Concepts embedded in the draft IS:800 for Compression members TTTI-14.02.07

Behaviour of columns and their design TTTI-14.02.07

PTF=PEX or PTF=PEY or PTF=PT TYPES OF COLUMN BEHAVIOUR CG SC x0 y0 Doubly symmetric PTF=PEX or PTF=PEY or PTF=PT CG SC CG SC x0 Singly symmetric PTF=PEX+PT or PTF=PEY Unsymmetric PTF=PEX+PEY+PT TTTI-14.02.07

INTRODUCTION TO THE DESIGN OF AXIALLY LOADED COLUMNS Teaching Resources for Steel Structures INTRODUCTION TO THE DESIGN OF AXIALLY LOADED COLUMNS Dominant factors affecting ultimate strength of practical columns: Initial imperfection Eccentricity of loading Residual stresses Lack of defined yield point Strain hardening l/r ratio Material Yield stress TTTI-14.02.07 © IIT Madras, SERC Madras, Anna Univ., INSDAG Calcutta

INTRODUCTION (Contd…) Teaching Resources for Steel Structures INTRODUCTION (Contd…) x Typical column design curve c fy Test data (x) from collapse tests on practical columns Euler curve Design curve Slenderness  (/r) x x x x x x x 200 100 50 100 150 L. Euler TTTI-14.02.07 © IIT Madras, SERC Madras, Anna Univ., INSDAG Calcutta

Teaching Resources for Steel Structures HISTORICAL REVIEW PERRY ROBERTSON EQUATION - a factor defining initial imperfection and load eccentricity =y / r2 If =L/1000 then =0.001 y/r L / r =   where =0.0012 for x-x =0.002 for y-y TTTI-14.02.07 © IIT Madras, SERC Madras, Anna Univ., INSDAG Calcutta

Effect of  on the strength of columns  = 0.001  = 0.002 = 0.003  = 0.004 300 250 200 150 Compressive strength c (Mpa) fy 100 50 50 100 150 200 250 Slenderness,  TTTI-14.02.07

PERRY ROBERTSON APPROACH Teaching Resources for Steel Structures PERRY ROBERTSON APPROACH c fy  Euler curve Design curve with  = 0.003 200 100 50 100 150 Robertson’s Design Curve TTTI-14.02.07 © IIT Madras, SERC Madras, Anna Univ., INSDAG Calcutta

MODIFICATION TO THE PERRY ROBERTSON APPROACH Teaching Resources for Steel Structures MODIFICATION TO THE PERRY ROBERTSON APPROACH c  fy        200 100     Euler curve       Design curve with  = (-0)      0 50 100 150 Robertson’s Design Curve TTTI-14.02.07 © IIT Madras, SERC Madras, Anna Univ., INSDAG Calcutta

MULTIPLE COLUMN CURVES IN IS:800  = 0.002  = 0.0035 = 0.0055  = 0.008 (Curve A) (Curve B) (Curve C) (Curve D) 300 250 200 150 Compressive strength c (Mpa) fy 100 50 50 100 150 200 250 Slenderness,  TTTI-14.02.07

Teaching Resources for Steel Structures Rolled steel sections (b) Double Angle (c) Tee (d) Channel (e) Hollow Circular Section (CHS) (f) Rectangular Hollow Section (RHS) (a) Single Angle Cross Section Shapes for Rolled Steel Compression Members TTTI-14.02.07 © IIT Madras, SERC Madras, Anna Univ., INSDAG Calcutta

EFFECTIVE LENGTH OF COLUMNS Teaching Resources for Steel Structures EFFECTIVE LENGTH OF COLUMNS Column fixed at both ends : e = 0.7  Column fixed at one end and hinged at the other : e = 0.85 (Note: These values are NOT the same as those contained in IS: 800-1984 which suggests 0.80  and 0.65  respectively.) TTTI-14.02.07 © IIT Madras, SERC Madras, Anna Univ., INSDAG Calcutta

EFFECTIVE LENGTHS OF COLUMNS IN A FRAME  TTTI-14.02.07

DRAFT IS:800 CONTENTS Section 1 General Section 2 Materials Section 3 General Design Requirements Section 4 Methods of Structural Analysis Section 5 Limit States Design Section 6 Design of Tension Members Section 7 Design of Compression Members Section 8 Design of Members Subjected to Bending Section 9 Member Subjected to Combined Forces Section 10 Connections Section 11 Working Load Design Format Section 12 Design and Detailing for Earthquake Loads Section 13 Fatigue Section 14 Design Assisted by Testing Cont... TTTI-14.02.07

