MATH: Reinforced Concrete Design 02

CHAPTER 6
Axially Loaded Columns

CLASSIFICATION OF COLUMNS
In general, columns are classified as short columns and long columns. If the height of
column is less than three times its least lateral dimension, it may be considered
as short compression blocks or pedestal, Pedestals may be designed without
reinforcement with a maximum permissible compressive strength of 0.850 f'c ,
where Ø is 0.70 (Sect. 5.10.15). If the compressive strength is greater than this value, the pedestal will have to be designed as a reinforced concrete short column.

If the reinforced concrete column fails due to initial material failure, it is classified as short columns, The load of the short columns depends on the dimension and the strength of the material of which it is made.
If the length of the column is increased, the chances that it will fail by lateral buckling will be increased. Columns that fail by buckling are called long columns.

P-delta Moment
When a column is subjected to primary moments M, such as thosde caused by applied loads or joint rotation, the axis of the member deflects laterally. This deflection causes additional moment applied to the column, which is equal to the column load times the lateral deflection. This moment is called secondary moment or P-delta moment, as shown in Figure 6.1.




If the secondary moment becomes too large, the column is said to be long column and it is necessary to design its section for the sum of both primary and secondary moments. However, the Code permits that columns be designed as short column if the secondary or PA effect does not reduce their strength by more than 5%.

Types of columns

Plain concrete pedestal - This may be used only if the height does not exceed three times the least lateral dimension.

(b) Tied columns - A column in which the longitudinal bars are braced with a series of closed ties.

(c) Spiral columns - a column in which the longitudinal bars and concrete core are wrapped with a closely spaced helix or spiral.

(d) Composite columns - These columns may contain a structural steel shape surrounded by longitudinal bars with ties or spirals or it may consist of high strength steel tubing filled with concrete.

Tied and spiral columns are the most common forms. Either type may be circular octagonal, square, or rectangular section. Tied columns may also be L, T or other irregular shape.

AXIAL LOAD CAPACITY OF COLUMNS

Axial load without moment is not a practical cease in design of columns, but the discussion of such case is necessary for explaining the theory involved in eccentrically loaded columns. For a column subjected purely by an axial load, the nominal load Pn that it can carry is the sum of the strength of steel which is fyAst, and the strength of concrete 0.85f'c(Ag -Ast ), where Ag - Ast is the net concrete area, or

Pn=0.85f'c Ag-Ast+ fyAst Eq.6-1

To counter the effect of possible eccentricities, the nominal strength Pn is multiplied by 0.80 for tied columns and 0.88 for spiral columns. Finally, the ultimate axial load capacity of the column Pn is ØPn, where Ø is 0.70 for tied columns and 0.75 for spiral columns.

TIED COLUMN



Pu = ØPn = Ø 0.80 [0.85f'c (AgAst)+ fy, Ast] Eq. 6-2

Where Ø=0.70
Ag=gross concrete area=bx t
Ast=area of steel reinforcement
These maximum load limits govern wherever the moment is small enough to keep the eccentricity under 0.10h where h is the column width parallel to the applied applied moment.

Limits of Reinforcement for Tied Columns (Section 510.9)

I. Ast shall not be less than 0.01Ag and Ast shall not be more than 0.06Ag.

II. The minimum number of longitudinal bars is 4 for bars within rectangular or circular ties, 3 for bars within triangular ties.

Sizes and Spacing of Main Bars and Ties

I. Clear distance between longitudinal bars shall be not less than 1.5db nor 40 - mm. (Section 57.6.3)

II. Use 10-mm diameter ties for 32-mm bars or smaller and at least 12 mm in size for 36 mm and bundled longitudinal bars. (Section 5.7.10.5.2)

III. Vertical spacing of ties shall be the smallest of the following:
(Sect. 5.7.10.5.2)

1. 16 x db (db, = longitudinal bar diameter)
2. 48 x tie diameter
3. least dimension of the column

IV. Ties shall be arranged such that every corner and alternate longitudinal bar shall have lateral support provided by the corner of the tie with an included angle of not more than 135° and no bar shall be farther than 150 mm clear on each side along the tie from such a laterally supported bar. Where longitudinal bars are located around the perimeter of a circle, a complete circular tie is allowed. (Section 5.7.10.5.3).



Pu= ØPn= Ø 0.85 0.85 f'c Ag-Ast+ fy Ast Eq. 6.3

Where Ø=0.75
This maximum load limit governs whenever is small enough to keep the eccentricity under 0.05h.

Sizes and spacing of spirals

I. For cast-in-place construction, size of spirals shall not be less than 10 mm [(Section 5.7.10.4.2)

II. Clear spacing between spirals shall not exceed 75 mm, nor less than 25 mm. (Section 5.7.10.4.3)

III. Anchorage of spiral reinforcement shall be provided by 1-½ extra turns of jspiral bar. (Section 5.7.10.4)

IV. Splices of spiral reinforcement shall be lap splices of 48db but not less than 300 mm or welded, (Section 5. 7.10.5)

V. The percentage of spiral steel s is computed from the following equation
Ps= volume of spiral in one loopvolume of concrete core for a pitch s Eq. 6.4
Ps= 4as (Dc-db)sDc2 Eq.6.5

where as is the cross-sectional area of spiral bar, D is diameter of the core to out of the spiral, arid db, is the diameter of the spiral bar.

VI. The minimum spiral percentage is given by: (Section 5.10.9.3)
ρs min=0.45 AgAc-1f'cfy Eq. 6.6
Where fy is the specified yield strength of spiral reinforcement but not more than 415 MPa.