as per IS 456-2000

1. Reinforced Concrete Columns
by
S.Praveenkumar
Assistant Professor
Department of Civil Engineering
PSG College of Technology
Coimbatore

2. 2
► Dr. H.J. Shah,Dr. H.J. Shah, “Reinforced Concrete Vol-1”“Reinforced Concrete Vol-1”, 8, 8thth
Edition, 2009.Edition, 2009.
► Dr. H.J. Shah,Dr. H.J. Shah, “Reinforced Concrete Vol-2”“Reinforced Concrete Vol-2”, 6, 6thth
Edition, 2012.Edition, 2012.
► S. Unnikrishna Pillai and Devadas Menon,S. Unnikrishna Pillai and Devadas Menon, “Reinforced Concrete Design”“Reinforced Concrete Design”,,
33rdrd
Edition, 2009Edition, 2009
► P.C.Varghese,P.C.Varghese, “Limit State Design of Reinforced Concrete”“Limit State Design of Reinforced Concrete”, PHI, 2, PHI, 2ndnd
edition, 2009edition, 2009
► Ashok K Jain,Ashok K Jain, “Reinforced Concrete, Limit State Design“Reinforced Concrete, Limit State Design”, Nem Chand and”, Nem Chand and
Bros, 7Bros, 7thth
Edition, 2012Edition, 2012
► M.L.Gambhir, “M.L.Gambhir, “Design of Reinforced Concrete StructuresDesign of Reinforced Concrete Structures”, PHI, 2008”, PHI, 2008
Reference booksReference books

3. 3
► Dr. B.C. Punmia et al,Dr. B.C. Punmia et al, “Limit State Design of Reinforced concrete”“Limit State Design of Reinforced concrete”, Laxmi,, Laxmi,
2007.2007.
► J.N. Bandyopadhyay,J.N. Bandyopadhyay, “Design of Concrete Structures”“Design of Concrete Structures”, PHI, 2008., PHI, 2008.
► N.Krishna Raju,N.Krishna Raju, “Structural Design and Drawing, Reinforced concrete and“Structural Design and Drawing, Reinforced concrete and
steel”steel”, Universities Press, 1992, Universities Press, 1992
► M.R. Dheerencdra Babu,M.R. Dheerencdra Babu, “Structural Engineering Drawing”“Structural Engineering Drawing”, Falcon, 2011, Falcon, 2011
► Bureau of Indian Standards,Bureau of Indian Standards, IS456-2000, IS875-1987, SP16, SP34IS456-2000, IS875-1987, SP16, SP34

4. IntroductionIntroduction
► A column is an important components of R.C. Structures.
► A column, in general, may be defined as a member carrying direct axial
load which causes compressive stresses of such magnitude that these
stresses largely control its design.
► A column or strut is a compression member, the effective length of
which exceeds three times the least lateral dimension.(Cl. 25.1.1)(Cl. 25.1.1)
► When a member carrying mainly axial load is vertical, it is termed as
column ,while if it is inclined or horizontal, it is termed as a strut.
► Columns may be of various shape such as circular, rectangular,
square, hexagonal etc.
► ‘‘Pedestal’ is a vertical compression member whose ‘effective length’ isPedestal’ is a vertical compression member whose ‘effective length’ is
less than three times its least lateral dimension [Cl. 26.5.3.1(h)].less than three times its least lateral dimension [Cl. 26.5.3.1(h)].
4

5. 5

6. 6

7. 7

8. 8

9. 9

10. 10

11. Classification of columnsClassification of columns
11
Based on Type of Reinforcement
a) Tied Columns-where the main
longitudinal bars are enclosed within
closely spaced lateral ties( all cross
sectional shapes)
b) Spiral columns-where the main
longitudinal bars are enclosed within
closely spaced and continuously wound
spiral reinforcement (Circular, square,
octagonal sections)
c) Composite Columns-where the
reinforcement is in the form of structural
steel sections or pipes, with or without
longitudinal bars

12. Based on Type of Loading
a) Columns with axial loading (applied concentrically)
b) Columns with uniaxial eccentric loading
c) Columns with biaxial eccentric loading
12

