1. SECTION 7 DESIGN OF COMPRESSION MEMBERS
IS 800: 2007
SECTION 7 DESIGN OF COMPRESSION MEMBERS
Dr S R Satish Kumar
Department of Civil Engineering
IIT Madras Chennai
© Dr S R Satish Kumar, IIT Madras

2. INTRODUCTION TO COLUMN BUCKLING
Elastic buckling of an ideal column
Strength curve for an ideal column
Strength of practical column
Concepts of effective lengths
Torsional and torsional-flexural buckling
Conclusions

3. INTRODUCTION Compression members: short or long
Squashing of short column
Buckling of long column
Steel members more susceptible to buckling compared to RC and PSC members

4. ELASTIC BUCKLING OF EULER COLUMN
Assumptions:
Material of strut - homogenous and linearly elastic
No imperfections (perfectly straight)
No eccentricity of loading
No residual stresss

5. ELASTIC BUCKLING OF EULER COLUMN
The governing differential
equation is
Lowest value of the critical load

6. STRENGTH CURVE FOR AN IDEAL STRUT
axially loaded initially straight pin-ended column B 1 f y A l c = /r
Plastic yield defined by s
Elastic buckling ( cr )
defined by p 2 E / C
Column fails when the compressive stress is greater than or equal to the values defined by ACB.
AC  Failure by yielding (Low slenderness ratios)
CB  Failure by bucking (  c )

7. STRENGTH CURVE FOR AN IDEAL STRUT/ f f y
Plastic yield
Elastic buckling
1.0 l
1.0
= ( f / s )
1/2 y cr
Strength curve in a non-dimensional form

8. FACTORS AFFECTING STRENGTH OF A COLUMN IN PRACTICE:
Effect of initial out of straightness
Effect of eccentricity of applied loading
Effect of residual stress
Effect of a strain hardening and the absence of clearly defined yield point
Effect of all features taken together

9. Residual Stresses

10. Effect of all features taken together

11. 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
Eccentricity for Stanchions and Columns
Splices
]7.4 Column Bases
Gusseted Bases
Slab Bases
7.5 Angle Struts
Single Angle Struts
Double Angle Struts
Continuous Members
Combined Stresses Cont...
© Dr S R Satish Kumar, IIT Madras

12. SECTION 7 DESIGN OF COMPRESSION MEMBERS
7.6 Laced Columns
General
Design of Lacings
Width of Lacing Bars
Thickness of Lacing Bars
Angle of Inclination
7.6.6 Spacing
Attachment to Main Members
End Tie Plates
7.7 Battened Columns
7.7.1 General
Design of Battens
Spacing of Battens
Attachment to Main Members
7.8 Compression Members Composed of Two Components
Back-to-Back end
© Dr S R Satish Kumar, IIT Madras

13. INTRODUCTION
Dominant factors affecting ultimate strength of columns subjected to axial compressive loading:
Slenderness ratio (/r)
Material yield stress (fy)
Dominant factors affecting ultimate strength of practical columns:
Initial imperfection
Eccentricity of loading
Residual stresses
Lack of defined yield point
Strain hardening
© Dr S R Satish Kumar, IIT Madras

14. Typical column design curve
INTRODUCTION c fy
Test data (x) from collapse tests
on practical columns
Euler curve
Design curve
Slenderness  (/r) x
x x
x x x
x x
200
100
Typical column design curve
© Dr S R Satish Kumar, IIT Madras

15. Cross Section Shapes for Rolled Steel Compression Members
(a) Single Angle
(b) Double Angle
(c) Tee
(d) Channel
(e) Hollow Circular
Section (CHS)
(f) Rectangular Hollow
Section (RHS)
© Dr S R Satish Kumar, IIT Madras

16. (f) Built-up Box Section
Cross Section Shapes for Built - up or
fabricated Compression Members
(b) Box Section
(c) Box Section
(d) Plated I Section
(e) Built - up I Section
(f) Built-up Box Section
(a) Box Section
© Dr S R Satish Kumar, IIT Madras

