# Stability of Structures

By BYJU'S Exam Prep

Updated on: September 25th, 2023

Before understanding the stability of structures, let’s first understand structure. A structure is something called the arrangement of its members in a proper manner. A structure can be classified as a stable structure or an unstable structure. An unstable structure is a mechanism that shows permanent deformation even before loading loads. The “stability of structures” theory has many applications in engineering, including civil, mechanical, and aerospace.

The stability of structures means that a structure is stable during the application of loads. A stable structure and redundant structure can withstand the effect of loads over it. But in the real world of designing structures, mostly redundant types of structures have been preferred because it is usable even if some reactions become zero during the application of loads.

## What is the Stability of Structures?

Stability means simply how the structure withstands the stresses due to external loads. During the application of load, it might not be able to withstand the effect of load; such a structure is called an unstable structure.

### Stability of Structures Meaning

A structure is said to be stable if it has sufficient reactions when subjected to external loading. The stability of structures can also be defined based on the determinacy of the structure. If the degree of determinacy is greater or equal to zero, then the structure is said to be stable, but if it is less than zero, it is said to be unstable.

The stability of structures shows a basic problem in solid mechanics, which is considered for the safety of structures against their failure. Failure can be of many types, like collapse, buckling, etc. Therefore, stability theory is important in designing space structures, foundations, etc.

## What are the Types of Stability of Structures?

The stability of structures can be classified into internal and external stability of structures. External stability deals with support reaction, and internal stability deals with the degree of freedom of structure.

### External Stability of Structures

The external stability of structures can be understood with the help of the following points.

• The minimum number of reactions required for a structure to be stable externally is 3.
• These three reactions must be non-concurrent and non-parallel.
• If three reactions are parallel, then rigid body translation takes place. If they are concurrent, then rigid body rotation takes place.
• If the structure becomes unstable due to the improper arrangement of three reactions, it is known as geometrically unstable.
• If the structure becomes unstable due to less than three support reactions, it is called statically unstable.

### Internal stability of structures

We can say Internal stability if a structure becomes unstable due to its internal reactions. For example, We can understand internal stability with the help of the following cases.

Case 1: Internal Stability of Beams

Internal floating hinge: In the case of an internal hinge structure can rotate about the hinge point and hence become unstable internally.

Case 2: Internal Stability of Trusses

In the case of trusses, if the following condition exists, it is classified as an unstable truss.

m<2j-3

Where,

• m = number of members in truss structure.
• j = number of joints in truss structure.

Case 3: Internal Stability of Frames

If reactions are parallel, the frame structure will be termed unstable. Because resisting capacity in this condition becomes zero, hence structure becomes unstable.

## When can it be said that the Structure is Stable?

A stable structure can maintain its shape when subjected to any load. However, to maintain its shape, it should be able to resist the stresses induced in the structure due to external loads.

It is important to establish the stability criteria to understand whether a structure is in a stable condition or an unstable condition. For example, if, on the application of load, the structure will not go into any permanent deformation, then it can be said that the structure is in its stable condition. On the other hand, if it goes through a significant amount of deformation, it can be said that the structure is unstable. An unstable structure can also be said to be a mechanism, and it can not resist any load and can not be used for civil engineering structures.

## How to Check the Structural Stability of a Building?

The design of civil engineering structure should be a stable structure for the proper dispersion of loads through it. Here some points are given which can be used to check the stability of structures.

• Check the determinacy of the structure; if determinacy is greater or equal to zero, then it can be said to be a stable structure.
• For the stable structure, there should be non-parallel and non-concurrent support reactions.

## Effect of Stability of Structures

As we now understand the meaning of stable structure and unstable structure. And we also understand the causes of stability and instability of the structure. So let’s understand the effect of stability of the structure.

Stability means how the structure withstands the stresses caused by the external loads. If a structure is more stable, it implies that it has more redundant reactions, making it more capable of withstanding external loads.

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