13. 13

14. 14

15. ► The occurrence of ‘pure’ axial compression in a column (due to
concentric loads) is relatively rare.
► Generally, flexure accompanies axial compression — due to ‘rigid
frame’ action, lateral loading and/or actual(or even,
unintended/accidental) eccentricities in loading.
► The combination of axial compression (P) with bending moment (M) at
any column section is statically equivalent to a system consisting of the
load P applied with an eccentricity e = M/P with respect to the
longitudinal centroidal axis of the column section.
► In a more general loading situation, bending moments (Mx and My) are
applied simultaneously on the axially loaded column in two
perpendicular directions — about the major axis (XX) and minor axis
(YY) of the column section. This results in biaxial eccentricities ex=
Mx/P and ey= My/P, as shown in [Fig.(c)]. 15

16. ► Columns in reinforced concrete framed buildings, in general, fall into
the third category, viz. columns with biaxial eccentricities.
► The biaxial eccentricities are particularly significant in the case of the
columns located in the building corners.
► In the case of columns located in the interior of symmetrical, simple
buildings, these eccentricities under gravity loads are generally of a
low order (in comparison with the lateral dimensions of the column),
and hence are sometimes neglected in design calculations.
► In such cases, the columns are assumed to fall in the first category,
viz. columns with axial loading.
► The Code, however, ensures that the design of such columns is
sufficiently conservative to enable them to be capable of resisting
nominal eccentricities in loading
16

17. Based on Slenderness Ratio (Cl. 25.1.2)(Cl. 25.1.2)
Columns (i.e., compression members) may be classified into the following
two types, depending on whether slenderness effects are considered
insignificant or significant:
1. Short columns
2. Slender (or long) columns.
 ‘Slenderness’ is a geometrical property of a compression member
which is related to the ratio of its ‘effective length’ to its lateral
dimension. This ratio, called slenderness ratio, also provides a
measure of the vulnerability to failure of the column by elastic
instability (buckling) — in the plane in which the slenderness ratio is
computed.. 17

18. 18

19.  Columns with low slenderness ratios, i.e., relatively short and stocky
columns, invariably fail under ultimate loads with the material
(concrete, steel) reaching its ultimate strength, and not by buckling.
 On the other hand, columns with very high slenderness ratios are in
danger of buckling (accompanied with large lateral deflection) under
relatively low compressive loads, and thereby failing suddenly.
19

20. Braced columns & unbraced column
In most of the cases, columns are also subjected to horizontal loads like
wind, earthquake etc. If lateral supports are provided at the ends of the
column, the lateral loads are borne entirely by the lateral supports.
Such columns are known as braced columns.(When relative
transverse displacement between the upper and lower ends of a
column is prevented, the frame is said to be braced (against sideway)).
Other columns, where the lateral loads have to be resisted by them, in
addition to axial loads and end moments, are considered as unbraced
columns. (When relative transverse displacement between the upper
and lower ends of a column is not prevented, the frame is said to be
unbraced (against sideway).
20

21. Design of Compression membersDesign of Compression members
21

24. A building structure safely transmits loads down to Earth
24

25. 25

28. Design of single storey public buildingDesign of single storey public building

36. Unsupported Length
Code (Cl. 25.1.3) defines the ‘unsupported length’ l of a column
explicitly for various types of constructions.
Effective length of a column
The effective length of a column in a given plane is defined as the
distance between the points of inflection in the buckled configuration of
the column in that plane.
The effective length depends on the unsupported length l and the
boundary conditions at the column ends
36

37. Effective lengths for idealised boundary conditions (Euler’s theory)
37

38. Code recommendations for idealised boundary conditions
(Cl. E–1)-Use of Code Charts
Charts are given in Fig. 26 and Fig. 27 of the Code for determining theCharts are given in Fig. 26 and Fig. 27 of the Code for determining the
effective length ratios of braced columns and unbraced columnseffective length ratios of braced columns and unbraced columns
respectively in terms of coefficientsrespectively in terms of coefficients 1 and 2 which represent theβ β1 and 2 which represent theβ β
degrees of rotational freedom at the top and bottom ends of thedegrees of rotational freedom at the top and bottom ends of the
column.column.
38

39. 39
In such cases,
the effective
length ratio k
varies between
0.5 and 1.0

40. 40
In such cases,
the effective
length ratio k
varies between
1.0 and infinity

