Compression Members
Compression members are structural
elements primarily
subjected
to axial
compressive
forces
and hence, their
design is guided by considerations
of
strength
and buckling.
examples: pedestal,
column, wall and strut.
while
pedestal,
column and wall carry the loads along its length
in vertical
direction,
the strut
in truss carries
loads in any direction.
These compression
members may be made of bricks
or reinforced
concrete.
10.21.2

Definitions

(a) Effective
length:
The vertical
distance
between the points
of inflection
of
the compression
member in the buckled configuration
in a plane is termed as
effective
length of that compression
member in that plane. The effective
length
is different
from the unsupported
length
L of the member, though it depends on
the unsupported
length and the type of end restraints.
The relation
between the effective
and unsupported
lengths
of any compression
member is
Le
kl

where K is the ratio
of effective
to the unsupported
lengths.
Clause 25.2 of IS
456 stipulates
the effective
lengths
of compression members (vide Annex E of IS
456). This parameter is needed in classifying
and designing
the compression
members.

(b) Pedestal:
Pedestal
is a vertical
9 does not exceed three times of its
26.5.3.1h,
Note). The other horizontal
of b(Fig.10.21.1a).
(c) Column: Column is
shall
not exceed sixty
the two ends. Further,
exceed 100bA2/D, where
restricted
up to four

compression member whose effective
length
least
horizontal
dimension b (cl.
dimension D shall
not exceed four times

a vertical
compression member whose unsupported
length
L
times of b (least
lateral
dimension),
if restrained
at
its unsupported
length of a cantilever
column shall
not
D is the larger
lateral
dimension which is also
times of b (vide cl. 25.3 of IS 456 and Fig.1 0.21 .1 b).

(d) wall:
wall is a vertical
compression
member whose effective
height H to
thickness
t(least
lateral
dimension)
shall
not exceed 30 (cl.
32.2.3 of IS 456).
The larger
horizontal
dimension i.e.,
the length of the wall L is more than 4t
(Fig.10.21.1c).

10.21.3 Classification
Based on the types
classified
into three
(i) Tied columns: The
closely
spaced lateral
(ii)
Columns with
reinforcement
bars are
spiral
reinforcement.
(Fig.10.21.2b).

of Columns Based on Types of Reinforcement
of reinforcement,
the reinforced
concrete
columns are
groups:
main longitudinal
reinforcement
bars are enclosed within
ties
(Fig.10.21.2a).
helical
reinforcement:
The main longitudinal
enclosed within
closely
spaced and continuously
wound
Circular
and octagonal
columns are mostly of this type

(iii)
Composite columns: The main longitudinal
reinforcement
of the composite
columns consists
of structural
steel sections
or pipes with or without
longitudinal
bars (Fig.20.21.2c
and d).
out of the three types of columns, the tied columns are mostly common
with different
shapes of the cross-sections
viz.
square,
rectangular,
T, L,
cross etc. Helically
bound columns are also used for circular
or octagonal
shapes of cross-sections.
Architects
prefer
circular
columns in some specific
situations
for the functional
requirement.
10.21.4 Classification
Columns are classified
(i) Columns subjected

of Columns Based on Loadings
into the three following
types
to axial
loads only (concentric),

based on the loadings:
as shown in

Fig.20.21.3a.

(ii)
Columns subjected
Fig.10.21.3b.
(iii)
Columns subjected
Fig.10.21.3c.

to combined
to combined

axial
axial

load
load

and uniaxial
and biaxial

bending,
bending,

as shown in
as shown in

/

Figure 10.21.4 shows the plan view of a reinforced
concrete
rigid
frame having
columns and inter-connecting
beams in longitudinal
and transverse
directions.
From the knowledge of structural
analysis
it is well known that the bending
moments on the left
and right
of columns for every longitudinal
beam will
be
comparable as the beam is continuous.
Similarly,
the bending moments at the two
sides of columns for every continuous
transverse
beam are also comparable.
All
internal
columns will
be designed for axial force only. The side columns will
have axial
forces with uniaxial
bending moment, while the four corner columns
shall
have axial
forces with biaxial
bending moments.
It is worth mentioning
that pure axial
forces in the inside
columns is a rare
case. Due to rigid
frame action,
lateral
loadings
and practical
aspects of
construction,
there will
be bending moments and horizontal
shear in all the
inside
columns also. Similarly,
side columns and corner columns will
have the
column shear along with the axial
force and bending moments in one or both
directions,
respectively.
The effects
of shear are usually
neglected
as the
magnitude is very small.
Moreover,
the presence of longitudinal
and transverse
reinforcement

