In classical working-stress approaches, the secant formula for compressive stress in a column is considered applicable up to what approximate slenderness ratio (L/r)?

Introduction / Context: The secant formula relates compressive stress to eccentricity and slenderness by accounting for second-order (P–Δ) effects via a secant term. Its practical range of applicability is limited to moderate slenderness; beyond that, simplified formulae lose accuracy and instability dominates.

Given Data / Assumptions:

• Slenderness ratio λ = L/r, based on effective length.
• We seek the upper bound of λ for which the secant formula is typically used in classical design problems.

Concept / Approach: For low to moderate slenderness, inelasticity and initial imperfections can be approximated by the secant formula without full stability analysis. Traditional teaching sets an approximate applicability up to λ ≈ 160 for routine calculations before more advanced column curves or stability checks are needed.

Step-by-Step Solution: Define slenderness ratio λ = L/r. Adopt the conventional upper limit λ ≈ 160 for secant-based checks. Choose 160 from the options.

Verification / Alternative check: Modern limit-state codes use calibrated buckling curves across all λ, but in older WSD contexts, λ up to about 160 is a common pedagogical threshold for secant use.

Why Other Options Are Wrong:

• 120–150: Conservative but below the widely cited upper bound.

Common Pitfalls:

• Applying secant formula at very high slenderness without considering overall instability and imperfections explicitly.

Final Answer: 160.