46

CHAPTER 3

BEHAVIOUR OF CFST COLUMNS AND

CODAL RECOMMENDATIONS

3.1 GENERAL

This chapter deals with the behaviour of composite columns and its

short term and long term behaviour are discussed elaborately. The modes of

failure and the bond between steel and concrete columns are discussed in the

subsequent headings comprehensively. Codal provisions and method of

design are also discussed in the last headings.

3.2 BEHAVIOUR OF COLUMNS

Short composite columns exhibit a failure mechanism characterized

by yielding of steel and crushing of concrete. Medium length columns behave

in-elastically and fail because of partial yielding of steel, crushing of concrete

in compression and cracking of concrete in tension. Stocky concrete filled

tubes are also susceptible to local buckling of the outer skin, and this is of

importance in very thin walled tubes which are nowadays often used in

building construction. A short or stocky column is so short that flexural

buckling will not occur, although local buckling may occur. Stocky columns

are designed primarily on the material strengths of the concrete and steel

elements.

The column is usually defined as a structural member who carries

only concentric axial compression. The member is a steel element and is

47

subjected to bending as well as axial compression, as occurs when the load is

applied eccentrically; it is referred to as a beam-column. The various national

standards present load - moment interaction equations which are slenderness-

dependent, and which must be satisfied for the strength limit state. Composite

members subject to both compression and bending are referred to as columns.

Because of the presence of both steel and concrete in a composite column, the

behaviour of such a member is akin both to a steel beam column and a

reinforced concrete column. Generally speaking, short or stocky composite

columns are treated by the reinforced concrete approach based on section

material strengths. Slender composite columns, which do not contain

appreciable bending actions are treated by the steel approach which is based

on a design strength that is affected by the slenderness of the column.

There are a few structural considerations that must be borne in

mind when comparing and contrasting the fundamental behaviour of encased

columns and concrete filled steel tubes. Firstly, concrete filled steel tubes are

susceptible to local buckling of the steel skin, the prospect of which in many

cases is very thin. The second point pertains to the lateral confinement

provided by the tube to the expansion of the concrete core in compression,

which enhances the strength of short columns, but it is insignificant in slender

columns. Thirdly, the steel skin inhibits the egress of moisture that contributes

to creep and shrinkage effects. Research into monitoring the time dependent

deformations of concrete filled tubes has indicated a reduced creep and

shrinkage induced response.

In all column analysis approaches used at both ultimate and

serviceability limits, it is assumed that there is full interaction between the

concrete element and the steel element. This implies that the strain profile

across the section remains uni-linear, so that there is no step change or slip-

strain across the steel / concrete interface, as is often assumed in composite

48

beam design. This assumption is reasonable, since the area of the interface is

generally and fairly large and hence a good bond is provided at relatively low

bond stresses. It is worth noting that the bond stresses in composite columns

are generally lower than those in beams, because the columns are mainly

subjected to compression.

3.3 SHORT TERM BEHAVIOUR

In a short concentrically loaded concrete filled steel tube, the

concrete core of the column is subjected to a confining stress, and as a result

the column can carry considerably larger axial forces than if the concrete was

unconfined. The results of triaxial tests on concrete have illustrated this,

where concrete subjected to a lateral confining pressure can carry a greater

axial load than unconfined concrete. Of course, this is utilized in reinforced

concrete construction where spirally reinforced columns provide a lateral

stress that increases the axial load carried by the concrete core. However, the

behaviour of an axially loaded steel tube filled with concrete will vary

according to the method in which the ends of the member are loaded as shown

in Figure 3.1. Essentially, there are three fundamentally different methods of

applying the loading, and these are discussed below.

(a) Load the Steel and not the Concrete - This condition of loading may not

increase the axial capacity of the column above that of the steel tube alone,

because the Poisson’s effect causes the steel tube to separate from the

concrete, once the adhesive chemical bond between the concrete and steel has

exceeded. The column will generally fail at the maximum load which the

hollow steel tube alone can carry, but the concrete core may tend to delay the

column local buckling. For slender columns, the failure load will increase

significantly due to the increase in flexural stiffness.

49

(b) Load the Concrete and not the Steel - In this principle, which is the

most favorable loading method, the concrete takes the maximum load as the

steel does not resist axial load, but only provides a confining stress to the

concrete in an analogous manner to a spirally reinforced concrete column.

However, since there is some adhesion between the steel and concrete, the

condition is hard to attain as some axial load is produced in the steel.

(c) Load the Steel and Concrete - This is the method most often encountered

in practice, and it may be enforced by welding stud shear connectors to the

inside of the steel tube where practicable. If the steel is axially stressed in

compression as well as circumferentially because of the expansion of the

concrete, it will be subjected to a state of biaxial stress which, in accordance

with the von Mises’ yield criterion, will reduce the yield stress in the

circumferential direction. This has the effect of lowering the confining effect,

and hence reduces the maximum load on the concrete. Though the reduction

in the confining effect is offset, since the steel now carries some of the

compressive force the load-carrying capacity of the column is increased by

this steel and concrete.