is

sufficient

to

resist

the

effect

of

column

shear

of

comparatively
low magnitude.
The effect
of some minimum bending moment, however, should be taken into account
in the design even if the column is axially
loaded. Accordingly,
cls. 39.2 and
25.4 of IS 456 prescribes
the minimum eccentricity
for the design of all
columns. In case the actual
eccentricity
is more than the minimum, that should
be considered
in the design.
10.21.5

Classification

of

Columns are classified

Columns

into

Based

the following

on

Slenderness

two types

Ratios

based on the slenderness

ratios:

(i)

Short

columns

(ii)

Slender

or long

columns

Figure 10.21.5 presents
the three modes of failure
of columns with different
slenderness
ratios
when loaded axially.
In the mode 1, column does not undergo
any lateral
deformation
and collapses
due to material
failure.
This is known as
compression
failure.
Due to the combined effects
of axial
load and moment a
short column may have material
failure
of mode 2. On the other hand,
a slender
column subjected
to axial
load only undergoes deflection
due to beamcolumn effect
and may have material
failure
under the combined action
of direct
load and bending moment. Such failure
is called
combined compression
and bending
failure
of mode 2. Mode 3 failure
is by elastic
instability
of very long column
even under small load much before the material
reaches the yield
stresses.
This
type of failure
is known as elastic
buckling.
The slenderness
ratio
of steel column is the ratio
of its effective
length
Le to
its least
radius of gyration
r. In case of reinforced
concrete
column, however,
IS 456 stipulates
the slenderness
ratio
as the ratio
of its effective
length
Le
to its least lateral
dimension.
As mentioned earlier
in sec. 10.21.2(a),
the
effective
length is different
from the unsupported
length,
the rectangular
reinforced

concrete

column

of

crosssectional

dimensions

b and

D shall

have

two

effective
lengths
in the two directions
of b and D. Accordingly,
the column may
have the possibility
of buckling
depending on the two values of slenderness
ratios
as given below:
Slenderness
ratio
about the major axis
Slenderness

ratio

about

the

minor

axis

Lex/D
Ley/b

A compression
member may be considered
as short when both the slenderness
ratios
Lex/D and Ley/b are less than 12 where Lex: effective
length in respect of the
major axis,
D = depth in respect of the major axis,
Ley effective
length in
respect of the minor axis,
and b = width of the member. It shall
otherwise
be
considered
as a slender
compression
member.
Further,
it is essential
to avoid the mode 3 type of failure
of columns so that
all columns should have material
failure
(modes 1 and 2) only. Accordingly,
cl.
25.3.1 of IS 456 stipulates
the maximum unsupported
length
between two
restraints
of a column to sixty
times its least lateral
dimension.
For
cantilever
columns, when one end of the column is unrestrained,
the unsupported
length is restricted
to 100bA2/D.

10.21.6

Braced

and

unbraced

columns

It is desirable
that the columns do not have to resist any horizontal
loads due
to wind or earthquake.
This can be achieved by bracing the columns as in the
case of columns of a water tank or tall
buildings
(Figs.10.21.6a
and b).
Lateral

tie

members

for

the

columns

of

water

tank

or

shear

walls

for

the

columns

of tall
buildings
resist
the horizontal
forces and these columns are called
braced columns. Unbraced columns are supposed to resist
the horizontal
loads
also.

