1. 1 by Katerina Laschober

2. 2 Obr. 1.1 Steel column. Load arrangement. In the book called Probabilistic assessment of Structures there I have found an example of the column eccentrically loaded. The authors calculated two component load effect combination in the critical section of the column, but the 2nd order analysis was not considered. I have tried to calculate the same according to the 1st and the 2 nd order analysis. The differences are gonna be specified and discussed.

3. 3 Factored (or design) load values according to EC are: dead load G snow load S wind load W Nominal length of column L Eccentricity of vertical loads e Sectional area A Moment of inertia I Plastic sectional modulus W Modulus of elasticity E

4. 4  Loading variation is expressed by histograms: Dlvar, Slvar, Wlvar  Variation of length and eccentricity is expressed by histograms: histograms: Lvar and evar Lvar and evar  Variation of yield point is expressed by histogram fyvar.

5. 5 Maximal load effect combination for axial force N and bending moment M (considering the 1 st and the 2 nd order analysis) is expressed by stress in extreme fibres of the critical section. In the probabilistic assessment (according the SBRA concept using the Anthill program) was used the reference level which was expressed by the onset of yielding.

6. 6 Safety function :SF = fy – abs(sigma) Resistance of the column is referred to the yield point: fy = 0.9 x fyvar Load combination in the critical section: sigma = N/A  M/W, where:N = G  Dlvar + S  Slvar A) the 2 nd order analysis is not considered: M = (G  Dlvar + S  Slvar)  (e  Evar) + (wind  Wlvar)  (L  Lvar) B) the 2 nd order analysis is considered M = N x (((1/cos(U x (L x Lvar))-1)) x (e x evar) +(tan(U x (L x Lvar))/ (U x (L x Lvar))-1) x ((Wind x Wvar) x (LxLvar)))/N+(e x evar))- ((Wind x Wvar) x (L x Lvar))

7. 7 pic.1.2 Safety function pic.1.3 AntHill program output Stress in the extreme fibres of the ctitical sections: sigma = N/A  M/W,

8. 8 pic.1.4 Safety function pic..1.5 AntHill program output Stress in the extreme fibres of the ctitical sections: sigma = N/A  M/W,

9. 9 The resulting load effect combinations calculated according to the SBRA concept using the Anthill program were given in Figures 1.2 – 1.5. The resulting load effect combinations calculated according to the SBRA concept using the Anthill program were given in Figures 1.2 – 1.5. 1) 1 st order analysis: probability of the failure (the stress in the extreme fibres is bigger than the yield point) is 0.000823 2) 2 nd order analysis: probability of the failure is 0.013125 Significant differences between the probabilities of failure according to the 1st and 2nd order analysis could be observed. It means that there is need to consider the 2nd order analysis in the assessment.