concrete 2001 perth - design of concrete columns to as 3600-2001 - wheeler bridge - final

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Design of Concrete Columns to AS 3600-2001

Conference Paper · September 2001

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2 authors:

Andrew Thomas Wheeler

ABES Australia

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Russell Q. Bridge

Western Sydney University

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https://www.researchgate.net/profile/Andrew_Wheeler2?enrichId=rgreq-cd4b27a8-decb-4a1f-801e-cf29e2819c59&enrichSource=Y292ZXJQYWdlOzI5MjQ3Njk2NTtBUzozMzAzNzk3OTkwODkxNTJAMTQ1NTc4MDA5MDEzMw%3D%3D&el=1_x_7https://www.researchgate.net/profile/Andrew_Wheeler2?enrichId=rgreq-cd4b27a8-decb-4a1f-801e-cf29e2819c59&enrichSource=Y292ZXJQYWdlOzI5MjQ3Njk2NTtBUzozMzAzNzk3OTkwODkxNTJAMTQ1NTc4MDA5MDEzMw%3D%3D&el=1_x_7https://www.researchgate.net/profile/Andrew_Wheeler2?enrichId=rgreq-cd4b27a8-decb-4a1f-801e-cf29e2819c59&enrichSource=Y292ZXJQYWdlOzI5MjQ3Njk2NTtBUzozMzAzNzk3OTkwODkxNTJAMTQ1NTc4MDA5MDEzMw%3D%3D&el=1_x_7https://www.researchgate.net/profile/Andrew_Wheeler2?enrichId=rgreq-cd4b27a8-decb-4a1f-801e-cf29e2819c59&enrichSource=Y292ZXJQYWdlOzI5MjQ3Njk2NTtBUzozMzAzNzk3OTkwODkxNTJAMTQ1NTc4MDA5MDEzMw%3D%3D&el=1_x_7https://www.researchgate.net/profile/Russell_Bridge?enrichId=rgreq-cd4b27a8-decb-4a1f-801e-cf29e2819c59&enrichSource=Y292ZXJQYWdlOzI5MjQ3Njk2NTtBUzozMzAzNzk3OTkwODkxNTJAMTQ1NTc4MDA5MDEzMw%3D%3D&el=1_x_7https://www.researchgate.net/profile/Russell_Bridge?enrichId=rgreq-cd4b27a8-decb-4a1f-801e-cf29e2819c59&enrichSource=Y292ZXJQYWdlOzI5MjQ3Njk2NTtBUzozMzAzNzk3OTkwODkxNTJAMTQ1NTc4MDA5MDEzMw%3D%3D&el=1_x_7https://www.researchgate.net/profile/Russell_Bridge?enrichId=rgreq-cd4b27a8-decb-4a1f-801e-cf29e2819c59&enrichSource=Y292ZXJQYWdlOzI5MjQ3Njk2NTtBUzozMzAzNzk3OTkwODkxNTJAMTQ1NTc4MDA5MDEzMw%3D%3D&el=1_x_7https://www.researchgate.net/profile/Russell_Bridge?enrichId=rgreq-cd4b27a8-decb-4a1f-801e-cf29e2819c59&enrichSource=Y292ZXJQYWdlOzI5MjQ3Njk2NTtBUzozMzAzNzk3OTkwODkxNTJAMTQ1NTc4MDA5MDEzMw%3D%3D&el=1_x_7https://www.researchgate.net/?enrichId=rgreq-cd4b27a8-decb-4a1f-801e-cf29e2819c59&enrichSource