Determinacy of Structures: Explained in 2-minutes

If the reactions of internal forces of a structure can be solved using just the force equilibrium equations, we refer to it as (i) statically determinate. If the structure is more complicated but still stable, we refer to it as (ii) statically indeterminate. Both of these are stable structures. In the latter case, we can consider compatability conditions to help us solve complex problems.

Besides there two categories, there is a third classification for structures which are inherently (iii) unstable (such as a cantilever beam with a pinned end). This third classification is also referred to as a mechanism.

This post explains how to assess the determinancy of a structure.

Determinancy of a Beam

We can determine the degree of determinancy for a beam using the following equation:

degree of determinancy,

Where r is the number of reactions, n is the number of equilibrium equations (3), and ec is the additional equilibrium equations due to internal hinges or internal rollers.

We can interpret the determinancy as follows:

Some examples of calculating determinancy of various structures are shown below.

Determinancy of a Frame Structures

Some examples of calculating determinancy of frames is shown below:

Determinancy of Arch Structures

Some examples of calculating the determinancy of arches is shown below:

Further Information

You can find more information at the links below:

https://learnaboutstructures.com/External-Indeterminacy

https://wethestudy.com/engineering/determinacy-structural-analysis/