Columns – Empirical Formula for Permissible Stress The empirical expression commonly used to estimate the permissible compressive stress in a column as a function of slenderness ratio is known as:

Introduction / Context:
Design codes historically used empirical relationships to estimate permissible compressive stress in columns considering slenderness. Perry’s formula is a well-known empirical relation bridging short and intermediate columns for allowable stress design.

Given Data / Assumptions:

• Axially loaded column.
• Working-stress (allowable stress) context.
• Slenderness effects reduce permissible stress below yield.

Concept / Approach:
Perry’s formula relates permissible stress to slenderness ratio using a form that penalizes increasing slenderness, reflecting instability effects prior to Euler buckling. It differs from ultimate load formulas (e.g., Rankine) that predict failure loads rather than allowable stresses.

Step-by-Step Solution:
Identify the target: permissible stress, not ultimate load.Among the listed relations, Perry’s is specifically used to compute allowable stress with slenderness corrections.Therefore, the named empirical formula is Perry’s formula.

Verification / Alternative check:
Rankine’s expression combines crushing and Euler loads to give ultimate capacity, not directly an allowable stress formula. Straight-line/parabolic items may refer to steel or concrete stress-strain idealizations and not the classic column permissible stress relation.

Why Other Options Are Wrong:

• Straight line / Parabolic formula: generic names without specific column permissible stress context.
• Rankine’s formula: predicts ultimate load, not allowable stress.
• Johnson’s parabolic formula: a capacity formula for columns rather than an allowable stress rule.

Common Pitfalls:
Confusing ultimate capacity formulas with allowable stress prescriptions can lead to unsafe designs.

Final Answer:
Perry's formula