DESIGN OF COMPRESSION MEMBERS

Sheela MalikAP (Civil)GITAM Kablana

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

Columns and Other Compression Members

• The strength of steel compression members is usually limited by their tendency to buckle.

• The load at which a compression • The load at which a compression member becomes unstable is the buckling load.

• The buckling load depends on the length, cross-section, and end conditions of the column and the stiffness of the material.

ELASTIC BUCKLING OF EULER COLUMN

Assumptions:

• Material of strut - homogenous and

linearly elastic

• No imperfections (perfectly straight)

• No eccentricity of loading

• No residual stresss

The governing differential equation is

02

2

yEI

P

dx

yd cr .

x

y

Pcr

ELASTIC BUCKLING OF EULER COLUMN

x2

2

EIPcr

Lowest value of the critical load

2

2

2

2

2

22

2

2

)/(

E

r

ErE

A

IE

A

P

cr

cr

cr

axially loaded initially straight pin-ended column

B1f

f yA

Plastic yield defined

by ff = y

Elastic buckling ( cr )

defined by

A C

STRENGTH CURVE FOR AN IDEAL STRUT

Column fails when the compressive stress is greater than or equal to the values defined by ACB.

AC Failure by yielding (Low

c = /r

defined by 2 E / 2

B

AC Failure by yielding (Low slenderness ratios)

CB Failure by bucking ( c )

f /fy

1.0 Elastic buckling

Plastic yield

STRENGTH CURVE FOR AN IDEAL STRUT

= (fy/cr )1/2

1.0

Strength curve in a non-dimensional form

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

Residual stresses in flanges

Residual stressesin web

Residual Stresses

Residual stresses distribution (no applied load)

INTRODUCTION

c

fy

Test data (x) from collapse testson practical columns

Euler curvex

x xxx

xx

x x x

x x

200

Typical column design curve

Design curve

Slenderness (/r)

x

xx

x x

x x

x xx x

100

50 100 150

(a) Single Angle (b) Double Angle (c) Tee

Cross Section Shapes for Rolled Steel Compression Members

(d) Channel (e) Hollow Circular Section (CHS)

(f) Rectangular HollowSection (RHS)

(b) Box Section (c) Box Section(a) Box Section

Cross Section Shapes for Built - up orfabricated Compression Members

(d) Plated I Section (e) Built - up I Section (f) Built-up Box Section

Cross Section Limits Buckling about axis

Buckling Curve

Rolled I-Sections h/b > 1.2 : tf 40 mm

40 < tf

7.1 DESIGN STRENGTH

Buckling Curves

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1fc

d/f

y

a

b

c

d

TABLE 7.1 IMPERFECTION FACTOR, α

Buckling Class a b c d

0.21 0.34 0.49 0.76

0

0.1

0.2

0.3

0 0.5 1 1.5 2 2.5 3Lamda

Effective Length of Compression Members

Boundary Conditions

Schematic represen

-tation

Effective Length

At one end At the other end

Translation Rotation Translation Rotation

Restrained Restrained Free Free

2.0L

Free Restrained Restrained FreeFree Restrained Restrained Free

Free Restrained Free 1.0L

Restrained Restrained Free Restrained 1.2L

Restrained Restrained Free 0.8L

Restrained Restrained Restrained 0.65 L

Restrained

Restrained

Restrained

• 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

BEHAVIOUR OF ANGLE COMPRESSION MEMBERS

V

V U

U

– 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

V U

U

ANGLE STRUTS

Basic compressive strength curve

• Curve C of Eurocode 3 • Slenderness Ratio:

concentric loading kL/r

Single leg Connection (kl/r)eqSingle 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.

23

221

2 kkk vve

LACED AND BATTENED COLUMNS

(a) Single Lacing (b) Double Lacing (c) Battens

Built-up column members