Case (a) Case (b) Case (c)

Figure 3.1 Loading conditions of specimens

50

3.4 LONG TERM BEHAVIOUR

The behaviour of concrete filled steel tubes when undergoing creep

and shrinkage caused by a sustained load is different from that of encased

I-section columns. The main difference is attributable to the reduction in

moisture loss that is directly related to the creep and especially the shrinkage

properties. In steel tubes with very thin walls the time-induced load shedding

may increase the compression in the steel markedly, and thus precipitate local

buckling. Researchers undertook a series of experiments to measure the creep

and shrinkage response of concrete in thin circular steel tubes. It was

concluded that the moisture loss that took place in these tubes might be very

small or could be eliminated totally, with a consequent reduction in the effects

of creep and shrinkage.

3.5 LOAD TRANSFER MECHANISM

It has been observed that the ultimate axial capacity of concrete

filled tubular columns is larger than the sum of uncoupled steel and concrete

at failure loads. The increase in failure load is caused by the confining effect

of steel tube on the concrete. The structural behaviour of concrete filled

tubular sections is considerably affected by the difference between the

Poisson’s ratios of the steel tube and concrete. In the initial stage of loading,

the Poisson’s ratio for the concrete is lower than that of steel. Thus the steel

tube has no confining effect on the concrete. As the longitudinal strain

increases, the lateral expansion of concrete gradually becomes greater than the

expansion of the steel tube. At this stage the concrete becomes tri-axially

stressed and the steel tube bi-axially stressed.

The steel tube under a biaxial state of stress cannot sustain the

normal yield stress, causing a transfer of load from the steel tube to the

concrete. In the first stage of loading, the steel tube sustains most of the load

51

until it yields. At this stage there is a load transfer from the steel tube to the

concrete. The steel tube exhibits a gradual decrease in load sharing until the

concrete reaches its maximum compressive strength. After the first stage of

loading there is a redistribution of load from the concrete to the steel tube,

whereas the steel exhibits a hardening behaviour which is almost same as the

uni-axial stress-strain hardening relationship.

3.6 STRESS - STRAIN RELATIONSHIP OF COMPOSITE

COLUMNS

Concrete filled circular tubular columns exhibit different patterns of

cross-sectional stress distribution in concrete. In the case of circular columns,

the cross-sectional stress distribution is uniform. The axial and lateral stress

distributions at the cross section are radially uniform. Circular hollow sections

provide a significant amount of confinement while this effect is negligible in

the case of rectangular sections. Additional strength occurs because of the

increase in compressive strength of the concrete core that is restrained

laterally by the surrounding steel tube. This increase in concrete strength out

weights the reduction in the yield strength of steel in vertical compression due

to the confinement tension needed to contain the concrete. Beyond this limit,

steel exhibits a strain softening behaviour until it reaches the plastic limit.

When the concrete reaches its maximum compression capacity, the steel tube

exhibits a softening behaviour because a decrease in the stiffness of concrete

core begins. The higher internal pressure causes larger hoop stress, which

results in a reduction in compressive stress in steel tube. Short composite

columns exhibit a failure mechanism characterized by yielding of steel and

crushing of concrete. Medium length columns behave inelastically and fail by

partial yielding of steel, crushing of concrete in compression and cracking of

concrete in tension.

52

3.7 ROLE OF STEEL TUBE IN COMPOSITE COLUMNS

In composite column with concrete filled circular sections, the

confinement effects of concrete increases the concrete resistance, but at the

same time reduces the axial resistance of the steel section. Strength and

ductility of plain concrete are highly dependent on the degree of confinement.

As concrete is axially compressed, the rate of lateral expansion is a function

of the axial shortening by a stable value of Poisson’s ratio upto approximately

50% of the compressive strength. During this stage, stable propagation of the

bond cracks between cement and aggregate occurs, and negative volumetric

strain indicates compaction of the concrete mass. Approximately 50% of the

strength, micro cracks develops within the matrix causing the concrete to

behave in highly non-linear manner and the lateral stain also increases in a

non-linear manner.

The volumetric strain is however, still negative upto the critical

stress level of approximately 87% of the compressive strength. Past this

loading stage, the volumetric strain, lateral strain start to increase at a much

higher rate of micro cracking, evolving into dominant cracks that propagate

within the concrete mass causing failure. It is therefore believed that

controlling the lateral expansion of concrete by confinement is the key to

enhance the strength and ductility of concrete. One of the methods used to

achieve confinement is to cast concrete in a steel tube. When the concrete is

axially loaded, lateral expansion is partially restrained by the tube, resulting in

radial pressure at the interface. The amount of radial pressure depends on the

stiffness of the steel tube in the circumferential direction. As the load

increases, the tendency for lateral expansion increases and the confining

pressure also increases. Because the material properties of the steel tubes are

typically linear and (or) elastic linearly, the induced confinement is variable.

For steel tubes, after the steel yields, the confining pressure is constant and

independent of the axial load level.