=Y292ZXJQYWdlOzI5MjQ3Njk2NTtBUzozMzAzNzk3OTkwODkxNTJAMTQ1NTc4MDA5MDEzMw%3D%3D&el=1_x_1https://www.researchgate.net/profile/Russell_Bridge?enrichId=rgreq-cd4b27a8-decb-4a1f-801e-cf29e2819c59&enrichSource=Y292ZXJQYWdlOzI5MjQ3Njk2NTtBUzozMzAzNzk3OTkwODkxNTJAMTQ1NTc4MDA5MDEzMw%3D%3D&el=1_x_7https://www.researchgate.net/institution/Western_Sydney_University?enrichId=rgreq-cd4b27a8-decb-4a1f-801e-cf29e2819c59&enrichSource=Y292ZXJQYWdlOzI5MjQ3Njk2NTtBUzozMzAzNzk3OTkwODkxNTJAMTQ1NTc4MDA5MDEzMw%3D%3D&el=1_x_6https://www.researchgate.net/profile/Russell_Bridge?enrichId=rgreq-cd4b27a8-decb-4a1f-801e-cf29e2819c59&enrichSource=Y292ZXJQYWdlOzI5MjQ3Njk2NTtBUzozMzAzNzk3OTkwODkxNTJAMTQ1NTc4MDA5MDEzMw%3D%3D&el=1_x_5https://www.researchgate.net/profile/Russell_Bridge?enrichId=rgreq-cd4b27a8-decb-4a1f-801e-cf29e2819c59&enrichSource=Y292ZXJQYWdlOzI5MjQ3Njk2NTtBUzozMzAzNzk3OTkwODkxNTJAMTQ1NTc4MDA5MDEzMw%3D%3D&el=1_x_4https://www.researchgate.net/profile/Andrew_Wheeler2?enrichId=rgreq-cd4b27a8-decb-4a1f-801e-cf29e2819c59&enrichSource=Y292ZXJQYWdlOzI5MjQ3Njk2NTtBUzozMzAzNzk3OTkwODkxNTJAMTQ1NTc4MDA5MDEzMw%3D%3D&el=1_x_7https://www.researchgate.net/profile/Andrew_Wheeler2?enrichId=rgreq-cd4b27a8-decb-4a1f-801e-cf29e2819c59&enrichSource=Y292ZXJQYWdlOzI5MjQ3Njk2NTtBUzozMzAzNzk3OTkwODkxNTJAMTQ1NTc4MDA5MDEzMw%3D%3D&el=1_x_5https://www.researchgate.net/profile/Andrew_Wheeler2?enrichId=rgreq-cd4b27a8-decb-4a1f-801e-cf29e2819c59&enrichSource=Y292ZXJQYWdlOzI5MjQ3Njk2NTtBUzozMzAzNzk3OTkwODkxNTJAMTQ1NTc4MDA5MDEzMw%3D%3D&el=1_x_4https://www.researchgate.net/?enrichId=rgreq-cd4b27a8-decb-4a1f-801e-cf29e2819c59&enrichSource=Y292ZXJQYWdlOzI5MjQ3Njk2NTtBUzozMzAzNzk3OTkwODkxNTJAMTQ1NTc4MDA5MDEzMw%3D%3D&el=1_x_1https://www.researchgate.net/publication/292476965_Design_of_Concrete_Columns_to_AS_3600-2001?enrichId=rgreq-cd4b27a8-decb-4a1f-801e-cf29e2819c59&enrichSource=Y292ZXJQYWdlOzI5MjQ3Njk2NTtBUzozMzAzNzk3OTkwODkxNTJAMTQ1NTc4MDA5MDEzMw%3D%3D&el=1_x_3https://www.researchgate.net/publication/292476965_Design_of_Concrete_Columns_to_AS_3600-2001?enrichId=rgreq-cd4b27a8-decb-4a1f-801e-cf29e2819c59&enrichSource=Y292ZXJQYWdlOzI5MjQ3Njk2NTtBUzozMzAzNzk3OTkwODkxNTJAMTQ1NTc4MDA5MDEzMw%3D%3D&el=1_x_2


