Masonry design: for a free-standing masonry wall (unsupported at the top and restrained only at the base), what effective height should be used when computing slenderness ratio?

Introduction / Context:Slenderness effects significantly influence the compressive capacity of masonry walls. Codes use an effective height (or length) to account for end restraint conditions. A free-standing wall behaves like a cantilever with one end fixed and the other free, increasing the effective height compared to a wall braced at both ends.

Given Data / Assumptions:

• Wall is free-standing (top unrestrained laterally).
• Base is effectively fixed at foundation level.
• Effective height is used in slenderness ratio λ = effective_height / effective_thickness.

Concept / Approach:For column/strut analogues, the effective length factors depend on end restraints: fixed–free members have an effective length of 2.0 L (twice the clear height). This increases slenderness and reduces allowable stress to reflect the higher propensity for buckling or instability.

Step-by-Step Solution:Recognize end conditions: fixed at base, free at top.Use standard effective length factor K = 2.0 for fixed–free condition.Therefore, effective height = K * L = 2.0 L.

Verification / Alternative check:Structural design handbooks and masonry codes list effective height multipliers; fixed–free consistently corresponds to 2.0.

Why Other Options Are Wrong:

• 0.5 L and 1.0 L reflect braced conditions with more restraint than present.
• 2.5 L overstates the cantilever effect beyond standard practice.

Common Pitfalls:Assuming the top has some bracing when it is explicitly free; using clear height directly without effective length factor.

Final Answer:2.0 L