In the practical scenario, there are three main categories of stability,

- Stable
- Unstable
- Neutral

Failure of structures may be also because of geometric instability. In the case of slender column, the slenderness or the stiffness of the column becomes more important. The capacity of material in the case of slender column is not fully utilized. The column fails due to buckling even before the column reaches the stress limit of the material.

## Buckling

It is the the critical load for a column, in pure buckling . By assuming that the beam acts as an ideal column, the critical load for the column is :

$$

P_{c r}=\frac{\pi^{2} E l}{\left(\beta L^{2}\right)}

$$

We can reduce buckling by reducing the length of the column. by providing bracing in columns we can reduce the column length. The brace can be of two types: elastic or ideal. An elastic brace takes on the load and deflects out as well as the bracing gets displaced from its origin. The displacement is dependent on the stiffness of the brace, when it becomes stiff enough it will remain in place and be considered as ideal.

### Stable equilibrium

When the value of load applied is less than the critical load (P < P_{cr}), the object will return to its original position, no change in the geometry of the column.

### Un-stable equilibrium

When the value of load applied is more than the critical load (P > P_{cr}), the object will move and will not return to its original position, Geometry changes drastically.

### Neutral equilibrium

When the value of load applied is equal to the critical load (P = P_{cr}), the object will move and stop at equilibrium position, Geometry changes.

## Column design

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- Detailed calculation steps presented for verification and validation.