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20th Biennial Conference of the Concrete Institute of Australia 2001 (Concrete 2001),Perth, Western Australia, 11 - 14 September 2001

1

Wheeler & Bridge

DESIGN OF CONCRETE COLUMNS TO AS 3600-2001

A. Wheeler and R.Q. Bridge

Centre for Construction Technology and Research, University of Western Sydney

Synopsis. Columns are an important structural element in reinforced concrete

structures. They are usually cast integrally with the framing concrete beams and slabs

although precast columns can be used in appropriate situations. They have to provide

resistance to both axial forces and bending moments generally resulting from load

applied to the floor beams and slabs. In the design procedure for columns, use is made

of the load-moment interaction diagrams which may be in the form of design charts or

generated by computer programs.

Important new design provisions have been included in a new edition of Australian

Standard AS 3600-2001, "Concrete Structures". Apart from improving the quality of

building construction, the new design provisions also allow designers to benefit

considerably from the move to high-strength 500 MPa reinforcing steels. The use of thehigher strength steels is of particular importance in the design of columns where the

predominant action to be resisted is axial force. Significant savings in steel can be

achieved leading to more economical solutions.

The new AS3600-2001 design provisions for columns take into account the change to

the higher strength steels. This paper presents the background to the changes and

includes important explanatory information. This will assist structural design engineers

to understand the engineering principles on which the design method is based and to

better realise the benefits that can be achieved through the use of the changes in

conjunction with the introduction of the high strength steels. These benefits are

highlighted through the presentation of a number of practical worked examples.Examples of new improved design charts are also presented.

1.0 INTRODUCTION

The introduction of the new Australian Concrete Structures Standard AS 3600-2001 [1]

and the corresponding introduction of 500 Grade reinforcing steel has resulted in a

number of significant changes in methods for calculating the ultimate strength of

members. While it may appear that the higher yield strength reinforcing steel can be

considered by substituting the yield stress ( f sy) into the existing calculation methods, it

should be pointed out that these methods are based on a number of assumptions that are

dependent on material properties. Consequently, a number of changes were made to the

standard to enable design with the higher grade reinforcing steel.

In this paper the changes made in AS 3600-2001 for the determination of the column

ultimate strength are discussed. The first of the changes is in the calculation of the

ultimate compressive strength of a column. According to AS 3600-1994 [2] the ultimate

compressive strength of a column is calculated by applying a constant strain of 2000

micro-strain to the cross-section. At this strain it is assumed that the concrete stress is

equal to the cylinder strength f c and that the reinforcing steel is at yield. However,

AS 3600-2001 increases the applied strain to 2500 micro-strain to invoke the additional

strength of the higher yielding reinforcing steel.

The second significant change is in the determination of the balance point. When

considering the column in combined compression and bending, the capacity reductionfactor is dependent on whether bending or axial compression is dominant, as determined


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Wheeler & Bridge

by the “balance point”. The values of this balance point are based on material properties

of the reinforcing. Consequently, they are altered with the introduction of higher grade

reinforcement.

Other significant changes with respect to columns discussed in this paper include

adjustment to the column stiffness when determining the buckling capacity, and the

increase in the maximum allowable concrete strength from 50 MPa to 65 MPa.

A design example is presented to demonstrate the economic benefits that may be

realised by utilising 500 grade reinforcement. Also presented is an improved “Column

Design Chart” that enables quick easy determination of reinforcement requirements for

standard columns.

2.0 CROSS-SECTIONAL STRENGTH

The cross-sectional strength of a member is dependent on a number of factors including

the size, relative configuration of the steel and concrete components and the material

properties of the both steel and concrete. While the size and layout of the cross-section

is critical in determining the capacity of a column, it is imperative that the stress-strainrelationships of both the steel and concrete be fully understood.

The common stress strain curve used for concrete is that defined by the Comite

Europeen de Beton [3]. Typical stress-strain curves for the current grades of concrete as

defined by AS 3600 [1] are shown in Figure 1. This Figure includes the 65 MPa

concrete as represented by the CEB curve. For all curves the strain corresponding to

maximum strength of the concrete occurs at a constant value of 0.0022. It should be

noted that the maximum strength of the concrete for determining strength of cross-

sections is taken as 0.85 f ’c, accounting for effects of long term loading and other site

conditions.

0 .

0 0 2 2

25 MPa

32 MPa

40 MPa

50 MPa

65 MPa

0

10

20

30

40

50

60

70

0 0.001 0.002 0.003 0.004 0.005

Strain

S t r e s s ( M P a )

Figure 1 - Stress Strain Relationship for Concrete

For reinforcing steels, a bi-linear elastic-plastic stress-strain relationship is utilised for

design, as shown in Figure 2. For design purposes, the elastic modulus ( E s) is taken as

200 000 MPa, the yield strength ( f sy) is based on the grade of reinforcement and the

yield strain (sy) is a function of the yield strength and the elastic modulus.


