Slenderness Ratio – Explanation, Calculators and Uses

Calculations are the base part of engineering. We need to make tons of calculations to obtain safe and financially optimized systems. Very basic structures and systems may require very detailed calculations, this is because we are engineers to do it. One of my master’s in university degrees once said; “Engineering is the art of optimization.” So, the slenderness ratio is one of these calculations.

Slendernes Ratio Calculator

Enter K :

Enter L :

Enter r_min :

Result :

How to Use Slenderness Ratio Calculator?

The use of a slenderness ratio calculator is very easy. You just need to enter the K value that you selected, the total length of your column application, and the minimum radius of gyration value of your column. Click on the ‘Calculate!’ button to calculate the slenderness ratio of your column. If you want to do another slenderness ratio calculation, click on the ‘Reset’ button as shown by the blue arrow above.

To obtain correct results from this calculator, you need to take care of your units. K has no unit, it is unitless. The unit of length and Rmin must be similar such as mm, cm, or m. The result will be also unitless. So consistency is very important.

Calculations are the base part of engineering. We need to make tons of calculations to obtain safe and financially optimized systems. Very basic structures and systems may require very detailed calculations, this is because we are engineers to do it. One of my master’s in university degrees once said; “Engineering is the art of optimization.” So, the slenderness ratio is one of these calculations.

Anyway, one person may think about columns, just prepare the mold then pour the concrete inside it… But the situation is not like this. To obtain a well-optimized column structure that must withstand potential loads and external effects. And we need to optimize them in terms of finance. 

So there are very deep calculations are created to design columns in this way. One of these calculations is the calculation of the slenderness ratio.  

What is the Slenderness Ratio?

In the structural means, columns may have different kinds of end fixities such as built-in fixity or pinned-pinned fixities. You can reach the types of fixities here. Because of these fixities, the type and mechanical strength of columns may change. One may think, that concrete column are generally fixed-fixed ends. But in steel structures, we can use other kinds of columns. 

If the end fixity of the column is clear, we can make the definition of the slenderness ratio; the Slenderness ratio is the ability of a column to withstand axial buckling loads. As you understand from its name, we are not expecting any buckling deformation from a column, if it is buckling, it is slender for the loads at stake. 

How to Calculate the Slenderness Ratio?

The slenderness ratio formula of columns is very easy actually. This formula is like that; 

In this formula, ‘K’ is the column constant that changes according to the end fixity type of the column. As you understand from this calculation, if ‘K’ increases, the slenderness of the column decreases. The minimum value of ‘K’ came from pinned-pinned end columns which withstand buckling loads in a better way compared with free-pinned ends. So the biggest value of the ‘K’ came from the free-pinned end fixities of the columns. 

Also, the column constant has a special calculation technique where we use elasticity modulus and yield strength values in the formulation. You can make comparisons between the calculated column constant and the constant according to the end fixities. This is very important in the slenderness ratio calculations.

As you understand, ‘L’ is the total length of the column. With the increasing value of the ‘L’, the slenderness of the column increases which means the ability to withstand buckling loads decreases.

Other Parameters

‘rmin’ is the minimum radius of gyration of the column. With the increasing radius of gyration, the slenderness ratio of the column decreases which also means the strength of the column increases. 

The radius of gyration depends on some factors. With the increasing amount of area moment of inertia of the column cross-section, the radius of gyration increases. So if the area moment of inertia increases, the strength of the column increases. But in a radius of gyration calculation, we divide the area moment of inertia by the area of the cross-section of the column. So while designing the column cross-section, it is better to select a cross-section that has a maximum amount of area moment of inertia, and a minimum amount of area. We calculate the slenderness ratio according to these aspects.

Where We Use the Slenderness Ratio?

As you understand from the definitions above, we use the slenderness ratio commonly in column design for structures and machinery. 

Designing an optimized column is not an easy thing. We need to calculate the various kinds of parameters. These calculations, the slenderness ratio is one of these calculations. 

In column design, we make different kinds of assumptions such as short-column and long-column. In these assumptions, we calculate slenderness ratios and compare them with column constant values to see whether the column is optimized or not. 

Take a look at the animation and explanation of the slenderness ratio with different examples from structural engineering; 

Why Do We Need the Slenderness Ratio?

This is a very important value to use in the column design. In the column design approach, we use the slenderness ratio. And column design in engineering is about safety. At which maximum load that the column will buckle?

So, in terms of the safe design of columns, we need to use these parameters and calculations.

Conclusion

So, the calculation of the slenderness ratio is a very important parameter in column design in engineering. We suggest that to use the calculators of column constant, slenderness ratio, and column design that we gave the links of them inside the article. 

Also, it is a very important phenomenon in column design. We need to consider the slenderness ratio effectively before deciding on the column applications.

We are using this value of columns in different kinds of areas. The most important area that we use, is civil engineering. But also, we use them in steel structures.

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