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What is slenderness ratio structural engineering?

Updated: 8/10/2023
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Ssritharan007

Lvl 1
9y ago

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The slenderness ratio is the ratio between the height or length of a structural element (such as a column, or strut) and the width or thickness of the element.

For example, if a rectangular column is 6m high, and 400mm by 600mm in cross-section, then its slenderness is 6000/600 = 10 in one direction and 6000/400 = 15 in the other direction.

The higher the slenderness ratio, the more slender the structural element is. How slender a structural element is allowed to be depends upon the material it is made from. Steel can be more slender than concrete, for example.

In structural engineering calculations, the slenderness is often denoted as the element's "effective" length divided by something called the radius of gyration. The radius of gyration is a measure of the average distance of the material from the centroid (centre of gravity) of the element's cross section. This can be calculated as r = (I/A)0.5, where I is the second moment of area, or second moment or inertia, of the cross section and A is the area of the cross section.

The effective length of an element is determined by how it is fixed at its ends. The effective length is the length of the column that will form half a sine wave if it buckles. If it is "pinned", or has hinged ends, the effective length is the true length of the element. If it is a cantilever (fixed at one end but free at the other), the effective length is twice the true length. If it is fully fixed at both ends the effective length is 0.7 times the true length, but this is in reality very difficult to achieve, so often a real structural element is considered to be only nominally fixed and the effective length is taken to be 0.85 times the true length.

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9y ago
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14y ago

The slenderness ratio refers to the capacity if a structural member in compression to resist warping or bowing by virtue of its length compared to its stiffness. This phenomenon is a case of Euler buckling.

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11y ago

It is the ratio of Length of Column ' L ' divided by Radius of Gyration ' r '.

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