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0 . 0

0 2 0

0 . 0

0 2 5

0

100

200

300

400

500

600

0 0.001 0.002 0.003 0.004 0.005Strain s

S t r e s s s

( M P a )

0.0025

0.002

Figure 2 - Stress Strain Relationship for Reinforcing Steel

In determining the ultimate capacities of columns when subjected to either bending

and/or axial force a number of assumptions are usually made. These are:

1. Plan sections remain plane2. Reinforcement is fully bonded to concrete3. Tensile strength of concrete is ignored4. Equilibrium and strain compatibility are satisfied

2.1 Axial Compression

The behaviour of a reinforced concrete cross-section subject to axial loading is easily

modelled by applying a uniform axial strain (a) to the cross-section. Using the stress-

strain relationships for the steel (Figure 2) and concrete (Figure 1), the stress in each

material may be determined and the resulting axial force expressed as

ccss A A N 1

The concrete stress (c) and steel stress (s) for the given strain (a) may be expressed as

)( ac f 2

),min(200000 syas f 3

From Figure 1 it is observed that the concrete stress strain relationship is non-linear with

the maximum strength of 0.85 f ’c occurring at a strain of 0.0022 while the steel is linear

elastic to the yield strain (sy) at which point the stress remains constant at the yield

stress ( f sy).

The ultimate strength ( N uo) of the cross-section in axial compression is determined by

increasing the axial strain a until the axial force N given in Eq. 1 reaches a maximum.

The strain corresponding to the ultimate axial strength N uo is defined as uo.

When the yield strain of the reinforcing steel is less than or equal to the strain resultingin a peak concrete load ( o), it can be seen that the steel yields before the concrete has


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reached its maximum strength. Thus the ultimate axial strength N ou in compression is

simply given as:

ccssyuo 850 A' f . A f N 4

For the 400 grade reinforcing bar this has been the case with a yield strain of sy = 0.002

which is less than the peak concrete strength strain o (=0.0022). This was reflected inClause 10.6.3 of AS 3600-1994 [2]. However, for steels with yield strains greater than

the strain o at peak concrete strength, such as the new 500 grade steels, the simplifiedmethod as described in Eq. 4 is no longer valid. Consequently, to fully utilise the

additional strength from increasing the steel strength, AS 3600-2000 recommends thatthe assumed applied axial strain is increased from 0.002 to 0.0025.

As shown in Figure 3, when a strain of 0.002 is applied to the cross-section, the

concrete stress is close to its peak stress but the stress in the steel is significantly below

the yield stress for a 500 grade steel. At a strain of 0.0025 (sy for 500 Grade steel) thereinforcement stress has peaked. However the concrete has passed its peak stress and

some loss in the concrete strength is observed. Consequently, the ultimate strength asdefined by Eq. 4 will generally give overestimates for the column capacities. The

magnitude of the overestimation is dependent on the percentage of reinforcement andthe strength of concrete, with the difference of approximately 2 percent occurring in a

column with 3 percent steel and 50 MPa concrete. However, when long term effects areconsidered these overestimations in ultimate strength are eliminated [4].

0 . 0

0 2 5

0

100

200

300

400

500

600

0 0.001 0.002 0.003 0.004 0.005 0.006

Strain

S t e e l S t r e s s ( M P a )

0

5

10

15

20

25

30

35

40

C o n c r e t e S t r e s s ( M P a )

31.6 MPa

Concrete

Steel

Figure 3 – Peak Stress and Strains

To accurately determine the short-term axial strength of a column cross-section it

should be noted that the ultimate strain (ou) at which the ultimate axial compressivestrength N uo is achieved is dependent on the geometric properties and the shape of the

concrete stress-strain relationship. For section typically with high percentages of steelthe ultimate load is achieved when the steel yields. Thus the ultimate axial compressive

strength N uo is expressed as


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Wheeler & Bridge

csyssyuo )( A f A f N 5

For cross-sections with lower percentages of reinforcement, ultimate axial compressive

strength N uo is reached before the steel yields. The steel remains elastic, with the axialcompressive strength N expressed as

casas )( A f A E N 6

where E s is the elastic modulus of the reinforcing steel.