The bracings can be
lateral
loads. It is
into account by the
(vide Annex E of IS

in one or more directions
depending on the directions
of the
worth mentioning that the effect
of bracing has been taken
IS code in determining
the effective
lengths of columns
456).

10.21.? Longitudinal
Reinforcement:
The longitudinal
reinforcing
bars carry the
compressive loads along with the concrete.
(a) The minimum amount of steel should be at least 0.8 per cent of the gross
cross sectional
area of the column required if for any reason the provided area
is more than the required area.
(b) The maximum amount of steel should be 4 per cent of the gross crosssectional
area of the column so that it does not exceed 6 per cent when bars
from column below have to be lapped with those in the column under
consideration.

(c) Four and six are the minimum number of longitudinal
bars in
rectangular
and circular
columns, respectively.
(d) The diameter of the longitudinal
bars should be at least 12 mm.
(e)

Columns having helical

bars

within

placed
the

and

in

Contact

reinforcement
with

the

shall

helical

have at least

reinforcement.

six longitudinal
The

bars

shall

equidistant
around its inner circumference.
(f) The bars shall be spaced not exceeding 300 mm along the periphery

be

of

column.

(g) The amount of reinforcement
for
the crosssectional
area provided.

pedestal

shall

be at least

0.15

per cent of

10.21.8 Transverse Reinforcement:
Transverse reinforcing
bars are provided in
forms of circular
rings, polygonal links (lateral
ties) with internal
angles not
exceeding 135° or helical
reinforcement.
The transverse
reinforcing
bars are
provided to ensure that every longitudinal
bar nearest to the compression face
has effective
lateral
support against buckling.
(a) Transverse reinforcement
shall only go round corner and alternate
bars if
the longitudinal
bars are not spaced more than 75 mm on either
side(Fig.10.21.7).
(b) Longitudinal
bars spaced at a maximum distance of 48 times the diameter of
the tie shall be tied by single tie and additional
open ties for in between
longitudinal
bars (Fig.10.21.8).
(c) For longitudinal
bars placed in more than one row (Fig.10.21.9):
(i)
transverse
reinforcement
is provided for the outer most row in accordance with
(a) above, and (ii)
no bar of the inner row is closer to the nearest compression
face than three times the diameter of the largest
bar in the inner row.
(d) For longitudinal
bars arranged in a group such that they are not in contact
and each group is adequately tied as per (a), (b) or (c) above, as appropriate,
the transverse
reinforcement
for the compression member as a whole may be
provided assuming that each group is a single longitudinal
bar for determining
the pitch and diameter of the transverse
reinforcement
as given in sec.10.21.9.
The diameter
(Fig.10.21.10).
10.21.9

(a)

of

Pitch

Pitch:

such

and

transverse

Diameter

of

The maximum pitch

reinforcement

Lateral

should

not,

however,

exceed

20 mm

Ties

of transverse

reinforcement

shall

be the least

of

the following:
(i) the least lateral
dimension
(ii)
sixteen
times the smallest
to be tied;
and (iii)
300 mm.

of the compression members;
diameter
of the longitudinal

reinforcement

bar

(b) Diameter:
The diameter
of the polygonal
links
or lateral
ties shall
be not
less than one fourth
of the diameter
of the largest
longitudinal
bar, and in no
case

less

than

10.21.10

6 mm.

Helical

Reinforcement

(a) Pitch:
Helical
reinforcement
shall
be of regular
formation
with the turns of
the helix
spaced evenly and its ends shall
be anchored properly
by providing
one
and a half extra turns of the spiral
bar. The pitch of helical
reinforcement
shall
be determined
as given in sec.10.21.9
for all cases except where an
increased
load on the column is allowed for on the strength
of the helical
reinforcement.
In such cases only,
the maximum pitch shall
be the lesser
of 75
mm and onesixth
of the core diameter
of the column, and the minimum pitch shall
be the lesser
of 25 mm and three times the diameter of the steel bar forming
the
helix.

(b)

Diameter:

The diameter

of the

helical

reinforcement

shall

be as mentioned

in

sec.10.21.9b.