53

3.8 COMPARISON OF CFST COLUMNS WITH HOLLOW

COLUMNS

The CFST columns increase earthquake resistant capabilities due to

the concrete filling inside the steel tubes and are particularly suitable for

buildings subjected to large axial compressive stress. More over, the columns

are fire resistant and reduce the thickness of traditional fire-resistant coating

or even eliminate the need for it. Thus the columns simplify the construction

process and increasing interior space in a building. Conventional structures

like reinforced concrete structures can be replaced by CFST structures system

with a high degree of generality and at the same time reduce costs to a

minimum. It is especially useful in high-rise buildings where high work speed

is required and flexibility of open space is desired for a maximum range of

applications. CFST columns may also be used in a situation where the cross

sections of hollow columns are unacceptably large. There are numerous

applications for which composite columns provide excellent solution to

structural problems when compared with hollow steel column. The composite

column has superior load retention at higher temperature, are more resistance

to local buckling, greater stiffness and abrasion resistance when compared

with hollow steel column. The composite column supports more thrust than

any other traditional reinforced concrete column of the same dimension.

3.9 EVALUATION OF MODES OF FAILURE

Composite columns are usually categorized by their modes of

failure. Short or stocky columns usually attain the cross-sectional strength, so

that their failure is governed by the yield strength fy of the steel and the

cylinder strength fck of the concrete. Stocky columns are therefore material -

dependant. Long or slender columns, on the other hand, fail by so called

flexural buckling in much the same way as a slender steel column. Under such

conditions, the composite column becomes unstable, and buckles sideways

54

with the buckling half wavelength being in the order of the length of the

column. Local buckling may also occur. However, if any of the steel elements

is free, then the steel element may buckle locally. However, the rigid concrete

medium forms a restraint against the free formation of buckles, so that local

buckling is less likely than if the concrete element was absent, as in a pure

steel member.

3.10 BOND BETWEEN STEEL AND CONCRETE COLUMNS

For axially compressed short CFST, bond strength may not be

necessary. It is needed only if there is significant shear force produced at the

interface. When the two elements only touch at an interface then they are

often tied together using mechanical forms of shear connection. When one

element encases the other element as in the columns and tube then the two

elements are tied together by interface forces, induced by the geometry of the

encasement and any bond strength. In all the cases, the bond must be designed

to resist the longitudinal shear forces at the steel / concrete interface.

However, the bond must also be designed to prevent separation between the

steel and concrete elements in order to ensure that the curvature in the steel

and concrete elements is the same. Hence the interface bond must be able to

resist both tensile forces normal to the steel / concrete interface, and shear

forces parallel to the steel / concrete interface.

3.11 THEORETICAL ANALYSIS

Concrete filled steel tubular columns are clearly an intermediate

between steel and reinforced concrete columns. However, the design

philosophy for each of these two structural members is fundamentally

different. Steel columns are treated as concentric in that they are loaded

through their centroids, but with due allowances being made for residual

stresses, initial out of straightness and slight eccentricities of the load. The

55

basis of the design of steel column is instability or buckling, and any moments

which act at the ends of the column are then incorporated by reducing the

axial load by way of an interaction equation.

The approach for RC column is quite different from that for steel

column in that the loads are considered to be eccentric to the centroid. The

failure is generally, but not always, attributable to cross-sectional and material

failure, and is based on the interaction curve as given in IS 456-2000. Because

of the similarity of CFST columns to both steel and concrete columns, there

has been a great deal to debate by researchers as to which approach should be

adopted. Short or stocky columns are clearly governed by cross section

failure, while long or slender columns are prone to buckling. Perhaps the most

logical treatment to date is that which is provided by the Eurocode4. The

behaviour of CFST columns can be best treated by a combination of both

approaches.

3.12 HISTORY OF DESIGN CODES

The publication of codes of practice tends to lag behind current

engineering thoughts. It is therefore not surprising that the first national code

(The American Association of State Highway Officials (AASHO) -

Specification for Composite Highway Bridges) was not published until 1944.

With its publication, official recognition and an approved design method were

available to designers and so an increasing number of composite highway

bridges were built in the USA over the years subsequently.

The soundness of the basic design principles available from a large

volume of concurrent research showed that there was a need for attention to

certain details. For this reason a new AASHO specification was published in

1957 and again in 1961. The other major country to develop an interest in

composite construction to the extent of publishing a Code of Practice (DIN

56

1078) was Germany. Here the pressure of steel shortage immediately

following 1945 world war, forced engineers to adopt the most economical

design methods available in order to be able to cope up with the very large

amount of reconstruction of bridges and buildings destroyed in the 1939-45

war.

With two major codes of practice available (the American and

Germany) other countries were able to draw up their own, basing them

generally on the provisions of one or other of the major codes. The AASHO

code was in many ways much simpler than the German code. Possibly

because steel was much more easily obtained in the USA, the Americans did

not attempt to incorporate the structural complexity or detailed analysis found

essential by the Germans. They preferred to avoid the difficulties of using

continuous beams or pre-stressed decks which in German practice were

necessary in order to obtain maximum economy in the material that is used

for construction.

Over the last two decades, researchers have suggested analytical

methods and design procedures for composite columns and design codes have

been formulated. Each of these codes is written so as to reflect the design

philosophies and practice in the respective countries. Over the last two

decades, different specific codes for the design of concrete filled steel tubular

columns have been used.

