1. by
S.Praveenkumar
Assistant Professor
Department of Civil Engineering
PSG College of Technology
Coimbatore
Design of Compression members-
Biaxial Bending

2. 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.
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3. 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.
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5. 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
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6. 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)
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Pu/Puz Between 0.2 and 0.8

7. 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.
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8. 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.
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9. 9
Simplified method as per BS8110Simplified method as per BS8110

10. 9
Simplified method as per BS8110Simplified method as per BS8110