Summary A risk‐targeted design spectral acceleration and the corresponding seismic design action for the force‐based design of structures is introduced by means of two formulations. The first one called direct formulation utilizes the seismic hazard function at the site of the structure. Because the seismic action defined in the codes is often associated with a designated return period, an indirect formulation is also introduced. It incorporates a risk‐targeted safety factor that can be used to define a risk‐targeted reduction factor. It is shown that the proposed formulations give analogical results and provide an insight into the concept of the reduction of seismic forces for the force‐based seismic design of structures if the objective is defined by a target collapse risk. The introduced closed‐form solution for the risk‐targeted reduction factor can be used to investigate how the target collapse risk, the seismic hazard parameters, the randomness of the seismic action, and the conventional parameters (ie, the overstrength factor and the deformation and energy dissipation capacity) affect the seismic design forces in the case of force‐based design. However, collaborative research is needed in order to develop appropriate models of these parameters. In the second part of the paper, the proposed formulations are demonstrated by estimating the risk‐targeted seismic design action for a six‐storey reinforced concrete building. By verifying the collapse risk of the designed structure, it is demonstrated that the risk‐targeted seismic action, in conjunction with a conventional force‐based design, provided structure with acceptable performance when measured in terms of collapse risk.

Summary Decision models for the verification of seismic collapse safety of buildings are introduced. The derivations are based on the concept of the acceptable (target) annual probability of collapse, whereas the decision making involves comparisons between seismic demand and capacity, which is familiar to engineering practitioners. Seismic demand, which corresponds to the design seismic action associated with a selected return period, can be expressed either in terms of an intensity measure (IM) or an engineering demand parameter (EDP). Seismic capacity, on the other hand, is defined by dividing the near‐collapse limit‐state IM or EDP by an appropriate risk‐targeted safety factor (γim or γedp), which is the only safety factor used in the proposed decision model. Consequently, the seismic performance assessment of a building should be based on the best possible estimate. For a case study, it is shown that if the target collapse risk is set to 10−4 (0.5% over a period of 50 years), and if the seismic demand corresponds to a return period of 475 years (10% over a period of 50 years), then it can be demonstrated that γim is approximately equal to 2.5 for very stiff buildings, whereas for buildings with long periods the value of γim can increase up to a value of approximately 5. The model using γedp is equal to that using γim only if it can be assumed that displacements, with consideration of nonlinear behavior, are equal to displacements from linear elastic analysis.

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Design of earthquake-resistant structures according to Eurocod 8 is not based on the concept of acceptable/tolerable probability of exceedance of the near collapse limit state. Rather than that standard introduces fundamental non-collapse and damage limitation requirements, which are associated with the design seismic action. It is foreseen that the noncollapse requirement is satisfied when the regular structure does not collapse in the case of an earthquake with a return period of 475 years. Probability of such an even in 50 years is 10%. Therefore it is obvious that probability of failure of structures, which would be designed strictly according to the fundamental non-collapse requirement, would be unacceptable for society. Due to factors of safety involved in design the structures withstand much stronger earthquakes in comparison to an earthquake with a period of 475 years. In order to assess which factor of safety have the greatest impact on the overall safety of code-conforming buildings, two multi-storey reinforced concrete buildings were investigated. The strength and the system ductility of the six variants of the structures were evaluated on the basis of the pushover analysis gradually taking into account the requirements of the Eurocode 2 and 8, as well as gradually excluding the design assumptions. Safety in design of the buildings was evaluated by the difference between the calculated and prescribed behaviour factor, by the ratio between the design ground acceleration and that associated with the near collapse limit state, which was assessed using the N2 method, and by the escalation of safety in terms of probability of exceedance of the near collapse limit state. The results of this analysis are discussed in the paper. For the investigated buildings it is shown that the design seismic action has the greatest impact on the yield strength of the structure and the peak ground acceleration, which cause the near-collapse limit state. On the other hand, the partial factors of material strength contribute around 50% to the return period of the near-collapse limit state, whereas the contribution of the capacity design principles to overall safety is minor.

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