3.13 DESIGN CODES

Currently comprehensive design standard can be utilized for the

design of CFST columns. Compact limits for most international design codes

limit the slenderness values to less than 40 (Brain Uy 2001). However, some

guidance for the design of CFST columns is provided by the European

Committee for Standardization, the American Concrete Institute and the

57

Chinese Code. The design codes are based on several different theories,

which can produce different results, and the assistance provided in terms of

application varies significantly. A number of design standards take local

buckling into account through the use of an effective diameter or an effective

area method. At present, there is no Indian Standard covering the design of

composite columns. The method of design suggested in this chapter largely

follows EC4, which incorporates the latest research on composite

construction. Indian Standards for composite construction (IS: 11384-1995)

does not make any specific reference to composite columns. The provisions

contained in IS: 456-2000 are often invoked for design of composite

structures. Extension of IS: 456-2000 to composite columns results in the

following equation:

Pp = Aa py + Ac pck + As psk (3.1)

where py = 0.87 fy ; pck = 0.4(fck)cu and psk = 0.67fy

The design of composite column is based on limit state method.

Eurocode4 is generally followed for composite column design as there is no

Indian Standard covering the design of composite columns. For structural

adequacy, the internal forces and moments resulting from the most

unfavourable load combination should not exceed the design resistance of the

composite cross-sections. While local buckling of the steel sections may be

eliminated, the reduction in the compression resistance of the composite

column due to overall buckling should definitely be allowed for, together with

the effects of residual stresses and initial imperfections. Moreover, the second

order effects in slender columns as well as the effect of creep and shrinkage of

concrete under long term loading must be considered, if they are significant.

The reduction in flexural stiffness due to cracking of the concrete in the

tension area should also be considered.

58

Isolated symmetric columns having uniform cross sections in

braced or non-sway frames may be designed by the simplified design method,

which adopts the European buckling curves for steel columns. However, this

method cannot be applied to sway columns. When a sufficiently stiff frame is

subjected to in-plane horizontal forces, the additional internal forces and

moments due to the consequent horizontal displacement of its nodes can be

neglected, and the frame is classified as “non-sway”.

3.13.1 American Concrete Institute (ACI 318-89)

The code ACI 318 uses the traditional reinforced concrete

approach, with a minimum load eccentricity used to determine the column

strength under nominal axial load. The American Standard excludes the

influence of concrete confinement by the steel tube and accounts for column

slenderness by a minimum load eccentricity. The code ACI 318 is appropriate

for the design of thick walled steel tubes filled with normal strength concrete.

The code ACI 318 is different in concept to the Eurocode4. However the

Australian Standards uses a similar approach to the code ACI 318.

According to ACI 318-89, a composite column is a concrete

column reinforced with a structural steel shape or tubing in addition to the

reinforcing. In order to consider the slenderness effects, an equivalent radius

of gyration and flexural stiffness are used with a parameter of sustained load

ratio, and hence without any sustained load, radius of gyration should be

taken as zero. A parameter for the softening influence of creep in concrete

that is subjected to sustain compressive loading is included.

3.13.2 Load and Resistance Factored Design Method (AISC-LRFD)

This is based on the same principles as ACI code. The design is

based on equations for steel columns. The nominal strength is estimated on

59

the basis of ultimate resistance to the load, and reduction factors are then

applied. The nominal axial load capacity is reduced according to the

slenderness ratio. Neither the ACI-318 nor the AISC-LRFD provisions

explicitly consider confinement effects on strength or ductility of members

analysed. ACI provisions for calculating the strength interaction between

axial and flexural effects are essentially the same as those for reinforced

concrete column, whereas AISC-LRFD recommendations are based on the

bilinear interaction formulae which have the same form as those of steel

columns. In the above design methods, flexural stiffness is under-estimated

and the confining effect of the steel tube on the concrete core is ignored. The

influence of creep is ignored for the concrete in composite columns according to AISC-LRFD specification.

3.13.3 Architectural Institute of Japan (AIJ)

A composite structural system using concrete and steel is called

‘Steel Reinforced Concrete’ (SRC) in Japan. In this country an allowable

stress design is primarily employed, in which working stresses are calculated

based on the elastic stiffness of members and allowable strength by the

superimposed strength formulae. Cross section strength is calculated by

superimposing the strength of both steel and concrete sections, thereby

neglecting the interaction between steel and concrete and the effect of

confinement. Euler buckling load is used with reduced concrete stiffness and

factors of safety for both concrete and steel. The method is applicable to

asymmetrical sections and columns under biaxial bending.

3.13.4 British Standard (BS 5400-Part 5)

Code provisions in BS 5400 are based on limit state design with

loading factors and material safety factors. The ultimate moment is calculated

from plastic stress distribution over the cross sections, and an approximation

for the interaction curve for axial load and moment is used. Reduced concrete

60

properties are used to account for the effects of creep and the use of un-

cracked concrete section in stiffness calculation. This method is applicable to

symmetrical sections only and restricted to the range of sections covered for

in the European buckling curves.

3.13.5 Australian Standards (AS)

Australian Standards are used in the ACI formula for calculating

the squash load. Neither code takes into consideration the concrete

confinement. The limiting thickness of steel tube to prevent local buckling is

based on achieving yield stress in a hollow steel tube under monotonic axial

loading which is not a necessary requirement for an in-filled composite

column.

