Uni and bi axial column and design

2. Generally a column is something which carries
load from beam and slab. In other words
columns are defined as the members that
carries load mainly in compression. columns
carry bending moment as well, about one or
both axes of the cross section.

3. COLUMNS ARE DEFINED ASMEMBERS THAT CARRYLOADS
CHIEFLYIN COMPRESSION.
SIMULTANEOUSLY BENDING MOMENTS ARE ALWAYS
PRESENT AS WELL ABOUT ONE OR BOTH AXES OF THE
CROSS SECTION.

5. SHORT COLUMN, FO R
WHICH LATERAL BUCKLING
NEED NOT BE CONSIDERED.
SLENDER COLUMN, FOR W H I C H THE
S T R E N G T H MAY BE SIGNIFICANTLY
REDUCED BYLATERAL
DEFLECTION, SO LATERALBUCKLING NEED
TO BE CONSIDERED.
USUALLY MOST COLUMNS IN PRESENT DAY
PRACTICE ARECONSIDERED AS SHORT COLUMN.

6. WHEN ACOLUMN IS SUBJECTED TO EITHER COMBINED
AXIAL COMPRESSION (P) AND MOMENT (M) ASIN
FIG-1 OR ONLY AXIAL LOAD (P) APPLIED AT AN
ECENTRICITY
e=(M/P) AS IN FIG-2 SO THAT THE COLUMN IS TRYING
TO BEND ABOUT ONLY ONE AXES OF THE COLUMN
CROSS SECTION IS KNOWN AS UNIAXIALLY LOADED
COLUMN.

7. In beam column slab, normally slab transfer loads to
beam and beam transfer loads to column and finally
column transfer loads to footing.

8. Short column:
In short column the strength is governed by strength of the
materials and the geometry of the cross section.
Slender column:
A column is said to be slender if its cross-sectional dimensions
are small compared with its length.

9. The column having axial load acting in such a way that the load is
eccentric about both the axes in the plane of the column then it is
called biaxially loaded column.

10. There are situations in which for
rectangular and square columns
axial compression is accompanied
by simultaneous bending about
both principal axes of the section.

11. Figure shows inter action diagram for compression plus biaxial
bending:
a) uniaxial bending about Y axis;
b) uniaxialbending about X axis;
c) biaxial bending about diagonal axis;d) interaction surface

12. An analysis of the damage observed in 24 reinforced concrete
(RC) columns tested under uniaxial and biaxial horizontal
loading . The test results show that for biaxial loading
conditions specific damage occurs for lower drift demands
when compared with the corresponding uniaxial demand .

13. Load contour method
Reciprocal load method
Strain compatibility method
Equivalent eccentricity method
45 slice through interaction surface

14. The 12 20 in column shown in fig is reinforced with
eight no.9 bars arranged around the column perimeter,
providing an area Ast = 8 in². A factored load Pu of
255 kips is to be applied with eccentricities
eʏ=3in,ex= 6in.
material strengths are ƒ’c = 4 ksi and ƒʏ= 60 ksi.
Check adequacy by trial design.

16. In a typical design situation given the size and reinforcement of
the trial column and the load eccentricities ex and ey following
steps should be followed
At first we need to calculate ratio γ then we shall calculate
e/h.
After that we shall calculate nominal loads Pnxo and Pnyo for
uniaxial bending around the X and Y axes respectively, and the
nominal load Po for concentric loading.
Then 1/Pn is computed from equation,
1/ Pn =1/ Pnyo+1/ Pnxo -1/Po

17. From the eqaution Pn is calculated, where Pn =approximate
value of nominal load in biaxial bending with eccentricities
ex and ey.
Ø The design requirement is that the factored load Pu must not
exceed ɸPn .
Ø ɸ = 0.65 for tied column and 0.70 for spiral column
according to ACI code.

18. By the reciprocal load method first considering bending about
the Y axis,
γ = 15/20 = 0.75 and e/h = 6/20 = 0.3
With the reinforcement ratio of Ast/bh= 8/240 = 0.033, using the
avg graps A.6 γ =0.7 and A.6 γ =0.8
Pnyo/ ƒ’cAg (avg) =0.62+0.66/2= 0.64 Pnyo= 0.64*4*240=
614kips
Po/ ƒ’cAg =1.31
Po=1.31*4*240=1258kips

19. Then for the bending about the X axis, γ = 7/12 = 0.6 and e/h = 3/12 =
0.25
Graph A.5 Appendix A gives Pnxo/ ƒ’cAg (avg) =0.65
P n x o = 0 . 6 5 * 4 * 2 4 0 = 6 2 4 k i p s P o / ƒ ’ c A g = 1 . 3 1
Po=1.31*4*240=1258kips

20. Now substituting these values in the equation 1/ Pn =1/ Pnyo+1/
Pnxo -1/Po
=1/624+1/614-1/1258
=0.00244
From which Pn =410 kips.
Thus according to Bresler method the design load,
Pu =0.65*4109 = 267 kips can be applied safely.

24. ØColumn is a structural element that transmits, through compression,
the weight of the structure above to other structural elements below. In
other words, a column is a compression member.
Ø The biaxial bending method discussed permit
rectangular column to be designed or analyzed if bending is
presentabout only one of the two principal axes of section.
Ø Axial compression is accompanied by simultaneous bending about
both principle axes of the section.
Ø It occurs in corner columns of building.

25. Fig: Biaxial bending plus compression

27. Equivalent Eccentricity of column
load
(a)Concentrically loaded column
(b)Eccentrically loaded column

28. Fig: Column subject to eccentric compression
(a)loaded column
(b)Strain distribution at section a-a (c)Stress and forces
at nominal strength

33. Interaction diagram for compression plus biaxial bending
(a) Uniaxial bending about y axis (b)Uniaxial bending about X axis
(c)Biaxial bending about diagonal axis (d)Interaction surface

35. Where
Where,

36. Fig: Interaction surface for the reciprocal load method

37. • The 12×20 in column shown in fig is reinforced with eight no.9 bars arranged
around the column perimeter, providing an area Ast=8 in². A factored
load Pu of 255 kips is to be applied with eccentricities
• = 3in,=6in.
• material strengths are ƒ’c = 4 ksi and ƒʏ=60 ksi.
• Check adequacy by trial design using
a. Reciprocal load method
b. Load contour method.

44. Thank you
Mr. VIKAS MEHTA
School of Mechanical and civil engineering
Shoolini University
Village Bajhol, Solan (H.P)
vikasmehta@shooliniuniversity.com
+91 9459268898