Building project rc column

Building Project (SPC1)
Design of RC Column
Done by: Eng.S.Kartheepan (M.Sc, B.Eng, AMIESL, AMIIESL)
Department of Civil Engineering
IET, Katunayake
E-mail: karthee2087@gmail.com

Introduction to column
• Columns act as vertical supports to beams and
slabs, and to transmit the loads to the
foundations.
• Columns are primarily compression members,
although they may also have to resist bending
moment transmitted by beams.
• Columns may be classified as short or slender,
braced or unbraced depending on various
dimensional and structural factors.

Column sections
• Common column cross sections are:
(a) Square
(b) Circular
(c) Rectangular section.
• The greatest dimension should not exceed four
times its smaller dimension. (h≤4b) – Clause 3.8.1
• For h>4b, the member should be regarded as a
wall for design purpose.

Failure modes of columns
Compression
failure
Buckling
Column Sections

Braced and unbraced column
The basic purpose of column is used to transfer the loads
in a vertical direction to the foundation. Columns can be
categorized into two types based on the lateral restrained.
Such as
1. Braced Column
2. Unbraced Column
Braced Column –
A column may be considered braced in a given plane if
lateral stability to the structure as a whole is provided by
walls or bracing (Clause 3.8.1.5)
Unbraced Column –
It should otherwise be considered as unbraced. It means if
there is no lateral strains then which column is considered
as unbraced column(Clause 3.8.1.5)

Braced and unbraced columns (Clause
3.8.1.5, BS 8110 – Part: 01, 1997)

• A braced column is classified as being short if :
• A column may be considered as short when both
the ratios lex/h and ley/b are less than 15
(braced)
Braced – Short column: Clause 3.8.1.3

• A column may be considered as short when both the
ratios lex/h and ley/b are less than 10 (unbraced). It
should otherwise be considered as Slender.
• Short – both lex/h and ley/b < 15 for braced columns
< 10 for unbraced columns
• Braced - If lateral stability to structure as a whole is
provided by walls or bracing designed to resist all lateral
forces in that plane then it is braced column
• Or else – Unbraced
Unbraced – Short column: Clause 3.8.1.3

• The effective height, le of a column in a given
plane may be obtained from the following
equation:
Where  is a coefficient depending on the fixity at
the column ends and lo is the clear height of the
columns.
• Effective height for a column in two plane
directions may be different.
Effective height of column (Clause - 3.8.1.6,
BS 8110 – Part: 01, 1997)

for unbraced column can be obtained from Table 3.20
Effective height of column (Clause - 3.8.1.6,
BS 8110 – Part: 01, 1997)
for braced column can be obtained from Table 3.19

End conditions (Clause 3.8.1.6.2, BS1997)
End 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 foundation, it
should be designed to carry moment.

• End condition 2 – The end of 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.

• End 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.

• End 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)

Determine the classification of braced column which is
shown in the figure below as short Column?
Example

Data’s: b = 250, h = 350 and Find the effective height.
Answer

Reinforcement details: longitudinal reinforcement
(Clause 3.12.5.3, BS 8110)
1. Size and minimum number of bars – bar size should not be
less than 12 mm in diameter. Rectangular column should
reinforced with minimum 4 bars; circular column should
reinforced with minimum 6 bars.
2. The longitudinal reinforcement should not exceed the
following amounts, calculated as percentages of the
gross cross-sectional area of the concrete: (Clause
3.12.6.2)
a) vertically-cast columns: 6 %;
b) horizontally-cast columns: 8 %;
c) laps in vertically- or horizontally-cast columns: 10 %.
3. Spacing of reinforcement – the minimum distance between
adjacent bars should not be less than the diameter of the
bar or hagg + 5 mm.

Reinforcement details – links (Clause 3.12.7.1, BS 8110)
• The axial loading on the column may cause buckling
of the longitudinal reinforcement and subsequent
cracking and spalling of concrete cover.
• Links are passing round the bars to prevent buckling.

1. Size and spacing of links – the diameter of the link
should be at least one quarter of the largest
longitudinal bar size or minimum 6 mm. The
maximum spacing is 12 times of the smallest
longitudinal bar.
2. Arrangement of links
Reinforcement details – links (Clause 3.12.7.1, BS 8110)

Theoretical strength of reinforced
concrete column
The equation is derived on the assumption that the axial load
is applied perfectly at the centre of the column.

Short column design
The short column are divided into three categories:
1. Columns resisting axial load only
B2 Column will resist an axial load only, as it supports
beams equal in length and symmetrically arranged.

Clause 3.8.4.3 Nominal eccentricity of short columns
resisting moments and axial force
• To allow for nominal eccentricity, BS 8110 reduce the
theoretical axial load capacity by about 10%.
• Short columns usually need only to be designed for the
maximum design moment about the one critical axis.
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:
• Design maximum axial load capacity of short column is
given in the above.

Clause 3.8.4.3 Nominal eccentricity of short columns
resisting moments and axial force
• Normally short columns only require to be designed for
the maximum moment about one critical axis in addition
to the axial load.
• In the case of a column supporting e.g. a rigid structure
or very deep beams, where it cannot be subjected to
significant moments, they may be designed in accordance
with Clause 3.8.4.3

Example - Axially loaded column
A short, braced column is subjected to an ultimate applied axial load
of 3000 kN and a nominal moment only. Using the design data given:
1. Check that the column is short
2. Determine the required area of main reinforcement
3. Determine the suitable links

Answer - Axially loaded column

2. Column supporting an approximately
symmetrical arrangement of beams
 C2 Column supports a symmetrical arrangement of
beams but which are unequal in length.
 If
(a) the loadings on the beam are uniformly
distributed,
(b) the beam spans do not differ by more than 15
percent, the column C2 belongs to category 2.

