7. DESIGN, QUALIFICATION AND RE-EVALUATION
7.6. Qualification by analysis
7.6.1. Evaluation of the external event demand for structures, systems and components for specified load combinations
It is common engineering practice to determine the demand for an analysed structure, system or component and for a specified load combination
based on the assumption that the structure, system or component 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 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, non-linear plastic analysis is widely used. A generic reference is provided in Ref. [5].
7.6.2. Capacity determination for qualified structures, systems and components For design purposes, the capacity determination of analysed structures, systems and components is based on the limits (stress and strength for materials and other appropriate characteristics) as given in the selected standards and codes (Table 10) relative to all potential critical failure modes for the analysed item. These limits are the same as those adopted by these standards and codes and by 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 for the evaluation of the failure for structures, systems and components. The design stress limits required by design codes for conventional risk facilities for normal loads such as dead load, live load, operating pressure, etc., vary between one half and two thirds of the yield stress of the material with a resulting median PF of about 10–4/a, corresponding to the design load.
Occasional or extreme loads, which typically have a probability of exceedance 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 PF in the range of 5 × 10–3/a to 10–2/a, assuming that 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 structure, system or component may be based on the 95% exceedance of actual material strength limits. If such test data are not available, the corresponding limits from the selected standards and codes (Table 10) are used if properly
verified by in situ investigations. Additional details for the seismic case are provided in Ref. [8].
7.6.3. Comparison of demand with capacity
The general acceptance criterion for comparison of demand with capacity can be written as follows:
(DNOC + DANOC + DAC + DEE) £ C (4)
where
DNOC is the demand on the structure, system or component in normal operation and normal environmental conditions (concurrent with the given external event);
DANOC is the demand on the structure, system or component due to an anticipated operational occurrence (if any, concurrent with the given external event);
DAC is the demand on the structure, system or component due to accident conditions (if any, concurrent with the given external event);
DEE is the demand on the structure, system or component due to a particular external event (or due to the effect of a rational combination of several external events resulting from the common initiating event);
C is the capacity of the structure, system or component.
For earthquakes, assuming that the structure, system or component behaves in a linear elastic manner, the general acceptance criterion would be:
DEE = DE = [(DE,i/kD )2 + (DE,a × kD,tot) 2] ½ (5) where demand means strength demand and
DEE = DE = [(DE,i × kD )2 + (DE,a )2] ½ (6) where demand means displacement demand and
DE,I is the demand on the structure, system or component 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 is the demand of the structure, system or component due to the anchor movement effect of an earthquake event (if any);
kD,tot = kD,g ×kD,l is the total inelastic energy absorption factor (ductility factor);
kD,g is the 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 (sample values are provided in Appendix III);
kD,l is the local inelastic energy absorption factor which relates to the local, member or element ductility associated with columns, beams, bracing members and equipment components (sample values are provided in Appendix III).
For application of Eq. (6) the following applies:
(a) To determine the demand DNOC, DANOC and DAC, the rules and provisions of the selected codes (standards) are to be used (see Table 11).
(b) The inelastic energy absorption factors can be applied only when the seismic response of the structure, system or component is calculated in a linear elastic manner.
Nearly all structures, systems and components 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 estimate of the seismic failure margin. Limited inelastic behaviour is usually permissible for those facilities with adequate design details, making ductile response possible, or for those facilities with redundant lateral load paths. For design class 3 structures, systems and components, 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 been proven to strongly influence the results of the seismic analyses of structures, systems and components. Because of the engineering judgement required in the definition of their value, recommended values are provided in Appendix III. Reference [5] provides typical earthquake design provisions and proper structural details that apply to research reactors and comparable facilities.
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 e = 2%.
If the structural element supports equipment that is meant to guarantee a safety function, the tensile plastic excursions can be limited to e = 1% defor-mation. In both previous cases, namely local and global design, the acceptance criterion for concrete in compression can be e = 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 of the plant protection are provided in Ref. [5].