The squash load is determined by Nu = 0.85 Ac fc + As fy (3.2)

3.13.6 Chinese Code (DL/T5085-1999)

The code DL/T5085 is based on the unified theory that considers

the CFST member as a composite member, as opposed to the separate

components. The properties of CFST columns depend on the properties of the

steel and concrete, and their dimensions. The composite indices and

geometric properties are then used directly to obtain the ultimate strength. The

Chinese code differs from both the Eurocode4 and the code ACI 318. The

code also includes for shear and torsion, in addition to bending and axial load.

A design by the code DL/T5085 and Eurocode4 give similar results for a

column subjected to a high axial load and a small moment.

3.13.7 European Committee for Standardization (Eurocode 4)

Eurocode 4 is the most recently completed international standard in

composite construction. The code is based on the rigid plastic method of

61

analysis which assumes fully crushed concrete and fully yielded steel. The

approach allows the full mean compressive strength of the cylinder to be

utilized. The code uses a column curve, similar to most modern steel design

codes, to determine the influence of slenderness in CFST columns. Local

buckling is ignored by limiting the plate slenderness to within compact plate

limits. The enhancement of the concrete due to confinement is included for

some specific cases and it is the only code that separately treats the effects of

long-term loading.

EC4 covers concrete encased and partially encased steel sections

and concrete filled sections with or without reinforcement. This code uses

limit state concepts to achieve the aims of serviceability and safety by

applying partial safety factor to loads and material properties. Based on

experimental results, it was recommended that the regulations of EC4

concerning factor of 0.85 should not be applied to hollow sections filled with

high strength concrete. All codes assume full interaction, but some impose

restrictions on the shear stress at all steel-concrete interface. It is customary to

use direct bearing or provide shear connectors, when the specified limiting

shear stress is exceeded. The code is appropriate for the design of thick-

walled steel tubes filled with normal strength concrete.

The ultimate axial force of a column is:

Nu0 = Aa fy η2 + Ac fc (1+ η1 (t fy /D fcy1)) (3.3)

3.14 METHOD OF DESIGN

The complexity of the local and global response of composite steel

- concrete systems, and the number of possible different situations in practice

led to the use of design methods developed by empirical processes. They are

based on, and calibrated against, a set of test data. Therefore, their

62

applicability is limited to the range of parameters covered by the specific

experimental background. This feature makes the reference to codes and in

particular to their application rules of substantial importance for any test dealing with the design of composite structures.

Several commonly used methods, which are now available for

designing composite columns, include Eurocode 4, BS 5400 and AISC-

LRFD. In the United States, design provisions for composite columns are

currently included in both the ACI-318 and LRFD specifications. The concept

of applying LRFD to composite columns was first presented by Furlong

(1967). The method of EC4 was based on the work of Roik and Bergmann

(1989) and others, while the recommendations given in the BS 5400 were

developed by Basu and Somerville (1969) and modified by Virdi and

Dowling (1973).

In general, a composite column must be designed for the ultimate

limit state. For structural adequacy, the internal forces and moments resulting

from the most unfavourable load combination should not exceed the design

resistances of the composite cross-sections. While local buckling of the steel

sections may be eliminated, the reduction in the compression resistance of the

composite column due to overall buckling should be allowed for, together

with the effects of residual stresses and initial imperfections. Moreover, the

second order effects in slender columns, as well as the effect of creep and

shrinkage of concrete under long-term loading, must be considered if they are

significant. The reduction of flexural stiffness due to cracking of the concrete

in the tension area should also be considered. These are provided either

explicitly or empirically, in EC4.

At present, there is no Indian Standard code covering composite

columns. The method of design suggested below largely follows EC4, which

incorporates the latest research in composite construction. Composite column

63

design method outlined here is valid for prismatic composite columns with

doubly symmetrical cross-sections. The plastic compression resistance of a

composite cross-section represents the maximum load that can be applied to a

short composite column. Concrete filled circular tubular sections exhibit

enhanced resistance due to the tri-axial confinement effects. Fully or partially

concrete encased steel sections and concrete filled rectangular tubular sections do not achieve such enhancement.

3.14.1 Basics of Design Method

In EC4-1-1, isolated columns are defined as compression members

that are integral parts of a braced or non-sway frame but which are considered

to be isolated for design purposes. As in other structural components, a

composite column must also be designed for the ultimate limit state. Isolated

symmetric columns having uniform cross-sections in braced or non-sway

frames may be designed by the simplified design method described in the next

section.

This method also adopts the European buckling curves for steel

columns as the basis of column design. It is formulated in such a way that

only hand calculation is required in practical design. The simplified method is

formulated for prismatic composite columns with doubly symmetrical cross-

sections. The calculations of various design parameters are covered and the

checks for structural adequacy of a composite column under applied loads are

presented below. Two methods of design for isolated composite columns in braced or, non-sway frames are given within EC4-1-1.

