1. Reinforced Concrete Design
Lecture 14
Dr. Nader Okasha

2. Design of Short Axially Loaded Columns

3. Columns
According to ACI Code, a structural element with a ratio of height-to least lateral dimension exceeding three used primarily to support compressive loads is defined as column.
Columns are vertical compression members of a structural frame intended to support the load-carrying beams. They transmit loads from the upper floors to the lower levels and then to the soil through the foundations. b l P h
Column
Beam
Loads
Footing
Soil
Slab

4. Columns
Usually columns carry bending moment as well, about one or both axes of the cross section, and the bending action may produce tensile forces over a part of the cross section
The main reinforcement in columns is
longitudinal, parallel to the direction of
the load and consists of bars arranged
in a square, rectangular, or circular shape

5. Length of the column in relation to its lateral dimensions
Columns may be divided into two categories
1- Short Columns, for which the strength is governed by the strength of the materials and the geometry of the cross section
2- Slender columns, for which the strength may be significantly reduced by lateral deflections.
3- Position of the load on the cross-section
Columns can be classified as
1-Concentrically loaded columns, are subjected to axial force only
2-Eccentrically loaded columns, are subjected to moment in addition to the axial force.

6. Column Load: Tributary area method

7. Column Load: Beam reaction method

8. Load Summation on Column Section for Design

9. Analysis and Design of Short Columns
Column Types:
Tied
Spiral
Composite

10. Behavior of Tied and Spirally-Reinforced Columns
Axial loading tests have proven that tied and spirally reinforced columns having the same cross-sectional areas of concrete and steel reinforcement behave in the same manner up to the ultimate load.
At that load tied columns fail suddenly due to excessive cracking in the concrete section followed by buckling of the longitudinal reinforcement between ties within the failure region. For spirally reinforced columns, once the ultimate load is reached, the concrete shell covering the spiral starts to peel off. Only then, the spiral comes to action by providing a confining force to the concrete core, thus enabling the column to sustain large deformations before final collapse occurs.

11. Behavior of Tied and Spirally-Reinforced Columns
Failure of a tied column
Failure of a spiral column
Deformation

12. Nominal Capacity and Design under Concentric Axial loads
Ag = gross area = b*h
Ast = area of long steel
fc = concrete compressive strength
fy = steel yield strength

13. Nominal Capacity and Design under Concentric Axial loads
Maximum Nominal Capacity for Design Pn
r = Reduction factor to account for accidental eccentricity
r = ( tied )
r = ( spiral )
ACI

14. Nominal Capacity and Design under Concentric Axial loads
f = 0.65 for tied columns
f = 0.75 for spiral columns (was 0.70 in ACI318-05)
r = ( tied )
r = ( spiral )

15. Nominal Capacity and Design under Concentric Axial loadsor

16. Nominal Capacity and Design under Concentric Axial loads
* when rg is known or assumed:

17. Nominal Capacity and Design under Concentric Axial loads
Reinforcement Requirements (Spiral)
Spiral Reinforcement Ratio, rs

18. Nominal Capacity and Design under Concentric Axial loads
Reinforcement Requirements (Spiral)

19. Reinforcement Requirements (Longitudinal Steel Ast)
Design Considerations
Reinforcement Requirements (Longitudinal Steel Ast)
ACI Code requires

20. Reinforcement Requirements (Longitudinal Steel Ast)
Design Considerations
Reinforcement Requirements (Longitudinal Steel Ast)
- Minimum Number of Bars ACI Code
min. of 6 bars in spiral arrangement
min. of 4 bars in rectangular or circular ties
min. of 3 bars in triangular ties

21. Reinforcement Requirements (Lateral Ties)
Design Considerations
Reinforcement Requirements (Lateral Ties)
ACI Code
size
f 8 bar if longitudinal bar f30 bar f12 bar if longitudinal bar f 32 bar f12 bar if longitudinal bars are bundled

22. Reinforcement Requirements (Lateral Ties)
Design Considerations
Reinforcement Requirements (Lateral Ties)
Vertical spacing: (ACI )
16 db ( db for longitudinal bars ) dstirrup least lateral dimension of column
s s s

23. Reinforcement Requirements (Lateral Ties)
Design Considerations
Reinforcement Requirements (Lateral Ties)
Arrangement Vertical spacing: (ACI )
1.)
At least every other longitudinal bar shall have lateral support from the corner of a tie with an included angle o.
No longitudinal bar shall be more than 15cm clear on either side from “support” bar.
2.)