41. Recommended effective length ratios for normal usage (Table 28,
Page 94)
1. columns braced against sideway:
a) both ends ‘fixed’ rotationally : 0.65
b) one end ‘fixed’ and the other ‘pinned : 0.80
c) both ends ‘free’ rotationally (‘pinned’) : 1.00
2. columns unbraced against sideway:
a) both ends ‘fixed’ rotationally : 1.20
b) one end ‘fixed’ and the other ‘partially fixed’ : 1.50
c) one end ‘fixed’ and the other free : 2.00
41

42. Reinforcement in columnReinforcement in column
► Concrete is strong in compression.Concrete is strong in compression.
► However, longitudinal steel rods are always provided to assist inHowever, longitudinal steel rods are always provided to assist in
carrying the direct loads.carrying the direct loads.
► A minimum area of longitudinal steel is provided in the column, whetherA minimum area of longitudinal steel is provided in the column, whether
it is required from load point of view or not.it is required from load point of view or not.
► This is done to resist tensile stresses caused by some eccentricity ofThis is done to resist tensile stresses caused by some eccentricity of
the vertical loads.the vertical loads.
► There is also an upper limit of amount of reinforcement in RC columns,There is also an upper limit of amount of reinforcement in RC columns,
because higher percentage of steel may cause difficulties in placingbecause higher percentage of steel may cause difficulties in placing
and compacting the concrete.and compacting the concrete.
► Longitudinal reinforcing bars are “tied” laterally by “ties” or “stirrups”Longitudinal reinforcing bars are “tied” laterally by “ties” or “stirrups”
at suitable interval so that the bars do not buckleat suitable interval so that the bars do not buckle
42

43. 43

44. Codal Provisions(IS-456-2000)Codal Provisions(IS-456-2000)
44
Page No:41 & 42 –IS 456-2000

45. 45
Page No:94–IS 456-2000

46. 46
Page No:42–IS 456-2000

47. 47
Clause26.53.1- Page No:48–IS 456-2000

48. 48

49. Functions of longitudinal reinforcementFunctions of longitudinal reinforcement
► To share the vertical compressive load, thereby reducing the overall
size of the column.
► To resist tensile stresses caused in the column due to (i) eccentric
load (ii) Moment (iii) Transverse load.
► To prevent sudden brittle failure of the column.
► To impart certain ductility to the column.
► To reduce the effects of creep and shrinkage due to sustained loading..
49

50. 50
Clause 26.53.3.2Page No:49–IS 456-2000

51. 51
Clause 26.5.3.2 Page No:49–IS 456-2000

52. 52
Clause 26.5.3.2 Page No:49–IS 456-2000

53. Functions of Transverse reinforcementFunctions of Transverse reinforcement
► To prevent longitudinal buckling of longitudinal reinforcement.
► To resist diagonal tension caused due to transverse shear due to
moment/transverse load.
► To hold the longitudinal reinforcement in position at the time of
concreting.
► To confine the concrete, thereby preventing its longitudinal splitting.
► To impart ductility to the column.
► To prevent sudden brittle failure of the columns.
53

54. 54
Clause 26.5.3.2 Page No:49–IS 456-2000
Cover to reinforcementCover to reinforcement
For a longitudinal reinforcing bar in a column, the nominal cover shall not
be less than 40mm, nor less than the diameter of such bar.
In the case of columns of minimum dimension of 200mm or under, whose
reinforcing bars does not exceed 12mm, a cover of 25mm may be used.
Clause 26.4.2.1 Page No:49–IS 456-2000

55. 55
SP 34- 1987 Page No:88

56. Assumptions in Limit State of Collapse -CompressionAssumptions in Limit State of Collapse -Compression
56
Clause 38.1 Page No:69–IS 456-2000

57. 57
Clause 38.1 Page No:69–IS 456-2000

58. 58
Clause 38.1 Page No:69–IS 456-2000

59. 59

60. 60

61. 61

62. 62
Detailing of columnsDetailing of columns

63. 63
a) Termination of column bars inside slab
b) Fixed end joint in a column

64. 64
c) Typical detail of beam column junction at external column

65. 65

66. 66

67. 67

68. 68

69. 69

70. Design of Compression members-
Uniaxial Bending

71. Based on Type of Loading
a) Columns with axial loading (applied concentrically)
b) Columns with uniaxial eccentric loading
c) Columns with biaxial eccentric loading
71

