no warning sign and cause sudden, catastrophic collapse.

34. Shear (clause 3.4.5, BS8110) Two principal shear failure mode: diagonal tension – inclined crack develops and splits the beam into two pieces. Shear link should be provide to prevent this failure. diagonal compression – crushing of concrete. The shear stress is limited to 5 N/mm 2 or 0.8(f cu ) 0.5 .

35. Shear (clause 3.4.5, BS8110) The shear stress is determined by: The shear resistance in the beam is attributed to (1) concrete in the compression zone, (2) aggregate interlock across the crack zone and (3) dowel action of tension reinforcement.

36. Shear (clause 3.4.5, BS8110) The shear resistance can be determined using calculating the percentage of longitudinal tension reinforcement (100As/bd) and effective depth

37. Shear (clause 3.4.5, BS8110) The values in the table above are obtained based on the characteristic strength of 25 N/mm 2 . For other values of cube strength up to maximum of 40 N/mm 2 , the design shear stresses can be determined by multiplying the values in the table by the factor (f cu /25) 1/3 .

38. Shear (clause 3.4.5, BS8110)

39. Shear (clause 3.4.5, BS8110) When the shear stress exceeded the 0.5  c, shear reinforcement should be provided. Vertical shear link A combination of vertical and inclined bars.

40. Shear (clause 3.4.5, BS8110) • S v ≤ 0.75d

41. Example 3.3 Design of shear reinforcement (Chanakya Arya, 2009) Design the shear reinforcement for the beam using high yield steel fy = 500 N/mm 2 for the following load cases: qk = qk = 10 kN/m qk = 45 kN/m

42. Example 3.3 Design of shear reinforcement (Chanakya Arya, 2009)

43. Example 3.3 Design of shear reinforcement (Chanakya Arya, 2009)

44. Example 3.3 Design of shear reinforcement (Chanakya Arya, 2009)

45. Example 3.3 Design of shear reinforcement (Chanakya Arya, 2009) Provide nominal shear link = 0.3

46. The links spacing Sv should not exceed 0.75d (0.75*547 = 410 mm). Use H8 at 300 mm centres. Example 3.3 Design of shear reinforcement (Chanakya Arya, 2009)

47. Example 3.3 Design of shear reinforcement (Chanakya Arya, 2009) Case 3 (qk = 45 kN/m)

48. Example 3.3 Design of shear reinforcement (Chanakya Arya, 2009) Provide H8 at 150 mm centres. Nominal shear links can be used from mid-span to position v = 1.05 N/mm 2 , to produce an economical design Provide H8 at 300 mm centres. For 2.172 m either side from centres.

49. Reinforcement detailing. Example 3.3 Design of shear reinforcement (Chanakya Arya, 2009)

50. D e flection For rectangular beam, The final deflection should not exceed span/250 Deflection after construction of finishes and partitions should not exceed span/500 or 20mm, whichever is the lesser, for spans up to 10 m. BS 8110 uses an approximate method based on permissible ratios of the span/effective depth.

51. Deflection (clause 3.4.6.3) This basic span/effective depth ratio is used in determining the depth of the reinforced concrete beam.

52. Reinforcement details (clause 3.12, BS 8110) The BS 8110 spell out a few rules to follow regarding: Maximum and minimum reinforcement area Spacing of reinforcement Curtailment and anchorage of reinforcement Lapping of reinforcement

53. Reinforcement areas (clause 3.12.5.3 and 3.12.6.1, BS 8110) Minimum area of reinforcement is provided to control cracking of concrete. Too large an area of reinforcement will hinder proper placing and compaction of concrete around reinforcement. For rectangular beam with b (width) and h (depth), the area of tensile reinforcement, A s should lie: • 0.24% bh ≤As ≤ 4% bh • 0.13% bh ≤As ≤ 4% bh for fy = 250 N/mm 2 for fy = 500 N/mm 2

54. Spacing of reinforcement (clause 3.12.11.1, BS 8110) The minimum spacing between tensile reinforcement is provided to achieve good compaction. Maximum spacing is specified to control cracking. For singly reinforcement simply supported beam the clear horizontal distance between tension bars should follow: h agg + 5 mm or bar size≤ s b ≤ 280 mm f y = 250 N/mm 2 h agg + 5 mm or bar size≤ s b ≤ 155 mm f y = 500 N/mm 2 (h agg is the maximum aggregate size)

55. Curtailment (clause 3.12.9, BS 8110) The area tensile reinforcement is calculated based on the maximum bending moment at mid- span. The bending moment reduces as it approaches to the supports. The area of tensile reinforcement could be reduced (curtailed) to achieve economic design.

56. Curtailment (clause 3.12.9, BS 8110) Simply supp o r t ed beam Co n tinuous beam (Chanakya Arya, 2009)

57. Anchorage (clause 3.12.9, BS 8110) At the end support, to achieve proper anchorage the tensile bar must extend a length equal to one of the following: 12 times the bar size beyond the centre line of the support 12 times the bar size plus d/2 from the face of support (Chanakya Arya, 2009)

58. Anchorage (clause 3.12.9, BS 8110) In case of space limitation, hooks or bends in the reinforcement can be use in anchorage. If the bends started after the centre of support, the anchorage length is at least 4  but not greater than 12  . If the hook started before d/2 from the face of support, the anchorage length is at 8r but not greater than 24  .

59. Continuous L and T beam For continuous beam, various loading arrangement need to be considered to obtain maximum design moment and shear force.

60. Continuous L and T beam The analysis to calculate the bending moment and shear forces can be carried out by using moment distribution method Provided the conditions in clause 3.4.3 of BS 8110 are satisfied, design coefficients can be used.

61. Clause 3.4.3 of BS 8110: Uniformly-loaded continuous beams with approximately equal spans: moments and shears

62. L- and T- beam Beam and slabs are cast monolithically, that is, they are structurally tied. At mid-span, it is more economical to design the beam as an L or T section by including the adjacent areas of the slab. The actual width of slab that acts together with the beam is normally termed the effective flange.

63. L- and T-beam At the internal supports, the bending moment is reversed and it should be noted that the tensile reinforcement will occur in the top half of the beam and compression reinforcement in the bottom half of the beam.

64. Clause 3.4.1.5: Effective width of flanged beam Effective span – for continuous beam the effective span should normally taken as the distance between the centres of supports

65. L- and T- beam The depth of neutral axis in relation to the depth of the flange will influence the design process. The neutral axis When the neutral axis lies within the flange, the breadth of the beam at mid-span( b ) is equal to the effective flange width. At the support of a continuous beam, the breadth is taken as the actual width of the beam.