Perry-Robertson formula is used to determine the design compressive stress of a compression member in IS 800, which is the Indian Standard code for general construction in steel. The formula is derived from the Euler formula, which is used to calculate the critical buckling load of a column.

The design compressive stress is the maximum stress that a compression member can sustain without failure. It is important to determine this value accurately to ensure the safety and stability of the structure.

The Perry-Robertson formula takes into account the slenderness ratio of the compression member, which is the ratio of its effective length to its radius of gyration. The slenderness ratio is a measure of how slender or stocky the member is, and it affects the buckling behavior of the member.

The Perry-Robertson formula is given by:

σ = (π² × E × Imin) / (K × Le)²

Where:
- σ is the design compressive stress
- E is the Young's modulus of the material
- Imin is the minimum moment of inertia of the member
- K is the effective length factor, which depends on the end conditions of the member
- Le is the effective length of the member, which is the actual length of the member multiplied by the effective length factor

The effective length factor, K, takes into account different end conditions of the member. It can be determined from various design tables provided in the IS 800 code.

By using the Perry-Robertson formula, the design compressive stress of a compression member can be calculated based on its slenderness ratio and end conditions. This helps in ensuring that the member can safely resist the compressive forces without buckling or failure.