Degrees of Freedom Explained: Why Walls Don't Move

A door can move. A wall cannot. The difference is degrees of freedom: the number of independent ways a structure can move. This video explains the idea in about 7 minutes, with animations, and shows why every structural engineer needs it.

What you will learn

• What a degree of freedom is. A block on a table has 3 (two slides and one spin). A body free in 3D has 6.
• Joints and members. Each joint of a 2D truss has 2 degrees of freedom, a 2D frame joint has 3, and a 3D frame joint has 6. The structure and its connections decide the count.
• Supports remove freedom. A roller removes 1, a pin removes 2, and a fixed support removes 3. Every restraint adds a reaction.
• Counting for stability. For a planar truss, compare the unknowns (members + reactions) with the equations (2 per joint). Fewer unknowns than equations means a mechanism, equal means statically determinate, more means indeterminate. A passing count is not enough: the arrangement of members and supports must also be stable.
• Degrees of freedom in analysis. In the stiffness method the unknowns are the free degrees of freedom, so their number sets the size of the matrix the software solves.
• Dynamics and vibration. A building has one degree of freedom per floor and one mode shape per degree of freedom. This is why natural frequency, mode shapes and resonance matter, and why bracing and dampers are used.

The idea in four lines

1. A structure's degrees of freedom are the ways it can move.
2. Supports take some of those ways away.
3. Counting equations against unknowns checks stability.
4. In dynamics, the degrees of freedom decide how the structure sways.

Who this is for

Civil and structural engineering students, and engineers who use structural analysis software such as ETABS, SAP2000 or Robot and want to understand what the model is doing.

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