› Note 5 Level 2
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Technical Technical Guidance Note
TheStructuralEngineer May 2013
Designing a concrete column Introduction
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 profiles, which are typically square, rectangular and circular.
ICON LEGEND
Principles of W concrete column design W Worked example
W Applied practice
W Further reading
W Web resources
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 fire protection
• Material properties Analysis of concrete columns Concrete 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 stiffness 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 simplification and explanation, this guide will only cover
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N
N
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.
determined. This is then used to calculate the bending moments that are being applied to the column due to pattern loading. Figure 2 explains how this is developed with the assumption that the end spans of the beams that frame into the column are simple pins.
Figure 1 Pattern loading to concrete columns
Provided the spans of beams and/or slabs framing into a column do not differ 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 stiffness of each element to another needs to be
Figure 2 Relative stiffness
The following equation defines how the bending moment is calculated by taking into account the relative stiffness of elements of the structure:
k k k = 2AB + 2BC = k col Where: k is the relative stiffness of the subframe in a braced, non-sway frame structure
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kAB is the stiffness of beam AB framing into the column as shown in Fig. 2 and is defined as:
I AB
I A
1 bh 3 = L AB 12L AB
If a beam frames into both sides of the column this expression can be altered thus:
the axis under consideration. This can be calculated using
k = k1 = k2 =
(I c /l) (I c /l) (I c /l) = = / 2 (I b /l) 2 # 2 (I b /l) 4 (I b /l)
Where:
Where: b and h are the overall width and depth of beam AB and LAB is the span. kBC is the stiffness of beam BC framing into the column as shown in Fig. 2 and is defined as:
1 bh 3 I BC L = 12L BC BC Where: b and h are the overall width and depth of beam BC and LBC is the span. kcol is the stiffness of the column, both above and below the level under consideration. This is defined as:
1 bh 3 I col L = 12L col col Where: b and h are the overall width and depth of the column and Lcol is its height.
Design of concrete column Like most vertical elements in a structure designed to support compression loads, slenderness λ is a key component in design. Concrete columns are no different in this regard and are defined by the following expression:
l m = i0 Where: l0 is the effective height of the column. i is the radius of gyration of the column about
bh 3 I = 12
and A is the cross section area of the column in its uncracked state.
As a general definition, 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 defined in Equation 5.15 of BS EN 1992-1-1 as:
‘Short’ columns A 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 first order moments. This is likely to be the case for braced structures with normal floor to floor 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 k k l 0 = 0.5l a 1 + 0.45 1+ k ka 1 + 0.45 2+ k k columns are determined to be 1 2 ‘short’. This criterion is based on the following expression, which is Where: k1 and k2 are the relative rigidities of the equation 5.13N in BS EN 1992-1-1: restrained ends of the column. This is m lim = 20 # A # B # C/ n based on the stiffness between the column and the beams that frame into it. Where: λlim is the limiting value of slenderness of a Assuming the columns above and below column before it can be considered to be the level at which the interface between ‘slender’ i.e. subject to second order effects. horizontal and vertical structural elements are being considered do not contribute to A is defined as: its stiffness, it is possible to simplify the 1/ (1 + 0.2{ ef ) derivation of k. Where: Provided the geometry does not vary φef is the effective creep ratio. If beyond 15% of each span of the column, not known then A can be taken to be 0.7. then the following expression is true: B is defined as:
column stiffness k = k 1 = k 2 = total beam stiffness =
(I c /l) / 2 (I b /l)
1 + 2~ Where:
ω is the mechanical reinforcement ratio:
Table 1: Effective lengths of columns with differing support conditions
A s fyd A c fcd
End condition at bottom of column
End condition at top 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
If not known then B can be taken to be 1.1.
C is defined as:
1.7 - rm Where:
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 fixed to a foundation the substructure must be designed to carry the resulting bending moment in order for this condition to be satisfied 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 flat slab floor construction structures
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rm is the ratio of first 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 defined as:
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N Ed A c fcd
TheStructuralEngineer May 2013
Technical Technical Guidance Note
E
Figure 3 Detailing 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’ columns Slender 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 deflects 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 requirements There 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.
be more than 150mm from a restrained bar. Figure 3 is a summary of these rules.
The two expressions that need to be used in order to read from the charts are as follows:
Designing columns for axial forces and bending moments
N M bhfck & bh 2 fck
Now 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 defined in BS EN 1992-1-1 or through an approximation. This guide focuses on the most frequently used method; the use of design charts.
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.
Worked example The minimum area of reinforcement is defined in BS EN 1992-1-1, Equation 9.12N as:
0.10N A s = 0.87f Ed $ 0.002A c yk 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.
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 fire 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.
The maximum area of steel reinforcement is defined as:
As A c 1 0.04 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
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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
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
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