1. SBRA method as a tool for reliability analysis of structural members exposed to multi-component load effects David Pustka VŠB – Technical University of Ostrava Faculty of Civil Engineering Ludvíka Podéště 1875, 708 00 Ostrava, Czech Republic

2. Introduction Current codes for design and assessment of building structures define the rules for determination of load effects using combination formulas. In case of multi-component load effects the determination of critical load effects combination according to these codes can be extremely difficult. The simply and efficient way of multi-component load effects analysis can be based on SBRA method - as is demonstrated on the following example.

3. Example assignment Random variable forces acting on vertical column fixed in the foot :

4. Load effects combination The load effects combination in any point of structure can be expressed by normal stress  x (if the shear forces are neglected) according to the equation: where N x, M y and M z are three components of internal forces (normal force and bending moments to corresponding axis). (1)

5. The equation of a “plane” in 3D space For any point of a structure and for selected probability P d can be found such equation of a “plane” in three-dimensional space, which represents infinity combinations of three-component load effects. Every point of this “plane” represents just one combination of internal forces N x, M y and M z. The “plane” can be constructed using the equation: where constants a, b, c and d are given by: (2)

6. 3D “AntHill” divided by the “plane”

9. Summary and conclusions Today’s codes for building structure design do not say, which values of N x, M y and M z should to be used in calculation according to the formula (1) so that the probability of combination of individual loads will be respected. The approach based on combination formulas does not lead to determination of one critical combination of loads, but to infinity number of combinations meet the formula (2). Thus, the application of interaction formulas in analysis of multi-component load effects according to today’s codes cannot lead to consistent and satisfactory results…

10. Thank you for attention …