Difficulty: Easy
Correct Answer: the reduced diameter of the column
Explanation:
Introduction:
In steel column base design, the thickness of a rectangular cap/base plate is determined from a bearing and bending check. The commonly used formula contains a diameter term d when the supported member is a solid round steel column. This question tests whether you know what that d physically represents.
Given Data / Assumptions:
Concept / Approach:
Base plates distribute axial load from the column to the concrete pedestal or foundation. The bending strip model uses the projection of the plate beyond the loaded area and the bearing pressure. For a round column, the loaded area is a circle defined by the column's effective (reduced) diameter at the interface after deducting machining tolerances or corrosion allowances. Hence, d refers to the column's reduced diameter, not the base dimensions.
Step-by-Step Solution:
1) Identify the loaded (bearing) area: circular area under the column end.2) Bending in the plate is governed by projection beyond this loaded circle.3) Therefore d must characterize the column's loaded circle, i.e., the reduced diameter.4) Base or top diameters of the plate are irrelevant to the bending calculation for the inner loaded area.
Verification / Alternative check:
Derivations treat the inner edge of the bending strip at the column–plate interface. Replacing d with base dimension would grossly overestimate thickness needs.
Why Other Options Are Wrong:
Base dimension or base diameter describe outer plate size, not the loaded circle. The top diameter is not a design variable for the plate's inner loaded area.
Common Pitfalls:
Confusing external plate size with internal loaded patch; ignoring machining allowance when selecting d.
Final Answer:
the reduced diameter of the column
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