Difficulty: Easy
Correct Answer: 20 mm
Explanation:
Introduction / Context:Columns are rarely loaded with perfectly concentric axial forces due to construction tolerances, load transfer paths, and second-order effects. Design standards therefore enforce a minimum eccentricity to avoid unconservative assessments of strength and to capture realistic bending moments even when axial load is intended to be concentric.
Given Data / Assumptions:
Concept / Approach:Minimum eccentricity protects against idealized zero-moment assumptions. Codes commonly prescribe e(min) based on overall dimensions (e.g., l/500 + D/30) but not less than a fixed floor value to account for practical misalignments. The fixed floor is widely taken as 20 mm to ensure a minimum bending moment is always present in design checks, enhancing safety against brittle compression failures.
Step-by-Step Solution:
Recognize that actual columns experience unintentional eccentricity due to tolerances and load path.Apply codal rule: compute e = geometric expression, but enforce a minimum of 20 mm.Select 20 mm as the required not-less-than limit from the options.Verification / Alternative check:
Design moment can be taken as P * e(min), guaranteeing non-zero bending even if the load is nominally axial.Why Other Options Are Wrong:
10 mm: too small to cover practical eccentricities.30 / 40 / 50 mm: larger than the standard minimum; these may arise in specific geometries but are not the universal floor.Common Pitfalls:
Ignoring minimum eccentricity and designing purely for axial compression.Confusing the geometric formula for eccentricity with the absolute minimum constraint.Final Answer:
20 mm
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