In this post, we will cover what support conditions are in structures. This is of major importance for all aspects of structural engineering in structures; varying from simple beam and column designs through to lateral stability and connections. From this, we will then explore what reactions will occur at these supports. To design any structure or individual members, you need a solid understanding of the types of supports and behaviors that these exhibit.
The post will be in two parts; the first part will be theory based an the second part will be examples. Don’t worry if you don’t grasp it all straight away, follow it through and look at the examples of free body diagrams. The examples will cover the three most fundamental supports, from which we can figure out the reactions. After the examples, you will be in a much better position to understand the theory.
Naturally, all structures are 3-dimensional (3-D) and solving problems in 3-D is a simple task with computer software. It is much better to have an understanding in 2-D using hand calculations before progressing though. Therefore this post will only cover 2-D examples.
What are Supports?
To explain what a support is, take an example of a simple beam. For the beam to be able to stay in position, supports are required to literally hold the beam in place. These can be found at any point of the beam and create different reactions. The reactions are related to the forces in the beam (axial and shear force as well as moments).
There are three primary types of supports; pinned, roller and fixed. A fourth support condition also exists, but it is seldom called a support. This is called a free support and these provide useful additional information about the beam or structure. Pinned and rollers have similar characteristics and transfer shear force. A fixed support can be seen as being fully encased (e.g in concrete), or a connection with adequate stiffness.
Pinned supports are the most common types of supports used in construction, especially steel structures. They are not required to have sufficient stiffness since they do not need to allow any rotation in the connection. This makes them one of the cheapest connections in an engineer’s arsenal.
In steel design, these supports are stated as simple or shear only connections. However, this is not entirely true. Pinned supports can also transfer translational forces.
The diagram to the right shows the common representation of a pinned support seen in structural analysis textbooks, physics textbooks and software.
A roller support is very similar to a pinned support. The only difference between them, is that a roller support cannot transfer translational forces.
In a beam configuration, a roller support and a pinned support create a simply supported beam. Shear force is at a maximum at these supports and the moment is zero.
To the right is the graphical representation of a roller support. Note the support appears to have rollers on the bottom. This is a good way to remember that if translational force was applied, it would move!
A fixed support is the stiffest support available. Imagine it has a steel beam fully encased in concrete, or two steel members fully welded together. This makes fixed supports the most expensive. Used efficiently though, they can reduce the cost of the overall structure.
A fixed support has sufficient stiffness to transfer any rotational forces from one member to the next. The designer must ensure the support has the capacity to transfer shear force, translational forces and moments from one member to the next. The rotational force in a support is the same as the moment force in the support.
To the right is the common graphical representation seen in textbooks and software. If the support condition is to be fully fixed, it allows the reactions to be in every direction.
In some software, a fixed support may be represented by a square or rectangular box.
What are Reactions?
The purpose of a support is to transfer the force from one structural member to another. For example, a beam to a column or a column to the foundations.
To transfer the force, the support creates a reaction. The different support conditions allow for different reactions. A quick example of this, a fixed support, allows for reactions in every different direction.
Pinned Support Reactions
Pinned supports have reactions in two directions. Axial force (force acting along a member) and shear force (force acting through a member).
We will not touch upon the 3-D analysis, but its good to be aware that shear force can be in two planes. The major axis and minor axis of the element.
To the right is a pinned support with all the possible forces acting upon it. These are equal and opposite to the forces being applied. Otherwise, the member would not be static. The A notation is linked to the name of the support, hence in all the following examples our support is named ‘Support A’.
Roller Support Reactions
Roller supports only have reactions in the X axis.
The roller support is similar to a pinned support and is known as a simple or shear only connection.
No moment transfer is possible.
Here is a great tip. Note that the support appears to have rollers on the bottom. This is a good way to remember that if translational force was applied, it would move. And we certainly don’t want our structure moving!
Fixed Support Reactions
Fixed supports have enough stiffness to transfer the rotational forces from one member to the next. Therefore, they allow a moment transfer through the structure.
We need fixed supports in structures to allow the lateral forces to be transferred down to the ground, into the foundations and distributed into the soil. An alternative to using fixed connections is to put bracing members in. However, constraints in the design brief will sometimes prohibit this.
As you would expect, the member not only allows translational forces and shear forces (orizontal and vertical), it also allows a moment. Fya, Fxa and Ma may not equal zero.
So, that”s the basic theory of support conditions and reactions. We have covered the three main types; pinned, roller and fixed supports.
Now we will look at basic beam arrangements and draw the free body diagrams showing all the reactions. No actual numbers are going to be used in the examples. Worked examples showing how to calculate the forces in the reactions will be presented in further posts.
Free Body Diagrams
To fully analyse reactions, a free body diagram is used. This is a diagram that shows reactions at the supports. In most cases, the diagrams also include the applied force. The applied force is the external force in the diagram below.
Simply Supported Beam – Ex.1
What is a simply supported beam? A beam that is simply supported (yes, I should of gone down the comedy root instead of engineering). A simply supported beam is supported at each end; one side a pin support and the other a roller support.
We are now going to break down each reaction in the beam.
First of all, we can tell from the supports that there can be no moments at the end, regardless of the external forces. Now from our knowledge of the supports, we know that pins and rollers can have vertical force. We add this to the free body diagram. We are also aware that pins can have horizontal forces.
From this we can deduce that the free body diagram should look like the following.
Please note that the force in the Y direction would only exist if an external force in that direct is applied, in accordance with Newton’s third law.
Fully Fixed Beam – Ex.2
Now we look at a fully fixed beam; a beam with two fixed supports (I know. Complete shocker).
We know that fixed supports are able to transfer moments and shear force in the vertical (Fy) and horizontal planes (Fx). Can you figure out what the free body diagram would look like?
Cantilever Beam – Ex.3
Time for one last example of a typical beam arrangement. All these arrangements can also be found in columns too. It’s the cantilever case! This is a beam that is only supported at one end and is completely free at the other end. Imagine holding a ruler in our hand from one end. Due to the principles of statics, the supported end must be fixed otherwise the beam would be an indeterminate beam. This basically means an unsolvable beam using static analysis, worthy of a topic in its own right.
Below is a the typical arrangement of a cantilever that you can expect to see in textbooks, tutorials and computer software.
So, finally, what would the free body diagram look like? We know the reactions we can expect at the fixed end, but what about the free end?
I hope you found the post useful, this is just the tip of the iceberg in being able to solve complex structures. By making everything as simple as possible in the analysis of a structure, it can give you a great estimate for the design going forward.
If you have any other questions please leave a comment. Further more, if you have any questions about this site, or in general Structures101.com, please get in touch via the contact form.