7.2.1. Evaluation of the external event demand for SSCs for specified load combinations
It is common engineering practice to determine the demand for an analysed SSC and for a specified load combination based on the assumption that the SSC behaves in a linear elastic manner. In such a case, the principle of superposition is applicable. When plastic behaviours are significant, the ductility (i.e. the ability to strain beyond the elastic limit) model still allows for linear modelling, provided suitable correction factors are applied (typically, the inelastic energy absorption factors). In other cases, such as the analysis of the response of civil structures that are subjected to high impact loads, the non-linear plastic analysis is widely used [21].
7.2.2. Capacity determination for qualified SSCs
For design purposes, the capacity determination of analysed SSCs is based on the limits (stress and strength for materials and other appropriate characteristics) in the selected codes and standards (Table 8) relative to all potential critical failure modes for the analysed item. These limits are the same as those employed in related engineering practices for extreme load combinations.
If the safety function is associated with a structural failure, the reference behaviour limit in terms of factors such as stress and strain needs to be defined in evaluating the failure for SSCs. The design stress limits required by design codes for conventional risk facilities for normal loads such as dead, live load and operating pressure vary between one half to two thirds of the yield stress of the material, with a resulting median probability of failure of about 10–4/a, corresponding to the design load. Occasional or extreme loads, which typically have a probability of exceeding in the range of 10–1/a to 10–2/a, have allowable stresses increased by between 20% and 33% and conditional probabilities of failure in the range of 2 × 10–4/a to 10–3/a.
For structures, the limiting behaviour levels are at yield or approximately 1.2 times yield, which give a probability of failure in the range of 5 × 10–3/a to 10–2/a, assuming stresses have been computed elastically. For mechanical components, higher stress levels are typically allowed up to twice the yield or 70% of the ultimate stress. However, there is some conservatism in the analysis such that the failure probability ranges between 10–2/a and 5 × 10–2/a, with the fragilities expressed as median capacities.
For re-evaluation purposes, the capacity determination of an analysed SSC may be based on the 95% exceeding of actual material strength limits. If such test data are not available, the corresponding limits from the selected codes and standards (Table 8) are used, if properly verified by in situ investigations.
Additional details are provided in IAEA Safety Standards Series No. NS-G-2.13, Evaluation of Seismic Safety for Existing Nuclear Installations [7] for the seismic case.
7.2.3. Comparison of demand with capacity
The general acceptance criterion for a comparison of demand with capacity can be written as follows:
(DNOC + DANOC + DAC + DEE) ≤ C (2)
where
DNOC = Demand on the SSC due to the effect of normal operation and normal environmental conditions (concurrent with the given external event);
DANOC = Demand on the SSC due to the effect of anticipated operational occurrence (if any, concurrent with the given external event);
DAC = Demand on the SSC due to the effect of accident conditions (if any, concurrent with the given external event);
DEE = Demand of the SSC due to the effect of a particular external event (or due to the effect of a rational combination of several external events resulting from the common initiating event);
C = Capacity of the SSC.
For earthquakes, and assuming that the SSC behaves in a linear elastic manner, the general acceptance criterion would be:
DEE = DE = [(DE,i / kD )2 + (DE,a
×
kD,tot) 2]½ (3) where demand means strength demand, andDEE = DE = [(DE,i
×
kD )2 + (DE,a ) 2]½ (4) where demand means displacement demand, andDE,i = Demand of the SSC due to the inertia effect of an earthquake event (or due to a combination of the inertia effect of an earthquake with other seismic induced effects);
DE,a = Demand of the SSC due to the anchor movement effect of an earthquake event (if any);
kD,tot = kD,g ×kD,l = Total inelastic energy absorption factor (ductility factor);
kD,g = Global inelastic energy absorption factor, which relates to the overall response of a structural system such as a space frame, a planar frame, a load bearing shear wall, a non–load bearing shear wall (example values are provided in Appendix III);
kD,l = Local inelastic energy absorption factor, which relates to the local, member, or element ductility associated with columns, beams, bracing members, equipment components (example values are provided in Appendix III).
Notes: To determine the demand DNOC, DANOC and DAC, the rules and provisions of the selected codes (standards) are to be used (see Table 8).
The inelastic energy absorption factors can be applied only when the seismic response of the SSC is calculated in a linear elastic manner.
Nearly all SSCs exhibit at least some ductility (i.e. the ability to strain beyond the elastic limit) before failure or even significant damage. Because of the limited energy content and oscillatory nature of earthquake ground motion, this energy absorption is highly beneficial in increasing the seismic margin against failure. Ignoring this effect will usually lead to an unrealistically low estimation of the seismic failure margin. Limited inelastic behaviour is usually permissible for those facilities with adequate design details such that ductile response is possible or for those facilities with redundant lateral load paths. For SSCs of design class 3, when the seismic input is considered in accordance with the conventional non-nuclear codes or standards, the designer needs to verify whether the global ductility is not latently considered, for instance by some reduction factors applied directly to the seismic input.
Damping values have a proven high influence on the results of the seismic analyses of SSCs. Because of the engineering judgement required in defining their value, suggested values are provided in Appendix III.
References [26, 33] provide typical earthquake design provisions and proper structural detailing that apply to research reactors and comparable facilities.
As an alternative to the specific methodologies presented above, many simplified procedures can be used for seismic design and re-evaluation purposes in the solution of special problems, such as:
● The assessment of the potential for liquefaction [26, 34–35];
● The assessment of soil–structure interaction [26, 36];
● The calculation of pulling forces on anchor devices [26];
● The seismic resistance of pipelines with the load coefficient method [37];
● The evaluation of sloshing effects in large free surface pools and tanks [24, 27].
However, any simplified approach needs to be validated for the application of interest, as it is usually heavily dependent on engineering judgement.
For aircraft crashes, the acceptance criteria for the stress–strain fields induced in a structural element depend on the safety function assigned to each structural element. For local design, if the only function of the element is to stop the aircraft and maintain the global stability of the building, it may be designed with plastic excursions of reinforced bars reaching a tensile deformation of ε = 2%.
If the structural element supports equipment that has to guarantee a safety function, the tensile plastic excursions can be limited to ε = 1% deformation. In both previous cases, namely local and global design, the acceptance criterion for concrete in compression can be ε = 0.35%.
If the element has a tightness function, no plastic excursion can be allowed, and elastic behaviour has to be guaranteed. In this case, however, it is more convenient to design a shielding structure able to protect the safety related buildings.
Detailed methodologies for structural design are provided in Refs [21, 26, 27].