Clause 3.8.4.4 Short braced columns supporting an
approximately symmetrical arrangement of beams
• The column is subjected to axial and small moment
when it supports approximately symmetrical
arrangement of beams:
• The design ultimate axial load for a short column of this
type may be calculated using the following equation:
• The design axial load capacity:

Clause 3.8.4.4 Short braced columns supporting an
approximately symmetrical arrangement of beams
• A reduction from the equation given in Clause 3.8.4.3 is
given to allow for moments which will arise from a
symmetrical loading on symmetrical beams and is given
in Clause 3.8.4.4 in the following equation:

3. Columns resisting axial loads and uniaxial or
biaxial bending
 If the column does not meet criteria (a) and (b), then
the column belongs to category 3.
 A column is considered
biaxially loaded
when the bending occurs
about the X and Y
axes, such as in the case of
the corner column C

Column resisting an axial load and uniaxial bending
• For column resisting axial load and bending moment at one
direction, the area of longitudinal reinforcement is
calculated using design charts in Part 3 BS 8110.
• The design charts are available for columns having a
rectangular cross section and symmetrical arrangement of
reinforcement.
• Design charts are derived based on yield stress of 460
N/mm2 for reinforcement steel but the area of
reinforcement obtained will be approximately 10% greater
than required.
• Design charts are available for concrete grades – 25, 30,
35, 40, 45 and 50.
• The d/h ratios are in the range of 0.75 to 0.95 in 0.05
increment.

Column resisting an axial load and biaxial bending
• The columns are subjected to an
axial and bending moment in
both x and y directions.
• The columns with biaxial
moments are simplified into the
columns with uniaxial moment
by increasing the moment about
one of the axes then design the
reinforcement according the
increased moment.

Column resisting an axial load and biaxial
bending (clause 3.8.4.5, BS 8110)
Symmetrically-reinforced
rectangular sections may be
designed to withstand an
increased moment about one axis
given by the following equations:

Slender column design
Column
Classification
Braced
Slender
Non-slender
Unbraced
Slender
Non-slender
Lateral stability to the structure
as a whole is provided by walls or
bracing – resist all lateral forces
Lateral loads are resisted
by the bending action of
the column

• Slender or Non-slender column depending on the
sensitivity to second order effect (P- effect)
• Use slenderness ratio,  to measure column
vulnerability by elastic instability or buckling
• Non-Slender:
a) Design action are not significantly affected by
deformation (P- effect is small)
b) P- effect can be ignored if  does not exceed a
particular value
c) P- effect can be ignored if  10% of the
corresponding first order moments
Classification of Columns

• Short column –  , crushing at ultimate strength
• Slender column –  , buckling under low compressive
load
Compression
failure
Buckling
failure

Major axis
(x-x)
Minor axis
(y-y)
Plane of
bending
Clear height, l Actual height

Design of slender Column
Load Evaluation in ULS (Ultimate Limit State)
• Load due to roof – design load of roof × Area of roof
• Load due to slab – design load in slab calculation × Area
of slab in the particular column location.
• Load due to Beam – design load in beam calculation ×
total length of beam
• Load due to Column – Column load in each floor level
1. 2nd Floor to Roof level Column
2. 1st Floor to 2nd Floor column
3. Foundation level to Ground Floor Column
Finally total Axial load is estimated in ULS on the column.

Find the stiffness factor (K)
Stiffness, K = EI/L
Relative Column Stiffness, k =
Kcol/2(Kbeam)
Moment of Inertia, I = bh3/12
BM (Mx)= Relative Column Stiffness × Fixed End BM

Minimum Eccentricity
 All design moment are to be not less than the
design ultimate axial load times the minimum
eccentricity, e(min), equal to 0.05 times the overall
dimension of the column in the plane of bending.
emin = 0.05h
 This eccentricity however should not be more than
20 mm.
 Where there is biaxial bending, it is only necessary
to consider the nominal eccentricity moment about
one axis at a time.
Mmin = N × emin

Deflection induced moments in slender columns
 The cross sections of the slender columns are
designed as short column but an account is taken
of the additional deflection moments.
 The deflection induced additional moment Madd is
given by Eq 35:
 The deflection άu for a rectangular column under
ultimate conditions is calculated by the following
(Eq 32):
 Here Ba is calculated by using the following Eq 34

Deflection induced moments in slender columns
 In the above, b is generally the smaller dimension of
the column except when considering biaxial bending
and designing in two directions it can be the h
dimension.
 K is a reduction factor that corrects the deflection to
allow for the influence of axial load and is calculated
by using Eq 33 as follows:

Design moments in braced columns bent about a single axis
Figure 3.20 of BS8110 shows the distribution of moments
assumed over the height of a typical braced column.
The initial moment at the point of maximum additional
moment (i.e. near mid-height of the column) is given by Eq
36:
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.

Design moments in braced columns bent about a single axis
Assuming the column is bent in double curvature, M1
should be taken as negative and M2 positive. As can be seen
from Fig 3.20 of BS 8110, the maximum design moment for
the column will be the greatest of these 4 values:
1) M2;
2) Mi + Madd;
3) M1 + Madd/2;
4) N emin.

Biaxial Bending
When designing columns in biaxial bending, symmetrically-
reinforced rectangular sections may be designed to
withstand an increased moment about one axis given by the
following two equations Eq 40 & Eq 41:
a) for Mx/h' >= My/b' Mx' = Mx + B' h'/b' My
b) for Mx/h' < My/b' My' = My + B' b'/h' Mx
where
• h' and b' are shown in Figure 3.22;
• B' is the coefficient obtained
from Table 3.22

Design chart for column resisting an axial load and
uniaxial bending moment, (Part 3, BS 8110)

Building project rc column

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