Slenderness ratio is an assessment of a structural member's ability to withstand buckling pressures. Engineers can determine it by dividing the length of the column by what is known as the radius of gyration, the distribution of weight around the center of the column. These calculations are important for supportive beams and other structural components, to make sure they will not fail and put a structure at risk of serious damage or collapse.
To determine the slenderness ratio, the engineer needs a measurement of the length of the column and must calculate the radius of gyration by looking at how the weight distributes around its center. This is determined by the width. If the column is very narrow, weight concentrates close to the center. Wide columns have more distributed weight and tend to be less prone to buckling.
It is possible to simply divide the length by the width for a quick estimation of the slenderness ratio. If the column is too slender, it will be prone to buckling, where the middle gives way even as the top and bottom remain solid. On the other hand, a very thick column may be so heavy that it causes structural problems itself. The weight of heavy supporting columns can be a significant issue in tall buildings.
There are some additional considerations to take into account with slenderness ratio. One is the material used to make the column. Wood structural members are more likely to bend than steel or concrete. They need a slightly different ratio to build in a margin of safety. Likewise, the level of support available to the column is important.
A very tall column supported for most of its width is less likely to bend than a shorter column with no support. Engineers may use effective length, looking just at the unsupported section, in a slenderness ratio calculation. They can also adjust the way a column performs in a structure by adding support to make it sturdier.
Engineers developing design specifications can use this formula to make sure the planned columns in a project will be adequate for the need. They can also check their math as a structure goes up, by sampling columns and calculating a slenderness ratio to determine if they are sufficient. If they are not, there is a risk the building could fall as it goes up. A building with inadequate supports may also fail to pass a building inspection. The builder might be required to retrofit or repair it and apply again for permission to start using the building.