# Simple steel column buckling calc - where am I going wrong? (Eurocode)

I'm trying to follow an example of this, but I get a wildly different answer than expected and I can't see where I'm going wrong.

The example I've got, is for a 2.8 m steel column (RHS 150 x 100 x 5mm) fixed both ends with a simple static vertical central load. Couldn't be easier for a beginner. My calculation is:

Relevant properties (section properties taken from [here][1]) normalising length to metres:

• Steel section: RHS 150 x 100 x 5mm. (unspecified hot or cold)
• L: Free length = 2.8 m
• E: 205 x 109 = 2.05 x 1011
• I (table): Least 2nd moment of area = 3.923 x 106 mm4 = 3.923 x 10-6 m4
• A (table): Area = 2373 mm2 = 2.373 x 10-3 m2
• r (table): Least radius of gyration (as double check): 40.7mm = 0.0407 m
• K: Effective length factor = 1 (fixed-fixed)
• s: Slenderness = L/r = 2.8/0.0407 = 68.8 (intermediate)

EUler buckling force, calculated using I,K,L:

• π2 x (E.I) / (KL)2
= (3.1422 x (2.05 x 1011) x (3.923 x 10-6) / (1 x 2.8)2
= 1.012 MN

Euler buckling force, calculated using A,s (as double check):

• π2 x (E.A) / (s2)
= π2 x (2.05 x 1011) x (2.373 x 10-3) / (68.8)2
= 1.014 MN

So the two calculations agree within the limits of the data table figures.

The problem is, the correct answer is apparently Pc (compressive strength) = 124 N/mm2 = 294 kN.

The answer does confirm that slenderness is 68.8, and that the least radius of gyration is 40.7 mm, so I know I'm on the right track.

But there's no actual full calculation, and the error isn't an obvious factor that might suggest the problem, so I don't actually understand where Ive gone wrong.

(The actual question is part of a longer worked example, so if I get stuck anywhere else I might need to update this. But for now, that's the point I'm stuck at... )

• Does Eurocode include a safety factor? A factor of about 3.5 would not be particularly conservative. Some people might prefer using 10 instead! Nov 16 '19 at 0:41
• No, this calc doesn't involve further safety factors, at least as far as I can see. Its pretty basic, e.g. K=1. In any case it would almost certainly involve some specific factor from a table or calculated from the above information, which is all one's told (as opposed to say an engineers personal preference in a given real-world situation), and a factor of 3.3 ~ 3.4x just doesn't seem to match anything obvious. Otherwise a " correct" answer would become "anything under 427, pick a number you like", which might be fair in real situations, but isn't likely here with a very specific answer = 124 Nov 16 '19 at 0:46
• You title says "Eurocode" not "Euler buckling." I'm a mech engineer not civil, but a quick google search brought up this eurocodes.jrc.ec.europa.eu/doc/2014_07_WS_Steel/presentations/… which implies that the Eurocode does specify safety factors to be applied to the standard Euler formulas. See the end of Example 1. Nov 16 '19 at 2:30
• idk if anyone checked this but 124 MPa ~= 294 kN / 2373 mm2 so Pc would be the stress calculated in a strength check. However you don't do this in EC3, you would calculate the NcRd = A * fy / gamma1. As for the Euler buckling force (Ncr) this seems to be OK but you have to use the reduction factors (slenderness -> relative slenderness -> buckling curve -> reduction factor) to get to NbRd, the buckling design resistance. The design resistance of the column will be min(NcRd, NbRd) so the answer may be correct if NcRd < NbRd. Feb 25 at 7:00

• Ohh! There's no mention of factors in the question or explanatory text. But the answer does definitely say Pc, and the value is then compared to the design stress (static load/area). The only other info is that it's an exercise from the UK (where I am), so it'll be UK specific data if anything, and also described as "the column is considered fixed top and bottom", and "is an end support for a fixed 200mm wide beam having a UDL with a reaction of 41.5 kN at each end". Combined with the OP info, is that enough information to know which factors to include and come to the correct answer? Nov 16 '19 at 10:17