17. 7.1 DESIGN STRENGTH
The design compressive strength of a member is given by
 = 0.5[1+ ( - 0.2)+ 2]
fcd = the design compressive stress,
λ = non-dimensional effective slenderness ratio,
fcc = Euler buckling stress = 2E/(KL/r)2
= imperfection factor as in Table 7
 = stress reduction factor as in Table 8
© Dr S R Satish Kumar, IIT Madras

18. Table 10 Buckling Class of Cross-sections
Limits
Buckling about axis
Buckling Curve
Rolled I-Sections
h/b > 1.2 : tf 40 mm
 40 < tf <100
z-z
y-y a b  b c
Welded I-Section
tf <40 mm
tf >40 mm
 z-z  c d
Hollow Section
Hot rolled
Cold formed
Any
Welded Box Section, built-up
Generally
Channel, Angle, T and Solid Sections
© Dr S R Satish Kumar, IIT Madras

19. 7.1 DESIGN STRENGTH a b c d
© Dr S R Satish Kumar, IIT Madras

20. 7.2 Effective Length of Compression Members (Table 11)
Boundary Conditions
Schematic represen
-tation
Effective Length
At one end
At the other end
Translation
Rotation
Restrained
Free
2.0L
1.0L
1.2L
0.8L
0.65 L
© Dr S R Satish Kumar, IIT Madras

21. 7.4 COLUMN BASES 7.4.2 Gusseted Bases 7.4.3 Slab Bases b a 2c+tf 2c+tw
© Dr S R Satish Kumar, IIT Madras

22. STEPS IN THE DESIGN OF AXIALLY LOADED COLUMNS
Design steps:
Assume a trial section of area A = P/150
Make sure the section is at least semi-compact !
Arrive at the effective length of the column.
Calculate the slenderness ratios.
Calculate fcd values along both major and minor axes.
Calculate design compressive strength Pd = (fcd A).
Check P < Pd
© Dr S R Satish Kumar, IIT Madras

23. BEHAVIOUR OF ANGLE COMPRESSION MEMBERS
Angles under compression
Concentric loading - Axial force
1. Local buckling
2. Flexural buckling about v-v axis
3. Torsional - Flexural buckling about u-u axis
Eccentric loading - Axial force & bi-axial moments
Most practical case
May fail by bi-axial bending or FTB
(Equal 1, 2, 3 & Unequal 1, 3) V U
© Dr S R Satish Kumar, IIT Madras

24. Basic compressive strength curve
7.5 ANGLE STRUTS
Basic compressive strength curve
Curve C of Eurocode 3
Slenderness Ratio:
concentric loading kL/r
Single leg Connection (kl/r)eq
Equivalent normalised slenderness ratio
Where, k1, k2, k3 are constants to account for different end conditions and type of angle.
© Dr S R Satish Kumar, IIT Madras

25. L = laterally unsupported length of the member
Where
L = laterally unsupported length of the member
rvv = radius of gyration about the minor axis
b1, b2 = width of the two legs of the angle
t = thickness of the leg
ε = yield stress ratio ( 250/fy)0.5
© Dr S R Satish Kumar, IIT Madras

26. No. of bolts at the each end connection
ANGLE STRUTS
Loaded through one leg
k1, k2, k3 = constants depending upon the end condition (Table 12)
No. of bolts at the each end connection
Gusset/Connec
-ting member Fixity† k1 k2 k3
> 2
Fixed
0.20
0.35 20
Hinged
0.70
0.60 5 1
0.75
1.25
0.50 60
Design ?
© Dr S R Satish Kumar, IIT Madras

27. DESIGN CONSIDERATIONS FOR LACED AND BATTENED COLUMNS
(a) Single Lacing
(b) Double Lacing
(c) Battens
Built-up column members
© Dr S R Satish Kumar, IIT Madras

28. LACED AND BATTENED COLUMNS
The effective slenderness ratio, (KL/r)e = 1.05 (KL/r)0,
to account for shear deformation effects.
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.
© Dr S R Satish Kumar, IIT Madras

29. Thank You SUMMARY 7.1 Design Strength
7.2 Effective Length of Compression Members
7.3 Design Details
7.4 Column Bases
7.5 Angle Struts
7.6 Laced Columns
7.7 Battened Columns
7.8 Compression Members Composed of Two Components Back-to-Back
Thank You
© Dr S R Satish Kumar, IIT Madras