1. Section 9 Members subjected to Combined Forces (Beam-Columns)

2. SECTION 9 MEMBER SUBJECTED TO
IS 800: 2007
SECTION 9 MEMBER SUBJECTED TO
COMBINED FORCES
9.1 General
9.2 Combined Shear and Bending
9.3 Combined Axial Force and Bending Moment
Section Strength
Overall Member Strength

3. 9.2 Combined Shear and Bending
Secondary effects on beam behaviour
Elastic
Bending stress
Elastic Shear stress
Plastic range a b c

4. 9.2 Combined Shear and Bending
Sections subjected to HIGH shear force > 0.6 Vd
a) Plastic or Compact Section
b) Semi-compact Section
Mfd = plastic design strength of the area of c/s excluding the shear area and considering partial safety factor
V = factored applied shear force; Vd = design shear strength

5. 9.3 Combined Axial Force and Bending Moment 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 Member Flexural Buckling
STEPS IN ANALYSING BEAM-COLUMNS
SUMMARY

6. Occurrence of Beam Columns
INTRODUCTION
Occurrence of Beam Columns
Eccentric Compression
Joint Moments in Braced Frames Rigid
Sway Moments in Unbraced Frames
Biaxial Moments in Corner Columns of Frames x y z

7. Py = Ag*fy Mp = Zp*fy SHORT BEAM-COLUMNS = Py Axial compression MP
Bending
moment
Fc M
Combined compression and bending, P & M fy + M P
Py = Ag*fy Mp = Zp*fy

8. P/Py + M/Mp  1.0 (conservative)
SHORT BEAM-COLUMNS O
1.0
Mo/Mp
Mmax/Mp
M/Mp
Short column
loading curve
Pcl /Py
P0/Py
P/Py
M / MP  1.0
P / Py M / MP  1.0
P/Py + M/Mp  1.0 (conservative)
Failure envelope
1.0
M = P e

9. Non – Sway Frame LONG BEAM COLUMNS Mmax = Mo + P  M0 P * 0 Linear
Non-Linear
Mmax = Mo + P

10. LONG BEAM-COLUMNS
Sway Frames 0  M0 M
M = Mo + P

11. Cm accounts for moment gradient effects
LONG BEAM-COLUMNS M0
0.5
0.8
P/Pcr = 0.0
1.0  O
P .
Pcr
M0/MP= 0.0  A
0.1 B
Cm accounts for moment gradient effects

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

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

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

15. IS 800: 2007 9.3 Combined Axial Force and Bending Moment
9.3.1 Section Strength
Plastic and Compact Sections
Semi-compact section fx.  fy /m0
9.3.2 Overall Member Strength
Bending and Axial Tension 
 Md

16. 9.3.2.2 Bending and Axial Compression
Cmy, Cmz = equivalent uniform moment factor as per table 18
Also CmLT

17. 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
Beam-Column Design
using equivalent axial load

18. 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