Minimum Amount in Concrete Columns

When I began to study the design of concrete, it was established by the ACI-318 design standard, and the Cuban design standard, that the minimum reinforcement ratio in columns was 1%. I participated in the elaboration of the Cuban HA design standards, which required the study of several design standards from other countries. This study, especially the one of ACI-318, allowed me to seek answers for the matter raised in this article.

The topic made me think that it was related to the amount required by a column working as a tensor. The sum of the tensile stresses at the moment of the first crack resulted in that 1%. However, I told myself this could not be the main reason for that 1%. For a long time, I was in doubt, until it finally came to light that columns can be subjected to bending, apart from axial loads, in the two main directions and in turn in both ways.

I found this in the comments of the design standard itself, which gives two reasons; one referring to the bending on each face of the column and the other is due to the effect of shrinkage, and also creep of the concrete, etc.

Starting from the first one, that is, bending on the four faces of the column, I came to the understanding that 1% steel is indeed required. But furthermore, the study of the subject led me to other interesting conclusions that I would like to share with practicing engineers.

In the article “Minimum Reinforcement Ratio in Concrete Columns” you can find the reasoning by which I reached the minimum 1% steel and other conclusions, as well as other findings that derive from this study.

I hope that, as it happened to me, this study will provide you the answer to the question indicated in the title, and that the other findings will be useful for your next designs.

Thank you very much,

Engineer Ernesto F. Valdés Avellaneda
Professor. Dr. Technical Sciences. Structural Specialist.
Graduated from the University of Havana, CUJAE, Cuba, 1966.

Minimum Reinforcement Ratio in Concrete Columns

The different versions of the ACI 318 code establish that the reinforcement ratio in column sections must be a minimum of 1% and a maximum of 8%.

In this work, we will focus our attention to the minimum reinforcement ratio of 1%.

In the code, it states that there are two fundamental causes that give rise to the minimum reinforcement ratio:

     a) Reinforcement is necessary to provide resistance to bending, which may exist despite the results of the structural calculations.

     b) To reduce the effect of the creep and shrinkage of concrete under the effect of the sustained compressions that tend to increase the stress on the reinforcement. 

I always asked myself where the 1% value came from and I even thought that it was due to the possibility that the column could be subjected to complete tension. 

Although it is possible, this situation does not always occur, and we tasked ourselves with finding a logical and rational explanation for this 1% value. 

Regardless, let’s see what happens in a column when it is subjected to axial tension: We will assume a 4000 psi concrete and 60000 psi steel.

        fc := 4000⋅psi              fy := 60000⋅psi

The tensile strength of concrete varies from 0.1 f’c to 0.15 f’c

For the most unfavorable condition, the tensile strength will be:

         ft := 0.15⋅fc                 ft = 600⋅psi

The condition of equilibrium at the instant of cracking of the concrete, ΣF = 0

          As⋅fy := Ac⋅ft

being ρcol = As/Ac the amount of reinforcement in the column, we have:

           ρcol :=  ft

                       fy

           ρcol = 1 %

Despite the logical result, it does not result in the general explanation we are looking for.

Analysis of the structural work of the columns

Each concrete column is connected to the foundation at its lowest level and as it rises, in each floor, anchors are placed to give it the necessary continuity throughout the height. This means that at each level there exists a kind of embedment capable of taking moments in all direction. 

In very few instances, the column-foundation connection is constructed as a pin connection; however, for the structural analysis it can be assumed that it is articulated if certain conditions are met.

For example, for a column with an isolated foundation subjected to axial load and moment, the effect of the moment is transmitted from the column to the foundation, and from the foundation to the ground. The foundation turns and the moment disappears. The final effect is equivalent to a joint. But it cannot be forgotten that it was the moment of the column that produced the turn due to the effect of bending. 

If we now consider that the foundation is continuous, isolated with connection beams, pile heads, or any other type that does not rotate, or is very small, then the bending moment of the column is transmitted to the foundation causing bending. 

Unless an articulated connection between foundation and column is designed, we will always have the action of the bending moments and the minimum amount of 1% must be take into account. 

This means that due to the effect of the lateral loads such as wind, distribution of live loads, etc. It is possible that bending is generated in the column on each of the sides of the column, independently or simultaneously. In other words, each side of the column can be subjected to bending and requires a minimum amount on each side. 

Minimum amount of reinforcement due to bending

Fig. 1 shows a diagram of the column with the moment acting in each direction. In this case, it has been assumed that each moment acts separately. 