(i) General Design Method

This comprehensive method is used for composite columns with

non-symmetrical or non-uniform cross-section over the column length. It is

also used for composite columns of doubly symmetrical and uniform cross-

64

section over the column height, when the limits of applicability for the

simplified design method are not satisfied. In these circumstances, some of

the important design issues which should be considered using the general

method are geometrical and material non-linearity, second order effects (on

slender columns), creep and shrinkage of the concrete under long-term

loading, contribution of the tensile strength of the concrete between cracks,

imperfections for the calculation of internal forces and moments about both

axes, distribution of internal forces and moments between the steel section

and the concrete by means of a clearly defined load path, transfer of

longitudinal shear stress at the interface between the steel section and the

concrete under large transverse shear and chemical bond and friction together

with mechanical shear connectors if necessary. In order to allow for these

design considerations, it is necessary to use sophisticated computer software,

which operate with both geometrical and material non-linearity. In general,

the design effort is considerable. Thus, this method is not preferred for use in

practical design.

(ii) Simplified Design Method

This method is used for composite columns of doubly symmetrical

and uniform cross-section over the column height. It is based on certain

assumptions relating to the geometrical configurations of the composite cross-

sections. Moreover, it also adopts the European buckling curves for steel

columns as the basis of column buckling design. It should be noted that this

method is formulated in such a way that only hand calculation is required in

practical design.

3.14.2 Local Buckling of Steel Hollow Sections

Before the plastic resistance of the concrete filled hollow section is

calculated, it should be ensured that local buckling of the steel does not occur.

65

In order to prevent premature local buckling, the width to thickness ratio of

the steel section in compression must satisfy the flowing limits:

For concrete filled rectangular hollow sections (RHS) h/t ≤ 52ε

For concrete filled circular hollow sections (CHS) d/t ≤ 90ε2

where

t is the wall thickness of the steel hollow section in mm.

h is the larger outer dimension of the rectangular hollow section in mm.

d is the outer diameter of the circular hollow section in mm.

ε = √(235/fy)

fy is the yield strength of the steel section in MPa.

Local buckling in some rectangular hollow section with large h/t

ratios may be critical. No specific design recommendation is given within

EC4, and design using sections which exceed the local buckling limits should

be verified by tests.

(i) Concrete filled Rectangular Hollow Sections (RHS)

The plastic resistance of a concrete filled rectangular hollow section (i.e., the so-called “squash load”) is given by the sum of the resistance of the components as follows:

Npl,Rd = Aa fy / γa + As fsk / γs + Ac fck / γc (3.4)

where

Aa is the area of the steel section

As is the area of the reinforcement

Ac is the area of the concrete

66

fy is the yield strength of the steel section

fsk is the characteristic yield strength of the steel reinforcement bars

fck is the characteristic compressive strength (cylinder) of the concrete

For ease of expression, fy / γa , fsk / γs and fck / γc are presented as

design strengths of the respective materials as fyd, fsd and fcd respectively. As

a result of this simplification, the above equation for the plastic resistance of

the composite column can be rewritten in the following compact form:

Npl,Rd = Aa fyd + As fsd + Ac fcd (3.5)

(ii) Concrete filled Circular Hollow Sections (CHS)

For composite columns with concrete filled circular hollow

sections, the increased resistance of concrete due to the confining effect of the

circular hollow section may be included. This restraint to transverse strain in a

three dimensional confinement results is increased concrete resistance. At the

same time, circular tensile stresses in the circular hollow section also arise,

which reduce its axial resistance.

In general, the resistance of a concrete filled circular hollow section

to compression may increase by upto 15 % under simple axial loads when the

effect of tri-axial confinement is considered. However, this effect on the

resistance enhancement of concrete depends also on the slenderness of the

composite columns and is significant only in stocky columns. For composite

columns with a non-dimensional slenderness of λ > 0.5 (where λ is defined

non-dimensional slenderness ratio), this effect should be neglected and the

plastic resistance assessed as for rectangular hollow sections.

In addition, further linear interpolation is necessary to take account

of any effective load eccentricities. However, the eccentricity, e of the applied

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load may not exceed the value d/10, where d is the outer diameter of the

circular hollow section.

e = Msd / Nsd (3.6)

where,

Msd is the maximum design moment (second order effects are ignored).

Nsd is the design applied load.

The plastic compression resistance of a concrete filled circular

hollow section may be obtained as follows:

Npl,Rd = Aa fyd η2 + As fsd + Ac fcd (1+ η1 (t fy /d fck)) (3.7)

where

t is the wall thickness of the steel hollow section in mm.

η1 = η10 (1-10e/d) for 0 < e ≤ d/10 η2 = η20 + (1- η20) 10e/d

η1 = 0 for e > d/10 η2 = 1.0

The basic values η10 and η20 depend on the non-dimensional

slenderness ratio , and are defined as follows:

η10 = 4.9 – 18.5 + 17 2 but η10 ≥ 0

η20 = 0.25 (3+2 ) but η20 ≤ 1.0

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If the eccentricity e exceeds the value d/10, or if the non-

dimensional slenderness ratio exceeds the value 0.5, then η10 = 0 and

η20 =1.0. Table 3.1 gives the basic values η10 and η20 for different values of .

