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Technical Guidance Note

Technical

May 2013

Note 5 Level 2

›

Principles of concrete column design

The principles of reinforced concrete design are explained in Technical Guidance

Note 3 (Level 2), which covers the design of concrete slabs. You are directed to that text prior to reading this guide in order to appreciate the concepts that are introduced within it. The key topics to note from that guide are:

• Concrete cover for bond, corrosion and fi re protection • Material properties

Analysis of concrete columnsConcrete columns are typically analysed as part of a sub-frame system. They work in conjunction with the horizontal elements of the structure. As the connection between the columns and all other elements is monolithic, it follows that they transfer bending moments either in part or whole, depending on the stiff ness of the elements that are framing into the columns.

The magnitude of that transfer is dependent upon whether or not the structure that the column forms part of is ‘braced’ or ‘unbraced’. Furthermore, if the structure is a sway frame then the connections within the structure are expected to transfer bending moments. For the purposes of simplifi cation and explanation, this guide will only cover

Designing a concrete columnIntroduction

The subject of this guide is the design of reinforced concrete columns to BS EN 1992-1-1 – Eurocode 2: Design of Concrete Structures – Part 1-1: General Rules for Buildings. It covers the design of columns of all cross section profi les, which are typically square, rectangular and circular.

W

W Worked example

W Applied practice

W Further reading

W Web resources

ICON LEGEND

Principles of concrete column design

columns that are in a braced, non-sway frame structure i.e. one where its lateral stability is provided by shear walls and/or bracing.

Provided the spans of beams and/or slabs framing into a column do not diff er by more than 30%, it is acceptable to treat the horizontal elements as being simply supported. The only bending moment that is developed is via pattern loading, with one span being subjected to a full imposed load while its neighbour is not. Figure 1 provides a further explanation of this.

When determining the bending moments in such sub-frames, the relative stiff ness of each element to another needs to be

determined. This is then used to calculate the bending moments that are being applied to the column due to pattern loading. Figure 2explains how this is developed with the assumption that the end spans of the beams that frame into the column are simple pins.

The following equation defi nes how the bending moment is calculated by taking into account the relative stiff ness of elements of the structure:

Where:k is the relative stiff ness of the subframe in a braced, non-sway frame structure

k k k k2 2AB BC

col= + =

N Figure 1Pattern loading to concrete columns N Figure 2

Relative stiff ness

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Design of concrete columnLike most vertical elements in a structure designed to support compression loads, slenderness λ is a key component in design. Concrete columns are no diff erent in this regard and are defi ned by the following expression:

Where:l0 is the eff ective height of the column.i is the radius of gyration of the column about

Table 1: Eff ective lengths of columns with diff ering support conditions

End condition

at top

of column

End condition at bottom of column

1 2 3

1 0.75 0.80 0.90

2 0.80 0.85 0.95

3 0.90 0.95 1.00

Condition 1 The elements that frame into the column are at least the same depth as the size of the column in the axis being considered. When fi xed to a foundation the substructure must be designed to carry the resulting bending moment in order for this condition to be satisfi ed

Condition 2* The elements that frame into the column are shallower than the column size

Condition 3* The elements that frame into the column do not provide anything more than a nominal restraint in terms of rotation

*These conditions are typically found in fl at slab fl oor construction structures

kAB is the stiff ness of beam AB framing into the column as shown in Fig. 2 and is defi ned as:

Where: b and h are the overall width and depth of beam AB and LAB is the span.kBC is the stiff ness of beam BC framing into the column as shown in Fig. 2 and is defi ned as:

Where: b and h are the overall width and depth of beam BC and LBC is the span.kcol is the stiff ness of the column, both above and below the level under consideration. This is defi ned as:

Where: b and h are the overall width and depth of the column and Lcol is its height.

I L Lbh1

12ABAB AB

3

=

I L Lbh1

12BCBC BC

3

=

I L Lbh1

12colcol col

3

=

il0m =

the axis under consideration. This can be calculated using

Where: and A is the cross section area of the column in its uncracked state.

As a general defi nition, the value of l0 can be determined using the restraints rules provided in Table 1, which are based on Figure 5.7 in BS EN 1992-1-1.

For columns that are considered over multiple storeys, a more rigorous approach must be adopted. For a column within a braced structure, the value of l0 is defi ned in Equation 5.15 of BS EN 1992-1-1 as:

Where:k1 and k2 are the relative rigidities of the restrained ends of the column. This is based on the stiff ness between the column and the beams that frame into it.

Assuming the columns above and below the level at which the interface between horizontal and vertical structural elements are being considered do not contribute to its stiff ness, it is possible to simplify the derivation of k.

Provided the geometry does not vary beyond 15% of each span of the column, then the following expression is true:

If a beam frames into both sides of the column this expression can be altered thus:

‘Short’ columnsA column is considered to be ‘short’ if the second order moments are small enough to be neglected; that is if they are less than 10% of the fi rst order moments. This is likely to be the case for braced structures with normal fl oor to fl oor distances unless the columns are particularly small in either dimension.

In order to determine whether or not a column is short, BS EN 1992-1-1 places a criterion against which columns are determined to be ‘short’. This criterion is based on the following expression, which is

equation 5.13N in BS EN 1992-1-1:

Where:λlim is the limiting value of slenderness of a column before it can be considered to be ‘slender’ i.e. subject to second order eff ects.

A is defi ned as:

Where: φef is the eff ective creep ratio. If not known then A can be taken to be 0.7.

B is defi ned as:

Where:ω is the mechanical reinforcement ratio:

If not known then B can be taken to be 1.1.

