Introduction
The purpose of this assignment is to define degree of freedom to a non-technical audience. This structural engineering term will be explained using parenthetical, sentence, and expanded definitions. These definitions are intended to be read as educational material by someone with minimal to no background in structural analysis with an understanding of basic math, including the cartesian coordinate system. Upon completing this assignment, students will have a better understanding of how to write a definition for a specific audience with an appropriate level of detail.
Parenthetical definition
In structural analysis, determining the degree of freedom (number of independent movements possible) of a part of a structure is important because it provides information on its stability (Balu, 2020).
Sentence definition
| Term | Class | Distinguishing Features |
| Degree of Freedom | a parameter | specifies the number of independent ways a part of a structure can move at a point |
The degree of freedom is a numerical parameter that specifies the number of independent ways a part of a structure can move at a point (Balu, 2020; Dlubal Software, 2022).
Expanded Definition for Non-Technical Readers
DEGREE OF FREEDOM
What is a degree of freedom?
The degree of freedom is a numerical parameter that specifies the number of independent ways a part of a structure can move at a point (Balu, 2020; Dlubal Software, 2022). It is a fundamental concept used in structural engineering to determine how a structure will respond when a force is exerted on it (American Welding Society, 2022). Specifically, it provides information on stability by indicating how many ways a certain part of a structure could move when a force is applied to it. Knowing how parts of a structure can move helps engineers determine how it might deform and fail. Thus, the degree of freedom is significant because it indicates the stability of a structure and how it could fail when a force is exerted on it.
The endpoints of a structural member (a part of a structure, for example, a beam or a column) are often called joints. Joints represent the point where the member ends or is connected to something else. The degree of freedom of a structural member at a joint is significant because it helps determine what is happening at that point in relation to the rest of the structure.
The degree of freedom of any part of a structure at a joint is between one and six (Balu, 2020). It accounts for the rotational and translational movements in the three coordinate directions (Balu, 2020; Dlubal Software, 2022), shown in Figures 1 and 2, respectively. Rotational movement can be thought of as a bar bending about a point. Figure 1 demonstrates how a bar would rotate around the joint centred on the x, y, and z axes. On the other hand, the translational movement can be imagined as a bar sliding in a specific direction. Figure 2 shows how a joint at the end of a bar could slide, or translate, along the x, y, and z axes. It is important to note that only movements in independent directions (x, y, z) are considered. Although the bar shown in Figure 2 can move up and down along the z-axis, there is only one degree of freedom possible for movement in the z-direction.
Figure 1: This diagram demonstrates the three rotational degrees of freedom possible (the way a bar would spin around the x, y, and z axes).
Figure 2: This diagram demonstrates the three translational degrees of freedom possible (the way the bar would slide along the x, y, and z axes).
How do we find the degree of freedom?
The degree of freedom (number of independent movements possible) of a structural member is dependent on how it is restrained (Balu, 2020). When determining the degree of freedom, we always assume that the part of the structure we are analyzing and any connections it has to its surroundings do not break.
A structural member fixed on both ends, like a beam fixed between two walls, is fully restained and, therefore, has zero degrees of freedom at each end. If the beam and the connections fixing it to the wall do not break, its endpoints cannot move side-to-side, up and down, or rotate. However, if one wall is removed, that end will no longer be restrained, and the degree of freedom at that point will change to six, as shown in Figure 3. This change is because the end of the beam now has the freedom to rotate and translate in each direction. The end of the beam that remains fixed to the wall will still have a degree of freedom of zero since it cannot move.
Figure 3: One end of this simplified beam is fully fixed, and the other is unrestrained. The degree of freedom of the fixed end is zero. The unrestrained end can rotate and translate in three directions, respectively. Therefore, its degree of freedom is six.
To determine the degree of freedom, it helps to imagine how the part in consideration can bend (rotation) or slide (translation). If it is difficult to imagine the possible movements try acting them out using a pencil. Consider how the part of the structure is connected to its surroundings, and how that connection prevents it from moving.
What is not a degree of freedom?
The degree of freedom helps engineers understand how a part of a structure will respond to a theoretical force. It is independent of the location or magnitude of the force because the degree of freedom is a parameter signifying the number of possible independent movements of the structure. It is simply a concept that represents the number of ways a part of the structure can move at a point. The degree of freedom of a part of a structure at a joint is not the actual motion resulting from the application of a force.
It is important to distinguish between the restraints and the degree of freedom at a joint. Adding a new restraint to a joint reduces the number of possible independent movements (Balu, 2020). For example, imagine one end of a beam that can rotate in all directions but cannot translate. At this joint, the degree of freedom is three, and the number of restraints is three. If it is changed so that the beam cannot rotate or translate, the degree of freedom and number of restraints become zero and six, respectively. Therefore, these concepts are related to each other but specify opposite things.
References
American Welding Society. (2022). Applied load. In American Welding Society Learning. https://awo.aws.org/glossary/applied-load/#:~:text=A%20force%20imposed%20on%20an%20object%20by%20a%20person%20or%20another%20object.
Balu, N. (2020, April 16). DEGREE OF FREEDOM. Civil Engineering. Retrieved June 5, 2022, from https://1civilengineering.blogspot.com/2020/04/degree-of-freedom.html
Dlubal Software. (2022, February 24). Degree of Freedom. Dlubal. Retrieved June 5, 2022, from https://www.dlubal.com/en/solutions/online-services/glossary/000234#:%7E:text=A%20degree%20of%20freedom%20is,rotation%20in%20a%20certain%20direction.
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