# column-59ccc90b8a42d

```Sabah Shawkat
Cabinet of Structural Engineering
2017
3.4 Reinforced concrete column
Design of reinforcement in reinforced concrete elements loaded concentric and
eccentric compression with a small eccentricity
Although the column is essentially a compression member, the manner in which it
tends to fail and the amount of load that causes failure depend on:
1. The material of which the column is made.
2. The shape of cross-section of the column.
3. The end conditions of the column.
As the loads on columns are never perfectly axial and the columns are not perfectly
straight, there will always be small bending moments induced in the column when it
is compressed.

Determining the buckling length of the column lo
Figure: 3.4-1
1. One end fixed in direction and position, the other free k = 2
2. Both ends pinned k = 1
3. One end pinned, the other fixed in direction and position k = 0.707
4. Both ends fixed in direction and position k = 0.5
The consideration of the two end conditions together results in the following
theoretical values for the effective length factor (the factor usually used in practice).
Columns and struts with both ends fixed in position and effectively restrained in
direction would theoretically have an effective length of half the actual length.
Sabah Shawkat
Cabinet of Structural Engineering
2017
However, in practice this type of end condition is almost never perfect and therefore
somewhat higher values for k are used and can be found in building codes. In fact,
in order to avoid unpleasant surprises, the ends are often considered to be pinned
(k = 1.0) even when, in reality, the ends are restrained or partially restrained in
direction.
In this case, the end conditions for buckling about the x-x axis are not the same as
about the y-y axis. There-fore both directions must be designed for buckling (Where
the end conditions are the same, it is sufficient to check for buckling in the direction
that has the least radius of gyration).
Although the buckling of a column can be compared with the bending of a beam,
there is an important difference in that the designer can choose the axis about which
a beam bends, but normally the column will take the line of least resistance and
buckle in the direction where the column has the least lateral unsupported dimension

Determination of basic characteristics
‘
slenderness:

i
lo
i
I
A c&acute;
‘
Ac‘= b . h
- rectangle:
- where I is the
moment of inertia of
I = 1/12.b.h3
the cross section

determine the minimum cross-sectional dimension columns in terms of
buckling
Figure 3.4-2
Sabah Shawkat
Cabinet of Structural Engineering
2017

Design of reinforcement in reinforced concrete columns

Stress in concrete [MPa] :
c = Nsd / Ac’
Total required area of reinforcement v [cm2] :
Arequired = c‘ .10 2
where  can be obtained from the following graph:

=5
=7,5
0.1
0.2
12.84472
13.14803
12.76732
13.06879
13.75465
13.67173
0.3
0.4
=10
13.28918
Minimum amount of
reinforcement:
=c
13.5888
• Determination of the maximum carrying capacity of cross-section
The maximum capacity of the cross section can be determined using the
following graph:
Aprovided . 10 2 / (Ac‘)


=5
=7,5
0.1
0.2
12.84472
13.14803
12.76732
13.06879
13.75465
13.67173
0.3
0.4
=10
13.28918
=b &lt; 0,6 . fck
13.5888

sdv
Ac‘ v
lo  v
i  v
Areq, Aprovided v
MN
m2
m
m
cm2
When the load on a column is not axial but eccentric, a bending stress is induced in the
column as well as a direct compressive stress. This bending stress will need to be considered
when designing the column with respect to buckling.
The relationship between the length of the column, its lateral dimensions and the end fixity
conditions will strongly affect the column’s resistance to buckling.
Sabah Shawkat
Cabinet of Structural Engineering
2017
Many countries have their own structural design codes, codes of practice or technical
documents which perform a similar function. It is necessary for a designer to become familiar
with local requirements or recommendations in regard to correct practice.
Figure 3.4-3
In low and normal strength concrete, significant non-linearities in the stress-strain
behaviour start to develop at about 0.001 strain and the slope of the curve is close to zero at
about 0.002 strain. The steel is therefore still in the elastic range, and is able to carry an
increasing part of the load, when the non-linearities in the concrete start to develop. The usual
range of the yield strength of ordinary reinforcement is 400 to 500 N/mm2. The reinforcement
thus starts to yield at about the same strain level as the concrete reaches its maximum
strength.
In high strength concrete the stress-strain curve is more linear, and the strain at maximum
stress is higher compared to lower strength concrete. The reinforcement in HSC columns will
therefore yield before the concrete reaches its maximum strength and will continue to yield at
about the same stress level until the concrete reaches its ultimate strain level.
Precast Concrete Columns can be circular, square or rectangular. For structures of five
storeys or less, each column will normally be continuous to the full height of the building. For
structures greater than five storeys two or more columns are spliced together. Precast concrete
columns may be single or double storey height. The method of connection to the foundation
Sabah Shawkat
Cabinet of Structural Engineering
2017
and to the column above will vary with manufacturer. Foundation connection may be via a
base plate connected to the column or by reinforcing bars projecting from the end of the
column passing into sleeves that are subsequently filled with grout. Alternatively, a column
may be set into a preformed hole in a foundation block and grouted into position.
Column-column connections may be by threaded rods joined with an appropriate
connector; with concrete subsequently cast round to the dimensions of the cross-section of the
column. Alternatively, bars in grouted sleeves, as described above, may be used. This results
in a thin stitch between columns while the previous approach requires a deeper stitch.
Connections may be located between floors, at a point of contra-flexure, or at floor level.
Columns are provided with necessary supports for the ends of the precast beams (corbels or
cast-in steel sections). There will also be some form of connection to provide beam-column
moment connection and continuity. For interior columns this may be by holes through which
reinforcing bars pass from one beam to another. For edge columns, some form of bracket or
socket is required. During erection columns must be braced until stability is achieved by
making the necessary connections to the beams and slabs.
Figure 3.4-4
Sabah Shawkat
Cabinet of Structural Engineering
2017
Sabah Shawkat
Cabinet of Structural Engineering
Figure 3.4-5
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Cabinet of Structural Engineering
Figure 3.4-6
Figure 3.4-7
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Sabah Shawkat
Cabinet of Structural Engineering
2017
Sabah Shawkat
Cabinet of Structural Engineering
Figure 3.4-8
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Cabinet of Structural Engineering
Figure 3.4-9
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Cabinet of Structural Engineering
Figure 3.4-10
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Cabinet of Structural Engineering
Figure 3.4-11
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Cabinet of Structural Engineering
Figure 3.4-12
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Sabah Shawkat
Cabinet of Structural Engineering
2017
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