Table 3.1 Basic values of η10 and η20 to allow for the effect to triaxial confinement in concrete filled circular hollow sections

Non-dimensional slenderness ratio 0.0 0.1 0.2 0.3 0.4 ≥0.5

η10 4.90 3.22 1.88 0.88 0.22 0 η20 0.75 0.80 0.85 0.90 0.95 1.00

3.14.3 Effective Flexural Stiffness

Composite columns may fail in buckling and one important parameter for the buckling design of composite columns is its elastic critical buckling load (Euler load), Pcr, which is defined as follows:

2 ecrP

2

EIl

(3.8)

where,

(EI) e is the effective elastic flexural stiffness of the composite column

l is the effective length of column which may be conservatively taken as system length L for an isolated non-sway composite column.

However, the value of the flexural stiffness may decrease with time due to creep and shrinkage of the concrete. Two design rules for the evaluation of the effective elastic flexural stiffness of composite column are given below.

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(i) Short-term Loading

The effective flexural stiffness of the composite column (EI)e is obtained from adding up the flexural stiffnesses of the individual components of the cross-section:

(EI)e = Ea Ia + Es Is + 0.6 Ecm Ic (3.9)

where,

Ia, Is and Ic are the second moment of area, about the appropriate

axis of bending, for the steel section, the reinforcement and the concrete

(assumed uncracked) respectively.

Ea and Es are the elastic moduli for the structural steel and the

reinforcement respectively.

0.6 Ecm Ic is the effective stiffness of the concrete component (the

factor 0.6 is an empirical multiplier, which has been determined from a

calibration exercise, to give good agreement with test results).

Ecm is the secant modulus of elasticity for structural concrete

(ii) Long-term Loading

For composite columns under long-term loading, the creep and

shrinkage of concrete will cause a reduction in the effective elastic flexural

stiffness of the composite column, there by reducing the buckling resistance.

However, this effect is only significant for slender columns; as a simple rule,

the effect of long-term loading should be considered if the buckling length to

depth ratio of a composite column exceeds 15.

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If the eccentricity of loading is more than twice the cross-section

dimension, the effect on the applied bending moment distribution caused by

increased deflections, due to creep and shrinkage of concrete, will be very

small. Consequently, it may be neglected and no provision for long term-

loading is necessary. Moreover, no provision is necessary if the non-

dimensional slenderness of the composite column is less than the limiting

values given in the Table 3.2 below.

Table 3.2 Limiting values of for long-term loading

Frame type Braced non-sway systems

Unbraced frames and/or sway frames

Concrete filled hollow sections

0.8

(1-δ)

0.5

(1-δ)

The steel contribution factor δ, given in Table 3.2 above is defined

as follows:

δ = Aa fyd / Npl,Rd (3.10)

If the eccentricity of loading is less than twice the cross-section

dimension and the non-dimensional slenderness of the composite column is

less than the limiting values given within Table 3.2, the effect of creep and

shrinkage of concrete should be allowed for by reducing the effective elastic

modulus of the concrete to the value:

Ec∞ = Ecd (1- (0.5 NG,Sd / NSd )) (3.11)

where,

NSd is the design applied load.

NG,Sd is the part of design load permanently acting on the column.

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Table 3.2 also allows the effect of long term loading to be ignored for

concrete filled hollow sections with ≤ 2.0, provided that δ is greater than 0.6

for braced (or non-sway) columns, and 0.75 for unbraced (and/or sway)

columns.

(iii) Slenderness Ratio

The definition of slenderness ratio in the codes of practice is important to note that the value of Ec used in evaluating the column slenderness ratio in LRFD does not include a factor of safety. However, in BS 5400, a partial factor of safety is included in the calculation of the column slenderness ratio. If the factored value of Ec is used, there will be a reduction in the column slenderness ratio, which will in turn lead to a reduction in the load carrying capacity.

The slenderness ratio in LRFD is expressed in terms of the modified radius of gyration, rm. The steel tube and the concrete portion of the composite sections both contribute to flexural resistance. If the steel dominates, the radius of gyration of the steel section should be used in calculating rm. On the other hand, if the reinforced concrete section dominates the flexural resistance, the radius of gyration of the concrete section should be used for calculating the slenderness parameter. In the absence of a more rigorous method, LRFD recommends that the larger of the radius of gyration values for steel or concrete be used in calculating the slenderness index l/rm.

Once the member slenderness of a composite column is determined, the compression resistance of the composite column may be evaluated. The column buckling curves, which are essentially the British Standards, are based on an extensive study. Their investigation highlighted the effect which the shape of the structural steel section and its method of fabrication have on its ultimate load carrying capacity. This is a result of the differences in geometry of cross-section, magnitude and distribution of

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residual stresses and the member initial out-of-straightness. These curves are identified as a, b and c and they have been found to apply equally well to composite columns. As for LRFD, only one strut curve is used and the position of the strut curve is close to the strut curve a, with a slightly smaller value for slenderness parameter, λ less than 1 and a slightly larger value for λ greater than 1.

(iv) Effect of Concrete Confinement

For composite column with concrete filled circular sections, the confinement effect of concrete increases the concrete resistance, but at the same time reduces the axial resistance of the steel section. In EC4, the reduction of concrete strength by 0.85 may be omitted for concrete filled composite columns since the development of concrete strength is better achieved due to protection against the environment and against splitting of concrete. The effect of confinement is considered when both the relative slenderness, λ is less than 0.5 and the eccentricity of the normal force does not exceed the value d/10, in which d is the outer diameter of the circular hollow section. In BS 5400, the limitation of the confinement effect is less restrictive than EC4. It is not dependent on the eccentricity of the axial loading and the confinement effect is neglected when λ is greater than 1.0. For most practical columns, λ = 1 corresponds to a length to diameter ratio between 24 and 29, but for simplicity, BS 5400 set the limit of l/d to 25. In LRFD, no confinement effect of concrete is taken into account for design of concrete filled circular hollow sections.