Fig. 1 Sections subjected to bending in both directions 

Fig. 2 Minimum reinforcement in concrete columns 

Each tensile zone requires a minimum bending reinforcement. This minimum bending reinforcement can be considered of the order of 0.0033 of the section of the column Ac (the effective section actually being b x d) and will be placed in each tensioned zone, then the total would be of the order of: 

          As/Ac = 4×0.0033 = 0.0132.

Taking into account that the corner bars will work for bending in a perpendicular direction, that is, 25% of the bars will work double, leaving behind 75% of the total effective bars, that is:

           As/Ac = 0.75×0.0132 = 0.01

which corresponds to the amount of 1% specified as the minimum by ACI 318. 

It has been clarified the origin of the 1% used as the minimum amount in the columns. 

Conclusions and recommendations

The analysis conducted has allowed us to reach certain conclusions of interest to the designer and the builder.

1.Minimum reinforcement ratio for column sections with high-strength concrete

For fc < 4440 psi the minimum amount due to bending is: 

.    fc := 4440•psi           fy := 60000•psi

.    ρmin := ((3•psi^0.5)•√fc)/(fy)        ρmin = 0.0033

For fc = 6000 psi the minimum amount due to bending is:

.  fc := 6000•psi        fy := 60000•psi

.  ρmin := ((3•psi^0.5)•√fc)/(fy)    ρmin = 0.0039

.  ρcol := 4•0.75•ρmin                  ρcol = 0.012                  1.2%

As can be seen, the minimum amount should increase as the quality of the concrete exceeds 4440 psi. It is recommended to increase the minimum amount as concrete strength increases above 5000 psi. 

 

2.Minimum reinforcement ratio when using high-strength steel

If the quality of the steel were greater than fy = 60000 psi, the amount of reinforcement necessary to compensate for the volume of tensions would decrease; therefore, the minimum amount would be less than 1%. Since this reinforcement is not used often, it is not worth establishing a different minimum. Hence why the value of 1% is maintained. However, we recommend complying with what was indicated in the previous point. 

3.Distribution of the minimum or greater reinforcement than the minimum in the section

When the minimum reinforcement is distributed in the column section, each side of the column should have the same number of bars of a same diameter. Consequently, they must be 4, 8, 12, etc. always multiples of 4 and the same bar diameter. 

Fig. 3 Reinforcement distribution in the column section 

In Fig. 3 a case is shown in which the distribution of the minimum bars must be modified. A 24 x 48 section requires a minimum reinforcement of:

achieved with: 

Fig. 3a shows the uniform distribution, so that on each face we have:

which complies with the minimum bending of 0.0033 

In Fig. 3b a non-uniform distribution is shown with 5 bars on the short side and 3 bars on the long side, 

With 3 bars on the long side, the minimum amount in bending should be met

which does not meet the minimum in bending. You will need to redistribute the uniform reinforcement or add the necessary bars on the long side to meet the minimum bending. 

Finally, if the column requires a greater amount of reinforcement than the minimum, the reinforcement can be redistributed according to the work of the column, but always keeping in mind that on the sides with fewer bars, the minimum reinforcement in bending must be met. It is recommended not to place reinforcement less than the minimum in bending on the sides with less loads so that the total amount of reinforcement is not increased. 

4. Case in which bending only occurs in one direction

In the case that the bending occurs in only one direction, as occurs in the columns within load-bearing walls (tie columns), the minimum amount must always be set to comply with the standard; however, the distribution of the reinforcement does not need to comply with the minimum bending reinforcement on the sides parallel to the bending plane. 

Fig. 4 Column bending in one direction.

In Fig. 4 it is shown a common case of a 8 in x 30 in section. The bending plane is perpendicular to the wall, so that the bars can be located on the long side. 

The minimum amount is:

Use 4 # 5 on both long sides 

The two remaining bars on the short side (no more than two are allowed in 8 in) do not have to meet the minimum amount in bending. 

which is acceptable as there is no bending on those sides. 

It is recommended not to vary the minimum amount of 1% since the standard only allows this variation for sections with very large dimensions compared to what is necessary for the given conditions. 

However, the minimum amount of bending is not necessary in this case. Short sides and the reinforcement can be increased for the sides that are more necessary. 

Thus concludes this work, we hope it will be useful for the designs of your next columns. 

Important Note:

In the work, the total section has been considered instead of the effective section to calculate the amount of bending. The objective of this work is to show the reason for the need of this reinforcement and the possible implications that each case has. That is why, in order to not unnecessarily complicate the exposition, it has been decided to assume this simplification. In actual calculations you should use the minimum amounts of bending with the values of b and d. 

Translation By: Ivet Llerena (Eastern Engineering Group)

Structural Drawings By: Eastern Engineering Group

© 2022 This article was written by Ernesto Valdes and published by Eastern Engineering Group. All rights reserved.