To determine the ultimate axial compressive strength N uo, Eq. 6 is differentiated with

respect to strain a and equating to zero gives the condition for maximum axial

compressive strength N uo where

0ca

ass

A

d

f d A E

d

dN ))((

a

7

Eq. 7 may be solved analytically if the stress-strain relationship c = f (a) is in a closedform solution and amenable to differentiation. Alternatively, Eq. 6 can be solved

numerically by varying a until a maximum value is obtained for N uo

There is no prior way of knowing if the steel yields prior to or after reaching the

ultimate axial compressive strength. However, the value of N uo from Equation 5 will be

less than or equal the value from Equation 6 and could be used conservatively for

design purposes. Alternative methods for determining an accurate value for N uo using

charts has also been developed [4].

2.2 Combined Compression and Bending

Moment

A x i a l L o a d

cu

k ud

Pure Moment ( M uo)

Pure Axial ( N uo)

cu

k uod o sy

Balance Point ( M ub, N u,)

d o

cu

( M ul, N ul)

Figure 4 – - Load Moment Strength Interaction Curve

The capacity of a column cross-section depends on the eccentricity of the applied load,

with the load decreasing as the eccentricity increases. General practice is to represent an

eccentric load as an axial load and a moment equivalent to the product of the appliedaxial load and the eccentricity. Consequently most design is done utilising the load


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Wheeler & Bridge

moment strength interaction curve of the type shown in Figure 4. A detailed description

of the theory and methods used is beyond the scope of this paper but can be found in a

number of publications [5][6].

Three key points on the load-moment strength interaction diagram, as shown in Figure

4, are of particular interest and use to designers. While the new standard has adjusted

some of the assumptions in determining the ultimate squash load N uo with respect to

applied strains, the ultimate strength in bending M uo still assumes that the strain cu on

the extreme compressive fibre is 0.003 [7]. At the so-called “balanced point” the

particular ultimate bending strength M ub and the corresponding ultimate axial

compression strength N ub are determined are determined for a particular depth of the

neutral axis (k uod o). At this point the value of k uo is such that this outermost layer of steel

has just reached yield at a strain of sy, and d o is the depth from the extreme compressive

fibre to the centroid of the outermost layer of tensile reinforcement. This point is usually

at or close to the “nose” of the load moment interaction diagram.

cu

k uod o sy

Figure 5 - Balance Point Strain Distribution

The strain distribution at the balance point is shown in Figure 5. From this figure the

required k uo at the balance point is determined and given by

sycu

cu

uok 8

In AS3600-1994, the normal type of bar reinforcement used in columns is 400Y with a

design yield stress f sy = 400 MPa and a yield strain sy = 0.002. The maximum

compressive strain cu in the concrete at ultimate strength is taken as 0.003. Using these

values in Eq. 8 gives a value of k uo = 0.6 which is the value that was used in AS3600-

1994 (see definitions of M ub and N ub in Clause 1.7). For 500N grade steel with a design

yield stress f sy = 500 MPa and a yield strain sy = 0.0025, then Eq. 8 gives a value of

k uo = 0.545. Consequently, AS 3600-2001 specifies the value of k uo according to Eq. 8.

3.0 BUCKLING LOAD

When considering slender columns, AS 3600 uses a moment magnifier to take into

account the slenderness effects. The moment magnifier for a braced column b is given

in Clause 10.4.2 of AS 3600 as

011 c

m b .

N N

k *

9

where k m is the coefficient is used to convert a column with unequal end moments, N * is

the applied axial load and N c is the column buckling loads defined as


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Wheeler & Bridge

2

e

c L

EI N

2 10

In determining the buckling load, the effective length Le is found using Clause 10.5.3 of

AS 3600-2001. However the stiffness EI of the column cross-section varies according to

the level of axial load and moment applied to the column. To simplify the design process, the secant stiffness for the column, based on the stiffness of the column cross-

section at the balance point ( M ub, N ub) is utilised to define this stiffness [8, 9]. The

secant stiffness has been shown to be relative constant for a wide range of points

( M u, N u) [10]. The secant stiffness for a typical moment-curvature relationship at a

constant axial force equal to the balanced value N ub is shown in Figure 6.

