Slenderness calculation: a stanchion has unsupported length 4 metres and least radius of gyration r = 5 cm. What is its slenderness ratio L/r?

Introduction / Context:
Slenderness ratio is a key parameter for column stability and determines which buckling curve or formula applies. It is the ratio of the member's effective length to the least radius of gyration of its cross-section, expressed in consistent units.

Given Data / Assumptions:

• Unsupported (effective) length L = 4 m.
• Least radius of gyration r = 5 cm.
• No end-restraint modification is specified; interpret L as given.

Concept / Approach:
The slenderness ratio λ is computed as L/r. Units must be consistent; convert metres to centimetres when r is in centimetres. Higher λ indicates greater susceptibility to buckling and lower allowable compressive stress for a given material and section.

Step-by-Step Solution:
Convert L to centimetres: L = 4 m = 400 cm.Compute λ = L / r = 400 / 5.Obtain λ = 80.

Verification / Alternative check:
A quick magnitude check: an 80:1 length-to-radius ratio is a moderate slenderness typical of rolled columns; it lies within ranges where inelastic buckling considerations may be relevant depending on the steel grade and code curve used.

Why Other Options Are Wrong:

• 60, 70, 90, 100: Do not match the straightforward calculation with correct unit conversion.

Common Pitfalls:

• Forgetting to convert L to the same unit system as r.
• Confusing least radius of gyration with least radius of curvature or with section depth.

Final Answer:
80.