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Civil Engineering QUESTION #2123
Question 1
In steel structural design, the slenderness ratio of a compression member is defined as \(\lambda = \dfrac{KL}{r}\), where \(r\) is the radius of gyration. The radius of gyration of a section is given by:
  • r = I/A
  • \(r = \sqrt{I/A}\)✔️
  • \(r = A/I\)
  • \(r = \sqrt{A/I}\)
Correct Answer Explanation
Radius of gyration \(r = \sqrt{\dfrac{I}{A}}\), where \(I\) = second moment of area and \(A\) = cross-sectional area. It represents the distribution of area about the axis — a larger \(r\) indicates area distributed farther from the neutral axis, giving greater bending and buckling resistance. For design, the minimum \(r\) (about the weak axis) governs the critical slenderness ratio and buckling load.