1. 1 BEAM-COLUMNS PROF. V. KALYANARAMAN Department of Civil Engineering Indian Institute of Technology Madras Chennai 600036 email: kalyan@civil.iitm.ernet.in

2. 2 DESIGN OF BEAM COLUMNS INTRODUCTION SHORT & LONG BEAM-COLUMNS Modes of failure Ultimate strength BIAXIALLY BENT BEAM-COLUMNS DESIGN STRENGTH EQUATIONS Local Section Flexural Yielding Overall MemberFlexural Buckling STEPS IN ANALYSING BEAM-COLUMNS ANALYSIS EXAMPLE SUMMARY

3. 3 INTRODUCTION Causes Of Bending In Beam Columns x y z  Eccentric Compression  Joint Moments in Braced Frames Rigid  Sway Moments in Unbraced Frames  Biaxial Moments in Corner Columns of Frames

4. 4 SHORT BEAM-COLUMNS P cs = A g * f y M P = Z * f y P = P cs Axial compression M P Bending moment F c M Combined compression and bending, P & M fyfy fyfy fyfy fyfy fyfy fyfy f y fyfy fyfy + M

5. 5 SHORT BEAM-COLUMNS Failure envelope 1.0 O M o /M p M max /M p M/M p Short column loading curve F cl /P cs F 0 /P cs F c /P cs Eqn. 3 M / M P  1.0 F c / P cs + 0.85 M / M P  1.0 Eqn 3

6. 6 LONG BEAM COLUMNS Linear Non-Linear  00 M0M0 P *  M0M0 Non – Sway Frame

7. 7 LONG BEAM-COLUMNS Sway Frames 00  M0M0 M

8. 8 LONG BEAM-COLUMNS B M0M0 0.5 0.8 P/P cr = 0.0 1.0  0.8 O 1.0 P. P cr M 0 /M P = 0.0  A 0.1 0.5

9. 9 LONG BEAM-COLUMNS Long columns loading curve Short column loading curve F cl /P cs F 0 /P cs F c /P cs Eqn. 3 Failure Envelope M o /M p M max /M p M / M P 1.0

10. 10 SLENDER BEAM-COLUMNS A After correction for (P-  ) effect F c /P cs F cl /P cs M y /M py Short column failure envelope After correcting for sway and bow (P-  and P-  ) 1.0 P*  P*  Minor axis bending 1.0 Major axis bending M x /M px F c /P cs F cl /P cs After correction for (P-  ) effect Short column failure envelope After correcting for sway and bow (P-  and P-  ) 1.0 Uniaxial Bending

11. 11 SLENDER BEAM-COLUMNS A MxMx  M px P/P y < 0.25 P/P y >0.5 Short Column Slender Column Fig. 7 Beam-column Moment Rotation Behaviour O B C C’ F F’ F’’ E D

12. 12 BEAM-COLUMNS / BIAXIAL BENDING F cl /P cs M y / M py M x /M px Fig. 8 beam-columns under Biaxial Bending /r = 0 /r increases

13. 13 DESIGN STRENGTH EQUATIONS Local Section Failure Overall Member failure

14. 14 STEPS IN BEAM-COLUMN ANALYSIS Steps in Beam-Column Analysis  Calculate section properties  Evaluate the type of section  Check using interaction equation for section yielding  Check using interction equation for overall buckling

15. 15 SUMMARY Short Beam-Columns Fail by Section Plastification Slender Beam-Columns may Fail By  Section Plstification  Overall Flexural Yielding  Overall Torsional-Flexural Buckling Intetaction Eqs. Conservatively Consider  P-  and P-  Effects Advanced Analysis Methods Account for P-  and P-  Effects, directly & more accuraely