M10l21

Module
10
Compression Members
Version 2 CE IIT, Kharagpur

Lesson
21
Definitions,
Classifications,
Guidelines and
Assumptions

Instructional Objectives:
At the end of this lesson, the student should be able to:
• define effective length, pedestal, column and wall,
• classify the columns based on types of reinforcement, loadings and
slenderness ratios,
• identify and explain the functions of bracing in a braced column,
• determine the minimum and maximum percentage of longitudinal
reinforcement,
• determine the minimum numbers and diameter of bars in rectangular and
circular columns,
• determine the longitudinal reinforcement in a pedestal,
• determine the type, pitch and diameter of lateral ties of columns after
determining the longitudinal steel,
• state the assumptions in the design of compression member by limit state
of collapse,
• determine the strain distribution lines of a compression member subjected
to axial load with or without the moments about one or both the axes,
• explain the need of the minimum eccentricity to be considered in the
design of compression members.
10.21.1 Introduction
Compression members are structural elements primarily subjected to axial
compressive forces and hence, their design is guided by considerations of
strength and buckling. Figures 10.21.1a to c show their examples: pedestal,
column, wall and strut. While pedestal, column and wall carry the loads along its
length l in vertical direction, the strut in truss carries loads in any direction. The
letters l, b and D represent the unsupported vertical length, horizontal lest
lateral dimension, width and the horizontal longer lateral dimension, depth. These
compression members may be made of bricks or reinforced concrete. Herein,
reinforced concrete compression members are only discussed.

This module is intended to explain the definition of some common
terminologies and to illustrate the design of compression members and other
related issues. This lesson, however, explain the definitions and classifications of
columns depending on different aspects. Further, the recommendations of IS 456
to be followed in the design are discussed regarding the longitudinal and lateral
reinforcing bars. The assumptions made in the design of compression member
by limit sate of collapse are illustrated.
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 le 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 = k l
(10.1)
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 compression member whose effective
length le does not exceed three times of its least horizontal dimension b (cl.
26.5.3.1h, Note). The other horizontal dimension D shall not exceed four times
of b (Fig.10.21.1a).
(c) Column: Column is a vertical compression member whose
unsupported length l shall not exceed sixty times of b (least lateral dimension),
if restrained at the two ends. Further, its unsupported length of a cantilever
column shall not exceed 100b2
/D, where D is the larger lateral dimension which
is also restricted up to four times of b (vide cl. 25.3 of IS 456 and Fig.10.21.1b).
(d) Wall: Wall is a vertical compression member whose effective height
Hwe 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 of Columns Based on Types of
Reinforcement

Based on the types of reinforcement, the reinforced concrete columns are
classified into three groups:
(i) Tied columns: The main longitudinal reinforcement bars are enclosed
within closely spaced lateral ties (Fig.10.21.2a).
(ii) Columns with helical reinforcement: The main longitudinal
reinforcement bars are enclosed within closely spaced and continuously wound
spiral reinforcement. Circular and octagonal columns are mostly of this type
(Fig.10.21.2b).
(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. This module, accordingly takes up these two types
(tied and helically bound) of reinforced concrete columns.

10.21.4 Classification of Columns Based on Loadings

Columns are classified into the three following types based on the
loadings:

(i) Columns subjected to axial loads only (concentric), as shown in
Fig.20.21.3a.
(ii) Columns subjected to combined axial load and uniaxial bending, as
shown in Fig.10.21.3b.
(iii) Columns subjected to combined axial load and bi-axial bending, as
shown in Fig.10.21.3c.
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
(neglecting small amounts due to differences of l1, l2, l3 and b1, b2, b3, b4).
Therefore, all internal columns (C1a to C1f) will be designed for axial force only.
The side columns (C2a to C2j) will have axial forces with uniaxial bending
moment, while the four corner columns (C3a to C3d) shall have axial forces with
bi-axial bending moments. Thus, all internal columns (C1a to C1f), side columns

(C2a to C2j) and corner columns (C3a to C3d) are the columns of type (i), (ii) and
(iii), respectively.
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 Based on Slenderness
Ratios
Columns are classified into the following two types 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 beam-
column 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 le is different from the unsupported length, the rectangular reinforced
concrete column of cross-sectional 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 = lex/D
Slenderness ratio about the minor axis = ley/b
Based on the discussion above, cl. 25.1.2 of IS 456 stipulates the
following:
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 100b2
/D where b and D are as defined earlier.

