100x10 SHS compression capacity VS economy with different grade steel

[Sunny17]

Q-The Hollow Square Section shown in the Figure below, has external dimensions 100mm x100mm x10 thick and is composed of 10mm thick steel welded plate.
It is being considered for use in propping applications where both ends can be considered to be effectively pinned. It will therefore be acting as a pin ended column without any intermediate lateral restraint.
Two alternatives steel grades are available for fabricating this cross section, viz: Type1 - Standard Grade 350MPa and Type 2 - QT 690MPa.
The cost of the Type 2 steel is 40% higher per lineal meter than the Type 1 steel.
You are asked to determine the height of the column (L) above which the Type 2 steel would no longer be cost-effective when compared with the Type 1 steel in this application.

Can someone help?

 

[jayrod12]

Well I would put my money on the buckling mode of failure governing in 95% of applications. Buckling has more to do with E, I and L than Fy, therefore in my opinion it would rarely make sense to use the higher strength steel.

 

[XR250]

Must be a homework problem.
For a short column, obviously the higher strength steel would have more capacity.
And, as Jayrod stated, for a slender column, the standard grade would make more sense.
I am guessing you will have to iterate on the intermediate height column formulas with each member until they converge.