›
Note 5 Level 2
22
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
TSE17_22-25.indd 22
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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›
Note 5 Level 2
24
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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