10.21.11

Assumptions

in

the Design

of Compression

Members by Limit

State

of

Collapse

Tied and helically
reinforced
short and slender columns subjected
to axial
loadings
with or without
the combined effects
of uniaxial
or biaxial
bending
will
be taken up. The assumptions
(i) to (v) given in sec.3.4.2
of Lesson 4 for
the design of flexural
members are also applicable
here. Further
more, the
following
are the additional
assumptions
for the design of compression
members
(cl.
39.1 of IS 456).
(i) The maximum compressive
strain
in concrete
in axial
compression
is taken as
0.002.

(ii)
The maximum compressive
strain
at the highly
compressed extreme fibre
in
concrete
subjected
to axial
compression
and bending and when there is no tension
on

the

section

shall

be

0.0035

minus

0.75

times

the

strain

at

the

least

compressed extreme fibre.
The assumptions
(i) to (v) of section
3.4.2 of Lesson 4 and (i) and (ii)
mentioned above are discussed
below with reference
to Fig.10.21.11a
to c
presenting
the cross-section
and strain
diagrams for different
location
of the
neutral

axis.

The discussion
made in sec. 3.4.2 of Lesson 4 regarding
the assumptions
(i),
(iii),
(iv)
and (v) are applicable
here also. Assumption
(ii)
of sec.3.4.2
is

also

applicable
here when kD, the depth of neutral
axis from the highly
compressed
right
edge is within
the section
i.e.,
K < 1. The corresponding
strain
profile
IN

in

Fig.10.21.11b
is for particular
value of P and M such that the maximum
compressive
strain
is 0.0035 at the highly
compressed right
edge and tensile
strain
develops at the opposite
edge. This strain
profile
is very much similar
to
that

of

a beam

in

flexure

of

Lesson

4.

The additional
assumption
(i) of this section
refers
to column subjected
axial
load P only resulting
compressive
strain
of maximum (constant)
value
0.002 and for which the strain
profile
is EF in Fig.10.21.11b.
The neutral
is

of
axis

at

infinity

(outside

the section).

Extending
the assumption of the strain
profile
IN (Fig.10.21.11b),
we can
draw another strain
profile
IH (Fig.10.21.11c)
having maximum compressive
strain
of 0.0035 at the right
edge and zero strain
at the left
edge. This strain
profile
1H along with EF are drawn in Fig.10.21.11c
to intersect
at V. From the
two similar
triangles
EVI and GHI, we have

EV/GH

3/7,

0.0015/0.0035

which

gives

EV = 3D/7

(10.2)

The point
the strain

V, where the two profiles
profiles
when the neutral

intersect
is assumed to act as a fulcrum
axis lies
outside
the section.
Another

for

strain

profile
axis is

JK drawn on this figure
passing through the fulcrum
outside
the section.
The maximum compressive
strain

V and whose neutral
GJ of this profile

is

related

to the minimum compressive

GJ = GI

similar
IJ/HK

IJ

= GI

0.75

triangles
= VENF

The value

strain

HK, as we can write

HK as explained
IJ

in

term

below.
of

HK from

two

JVI and HVK:

= 0.75.

of the maximum compressive

strain

GJ for

the

profile

JK is,

therefore,
0.0035 minus 0.75 times the strain
HK on the least
compressed
This is the assumption
(ii)
of this section
(cl.
39.1b of IS 456).
10.21.12

Minimum

Eccentricity:

In

practical

construction,

columns

are

edge.

rarely

truly
concentric.
Even a theoretical
column loaded axially
will
have accidental
eccentricity
due to inaccuracy
in construction
or variation
of materials
etc.
Accordingly,
all axially
loaded columns should be designed considering
the
minimum eccentricity
as stipulated
in cl. 25.4 of IS 456 and given below
(Fig.10.21.3c)

em,-,,
2 greater
of )I/500
+ D/30) or 20 mm
eymjn 2 greater
of )I/500
+ b/30) or 20 mm
where L, D and b are the unsupported
length,
larger
lateral
dimension,
respectively.

lateral

dimension

and least