24. Examples of lateral ties
Design Considerations
Examples of lateral ties

25. Reinforcement Requirements (Spirals )
Design Considerations
Reinforcement Requirements (Spirals )
ACI Code
size
10 mm diameter
ACI
clear spacing between spirals
2.5cm
7.5cm

26. Design Considerations
Clear Distance between Reinforcing Bars
ACI Code specify that for tied or spirally reinforced columns, clear distance between bars, shown in Figure, is not to be less than the larger of 1.50 times bar diameter or 4 cm. This is done to ensure free flow of concrete among reinforcing bars.

27. Design Considerations
Concrete Protection Cover
ACI Code specifies that for reinforced columns, the clear concrete cover is not to be taken less than 4 cm for columns not exposed to weather or in contact with ground. It is essential for protecting the reinforcement from corrosion or fire hazards.
Minimum Cross Sectional Dimensions
The ACI Code does not specify minimum cross sectional dimensions for columns. Column cross sections 20 × 25 cm are considered as the smallest practicable sections. For practical considerations, column dimensions are taken as multiples of 5 cm.
Lateral Reinforcement
Ties are effective in restraining the longitudinal bars from buckling out through the surface of the column, holding the reinforcement cage together during the construction process, confining the concrete core and when columns are subjected to horizontal forces, they serve as shear reinforcement.

28. Design Considerations
Factored Loads
For gravity loads only,
Pu = 1.2 PD+1.6 PL
For dead, live and wind loads,
Pu = 1.2 PD+1.0 PL+1.6 PW
For dead and wind loads,
Pu = 0.9 PD PW or Pu = 1.2 PD PW
For dead, live and earthquake loads,
Pu = 1.2 PD+1.0 PL+1.0 PE
For dead and earthquake loads,
Pu = 0.9 PD PE

29. Design Procedure for Short Axially Loaded Columns
Evaluate the factored axial load Pu acting on the column.
Decide on a reinforcement ratio ρg that satisfies ACI Code limits. Usually a 1 % ratio is chosen for economic considerations.
Determine the gross sectional area Ag of the concrete section.
Choose the dimensions of the cross section based on its shape.
Readjust the reinforcement ratio by substituting the actual cross sectional area in the respective equation. This ratio has to fall within the specified code limits.
Calculate the needed area of longitudinal reinforcement ratio based on the adjusted reinforced ratio and the chosen concrete dimensions.

30. Design Procedure for Short Axially Loaded Columns
From reinforcement tables, choose the number and diameters of needed reinforcing bars. For rectangular sections, a minimum of four bars is needed, while a minimum of six bars is used for circular columns.
Design the lateral reinforcement according to the type of column, either ties or spirals.
Check whether the spacing between longitudinal reinforcing bars satisfies ACI Code requirements.
Draw the designed section showing concrete dimensions and with required longitudinal and lateral reinforcement.

31. Example 1
The cross section of a short axially loaded tied column is shown in Figure. It is reinforced with 6 16mm bars. Calculate the design load capacity of the cross section.
Use fc′=280 kg/cm2 and fy = 4200 kg/cm2.
Solution:
Clear distance between bars Sc
Only, one ties is required for the cross section
Figure [1]
6Φ16 25 40
Ties
Sc=12.8 cm
6Φ16 25 40

32. Example 1 The spacing between ties is not exceed the smallest of
16 db =16(1.6) = 25.4 cm
48 ds = 48(0.8) = 38.4 cm
25 cm
Thus, ACI requirements regarding reinforcement ratio, clear distance between bars and tie spacing are all satisfied.
The design load capacity ΦPn
Φ 8mm ties 25 cm

33. Example 2
Design a short tied column to support a factored concentric load of 1000 kN, with one side of the cross section equals to 25 cm.
Solution

34. Check spacing

35. Stirrup design

36. Example 3
Design a short, spirally reinforced column to support a service dead load of 800 kN and a service live load of 400 kN.
Solution

37. Check spacing between longitudinal bars
Solution
Check spacing between longitudinal bars
D’ =35-2(4)-2(0.8)-1.4=24cm

38. Design the needed spiral, try f 8