KEY DESIGN DATA FOR RC COLUMNS DESIGN

A column may be considered as short when both the ratios lex/h and ley/b are less than 15 (braced) and 10
(unbraced). It should otherwise be considered as slender.
Effective height of a column
The effective height, le, of a column in a given plane may be obtained from the following equation: le =
β.lo
lo = clear height between end restraints.

End conditions
The four end conditions are as follows.
a) Condition 1. The end of the column is connected monolithically to beams on either side which are at
least as deep as the overall dimension of the column in the plane considered. Where the column is
connected to a foundation structure, this should be of a form specifically designed to carry moment.
b) Condition 2. The end of the column is connected monolithically to beams or slabs on either side which
are shallower than the overall dimension of the column in the plane considered.
c) Condition 3. The end of the column is connected to members which, while not specifically designed to
provide restraint to rotation of the column will, nevertheless, provide some nominal restraint.
d) Condition 4. The end of the column is unrestrained against both lateral movement and rotation (e.g. the
free end of a cantilever column in an unbraced structure).
Slenderness limits for columns
Generally, the clear distance, lo, between end restraints should not exceed 60 times the minimum
thickness of a column.
Slenderness of unbraced columns
If, in any given plane, one end of an unbraced column is unrestrained (e.g. a cantilever column), its clear
height, lo, should not exceed:
Minimum percentage of steel: 100 Asc/Acc = 0.4
where Asc = Area of longitudinal steel in compression
Acc = Area of concrete in compression
Maximum area of reinforcement:
For vertically cast column: should not exceed 6% of the gross cross-sectional area
For laps in columns: should not exceed 10% of the gross cross-sectional area
Links:
The diameter of links should not be less than 6 mm or one-quarter of the diameter of the largest
longitudinal bar;
The maximum spacing is to be 12 times the diameter of the smallest longitudinal bar
The links should be arranged so that every corner bar and each alternate bar in an outer layer is supported
by a link passing round the bar and having an included angle of not more than 135°. No bar is to be
farther than 150 mm from a restrained bar.

Length of compression laps = 1.25 * Anchorage length in compression

Laps in columns are located above the base and floor levels as shown in figure below.

Short columns
Short braced columns supporting an approximately symmetrical arrangement of beams
The design ultimate axial load for a short column of this type may be calculated using the following
equation:
N = 0.35fcuAc + 0.67Ascfy
where
a) the beams are designed for uniformly distributed imposed loads; and
b) the beam spans do not differ by more than 15 % of the longer.

Where, due to the nature of the structure, a column cannot be subjected to significant moments, it may be
designed so that the design ultimate axial load does not exceed the value of N given by:
N = 0.4fcuAc + 0.75Ascfy
The above equation allows for small eccentricity of axial load

If the load applied is assumed to be perfectly axial, the capacity of the column cross section can be based
on the design strength of concrete and steel, thereby the design ultimate axial load shall not exceed
N = 0.45fcuAc + 0.87fyAsc
In all the above expressions for N,
Ac = net cross-sectional area of concrete in the column and
Asc = area of vertical reinforcements
Biaxial bending
For biaxial bending column, it is considered as an uniaxial bending column about any one axis by
increasing the moment about that axis.
h'
if Mx/My ≥ h′/b′: the enhanced design moment, about the x–x axis, M ' x = M x + My
b'
if Mx/My < h′/b′, the enhanced design moment, about the y–y axis, M ' y = M y + b' M x
Where b′ and h′ are the effective depths h'
Values of enhancement coefficient β

Rigorous method of determination of effective height of column

I = second moment of area of the section
l = effective height in the plane considered
e
l = clear height between end restraints
0
α = ratio of the sum of the column stiffnesses to the sum of the beam stiffnesses at
c1
the lower end
α = ratio of the sum of the column stiffnesses to the sum of the beam stiffnesses at
c2
the upper end
α = the lesser of α and α
c min c1 c2
I/l = stiffness of member (both column and beam)
0

For simply supported beams framing into a column, αc=10;

For the connection between column and base designed to resist only nominal moment, αc=5;
For the connection between column and base designed to resist column moment, αc=1.0.
1. For braced columns the effective height is the lesser of
le = l0 [0.7 + 0.05(αc1 + αc2)] < l0
le = l0 (0.85 + 0.05αc min) < l0
2. For unbraced columns the effective height is the lesser of
le = l0[1.0 + 0.15(αc1 + αc2)]
le = l0(2.0 + 0.3αc min)
 Slender columns

In general, a cross-section of a slender column may be designed by the methods given for a short
column but in the design, account has to be taken of the additional moment induced in the column by
its deflection.
2
1  le 
The deflection of slender column at ultimate stage ɑu = βaKh, a   
2000  b' 
βa can be determined by the following expression or from the table 3.21 given in code as below.

In the above expression for βa the value of b’ is the least dimension of the column cross section.

K is a reduction factor that corrects the deflection to allow for the influence of axial load. K is derived
from the following equation:
N uz  N
K 1
N uz  N bal
Where, Nuz = 0.45fcuAc + 0.87fyAsc is the axial load capacity of the column when the axial load is
perfectly axial.

Nbal = 0.25fcu.b.d.

K has to be found by iterations; otherwise, conservatively, may be taken as 1.

The deflection induces an additional moment given by:

Madd = N. ɑu

Design moments in braced columns bent about a single axis

Figure 3.20 shows the distribution of moments assumed over the height of a typical braced column.
It may be assumed that the initial moment at the point of maximum additional moment (i.e. near
mid-height of the column) is given by:

Mi = 0.4M1 + 0.6M2 ≥ 0.4M2

Where, M1 is the smaller initial end moment due to design ultimate loads;

M2 is the larger initial end moment due to design ultimate loads.

If the column is bent in double curvature, M1 should be taken as negative and M2 positive.

It will be seen from Figure 3.20 of the code that the maximum design moment for the column will be
the greatest of a) to d):

a) M2;

b) Mi + Madd;

c) M1 + Madd/2;

d) eminN.
emin, equal to 0.05 times the overall dimension of the column in the plane of bending considered but
not more than 20 mm

(a) Slender columns bent about a single axis (major or minor)

If the h < 3b for columns bent about the major axis and le/h ≯ 20, the design moment is Mi+Madd as
set out above.

(b) Columns where le/h>20 bent about the major axis

The section is to be designed for biaxial bending. The additional moment occurs about the minor axis.

(c) Columns bent about their major axis

If h > 3b, the section is to be designed for biaxial bending as in (b) above.

(d) Slender columns bent about both axes

Additional moments are to be calculated for both directions of bending. The additional moments are
added to the initial moments about each axis and the column is designed for biaxial bending.

In this case, for each direction, b’ in Table 3.21 should be taken as the dimension of the column in the
plane of bending considered.

Unbraced structures

The distribution of moments in an unbraced column is shown in Fig. 3.21 of the code. The additional
moment is assumed to occur at the stiffer end of the column. The additional moment at the other end
is reduced in proportion to the ratio of joint stiffnesses at the ends.