TTTI-14.02.07

SECTION 7 DESIGN OF COMPRESSION MEMBERS 7.1 Design Strength 7.2 Effective Length of Compression Members 7.3 Design Details 7.3.1 Thickness of Plate Elements 7.3.2 Effective Sectional Area 7.3.3 Eccentricity for Stanchions and Columns 7.3.4 Splices ]7.4 Column Bases 7.4.1 Gusseted Bases 7.4.2 Slab Bases 7.5 Angle Struts 7.5.1 Single Angle Struts 7.5.2 Double Angle Struts 7.5.3 Continuous Members 7.5.4 Combined Stresses Cont... TTTI-14.02.07

SECTION 7 DESIGN OF COMPRESSION MEMBERS 7.6 Laced Columns 7.6.1 General 7.6.2 Design of Lacings 7.6.3 Width of Lacing Bars 7.6.4 Thickness of Lacing Bars 7.6.5 Angle of Inclination 7.6.6 Spacing 7.6.7 Attachment to Main Members 7.6.8 End Tie Plates 7.7 Battened Columns 7.7.1 General 7.7.2 Design of Battens 7.7.3 Spacing of Battens 7.7.4 Attachment to Main Members 7.8 Compression Members Composed of Two Components Back-to-Back Cont... TTTI-14.02.07

APPENDIX E E.1 Method for Determining Effective Length of Columns in Frames E.2 Method For Determining Effective Length For Stepped Columns E.2.1 Single Stepped Columns E.3 Effective Length for Double Stepped Columns 7.1.2 The design compressive strength of a member is given by Pd = Ae fcd 7.1.2.1 The classification of different sections under different buckling class a, b, c or d, is given below. a b c d TTTI-14.02.07

λ = non-dimensional effective slenderness ratio, 7.1.2.2 The design compressive stress, fcd, of axially loaded compression members λ = non-dimensional effective slenderness ratio, fcc = euler buckling stress = 2E/(KL/r)2 Cont...  = 0.5[1+ ( - 0.2)+ 2] TTTI-14.02.07

c 7.6 Laced Columns 7.7 Battened Columns 7.6.1.5 The effective slenderness ratio, (KL/r)e, of the laced column shall be taken as 1.05 times the (KL/r)0, the actual maximum slenderness ratio in order to account for shear deformation effects. 7.7 Battened Columns 7.7.1.4 The effective slenderness ratio of battened column, shall be taken as 1.1 times the (KL/r)0, where (KL/r)0 is the maximum actual slenderness ratio of the column, to account for shear deformation effects. Cont... c TTTI-14.02.07

7.4.2 Slab Bases 7.5 Angle Struts 7.4.2.1 The minimum thickness, ts, of rectangular slab bases, supporting columns under axial compression shall be 7.5 Angle Struts 7.5.1.2 Loaded through one leg  k1, k2, k3 = constants depending upon the end condition and TTTI-14.02.07

STEPS IN THE DESIGN OF AXIALLY LOADED COLUMNS Teaching Resources for Steel Structures STEPS IN THE DESIGN OF AXIALLY LOADED COLUMNS Design steps: Assume a suitable trial section. Arrive at the effective area of the column Ae (No Classification) Arrive at the effective length of the column. Decide the appropriate column curve Calculate the slenderness ratio  and factor  Calculate fcd TTTI-14.02.07 © IIT Madras, SERC Madras, Anna Univ., INSDAG Calcutta

STEPS IN THE DESIGN OF AXIALLY LOADED COLUMNS Teaching Resources for Steel Structures STEPS IN THE DESIGN OF AXIALLY LOADED COLUMNS Calculate fcd values along both major and minor axes. Compute the load that the compression member can resist Ae fcd Check TTTI-14.02.07 © IIT Madras, SERC Madras, Anna Univ., INSDAG Calcutta

Summary Concepts which are embedded in the draft IS:800 has been briefly outlined. The limit state design appears to be a promise and it presents an open ended design route. TTTI-14.02.07