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IS:800 2007 LATERALLY UNSUPPORTED BEAMS Prepared by C.MAKENDRAN Assistant professor :

1 IS:800 2007 LATERALLY UNSUPPORTED BEAMS Prepared by C.MAKENDRAN Assistant professor

Slide2:

2 SECTION 8 DESIGN OF MEMBERS SUBJECTED TO BENDING 8.2.2 Laterally Unsupported Beams 8.3 Effective Length of Compression Flanges

LATERAL BUCKLING OF BEAMS :

3 LATERAL BUCKLING OF BEAMS FACTORS TO BE CONSIDERED Distance between lateral supports to the compression flange. Restraints at the ends and at intermediate support locations (boundary conditions). Type and position of the loads. Moment gradient along the unsupported length. Type of cross-section. Non-prismatic nature of the member. Material properties. Magnitude and distribution of residual stresses. Initial imperfections of geometry and eccentricity of loading.

END SUPPORT CONDITIONS:

4 END SUPPORT CONDITIONS Torsional (Rotational) Restraint: Warping Restraint: The end restraint elements shall be capable of safely resisting, in addition to wind and other applied external forces, a horizontal force acting in the plane in a direction normal to the axis of compression flange of the beam at the level of the centroid of the flange and having a value not less than 2.5 percent of the maximum compressive force occurring in the flange.

LATERAL TORSIONAL RESTRAINT AT SUPPORTS:

5 LATERAL TORSIONAL RESTRAINT AT SUPPORTS Bearing Stiffener

WARPING RESTRAINT AT SUPPORTS:

6 WARPING RESTRAINT AT SUPPORTS

EFFECTIVE LENGTH (Simply Supported):

7 EFFECTIVE LENGTH (Simply Supported) Effective Length of Compression Flanges Boundary Condition Effective Length (kL) Each end – torsional restraint L Full torsional and Partial Warping restraint 0.85 L Full Torsional & Warping Restraint 0.75 L

EFFECTIVE LENGTH (Cantilever):

8 EFFECTIVE LENGTH (Cantilever) kL = 0.85 L kL = 0.75 L kL = 0.5 L kL = L kL = 2 L kL = 3 L

LATERAL RESTRAINT:

9 LATERAL RESTRAINT Restraint against torsion in these beams can be provided by: web or flange cleats bearing stiffeners acting in conjunction with the bearing of the beam lateral end frames or external supports provide lateral restrain to the compression flanges at the ends Restraint Against Warping Being built into walls Flange rotationally restrained in plan by framing beams

INTERMEDIATE LATERAL SUPPORTS:

10 INTERMEDIATE LATERAL SUPPORTS Location of Lateral Restraints: At the location of plastic hinges At a distance from plastic hinges less than 0.4 l

INTERMEDIATE RESTRAINT:

11 INTERMEDIATE RESTRAINT Effective lateral restraint to the compression flange at intervals along the span shall be capable of resisting a force of 2.5 percent of the maximum force in the compression flange taken as divided equally between the number of points at which the restraint members occur. the sum of the restraining forces required shall be taken as 2.5 percent of the maximum flange force in one beam only. In the case of a series of latticed beams, girders or roof trusses which are connected together by the same system of restraint members, the sum of the restraining forces required shall be taken as 2.5 percent of the maximum force in the compression flange plus 1.25 percent of this force for every member of the series other than the first, up to a maximum total of 7.5 percent.

POSITION OF LOADS:

12 POSITION OF LOADS EFFECT OF MOMENT GRADIENT

TYPE OF CROSS SECTION:

13 TYPE OF CROSS SECTION Unsymmetric Section Non-Prismatic Member

ELASTIC LATERAL BUCKLING MOMENT:

14 ELASTIC LATERAL BUCKLING MOMENT

Slide15:

15 EFFECT OF RESIDUAL STRESSES & IMPERFECTIONS Rolled Welded

Slide16:

16 APPENDIX F ELASTIC LATERAL TORSIONAL BUCKLING F.1 Elastic Critical Moment F.1.1 Basic F.1.2 Elastic Critical Moment of a Section Symmetrical about Minor Axis 8.2 Design Strength in Bending (Flexure) The factored design moment, M at any section, in a beam due to external actions shall satisfy 8.2.1 Laterally Supported Beam The design bending strength as governed by plastic strength, M d , shall be taken as M d =  b Z p f y /  m0  1.2 Z e f y /  m0 8.2.1.4 Holes in the tension zone ( A nf / A gf )  ( f y /f u ) (  m1 /  m0 ) / 0.9 Cont...

Slide17:

17 8.2.2 Laterally Unsupported Beams The design bending strength of laterally unsupported beam is given by: M d =  b Z p f bd f bd = design stress in bending, obtained as , f bd =  LT f y /γ m0  LT = reduction factor to account for lateral torsional buckling given by:  LT = 0.21 for rolled section,  LT = 0.49 for welded section Cont…

Slide18:

18 8.2.2.1 Elastic Lateral Torsional Buckling Moment

SUMMARY:

19 SUMMARY Determine Torsional & Warping Supports Laterally Unsupported Length Spacing to ensure the Laterally supported beam behaviour Strength to ensure laterally adequate support Determination of Section Properties Determination of other effects Determination of Elastic Critical Moment Capacity Determination of Design Strength using imperfection Parameter

Slide20:

20 Thank You

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