1. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 1 COLD FORMED STEEL SECTIONS - I

2. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 2 COLD FORMED STEEL SECTIONS- I  Introduction  Advantages of cold formed sections  Stiffened and unstiffened Elements  Local buckling, Effective width concepts  Beams  Design considerations: web crushing, web buckling and lateral buckling  Conclusion

3. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 3 INTRODUCTION –extensively used in building industry –manufactured by forming thin steel sheets in cold state –also called Light Gauge Steel Sections or Cold Rolled Steel Sections –number of pairs of rolls (called stages) depends on the complexity of the cross sectional shape –alternative method of forming is press – braking –galvanising provides protection against corrosion –normally, yield strength is at least 280 N/mm 2

4. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 4

5. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 5

6. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 6

7. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 7 ADVANTAGES Cross sectional shapes formed to close tolerances and can be consistently repeated for as long as required. Any desired shape of any desired length can be produced. Pre-galvanised or pre-coated metals have high resistance to corrosion, besides having an attractive surface finish. All conventional jointing methods, (i.e. riveting, bolting, welding and adhesives) can be employed. High strength to weight ratio. light and easy to transport and erect.

8. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 8 Typical Cold Formed Steel Profiles

9. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 9 - stiffened element - an element which is supported by webs along both its longitudinal edges. - unstiffened element - supported along one longitudinal edge only with the other parallel edge being free to displace - intermittently stiffened element - made of a very wide thin element divided into two or more narrow sub elements by the introduction of intermediate stiffeners, formed during rolling. Stiffened and Unstiffened Elements

10. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 10 Stiffened and Unstiffened Elements - 2 Stiffened and Unstiffened Elements Stiffened element Unstiffened element Intermediate stiffener Intermittently stiffened element Edge stiffened element Lips

11. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 11 LOCAL BUCKLING Elastic Buckling of Thin Plates A flat plate simply supported on all edges and loaded in compression will buckle at an elastic critical stress given by

12. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 12 Local Buckling- 2 Supported edge (a) Axially compressed plate simply supported on all edges (b) Axially compressed plate with one edge supported and the other edge free to move Supported edge Edge free to move

13. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 13 Local Buckling - 3 The technique of stiffening the element Unstiffened element with an edge free to move Internal element Section with unstiffened element Edges stiffened to prevent free movement Internal element with supported edges The same section with stiffened outstands Edge stiffened element

14. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 14 Local Buckling - 4 Post - Critical Behaviour   (c) Effective width M M (a) Buckled Shape   (b) Stress Distribution b Local Buckling Effects

15. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 15 Local Buckling - 5 flat plates would buckle instantaneously at the elastic critical load. Under incremental loading, plate elements which are not perfectly flat will begin to deform out of plane from the beginning rather than instantaneously at the onset of buckling and fail at a lower load. a non-uniform state of stress exists throughout the loading regime. This tendency is predominant in plates having b/t (breadth/thickness) ratios of 30-60. for plates having a b/t value in excess of 60, “membrane stresses” resist further buckling.

16. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 16 Local Buckling - 6 Mean stress Vs Lateral deflection relation Flat plates Plates with initial imperfections Lateral deflection  Mean stress p cr Initial imperfection

17. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 17 Local Buckling - 7 Effective Width Concept Lightly stressed regions at the centre are least effective. Regions near the supports are far more effective. The effective width, (b eff ) multiplied by the edge stress (  e ) is the same as the mean stress across the section multiplied by the total width (b) of the compression member.

18. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 18 The effective width of an element under compression is dependent on the magnitude of the applied stress f c, the b/t ratio of the element and the edge support conditions. BS 5950 Code Provisions when f c > 0.123 p cr, then when f c < 0.123 p cr, then b eff = b Local Buckling - 8

19. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 19 Local Buckling - 9 Ratio of effective width to flat width (f y = 280 N/mm 2 ) of compression plate with simple edge supports 50 100 150 200 250 b / t b eff / b 1.0 0.8 0.6 0.2 0.4

20. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 20 Local Buckling - 10 Buckling coefficient, K (BS 5950, Part 5) for channel element Lipped channel B1B1 B2B2 For the member having the width of B 1 For the member having the width of B 2 wh ere h = B 2 / B 1

21. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 21 Local Buckling - 12 2. Plain channel (without lips) for the element of width B 1 B1B1 B2B2 for the element of width B 2

22. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 22 Local Buckling - 13 Maximum width to thickness ratios (IS: 801 and BS 5950, Part 5 ) Stiffened elements with one longitudinal edge connected to a flange or web element and the other stiffened by a simple lip: 60 Stiffened elements with both longitudinal edges connected to other stiffened elements: 500 Unstiffened compression elements: 60

23. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 23 Local Buckling - 14 Treatment of Elements with Stiffeners Edge Stiffeners Elements having b/t  60 and provided with simple lip having one fifth of the element width may be regarded as a stiffened element If b/t > 60, then the lip itself may have stability problems. Therefore “compound” lips are designed.

24. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 24 Local Buckling - 15 Intermediate stiffeners The required minimum moment of inertia of the stiffener about the axis 0-0 w t o o Intermediate stiffener Intermediate stiffeners is used to transform a wide and ineffective element into highly effective element

25. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 25 Local Buckling - 17 Proportioning of Stiffeners Performance of unstiffened elements can be substantially improved by  introducing stiffeners such as lip.  introducing intermediate stiffeners.  According to BS 5950, an unstiffened element can be regarded as a stiffened element, when the lip or the edge stiffener has a moment of inertia about an axis through the plate middle surface equal to or greater than

26. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 26 Local Buckling - 18 The Indian standard IS: 801-1975 prescribes a minimum moment of inertia for the lip given by I min should not be less than 9.2 t 4. For a simple lip bent at right angles to the stiffened element, the required overall depth d min is given by d min should be less than 4.8 t

27. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 27 Local buckling - 19 Intermediate Stiffeners.  used to split a wide element into a series of narrower and therefore more effective elements. (For Equations, please refer the paper)

28. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 28 Beams Laterally stable beams - Beams, which do not buckle laterally. Designs may be carried out using simple beam theory, making modifications for local buckling of the webs. This is done by imposing a maximum compressive stress,(which may be considered to act on the bending element ) given by

29. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 29 Beams - 3 Other Beam Failure Criteria 1.Web Crushing Generally occurs under concentrated load or at support point when deep slender webs are employed. (a) Web crushing Space between bottom flange and supporting beam Web cleat used to avoid web crushing (b) Cleats to avoid web crushing Web crushing and how to avoid it

30. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 30 Beams - 3  Shear Buckling W Web buckling Thin webs subjected to predominant shear will buckle. The maximum shear in a beam web is invariably limited to 0.7 times yield stress in shear. In deep webs, where shear buckling can occur, the average shear stress (p v ) must be less than

31. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 31 Beams - 4 Lateral Buckling  The great majority of cold formed beams are (by design) restrained against lateral deflections.  Lateral buckling will not occur if the beam under loading bends only about the minor axis.  Lateral buckling occurs only in "long" beams and is characterised by the beam moving laterally and twisting when a transverse load is applied

32. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 32 Beams - 5 Lateral Buckling Bending and twisting

33. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 33 Beams - 6 The design approach is based on the "effective length" of the beam for lateral buckling, which is dependent on support and loading conditions. The elastic lateral buckling moment capacity, where, C b = 1.75 - 1.05  + 0.3  2  2.3.  = ratio of the smaller end moment to the larger end moment

34. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 34 Beams - 7 Single and Double Curvature Bending M  M Single Curvature M  M Double Curvature

35. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 35 Beams - 8 Perry-Robertson type equation is employed for evaluating the Moment Resistance of the beam M y = First yield moment given by the product of yield stress (f y ) and the Elastic Modulus (Z c ) of the gross section. M E = Elastic lateral buckling resistance moment  = Perry coefficient

36. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 36 CONCLUSION The difference between cold rolled steel and hot rolled steel has been discussed and the merits of the former are outlined The concepts of "effective width" and "effective section" employed in the analysis and design of cold rolled section are explained. The difference between "stiffened" and "unstiffened" elements is explained. Considerations in the design of cold rolled beams have been explained

37. ©Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 37 THANK YOU