Reliability assessment of ‘simple’ statically indeterminate structures

Abstract

Probability calculations are used to determine the possible failure of civil structures which includes bridges. The Eurocode uses a conservative form of these probability calculations and this could have a negative economic impact. Having said this, more advanced probability calculation methods are developed to decrease the negative economic impact this could have.
Nowadays structural analysis in daily practise is mostly done through the finite element method. The finite element method uses either linear or non-linear structural analysis. The latter mentioned analysis is used for the analysis of materials in which the nonlinear effects have significant impact. However not only finite element analyses are used to determine structural behaviour. Analytical models remain an important tool to examine civil structures. Since the analytical models cannot address all the influences of the nonlinear parameters, conservative assumptions were made.
On the one hand the modern design code uses semi-probabilistic in combination with the analytical model. Finite element analysis together with semi-probabilistic assessment is a possible use for design purposes as well. On the other hand full-probabilistic assessments, are not possible to execute in combination with nonlinear, finite element analyses. The reason for that the computation time becomes too large.
The research question that is tried to answer in this thesis: “How does a semi-probabilistic compare to a full-probabilistic safety assessment for a statically indeterminate beam structure?”
The 2-span statically indeterminate reinforced concrete beams that are studied in this thesis find their origin from the research done by Monnier between 1965 and 1970. This research had as goal to see what the influence of shear force would be on the bending capacity. This specific research is chosen because here statically indeterminate beams are dealt with. The experiments’ data generated during the execution of the four-point bending test is the starting point of this thesis.
To answer the research question, the components of a reliability model have been investigated. The levels of model approximation (LoA) as stated in the model code 2010 together with the level of reliability calculations (Steenbergen 2011) were used. Two combinations between LoA and reliability methods have been analysed to assess their strengths and weaknesses. These two reliability analyses were both were based on an analytical model (LoA I). The reliability level I and III, the so called semi-probabilistic and full-probabilistic, calculations were used.
In conclusion, the full-probabilistic reliability calculation is all cases applicable to determine the probability of failure of a statically indeterminate structure. However, semi-probability reliability are useful as well but it does allow only partly redistribution of forces. In case of statically indeterminate structures this can have significant impact on the failure load. The best reliability method for a statically indeterminate structure is dependent on the amount of redistribution of forces.
The semi-probabilistic calculations treat structures, where a lot of redistribution can occur, conservatively. For instance, the semi-probabilistic calculation procedure that is used in this thesis allows for only partly redistribution of forces. The full-probabilistic calculation procedure is therefore beneficial to use for structures where a lot of redistribution can occur in the ultimate limit state.
It turned out that the full-probabilistic calculation determines a higher reliability of the structure. In the full-probabilistic analysis, the limit state function is used in its analytical form. Whereas in the semi-probabilistic analysis is made with the use of approximations of the limit state function. However, when the cross-section of a statically indeterminate structure is designed in such a way that little redistribution will take place, the difference between the full- and semi-probabilistic is insignificant.