Curvature

M o m e n t

Slope = EI

M ub

ub

N ub = Constant

Figure 6 - Moment-Curvature Relationship for Constant Balanced Axial Force Nub

From this figure the secant stiffness EI at the balance point is expressed as

ub

ub

M EI 11

From the strain diagram shown in Figure 5 at the balance point, the curvature ub (slope

of the strain distribution) is given by

ouo

cuub

d k

12

Substituting the value of k uo from Eq. 8 into Eq. 12 then substituting this value of ub

into Eq. 11 gives the secant stiffness EI

sycu

oub

d M EI 13

In AS3600-1994, the normal type of bar reinforcement used in columns is 400Y with adesign yield stress f sy = 400 MPa and a yield strain sy = 0.002, and the maximum

compressive strain cu in the concrete at ultimate strength is taken as 0.003. Using these


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Wheeler & Bridge

values in Eq. 13 then

EI = 200d o M ub 14

When the same procedure is applied to 500N grade steel with a design yield stress f sy =

500 MPa and a yield strain sy = 0.0025, and taking the strain cu in the concrete at

ultimate strength as 0.003, then substitution into Eq. 13 gives the design value for EI as

EI = 182d o M ub 15

Finally the stiffness is corrected to account for creep due to sustained loading, a reduced

concrete elastic modulus, resulting in a column stiffness of

EI = 200d o( M ub)/(1+ d ) for 400 Grade 16

EI = 182d o( M ub)/(1+ d ) for 500 Grade 17

where d is the creep factor and M ub is the design strength.

4.0 DESIGN EXAMPLE

To demonstrate how savings can be achieved by using the 500 grade reinforcement, a

typical design example is presented. For the case chosen a re-design of a 400 grade

column into 500 grade reinforcement is required. The column had external dimensions

of 450 x 700 mm, 50 MPa concrete, with the reinforcement consisting of 12Y36 barswith a cover of 35 mm to reinforcement as shown in the insert in Figure 7.

The load-moment strength interaction diagram for the column using 400 grade

reinforcement is shown by the bold line in Figure 7. For this particular example three

alternatives using 500 grade reinforcement were determined.

The first was a simple substitution of 12N36 (500 grade) bars for the existing 12Y36 bars. This solution represented by the dash line results in a column with an increase of 5

percent in axial capacity and up to 20 percent increase in moment capacity.

The second alternative is to reduce the bar diameter and use 12N32 bars; this equates to

a reinforcement reduction of approximately 21 percent. As represented in Figure 7 by

the dash-dot-dot line, this alternative presents a load moment strength curve a little

lower than that of the original column with a decrease in axial capacity of

approximately 1 percent and decrease in moment capacity of 2 percent. If within the

tolerance of design, these variations may acceptable. Consequently a 21 percent saving

in steel may obtained.


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Wheeler & Bridge

0

2000

4000

6000

8000

10000

12000

0 500 1000 1500

Moment Strength M u (kNm)

A x i a l S t r e n g t h

N u

( k N )

12N36500 Grade

12Y36400 Grade

12N32500 Grade 10N36

500 Grade

12 bars 10 bars

450 x 700

50 MPa ConcreteCover 35 mm

Figure 7 – Load-Moment Strength Interaction ( Ast Equal)

The third alternative is to replace the 12Y36 bars with 10N36 bars in the configuration

shown in Figure 7. In this case the load moment strength curve, the dash-dot line,

closely represents the curve for the existing column design with a saving of 17 percent

of reinforcement realised. For the given example, the designer must also check the

design for bending in the y direction to ensure that it is also adequate.

5.0 COLUMN DESIGN CHARTS

To assist the designer in selecting the correct column based on design action effects, a

number of publications exist that enable quick selection of the correct percentages of

reinforcement using charts. A typical design chart is presented in Figure 8 for a

rectangular column reinforced equally on all four faces.

The design charts are generated using an advanced analysis method, with material

assumptions as specified by AS 3600-2001. The stress distributions in the concrete were

determined from the CEB stress strain relationship, with a maximum stress of 0.85 f 'c.

