Column Interaction Diagram Example

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Hollie Kipps

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Aug 3, 2024, 3:44:50 PM8/3/24

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Vertical members that are part of a building frame are subjected to combined axial loads and bending moments. These forces develop due to external loads, such as dead, live, and wind loads. Simply put, an interaction diagram (or curve) displays the combinations of the acceptable moment and axial capacities of a structural member.

To consider this curve SkyCiv considers the necessary number of intermediate points. Typically, there are three main points: maximum axial tension (point G), maximum axial compression (point A), and balanced condition (point D). Then intermediate points are considered from balanced condition to maximum tension (points D-G) and from balanced condition to maximum compression (points D-A). To calculate all that points as per design codes used the next assumptions:

The strength of a column cross-section can be determined from the geometry of the cross-section, the constitutive relationships of the concrete and steel and consideration of equilibrium and strain compatibility. For the calculation of intermediate M-N curve points that describe the strength of section the SkyCiv uses an iterative process. The next steps are involved in this process as per ACI code:

For the design of a column to be considered adequate (safe), the combination of action effects (M, P) must be less than the combination of design strengths (M, P) from the interaction curve. This means that if the position of the M,P point on the plot is outside of the curve it is deemed as not meeting this criterion and considered unsafe.

In SkyCiv RC Design Module, SkyCiv uses both the major and minor axis to calculate the balance point. The module defines the point of intersection with a 3D interaction diagram (green point in the below picture). The coordinates of this point provides the axial and flexure capacities for the section.

SkyCiv offers a fully featured Reinforced Concrete Design software that allows you to check concrete beam and concrete column designs as per ACI 318, AS 3600, and EN2 Design Standards. The software is easy-to-use and fully cloud-based; requiring no installation or downloading to get started!

The document provides information on constructing interaction diagrams for reinforced concrete columns. It defines an interaction diagram as a graph showing the relationship between axial load (Pu) and bending moment (Mu) for different failure modes of a column section. The document outlines the design procedure for constructing interaction diagrams, including considering pure axial load, axial load with uniaxial bending, and axial load with biaxial bending. An example is provided to demonstrate constructing the interaction diagram for a given reinforced concrete column cross-section.Read less

Often a summary refresher helps keep us grounded in the fundamentals of elements that we commonly design. Owing to many requests from peers, this article is provided as a summary of the steps that may be taken for the development of a typical reinforced concrete column interaction diagram.

The methodology outlined below reflects the provisions of ACI 318, but it is not the only viable method. In fact, ACI 318 does not explicitly require an interaction diagram for column design. However, most structural engineers understand that such a tool is the most convenient form of expressing the nominal axial and flexural capacities, as well as the best tool for helping us know how axial loads and bending loads influence and affect one another.

Assume, just for the sake of argument, that the factored load effect for the design of a tied concrete column is a trivial matter, and that we have the results for Mu and Pu. The next step that we might follow would be to examine a generated interaction diagram and see whether our interactive load (represented by Mu and Pu) falls within the capacity boundary of our trial column.

The series of strains (tensile and compressive) are then assigned to the layer of reinforcement opposite the concrete compressive failure surface. For any one particular level of strain that we have arbitrarily assigned, we can follow ACI 318 criteria and connect the two opposing points of strain on a diagram with a straight line, thus assuming that the strain is distributed linearly across with column width. This makes for simple calculation of the strain in the remaining layers of reinforcement, using the simple formulas for similar triangles that we learned in high school math.

The result is a strain for each and every bar in the column as it correlates to the level of strain that was arbitrarily assigned to the layer of reinforcement opposite the compression surface. This also helps us know where the theoretical neutral axis for the column is for this strain condition, which occurs where the aforementioned line intersects the vertical axis of the strain diagram. Once the strain levels and the neutral axis are known, the design may proceed to the next step.

Once the stress in each layer of reinforcement is known, as well as the dimensions of the concrete compressive stress region, the resultant forces in each are calculated simply by multiplying the stresses by the respective areas. Summing the result yields a total force Pn, the nominal axial capacity of the column as it correlates to this level of strain. Multiplying these same forces by their relative distances from the centroid of the gross column section and summing the result yields the nominal moment capacity Mn.

The final step for this one iteration of design is to determine the strength reduction factor that is appropriate for the level of strain under consideration. This is a function of the net tensile strain arbitrarily assigned earlier; it has a value of 0.9 for net tensile strains of 0.005 or more and a value of 0.65 for net tensile strains of 0.002 or less. Intermediate values are linearly interpolated. The strength reduction factor is then multiplied by each of the Mn and Pn values calculated previously to determine the resulting φMn and φPn that define this one point on the interaction diagram.

The entire process is repeated several times, with varying levels of strain assigned to produce a series of points that define the interaction diagram boundary. Figure 1 depicts the superimposed strain conditions as recommended by prominent textbook authors. For each level of strain, the calculations described herein are repeated. For each level of strain, a corresponding point on an interaction diagram can be determined. Interconnecting the points results in the interaction diagram (potentially similar to Figure 3) on which we can plot Mu, Pu and assess whether the column is sufficient.

Jerod G. Johnson is a Principal at Reaveley Engineers in Salt Lake City. He was the engineer of record for recent updates to the base isolation system for the Salt Lake City & County Building. He was the principal investigator of the comprehensive isolator testing of May 2011. (jjoh...@reaveley.com)

Previously, as we talk about the Column Design Principles in our previous post, we found out that a lot of things to consider in the column design. It is always okay to consider the first assumption that we learn in the previous article to get the number of bars in the column we are designing which is the 1 to 8 percent ratio of reinforcement to the gross area of the column. But Column design makes it even more complicated when there is an eccentricity or bending being considered. This tends the designer to rely on structural software to analyze it easier, oops we are not going to talk about what are the different software that can be used in column design because I am sure you already knew about it. We are here to discuss the column interaction diagram. Perhaps the most practical way for a column design is to analyze the column interaction diagram, but how we are going to interpret it?

An interaction Diagram in a column is a graph that shows a plot for the axial load Pn that a column could carry versus its moment capacity, Mn. This diagram is very useful in analyzing the strength of the column which varies according to its loads and moments. This can easily be interpreted as: the load combinations under any case that falls inside the curve are satisfactory while the load combination under any case that falls outside the curve represents a failed design.

The diagram is made by plotting the axial load capacity of the column at point A, then the balanced loading at point B, then the bending strength of the column. If it is subjected to a pure bending moment only at point C. In between points A and C, the column fails due to axial and bending moment combinations. Point B is called the balanced point. In reference to point D, the vertical and horizontal lines represent the particular load combinations of axial load and moment.

This sequence diagram tutorial is to help you understand sequence diagrams better; to explain everything you need to know, from how to draw a sequence diagram to the common mistakes you should avoid when drawing one.

There are 3 types of Interaction diagrams; Sequence diagrams, communication diagrams, and timing diagrams. These diagrams are used to illustrate interactions between parts within a system. Among the three, sequence diagrams are preferred by both developers and readers alike for their simplicity.

Sequence diagrams, commonly used by developers, model the interactions between objects in a single use case. They illustrate how the different parts of a system interact with each other to carry out a function, and the order in which the interactions occur when a particular use case is executed.

Sequence diagrams are commonly used in software development to illustrate the behavior of a system or to help developers design and understand complex systems. They can be used to model both simple and complex interactions between objects, making them a useful tool for software architects, designers, and developers.

A sequence diagram is structured in such a way that it represents a timeline that begins at the top and descends gradually to mark the sequence of interactions. Each object has a column and the messages exchanged between them are represented by arrows.