3.14.4 Column Buckling Resistance

The plastic resistance to compression of a composite cross-section Npl,Rd represents the maximum load that can be applied to a short column. However, for slender columns, with low elastic critical load, overall buckling considerations may be more significant.

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In Figure 3.2 (b), the buckling resistance of a column is expressed as a proportion χ of the plastic resistance to compression Npl,R, thereby non-dimensionalising the vertical axis compared to Figure 3.2 (a). The horizontal axis may be non-dimensionalised similarly by use of the Euler buckling load Ncr as is also shown in Figure 3.2 (b).

By incorporating the effects of both residual stresses and geometric imperfections, the European buckling curves were developed on this basis as shown in Figure 3.2 (c). These curves form the basis of column buckling design for both steel and composite columns.

(a) (b)

(c)

Figure 3.2 (a) Idealized column buckling curve, (b) Non-dimensionalised column buckling curve, (c) European buckling curves according to EC3

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The buckling resistance is calculated from the plastic resistance

and the Euler (elastic) critical load using the EC3-1-1 buckling curve 'a'. The

Euler buckling load is given by:

2 ecr 2

EIN

l (3.12)

where

(EI)e is the effective elastic flexural stiffness of the composite column.

l is the buckling length of the column.

EC4-1-1 suggests that the buckling length l of an isolated non-sway

composite column may conservatively be taken as equal to its system length

L. Alternatively, the buckling length may be determined using Annex E of

EC3-1-1.

The non-dimensional slenderness ratio is given by:

pl R

cr

,NN

(3.13)

where

Npl,R is the plastic resistance of the composite cross-section to

compression.

The resistance of a composite column in axial compression

(buckling load) is obtained from:

NRd = χ Npl,Rd (3.14)

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where

χ is the reduction co-efficient for buckling obtained from curve ’a’

of EC3, and is dependant on the non-dimensional slenderness ratio

The reduction co-efficient may be determined from:

2 2

1χ = but χ 1.0 Φ + Φ – λ

(3.15)

where

Φ = 0.5 [1 + α (λ – 0.2) + λ2 ]

α is an imperfection parameter depending on the buckling curve

considered.

3.14.5 Relevant Buckling Curves and Imperfection Factors

According to prEN 1994-1-1, circular or rectangular hollow section

columns filled with plain concrete or containing up to 3% reinforcement can

be designed using buckling curve 'a' with an imperfection factor, α = 0.21.

However, concrete filled sections containing between 3% to 4%

reinforcement must be designed using buckling curve 'b' with an imperfection

factor, α = 0.34 (see Figure 3.3 (a) and (b) and Table 3.3 below).

In addition, concrete filled circular hollow section columns as

shown in Figure 3.3 (c) containing an additional open section used as primary

steel can also be designed as a composite section using buckling curve 'b'

with an imperfection factor, α = 0.34.

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Figure 3.3 Typical column cross-sections

The European buckling curves illustrated in Figure 3.2 (c) are

proposed to be used in composite columns. They are selected according to the

types of the steel sections and the axis of bending.

Curve a for concrete filled steel tubular sections.

Curve b for fully or partially concrete encased I-sections buckling

about the strong axis of the steel sections (x-x axis)

Curve c for fully and partially concrete encased I-sections bucking

about the weak axis of the steel sections (y-y axis)

Table 3.3 Imperfection factor α for the buckling curves

European Buckling curve a b c

Imperfection factor α 0.21 0.34 0.49

Although not explicitly stated, Clause 4.8.3.2 of EC4-1-1, while

defining the partial safety factors implies that isolated non-sway composite

columns need not be checked for buckling, if any of the following conditions

is satisfied:

(i) the axial force in the column is less than 0.1 Ncr ; or

(ii) the non-dimensional slenderness ratio is less than 0.2.

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3.14.6 Restrictions on the Simplified Design Method

The limits of applicability of this method are given in EC4, when

the limits are not satisfied, general design method should be used. The

application of the simplified design method is subjected to various

restrictions, as follows:

(a) The column is doubly-symmetrical and is of uniform cross-

section over the height of the column.

(b) The steel contribution ratio δ must satisfy the following

conditions: 0.2 ≤ δ ≤ 0.9

If δ is less than 0.2, the column may be designed according to

EC2. If δ is larger than 0.9, the concrete is ignored in the

calculations, and the column is designed as a bare steel

section.

(c) The maximum non-dimensional slenderness ratio of the

composite column is limited to 2.0.

(d) The maximum amount of longitudinal reinforcement that can

be considered in the analysis is 6 % of the concrete area.

However, if design for fire resistance is not needed, according

to EC4, no minimum amount of reinforcement is normally

necessary within a filled SHS column; in other words: 0 %

≤ As / Ac ≤ 6 %.