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1. Beams

2. BEAMS A structural member loaded in the transverse direction to the longitudinal axis. The beams are designed for maximum BM and checked for maximum SF, local effects such as vertical buckling and crippling of webs and deflection Internal Forces: Bending Moments and Shear

3. Support Floor Deck

4. Floor Beams Beams that support joists

5. Floor Beams

6. Girders: Support most load in a floor system

7. Over Windows and Door Openings Support portion of wall above opening

8. Purlins Support Roof Surface

9. Roof Beams

10. Spandrel Beams Support outside edges of a floor deck and outside walls of buildings

11. 12 2.0 1.7 1.27 1.14 1.5 Some typical shape factor

12. Types of beam cross sections I sections are used for normal spans and loadings with all the geometrical properties available in IS 800 : 2007.

13. I section with cover plates are used when the loads are heavy and the spans are large. Additional cover plates increases the lateral load resistance with increase

14. Two I sections with cover plates can be used when very heavy loads and spans act on the beam.

15. Two I sections placed one above the other are used when the loads are light with large spans , where deflection is the main criteria Design own design

16. Gantry girders are used in industrial buildings to lift loads and typical sections

17. C/S OF PLATE GIRDERS Plate girders are used where the spans exceed 20m and the loads are heavy

18. Castellated beams are special sections fabricated from I sections and are used for light loads and large spans

19. Box sections have large torsional rigidity and can be used as single cell, twin cellor multi - cell sections.

20. Limit States Flexure Elastic Plastic Stability (buckling) Shear Deflection Fatigue Supports

21. 22 Limit states for LR beams Limit state of flexure Limit state of shear Limit state of bearing Limit state of serviceability

22. Structural Steel – expected failures Buckling: Instability due to slenderness

23. Elastic Buckling

24. Elastic failure

25. Lateral Stability of Beams A beam transversely loaded in its own plane can attain its full capacity (Plastic moment) only if local and lateral instabilities are prevented Local buckling of beams can be due to web crippling and web buckling. Lateral stability of beams is affected by span of the beam, moment of inertia and the support conditions .

26. 27 Lateral Stability of Beams

27. Factors affecting lateral stability Type of C/S Support conditions Effective length

28. Few minor failures

29. Local failures of flanges (Secondary design checks The local failure of flanges (plates) reduces the plastic moment capacity of the section due to buckling and is avoided by limiting the outstand to thickness ratios as given in IS 800: 2007 .

30. Local failures of web (Secondary design checks The web of a beam is thin and can fail locally at supports or where concentrated loads are acting. There are two types of web failure – Web Crippling (or Crimpling) Web Buckling

31. Web Crippling (or Crimpling) Web crippling causes local crushing failure of web due to large bearing stresses under reactions at supports or concentrated loads. Web crippling is the crushing failure of the metal at the junction of flange and web. Web crippling causes local buckling of web at the junction of web and flange.

32. 33 Shear yielding near support Web buckling Web crippling

33. Web Buckling The web of the beam is thin and can buckle under reactions and concentrated loads with the web behaving like a short column fixed at the flanges.

34. 35 45 d / 2 d / 2 b 1 n 1 Effective width for web buckling

35. 36 b 1 n 2 1:2.5 slope Root radius Effective width of web bearing Web Crippling in beams

36. 37

37. Shear lag effects In simple theory of bending, plane sections remain plane before and after bending require that no SF is present in the beam This results in non uniform distribution of flexural stresses in the flanges with stress being greater at the junction of flange and web. This is known as shear lag effect.

38. Section Classification There are four classes of section namely Plastic, Compact, Semi - Compact and Slender sections as given in IS 800 : 2007. [cl. 3.7.2 pp - 17] For design of beams, only Plastic and Compact sections are used.

39. 41 Moment ‘M’ Curvature M Y Moment curvature characteristics of the simply supported beam Yield moment M P Plastic moment Effect of strain hardening may occur after large rotation

40. 42

41. 43

42. Main failure modes of hot-rolled beams

43. 48 DESIGN OF FLEXURAL MEMBER AND BENDING WITH HIGH SHEAR

44. Types of beams 1.Laterally Supported (Restrained) beams 2.Laterally unsupported beams (unrestrained)

45. 1.Laterally Supported (Restrained) beams Beams subjected to BM develop compressive and tensile forces and the flange subjected to compressive forces has the tendency to deflect laterally. This out of plane bending is called lateral bending or buckling of beams . The lateral bending of beams depends on the effective span between the restraints, minimum moment of inertia (IYY)and its presence reduces the plastic moment capacity of the section. Beams where lateral buckling of the compression flange are prevented are called laterally restrained beams

46. 2.Laterally unsupported beam Beams subjected to BM develop compressive and tensile forces and the flange subjected to compressive forces has the tendency to deflect laterally. This out of plane bending is called lateral bending or buckling of beams. Lateral buckling of beams involves three kinds of deformations namely lateral bending, twisting and warping

47. Behaviour of beams If the web is too thin, the beam can fail in shear due to diagonal compression . The beam can also fail due to local effects such as web buckling, web crippling or distortion of flanges if these effects are not considered in the design. If the beam is not restrained laterally, the beam can undergo elastic lateral torsional buckling and can fail due to instability with large lateral deflections, rotations and warping.

48. Shear strength of Beams Shear forces always exists with BMs and the maximum shear stress has to be checked with the shear yield stress ..

49. Maximum Deflection Excessive deflection causes problems in the functioning of the structure. It can harm floor finishes, cause cracks in partitions and excessive vibrations in industrial buildings and ponding of water in roofs. Cl.5.6. 1, 5.6.1.1 and Table 6 gives relevant specifications

50. 59 1 2 3 4 Plastic Hinge Simply supported beam and its deflection at various stages W

51. 60 Table showing Partial safety factors for materials γ m

52. 61 Flexural members Laterally supported beam Elastic Analysis Plastic Analysis When factored design shear ≤ 0.6V d and

53. 62 Local Buckling In IS:800 (1984) the local buckling is avoided by specifying b/t limits. Hence we don’t consider local buckling explicitly However in IS:800(2007) limit state design, the local buckling would be the first aspect as far as the beam design is concerned How do we consider? By using section classification

54. 63 DESIGN OF BEAM COLUMN Combined action of bending and axial force (tension or compression) occurs in following situations. Any member in a portal frame. Beam transferring reaction load to column. Effect of lateral load on a column due to wind, earthquake Effect of eccentric load by crane loading due to bracket connection to column. In case of principal rafter, purlins not placed exactly over joint of roof truss.

55. 64 IS : 800 – 2007 CODAL PROVISIONS Minimum eccentricity of load transferred by beam to column is specified by clause 7.3.3 (p. no. 46) Section-9, Member subjected to combined forces. clause 9.3 for combined axial force and bending moment (p. no. 70) recommends check for section a) By material failure clause 9.3.1 b) By overall buckling failure clause 9.3.2