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BEAM-COLUMNS

BEAM-COLUMNS. PROF. V. KALYANARAMAN Department of Civil Engineering Indian Institute of Technology Madras Chennai 600036 email: kalyan@civil.iitm.ernet.in. DESIGN OF BEAM COLUMNS. INTRODUCTION SHORT & LONG BEAM-COLUMNS Modes of failure Ultimate strength

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BEAM-COLUMNS

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

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

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

  4. fy fy fy fy = + M fy fy fy fy fy Fc M Combined compression and bending, P & M Pcs Axial compression MP Bending moment SHORT BEAM-COLUMNS Pcs = Ag * fy MP = Z * fy P

  5. Short column loading curve Fc/Pcs F0/Pcs Fcl /Pcs Eqn. 3 M/Mp O Mmax/Mp 1.0 Mo/Mp M / MP  1.0 Fc / Pcs + 0.85 M / MP 1.0 Eqn 3 SHORT BEAM-COLUMNS 1.0 Failure envelope

  6. M0  M0 P * 0 Linear Non-Linear LONG BEAM COLUMNS Non – Sway Frame

  7. M 0 M0 LONG BEAM-COLUMNS Sway Frames

  8. M0/MP= 0.0 P/Pcr = 0.0 A 1.0 0.5 M0 0.1 P . Pcr 0.5 0.8 1.0 0.8  O  LONG BEAM-COLUMNS B

  9. Failure Envelope LONG BEAM-COLUMNS 1.0 Short column loading curve Fc/Pcs F0/Pcs Long columns loading curve Fcl /Pcs Eqn. 3 1.0 Mmax/Mp Mo/Mp M / MP

  10. After correcting for sway and bow (P- and P-) 1.0 Short column failure envelope Fc/Pcs After correction for (P-) effect Fcl/Pcs 1.0 Mx/Mpx Major axis bending SLENDER BEAM-COLUMNS Uniaxial Bending After correcting for sway and bow (P- and P-) 1.0 Short column failure envelope Fc/Pcs After correction for (P-) effect Fcl/Pcs A P*  P* 1.0 My/Mpy Minor axis bending

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

  12. Fcl/Pcs /r = 0 /r increases Mx/Mpx My/ Mpy Fig. 8 beam-columns under Biaxial Bending BEAM-COLUMNS / BIAXIAL BENDING

  13. DESIGN STRENGTH EQUATIONS Local Section Failure Overall Member failure

  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. 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

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