Design of slender columns as per IS 456-2000
16 likes12,516 views
The document discusses the design of slender columns. It defines a slender column as having a slenderness ratio (length to least lateral dimension) greater than 12. Slender columns experience appreciable lateral deflection even under axial loads alone. The design of slender columns can be done using three methods - the strength reduction coefficient method, additional moment method, or moment magnification method. The document outlines the step-by-step procedure for designing a slender column using the additional moment method, which involves determining the effective length, initial moments, additional moments, total moments accounting for a reduction coefficient, and redesigning the column for combined axial load and bending.
Design of slender columns as per IS 456-2000
- 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. 2
- 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. 3 Methods of Design of Slender ColumnsMethods of Design of Slender Columns
- 5. Determination of Total MomentDetermination of Total Moment 5
- 6. 6
- 7. Bending of columns in framesBending of columns in frames 7 (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 8
- 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 9
- 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. 10