I want to design a fixture. The fixture will have 4 stands (columns). Its cross-section will be steel pipe or steel bar. The length of the bar will be 150mm. How to calculate the critical load the stands capable of resisting? Is it possible to use Euler’s formula in this case? what are the criteria to say long or short columns?
You did not give the details. The cross section and consequently the least dimension of stands are not known. Also the joint condition ( fixed or hinged) of fixture and the stand is not mentioned. Depending on the joint conditions (both end hinged or both end fixed or one end fixed and the other end free or, one end fixed and the other end hinged ) you have to choose the formula. If it is a long column, column fails by buckling alone and the effective length to least lateral dimension is very large, you can use Euler's formula.
For your information, a column is said to be a short column if the ratio of effective length to its least lateral dimension is less than or equal to 12. Also the ratio of effective length to radius of gyration of a short column is less than or equal to 40. Note also that a short column usually fails by compression rather than by buckling.
A column is said to be a long column if the ratio of effective length to its least lateral dimension is greater than 12. Also the ratio of effective length to radius of gyration of a long column is greater than 40. A long column usually fails by buckling.
Hope this will help.
Thank You for your valuable information.How about short column? I think if the column is short J. B. Johnson formula will be used.
I suggest you proceed as follows,
1. make sure whether you have a short or slender column
1a. If short, ignore Euler's equation
1b. If slender, then look at the relevant design code to address point 2
2. See how you calculate the magnified bending moment
3. Once there, identify the relevant interaction diagram to estimate As - where As is the required area of steel.
I hope this helps
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