Parenthetical definition
The degree of freedom (number of independent movements possible) of a structural member is dependent on its restraints.
Sentence definition
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Term |
Class | Distinguishing Features |
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Degree of Freedom |
a parameter |
specifies the number of independent ways a structural member can move at a point |
The degree of freedom is a numerical parameter that specifies the number of independent ways a structural member can move at a point.
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 structural member can move at a point (Balu, 2020; Dlubal Software, 2022). It is a fundamental concept used in structural analysis to determine how a structure will respond to an applied load (a force exerted on it) (American Welding Society, 2022).
The points on a member are often called joints. Joints represent the location where the member ends or is restrained by a connection. The degree of freedom of a structural member at a joint is significant because it helps determine the stability of the structure.
The degree of freedom of any structure or structural member 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.
Figure 1: This diagram demonstrates the three rotational degrees of freedom possible.
Figure 2: This diagram demonstrates the three translational degrees of freedom possible.
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). A structural member fixed on both ends, like a beam fixed between two walls, has zero degrees of freedom at each end. If the beam remains rigid and does not break, its endpoints cannot move side-to-side, up, and down, or rotate. However, the degree of freedom at one end will change to six if all the restraints are removed, as shown in Figure 3. This is because the end of the beam now has the freedom to rotate and translate in each direction. The remaining fixed end 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.
What is not a degree of freedom?
The degree of freedom helps engineers understand how a structural member will respond to an applied load. However, it is independent of the location or magnitude of the forces applied. This is because it is a theoretical parameter signifying the possible independent movements of the structure. The degree of freedom of a structural member at a joint is not the actual motion resulting from an applied load.
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.
Expedition Workshed. (2022). ENCASTRE BEAM [Image]. PushMePullMe. https://expeditionworkshed.org/workshed/push-me-pull-me/
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