1. Section 9 Members subjected to Combined Forces (Beam-Columns)
Dr S R Satish Kumar
Dept. of Civil Engineering
I I T Madras, Chennai-36
Dr S R Satish Kumar, IIT Madras

2. SECTION 9 MEMBER SUBJECTED TO COMBINED FORCES
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
Dr S R Satish Kumar, IIT Madras

3. 9.2 Combined Shear and Bending
Secondary effects on beam behaviour
Elastic
Bending stress
Elastic Shear stress
Plastic range a b c
Dr S R Satish Kumar, IIT Madras

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
Dr S R Satish Kumar, IIT Madras

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
Dr S R Satish Kumar, IIT Madras

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
Dr S R Satish Kumar, IIT Madras

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
Dr S R Satish Kumar, IIT Madras

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
Dr S R Satish Kumar, IIT Madras

9. Non – Sway Frame LONG BEAM COLUMNS Mmax = Mo + P  M0 P * 0 Linear
Non-Linear
Mmax = Mo + P
Dr S R Satish Kumar, IIT Madras

10. Sway Frames 0  M0 M LONG BEAM-COLUMNS M = Mo + P
Dr S R Satish Kumar, IIT Madras

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
Dr S R Satish Kumar, IIT Madras

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
Dr S R Satish Kumar, IIT Madras

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
Dr S R Satish Kumar, IIT Madras

14. SLENDER BEAM-COLUMNS Mx  Mpx P/Py < 0.25 P/Py >0.5 Short Column
Slender Column
Fig. 7 Beam-column Moment Rotation Behaviour O B C C’ F F’
F’’ E D A
Dr S R Satish Kumar, IIT Madras

15. BEAM-COLUMNS / BIAXIAL BENDING
Fcl/Pcs
My/ Mpy
Mx/Mpx
Fig. 8 beam-columns under Biaxial Bending
/r = 0
/r increases
Dr S R Satish Kumar, IIT Madras

16. IS 800: 2007  Md 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
Bending and Axial Compression 
Dr S R Satish Kumar, IIT Madras

17. 9.3.2.2 Bending and Axial Compression
Cmy, Cmz = equivalent uniform moment factor as per table 18
Also CmLT
Dr S R Satish Kumar, IIT Madras

18. 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
Dr S R Satish Kumar, IIT Madras

19. 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
Dr S R Satish Kumar, IIT Madras