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 in one or more directions depending on the directions of the
lateral loads. It is worth mentioning that the effect of bracing has been taken into
account by the IS code in determining the effective lengths of columns (vide
Annex E of IS 456).
10.21.7 Longitudinal Reinforcement
The longitudinal reinforcing bars carry the compressive loads along with
the concrete. Clause 26.5.3.1 stipulates the guidelines regarding the minimum
and maximum amount, number of bars, minimum diameter of bars, spacing of
bars etc. The following are the salient points:
(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 cross-
sectional 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 reinforcement shall have at least six
longitudinal bars within and in contact with the helical reinforcement. The bars
shall be placed equidistant around its inner circumference.
(f) The bars shall be spaced not exceeding 300 mm along the periphery
of the column.
(g) The amount of reinforcement for pedestal shall be at least 0.15 per
cent of the cross-sectional area provided.
10.21.8 Transverse Reinforcement
Transverse reinforcing bars are provided in forms of circular rings,
polygonal links (lateral ties) with internal angles not exceeding 135o
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. Clause 26.5.3.2 stipulates the guidelines of the arrangement of
transverse reinforcement. The salient points are:
(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 of such transverse reinforcement should not, however,
exceed 20 mm (Fig.10.21.10).
10.21.9 Pitch and Diameter of Lateral Ties
(a) Pitch: The maximum pitch of transverse reinforcement shall be the
least of the following:
(i) the least lateral dimension of the compression members;
(ii) sixteen times the smallest diameter of the longitudinal
reinforcement bar to be tied; and
(iii) 300 mm.
(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 6 mm.
10.21.10 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 one-sixth 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
It is thus seen that reinforced concrete columns have different
classifications depending on the types of reinforcement, loadings and
slenderness ratios. Detailed designs of all the different classes are beyond the
scope here. 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. However, the basic assumptions of the design of any of the
columns under different classifications are the same. The assumptions (i) to (v)
given in sec.3.4.2 of Lesson 4 for the design of flexural members are also
applicable here. Furthermore, 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 of
0.002 and for which the strain profile is EF in Fig.10.21.11b. The neutral axis is 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 = 0.0015/0.0035 = 3/7, which gives
EV = 3D/7
(10.2)
The point V, where the two profiles intersect is assumed to act as a fulcrum for
the strain profiles when the neutral axis lies outside the section. Another strain
profile JK drawn on this figure passing through the fulcrum V and whose neutral
axis is outside the section. The maximum compressive strain GJ of this profile is
related to the minimum compressive strain HK as explained below.
GJ = GI – IJ = GI – 0.75 HK, as we can write IJ in term of HK from two
similar triangles JVI and HVK:
IJ/HK = VE/VF = 0.75.
The value 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 edge.
This is the assumption (ii) of this section (cl. 39.1b of IS 456).

10.21.12 Minimum Eccentricity
Section 10.21.4 illustrates that in practical construction, columns are 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)
ex min ≥ greater of )l/500 + D/30) or 20 mm
(10.3)
ey min ≥ greater of )l/500 + b/30) or 20 mm
where l, D and b are the unsupported length, larger lateral dimension and least
lateral dimension, respectively.
10.21.13 Practice Questions and Problems with Answers
Q.1: Define effective length, pedestal, column and wall.
A.1: See sec. 10.21.2.
Q.2: Classify the columns based on types of reinforcement.
A.2: See sec. 10.21.3
Q.3: Classify the columns based on loadings.
A.3: See sec. 10.21.4.
Q.4: Classify the columns based on slenderness ratios.
A.4: See Sec. 10.21.5
Q.5: Explain braced and unbraced columns.
A.5: See sec. 10.21.6.
Q.6: Answer the following:
(a) What are the minimum and maximum amounts of longitudinal
reinforcement in a column?

