For determining allowable compressive stress in axially loaded steel columns, which column formula is adopted in Indian Standard practice (classical approach)?

Introduction / Context: Allowable compressive stress in columns depends on slenderness and residual imperfections. Classical Indian Standard practice for working-stress design used an empirical-rational column curve based on the Perry–Robertson (modified Rankine type) approach to cover inelastic buckling and imperfections more realistically than Euler’s ideal formula.

Given Data / Assumptions:

• Axially compressed, prismatic steel columns.
• Working-stress/allowable-stress design context in traditional IS code.

Concept / Approach: Euler's formula applies only to perfectly straight, elastic columns with high slenderness. Real columns have residual stresses and imperfections; Perry–Robertson modifies the ideal curve to provide allowable stresses across a wide slenderness range. Indian practice historically adopted this basis to generate column curves used in design tables.

Step-by-Step Solution: Recognize limitations of Euler for stocky/intermediate columns. Identify Indian code's classical adoption of Perry–Robertson-type curves for allowable stress. Select Perry–Robertson as the correct answer.

Verification / Alternative check: Later limit-state versions (e.g., IS 800:2007) use buckling curves calibrated to tests; the historical working-stress framework is consistent with Perry–Robertson lineage for allowable stress values in older editions and exam problems.

Why Other Options Are Wrong:

• Euler: valid only for very slender, ideal columns.
• Rankine/Engesser/Secant: related formulations exist but Indian allowable-stress tables were based on Perry–Robertson-type curves.

Common Pitfalls:

• Confusing modern limit-state buckling curves with older allowable-stress foundations.

Final Answer: Perry–Robertson formula.