72. Column under axial compression and Uni-axialColumn under axial compression and Uni-axial
BendingBending
► Let us now take a case of a column which is subjected to combinedLet us now take a case of a column which is subjected to combined
action of axial load (Paction of axial load (Puu) and Uni-axial Bending moment (M) and Uni-axial Bending moment (Muu).).
► This case of loading can be reduced to a single resultant load PThis case of loading can be reduced to a single resultant load Puu actingacting
at an eccentricity e such that e= Mat an eccentricity e such that e= Muu / P/ Puu ..
► The behavior of such column depends upon the relative magnitudes ofThe behavior of such column depends upon the relative magnitudes of
MMuu and Pand Puu , or indirectly on the value of eccentricity e., or indirectly on the value of eccentricity e.
► For a column subjected to load PFor a column subjected to load Puu at an eccentricity e, the location ofat an eccentricity e, the location of
neutral axis (NA) will depend upon the value of eccentricity e.neutral axis (NA) will depend upon the value of eccentricity e.
► Depending upon the value of eccentricity and the resulting position (XDepending upon the value of eccentricity and the resulting position (Xuu))
of NA., We will consider the following cases.of NA., We will consider the following cases.
72

73.  Case ICase I :: Concentric loading: Zero Eccentricity or nominalConcentric loading: Zero Eccentricity or nominal
eccentricity (Xeccentricity (Xuu =∞)=∞)
 Case IICase II :: Moderate eccentricity (XModerate eccentricity (Xuu > D)> D)
 Case IIICase III :: Moderate eccentricity (XModerate eccentricity (Xuu = D)= D)
 Case IVCase IV :: Moderate eccentricity (XModerate eccentricity (Xuu < D)< D)
Case I (e=0 and e<eCase I (e=0 and e<eminmin ))
73

74. 74
Case II (Neutral axis outside the sectionCase II (Neutral axis outside the section)

75. 75
Case III (Neutral axis along the edge)Case III (Neutral axis along the edge)

76. 76
Case IV (Neutral Axis lying within the section)Case IV (Neutral Axis lying within the section)

77. Modes of Failure in Eccentric CompressionModes of Failure in Eccentric Compression
► The mode of failure depends upon the relative magnitudes ofThe mode of failure depends upon the relative magnitudes of
eccentricity e. (e = Meccentricity e. (e = Muu / P/ Puu ))
77
Eccentricity Range Behavior Failure
e = Mu / Pu
Small Compression Compression
e = Mu / Pu
Large Flexural Tension
e = Mu / Pu
In between
two
Combination Balanced

78. Column Interaction DiagramColumn Interaction Diagram
► A column subjected to varying magnitudes of P and M will act with itsA column subjected to varying magnitudes of P and M will act with its
neutral axis at varying points.neutral axis at varying points.
78

79. Method of Design of Eccentrically loaded short columnMethod of Design of Eccentrically loaded short column
79
The design of eccentrically loaded short column can be done by two
methods
I) Design of column using equations
II) Design of column using Interaction charts

80. Design of column using equationsDesign of column using equations
80

81. 81

82. 82
Design of column using Interaction chartsDesign of column using Interaction charts

83. 83

84. 84

85. Design of Compression members-
Biaxial Bending

86. IntroductionIntroduction
► A column with axial load and biaxial bending is commonly found inA column with axial load and biaxial bending is commonly found in
structures because of two major reasons:structures because of two major reasons:
Axial load may have natural eccentricities, though small, withAxial load may have natural eccentricities, though small, with
respect to both the axes.respect to both the axes.
Corner columns of a building may be subjected to bendingCorner columns of a building may be subjected to bending
moments in both the directions along with axial loadmoments in both the directions along with axial load
ExamplesExamples
1)1) External façade columns under combined vertical and horizontalExternal façade columns under combined vertical and horizontal
loadload
2)2) Beams supporting helical or free-standing stairs or oscillating andBeams supporting helical or free-standing stairs or oscillating and
rotary machinery are subjected to biaxial bending with or withoutrotary machinery are subjected to biaxial bending with or without
axial load of either compressive or tensile stress.axial load of either compressive or tensile stress.
86