(b) What are the minimum numbers of longitudinal bars in rectangular and
circular columns?
(c) What is the amount of longitudinal reinforcement in a pedestal?
(d) What is the maximum pitch of transverse reinforcement in a column?
(e) What is the diameter of lateral ties in a column?
A.6: (a) 0.8% and 4%
(b) 4 and 6
(c) 0.15% of cross-sectional area of the pedestal
(d) See sec. 10.21.9(a)
(e) See sec. 10.21.9(b).
Q.7: Explain the assumptions of determining the strain distribution lines in a
column subjected to axial force and biaxial bending.
A.7: See sec. 10.21.11(i) and (ii).
Q.8: State the minimum eccentricity of a rectangular column for designing.
A.8: See sec. 10.21.12.
10.21.14 References
1. Reinforced Concrete Limit State Design, 6th
Edition, by Ashok K. Jain,
Nem Chand & Bros, Roorkee, 2002.
2. Limit State Design of Reinforced Concrete, 2nd
Edition, by P.C.Varghese,
Prentice-Hall of India Pvt. Ltd., New Delhi, 2002.
3. Advanced Reinforced Concrete Design, by P.C.Varghese, Prentice-Hall of
India Pvt. Ltd., New Delhi, 2001.
4. Reinforced Concrete Design, 2nd
Edition, by S.Unnikrishna Pillai and
Devdas Menon, Tata McGraw-Hill Publishing Company Limited, New
Delhi, 2003.
5. Limit State Design of Reinforced Concrete Structures, by P.Dayaratnam,
Oxford & I.B.H. Publishing Company Pvt. Ltd., New Delhi, 2004.
6. Reinforced Concrete Design, 1st
Revised Edition, by S.N.Sinha, Tata
McGraw-Hill Publishing Company. New Delhi, 1990.
7. Reinforced Concrete, 6th
Edition, by S.K.Mallick and A.P.Gupta, Oxford &
IBH Publishing Co. Pvt. Ltd. New Delhi, 1996.

8. Behaviour, Analysis & Design of Reinforced Concrete Structural Elements,
by I.C.Syal and R.K.Ummat, A.H.Wheeler & Co. Ltd., Allahabad, 1989.
9. Reinforced Concrete Structures, 3rd
Edition, by I.C.Syal and A.K.Goel,
A.H.Wheeler & Co. Ltd., Allahabad, 1992.
10.Textbook of R.C.C, by G.S.Birdie and J.S.Birdie, Wiley Eastern Limited,
New Delhi, 1993.
11.Design of Concrete Structures, 13th
Edition, by Arthur H. Nilson, David
Darwin and Charles W. Dolan, Tata McGraw-Hill Publishing Company
Limited, New Delhi, 2004.
12.Concrete Technology, by A.M.Neville and J.J.Brooks, ELBS with
Longman, 1994.
13.Properties of Concrete, 4th
Edition, 1st
Indian reprint, by A.M.Neville,
Longman, 2000.
14.Reinforced Concrete Designer’s Handbook, 10th
Edition, by C.E.Reynolds
and J.C.Steedman, E & FN SPON, London, 1997.
15.Indian Standard Plain and Reinforced Concrete – Code of Practice (4th
Revision), IS 456: 2000, BIS, New Delhi.
16.Design Aids for Reinforced Concrete to IS: 456 – 1978, BIS, New Delhi.
10.21.15 Test 21 with Solutions
Maximum Marks = 50, Maximum Time = 30 minutes
Answer all questions carrying equal marks.
TQ.1: Define effective length, pedestal, column and wall.
A.TQ.1: See sec. 10.21.2.
TQ.2: Classify the columns separately based on loadings and slenderness
ratios.
A.TQ.2: See secs. 10.21.4 and 5.
TQ.3: Explain braced and unbraced columns.
A.TQ.3: See sec. 10.21.6.
TQ.4: Answer the following:
(a) What are the minimum and maximum amounts of longitudinal
reinforcement in a column?
(b) What are the minimum numbers of longitudinal bars in rectangular
and circular columns?

(c) What is the amount of longitudinal reinforcement in a pedestal?
(d) What is the maximum pitch of transverse reinforcement in a column?
(e) What is the diameter of lateral ties in a column?
A.TQ.4: (a) 0.8% and 4%
(b) 4 and 6
(c) 0.15% of cross-sectional area of the pedestal
(d) See sec. 10.21.9(a)
(e) See sec. 10.21.9(b).
TQ.5: Explain the assumptions of determining the strain distribution lines in a
column subjected to axial force and biaxial bending.
A.TQ.5: See sec. 10.21.11(i) and (ii).
10.21.16 Summary of this Lesson
This lesson defines the effective length, pedestal, column and wall. Three
different classifications of columns based on types of reinforcement, loadings
slenderness ratio are explained. The need and functions of bracings are
illustrated. The guidelines of IS 456 are discussed regarding the types,
arrangement, minimum numbers and diameter of bars, pitch and other aspects of
longitudinal and transverse reinforcement of columns. The assumptions needed
for the design of compression members are illustrated. The determination of
strain distribution lines are explained depending on the location of the neutral
axis. The need for considering the minimum eccentricity and its amount are
explained.

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