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]) 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/mm
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... )