C is defi ned as:

Where: rm is the ratio of fi rst order bending moments

at the end of the column. If this is not known then the value of C can be taken as 0.7. This factor has the biggest impact on the design of the column and to take the default value can result in conservatively sized columns. Considering the fact that during the design of a column, it is unlikely that the bending moments are not known, it is recommended that C is calculated in order to avoid oversizing columns.

n is the relative normal force and is defi ned as:

AI

I bh12

3

=

. . .l l kk

kk0 5 1 0 45 1 0 450

1

1

2

2= + + + +a ak k

( / )( / )

k k k total beam stiffnesscolumn stiffness

I lI l2 b

c1 2= = = = /

( / )( / )

( / )( / )

( / )( / )

k k kI l

I lI l

I lI l

I l2 2 2 4b

c

b

c

b

c1 2

#= = = = =/

/A B C n20lim # # #m =

/( . )1 1 0 2 ef{+

. r1 7 m-

1 2~+

A fA f

c cd

s yd

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Technical Guidance Note

Technical

May 2013

Note 5 Level 2

›

E Figure 3Detailing requirements for columns

which is the ratio of the design ultimate axial load to the area of uncracked concrete section multiplied by the compression strength of the concrete.

‘Slender’ columnsSlender columns are those that fall outside the value of λlim and are therefore subject to buckling failure as opposed to crushing, which is the case for short columns.

When a column is slender a bending moment is induced into it as the axial load is applied. The column defl ects due to the axial load and as it does so, this additional bending moment causes the column to buckle. The analysis of such columns is beyond the scope of this guidance note, but it will be the subject of a future text.

Detailing requirementsThere are very strict guidelines with regards to reinforcement detailing of columns. A minimum of 4 bars are required in a square column and 6 bars for a circular column unless it is quite small. The minimum size of bars is 12mm.

The minimum area of reinforcement is defi ned in BS EN 1992-1-1, Equation 9.12N as:

Where:As is the area of reinforcement steel.NEd is the design ultimate axial load.fyk is the characteristic yield strength of steel reinforcement, taken to be 500 N/mm2 in the UK.Ac is the cross sectional area of the concrete column in an uncracked state.

The maximum area of steel reinforcement is defi ned as:

Links in columns are there to primarily hold the bars together as they work to resist the axial load. They should be no less than 0.25 times the diameter of the compression reinforcement. Spacing is limited to 20 times that of the diameter of compression reinforcement or the smaller column dimension b or 400mm, whichever is smallest. However, for a distance h above and below the junction with a beam or slab, the spacing should be closed up to a factor of 0.6 of the spacing required for the rest of the column. All compression reinforcement must be restrained by transverse bars and cannot

A fN

c cd

Ed

.. .A f

N A0 870 10 0 002s

yk

Edc$=

.AA 0 04

c

s 1

Worked example

be more than 150mm from a restrained bar. Figure 3 is a summary of these rules.

Designing columns for axial forces and bending momentsNow that the forces in the column have been established and the detailing requirements are understood, the required reinforcement in the column can be calculated.

This can be done by using design charts that plot bending moments against axial forces, design equations as defi ned in BS EN 1992-1-1 or through an approximation. This guide focuses on the most frequently used method; the use of design charts.

The two expressions that need to be used in order to read from the charts are as follows:

These values are read against the design chart. Each chart is based on the ratio of d2/h and is therefore selected using this value. These charts can be downloaded from the Concrete Centre’s website at: www.eurocode2.info.

When considering biaxial bending in columns, you are directed to Technical

Guidance Note 22 (Level 1) which covers the analysis of such columns.

&bhfN

bh fM

ck ck2

A 4m high 600mm square column is supporting an axial load of 2500kN and a bending moment of 600kNm about one axis. It has a fi re rating of 1 hour and the grade of concrete is C30/37. It is not directly exposed to water. Determine the compression reinforcement and containment links required in the column.

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Glossary and further reading

Containment link – A form of reinforcement that consists of a hoop or series of hoops that provides the containment to compression reinforcement in a column.

Short column – A vertical element whose geometry and applied load conditions would lead it to fail in compression and not buckling.

Further Reading The Institution of Structural Engineers (2006) Manual for the design of concrete

building structures to Eurocode 2 London: The Institution of Structural Engineers

The Concrete Centre (2009) Worked

Examples to Eurocode 2: Volume 1 [Online] Available at: www.concretecentre.com/pdf/Worked_Example_Extract_Slabs.pdf (Accessed: February 2013)

Mosley W., Bungey J. and Hulse R. (2007) Reinforced Concrete Design to Eurocode

2 (6th ed.) Basingstoke, UK: Palgrave Macmillan

Reynolds C.E., Steedman J.C. and Threlfall A.J. (2007) Reynolds’s Reinforced Concrete

Designer’s Handbook (11th ed.) Oxford, UK: Taylor & Francis

The Institution of Structural Engineers (2012/13) Technical Guidance Notes 1-5, 17 and 22 (Level 1) and 3 (Level 2) The

Structural Engineer 90 (1-3, 10) and 91 (1, 3)

Eurocode 0.Web resources

The Concrete Centre: www.concretecentre.com/

The Institution of Structural Engineers library:www.istructe.org/resources-centre/library

Eurocode 0.Applied practice

BS EN 1992-1-1 Eurocode 2: Design of Concrete Structures – Part 1-1: General Rules for Buildings

BS EN 1992-1-1 UK National Annex to

Eurocode 2: Design of Concrete Structures – Part 1-1: General Rules for Buildings

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