What does statically determinate mean?
A structure is statically determinate when all of its support reactions and internal forces can be calculated from the equilibrium equations alone. In two dimensions there are three: the sum of horizontal forces is zero, the sum of vertical forces is zero and the sum of moments is zero. If the structure has exactly as many unknown reactions as these equations can solve, and it is not a mechanism, it is statically determinate.
Examples
- Statically determinate: a simply supported beam with a pinned support at one end and a roller at the other. Also a cantilever fixed at one end, and a three-hinged frame or arch.
- Statically indeterminate: a continuous beam over three or more supports, or a beam fixed at both ends. There are more unknowns than equations, so deformation has to be included in the calculation.
- Mechanism (unstable): too few supports or connections, so the structure can slide or collapse, such as a beam on two rollers.
Pros and cons in practice
- Statically determinate: simple to analyse and insensitive to settlement of a support or thermal expansion; these movements cause no additional stresses. But there is no reserve: if one member or support fails, the structure fails.
- Statically indeterminate: usually stiffer and more economical, often with an alternative load path (redundancy). But sensitive to differential settlement and temperature differences.
| Statically determinate | All reactions follow from the equilibrium equations alone. Simple to analyse, insensitive to support settlement or thermal expansion, but no reserve: if one member or support fails, the structure fails. Example: simply supported beam, cantilever, three-hinged frame or arch. |
|---|---|
| Statically indeterminate | More unknowns than equations, so deformation has to be included. Usually stiffer and more economical, often with an alternative load path, but sensitive to differential settlement and temperature differences. Example: continuous beam over three or more supports, beam fixed at both ends. |
| Mechanism (unstable) | Too few supports or connections, so the structure can slide or collapse. Example: a beam on two rollers. |
Application
- Recognise it in alterations. A steel beam on two bearings is usually statically determinate and straightforward to design.
- Be careful with extra supports. An extra prop or wall under an existing beam seems safe but changes the load path: a hogging moment can develop over the new support that the beam was not designed for.
- Leave the calculations to a structural engineer once multiple supports, fixed ends or connections are involved.
Common mistake: propping a reinforced concrete beam at midspan afterwards. The reinforcement is then in the wrong place, which can lead to cracking on the top face.
Related terms
- Pinned support
- Roller bearing support
- Fixed support
- Three-hinged arch
- Bending moment diagram
- Structural redundancy
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