87. Biaxial EccentricitiesBiaxial Eccentricities
►Every column should be treated as beingEvery column should be treated as being
subjected to axial compression along withsubjected to axial compression along with
biaxial bending by considering possiblebiaxial bending by considering possible
eccentricities of the axial load with respecteccentricities of the axial load with respect
to both the major axis(xx-axis) as well asto both the major axis(xx-axis) as well as
minor axis (yy-axis).minor axis (yy-axis).
►These eccentricities, designated as eThese eccentricities, designated as exx andand
eeyy with respect of x and y axes, may bewith respect of x and y axes, may be
atleast eatleast eminmin though in majority of cases ofthough in majority of cases of
biaxial bending, these may be much morebiaxial bending, these may be much more
then ethen emin.min.
87

88. 88

89. Method Suggested by IS 456-2000Method Suggested by IS 456-2000
►The method set out in clause 39.6 of the code is based on anThe method set out in clause 39.6 of the code is based on an
assumed failure surface that extends the axial load-momentassumed failure surface that extends the axial load-moment
diagram (Pdiagram (Puu-M-Muu) for single axis bending in three dimensions.) for single axis bending in three dimensions.
Such an approach is also known as Breslar’s Load contourSuch an approach is also known as Breslar’s Load contour
method.method.
►According to the code, the left hand side of the equationAccording to the code, the left hand side of the equation
89

90. Shall not exceed 1. Thus we haveShall not exceed 1. Thus we have
The code further relatesThe code further relates ααnn to the ratio of Pto the ratio of Puu/P/Puzuz
as under:as under:
For intermediate values, linear interpolationFor intermediate values, linear interpolation
may be done from figure.may be done from figure.
Load PLoad Puzuz is given byis given by
Load PLoad Puzuz may be evaluated from chart 63 of ISImay be evaluated from chart 63 of ISI
Handbook(SP-16-2000)Handbook(SP-16-2000)
90
Pu/Puz Between 0.2 and 0.8

91. Design of ColumnDesign of Column
Step-1Step-1-Assume the cross-section of the column and the area of-Assume the cross-section of the column and the area of
reinforcement along with its distribution, based on moment Mreinforcement along with its distribution, based on moment Muu
given by equationgiven by equation
where a may vary between 1.10 to 1.20- lower of awhere a may vary between 1.10 to 1.20- lower of a
for higher axial loading (Pfor higher axial loading (Puu/P/Puzuz))
Step-2Step-2- Compute P- Compute Puzuz either using Equation or chart. Find ratio ofeither using Equation or chart. Find ratio of
PPuu/P/Puz.uz.
Step-3Step-3- Determine Uniaxial Moment Capacities M- Determine Uniaxial Moment Capacities Mux1ux1 and Mand Muy1uy1
combined with axial load Pcombined with axial load Puu , using Appropriate Interaction, using Appropriate Interaction
curves(Design charts) for case of column subjected to axialcurves(Design charts) for case of column subjected to axial
load (Pload (Puu ) and Uniaxial Moment.) and Uniaxial Moment.
91

92. Step-4Step-4-Compute the values of M-Compute the values of Muxux/M/Mux1ux1 and Mand Muyuy/M/Muy1uy1 from chart 64 offrom chart 64 of
SP-16, Find the permissible value of MSP-16, Find the permissible value of Muxux/M/Mux1ux1 corresponding topcorresponding top
the above values of Mthe above values of Muyuy/M/Muy1uy1 and Pand Puu/P/Puzuz .If actual value of M.If actual value of Muxux/M/Mux1ux1
is more than the above value found from chart 64 of SP 16, theis more than the above value found from chart 64 of SP 16, the
assumed section is unsafe and needs revision. Even if theassumed section is unsafe and needs revision. Even if the
assumed value is over safe, it needs revision for the sake ofassumed value is over safe, it needs revision for the sake of
economy.economy.
92