The reinforcing steel utilises a bi-linear relationship and a yield stress of 500MPa. The

balance moment M ub and corresponding axial load N ub were determined when

k uo = 0.545.


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Wheeler & Bridge

0 . 0

8

0 . 0

7

0 . 0

6

0 . 0

5

0 . 0

4

0 . 0

3

0 . 0 2

0. 0 1

0. 0 0

0

10

20

30

40

0 2 4 6 8 10 12

Mu /AgD (MPa)

N u

/ A g

( M P a )

Minimum eccentricity

Locus Nub, Mub

Figure 8 – Rectangular Column f 'c = 40 MPa, g = 0.9

To determine the required percentage of steel the design action effects are taken and

non-dimensionlised using the depth and width of the cross section. These values are

then plotted on the chart and the corresponding percentage of steel determined. A series

of the charts for three general cross-sections may be found in the Guide to ReinforcedConcrete Design Booklet “Cross-section Strength of columns” [11].

6.0 CONCLUSIONS

With the introduction of the AS 3600 - 2001 and the ability to design using 500 grade

reinforcement, a number of subtle changes in the procedure for determining ultimate

strength and stiffness of column cross-sections have been introduced.

The changes with respect to columns include

Calculation of N uo - The ultimate strength in compression N uo shall be calculated by

assuming that the uniform concrete compressive stress in the concrete is equal to 0.85 f c

and that the maximum strain in the steel and concrete is 0.0025.

Definition of kuo - The value of k uo for the determination of the balance point and

buckling stiffness is now dependent on the yield strength of the reinforcement as

defined by Eq. 8. This results in the value of k uo being equal to 0.6 and 0.545 for 400

grade and 500 grade reinforcement respectively. The column buckling loads also vary

with the reinforcement grade.

7.0 REFERENCES

1 Standards Australia, (2001), “ AS3600-2001 – Concrete Structures”, Standards

Australia, Sydney.

2 Standards Australia, (2001), “ AS 3600-1994 – Concrete Structures”, Standards

b

DgD


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Wheeler & Bridge

Australia, Sydney.

3 CEB (1973), “Deformability of Concrete Structures – Basic Assumptions”, Bulletin

D’Information No. 90, Comite Europeen du Beton.

4 Wheeler A. and Bridge R., (2001) “Column Axial Compressive Strength and

AS 3600-2001”, Proceedings, The Australasian Structural Engineering Conference, Gold Coast 2001, pp. 359-366.

5 Bridge, R.Q. and Roderick, J.W. (1978), “The Behaviour of Built-up Composite

Columns”, Journal of the Structural Division, ASCE, Vol. 104, No. ST7, July, pp.

1141-1155.

6 Wheeler A. T. and Bridge R. Q., (1993) “Analysis of Cross-sections in Composite

Materials”. Proceedings, Thirteenth Australasian Conference on the Mechanics of

Structures and Materials, Wollongong, Australia, University of Wollongong, pp 929-

937.

7 Bridge, R.Q. and Smith, R.G. (1984), “The Ultimate Strain of Concrete”, Civil

Engineering Transactions, IEAust, Vol. CE26, No. 3, pp. 153-160.

8 Smith, R.G and Bridge, R.Q. (1984) “The Design of Concrete Columns”, Top Tier

Design Methods in the Draft Unified Code, Lecture 2, Postgraduate Course Notes,

School of Civil and Mining Engineering, University of Sydney, pp. 2.1-2.95

9 Bridge, R.Q. (1986), “ Design of Columns”, Short Course, Design of Reinforced

Concrete, School of Civil Engineering and Unisearch Ltd., University of New South

Wales, Lecture 8, pp. 8.1-8.36

10 Smith, R.G. and Bridge, R.Q. (1984), “Slender Braced Reinforced and Prestressed

Concrete Columns – A Comparative Study”, Research Report No. 472 , School of

Civil and Mining Engineering, University of Sydney, April, 51p.11 Bridge, R. and Wheeler A. (2000), “Guide to Reinforced Concrete Design – Cross-

section Strength of Columns – Part 1: AS 3600 Design”, OneSteel Reinforcing,

Sydney.
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concrete 2001 perth - design of concrete columns to as 3600-2001 - wheeler bridge - final

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