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

2. 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.
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3.  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.
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Methods of Design of Slender ColumnsMethods of Design of Slender Columns

4. 4
Page no:71,72-IS 456-2000

5. Determination of Total MomentDetermination of Total Moment
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6. 6

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

8. 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
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9. (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
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10. 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.
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