93. 93
Simplified method as per BS8110Simplified method as per BS8110

94. 94

95. 95

96. 96

97. 97

98. Design of Slender Columns

99. IntroductionIntroduction
► A Compression member may be considered as slender or long whenA Compression member may be considered as slender or long when
the slenderness ratio lthe slenderness ratio lexex/D and l/D and leyey/b are more than 12./b are more than 12.
► Thus, if lThus, if lexex/D > 12, the column is considered to be slender for bending/D > 12, the column is considered to be slender for bending
about x-x axis, while if labout x-x axis, while if leyey/b > 12, the column is considered to be slender/b > 12, the column is considered to be slender
for bending about y-y axis.for bending about y-y axis.
► When a short column is loaded even with an axial load, the lateralWhen a short column is loaded even with an axial load, the lateral
deflection is either zero or very small.deflection is either zero or very small.
► Similarly when a slender column is loaded even with axial load, theSimilarly when a slender column is loaded even with axial load, the
lateral deflection ∆, measured from the original centre line along itslateral deflection ∆, measured from the original centre line along its
length, becomes appreciable.length, becomes appreciable.
99

100.  The design of a slender column can be carried out by followingThe design of a slender column can be carried out by following
simplified methodssimplified methods
1) The Strength Reduction Coefficient method1) The Strength Reduction Coefficient method
2) The Additional moment Method2) The Additional moment Method
3) The Moment Magnification Method3) The Moment Magnification Method
The reduction coefficient method, given by IS 456-2000 isThe reduction coefficient method, given by IS 456-2000 is
recommended for working stress design for service load and is basedrecommended for working stress design for service load and is based
on allowable stresses in steel and concrete.on allowable stresses in steel and concrete.
The additional moment method is recommended by Indian and BritishThe additional moment method is recommended by Indian and British
codes.codes.
The ACI Code recommends the use of moment magnification method.The ACI Code recommends the use of moment magnification method.
100
Methods of Design of Slender ColumnsMethods of Design of Slender Columns

101. 101
Page no:71,72-IS 456-2000

102. Determination of Total MomentDetermination of Total Moment
102

103. 103

104. Bending of columns in framesBending of columns in frames
104
(a) Braced (b) unbraced

105. Procedure for Design of Slender ColumnProcedure for Design of Slender Column
Step-1-Step-1- Determine the Effective Length and Slenderness Ratio in eachDetermine the Effective Length and Slenderness Ratio in each
directiondirection
Step-2-Step-2- (a) Determine Initial Moment (M(a) Determine Initial Moment (Muiui) from given primary end) from given primary end
moments Mmoments Mu1u1 and Mand Mu2u2 in each direction.in each direction.
(b) Calculate e(b) Calculate eminmin and Mand Mu,minu,min in each direction.in each direction.
(c) Compare moments computed in steps (a) and (b) above and take the(c) Compare moments computed in steps (a) and (b) above and take the
greater one of the two as initial moment Mgreater one of the two as initial moment Muiui ,in each direction.,in each direction.
Step-3-Step-3- (a) Compute additional moment (M(a) Compute additional moment (Maa) in each direction, using) in each direction, using
equationequation
105

106. (b) Compute total moment (M(b) Compute total moment (Mutut ) in each direction from using equation) in each direction from using equation
without considering reduction factor (kwithout considering reduction factor (kaa))
(c) Make Preliminary design for P(c) Make Preliminary design for Puu and Mand Mutut and find area of steel. Thus p isand find area of steel. Thus p is
known.known.
Step-4-Step-4- (a) Obtain P(a) Obtain Puzuz. Also obtain P. Also obtain Pbb in each direction, for reinforcementin each direction, for reinforcement
ration p determined above.ration p determined above.
(b) Determine the value of k(b) Determine the value of kaa in each direction.in each direction.
(c) Determine the Modified design value of moment in each direction(c) Determine the Modified design value of moment in each direction
MMutut = M= Muiui + k+ kaa MMaa
106

107. Step-5-Step-5- Redesign the column for PRedesign the column for Puu and Mand Mutut . If the column is slender about. If the column is slender about
both the axes, design the column for biaxial bending, for (Pboth the axes, design the column for biaxial bending, for (Puu , M, Muxtuxt) about) about
x-axis and (Px-axis and (Puu , M, Muytuyt) about y-axis.) about y-axis.
Note-When external moments are absent, bending moment due toNote-When external moments are absent, bending moment due to
minimum eccentricity should be added to additional moment about theminimum eccentricity should be added to additional moment about the
corresponding axes.corresponding axes.
107

108. 108