7. Target Reliability¶
here are my edits and suggestions
7.1. General Aspects¶
In terms of a reliability based approach the structural risk acceptance criteria correspond to a required minimum reliability herein defined as target reliability. The requirements to the safety of the structure are consequently expressed in terms of the accepted minimum reliability index or the accepted maximum failure probability.
In a rational analysis the target reliability is considered as a control parameter subject to optimization. The parameter assigns a particular investment to the material placed in the structure. The more material - invested in right places - the less is the expected loss. Such optimization is mainly possible when economic loss components dominate over life, injury, and culture components. When the expected loss of life or limb is important, the optimal reliability level becomes more controversional. Frequently, this leads to the problem of the economic equivalent of human life; risk-benefit analyses are then applied to circuvent this difficulty; the reliability of the system is translated into the cost per life saved. The target reliability may then be chosen such that the cost per life saved is at acceptable levels (for example comparable to other similar systems).
In a practical approach the required reliability of the structure is controlled by:
i) a set of assumptions about quality assurance and quality management measures; these measures are for example related to design and construction supervision and are intended to avoid gross errors.
ii) formal failure probability requirements, conditional upon these assumptions, defined by specified target values for the various classes of structures and structural members.
7.2. Recommendations¶
Target reliability values are provided in the next paragraphs. They are based on optimization procedures and on the assumption that for allmost all engineering facilities the only reasonable reconstruction policy is systematic rebuilding or repair.
7.2.1. Ultimate Limit States¶
Target reliability values for ultimate limit states are proposed in Table 1. The values in Table 1 are obtained based on cost benefit analysis for the public at characteristic and representative but simple example structures and are compatible with calibration studies and statistical observations.
The shadowed value in Table 1 should be considered as the most common design situation. In order to make the right choice in this table the following guidelines may be of help:
Consequence classes
A classification into consequenze classes is based on the ratio \(\rho\) defined as the ratio between total costs (i.e. construction costs plus direct failure costs) and construction costs.
Class 1 Minor Consequences: \(\rho\) is less than approximately 2
Risk to life, given a failure, is small to negligible and economic consequences are small or negligible (e.g. agricultural structures, silos, masts);
Class 2 Moderate Consequences: \(\rho\) is between 2 and 5.
Risk to life, given a failure, is medium or economic consequences are considerable (e.g. office buildings, industrial buildings, apartment buildings).
Class 3 Large Consequences: \(\rho\) is between 5 and 10.
Risk to life, given a failure, is high, or economic consequences are significant (e.g. main bridges, theaters, hospitals, high rise buildings).
If \(\rho\) is larger than 10 and the absolute value of H also is large, the consequences should be regarded as extreme and a full cost benefit analysis is recommended. The conclusion might be that the structure should not be build at all.
One should be aware of the fact that failure consequences also depend on the type of failure, which can be classified according to:
a) ductile failure with reserve strength capacity resulting from strain hardening
b) ductile failure with no reserve capacity
c) brittle failure
Consequently a structural element which would be likely to collapse suddenly without warning should be designed for a higher level of reliability than one for which a collapse is preceded by some kind of warning which enables measures to be taken to avoid severe consequences.
The values given relate to the structural system or in approximation to the dominant failure mode or structural component dominating system failure. Therefore, structures with multiple, equally important failure modes should be designed for a higher level of reliability.
Relative cost of safety measures classificaton
The normal class (B) should be associated with:
medium variabilities of the total loads and resistances (0.1 < V < 0.3),
relative cost of safety measure
normal design life and normal obsolesce rate composed to construction costs of the order of 3%
The given values are for structures or structural elements as designed (not as built). Failures due to human error or ignorance and failures due to non-structural causes are not covered by table 1.
Values outside the given ranges may lead to a higher or lower classification. In particular attention may be given to the following aspects:
Degree of Uncertainty
A large uncertainty in either loading or resistance (coefficients of variation larger then 40 %), as for instance the case of many accidental and seismic situations, a lower reliability class should be used. The point is that for these large uncertainties the additional costs to achieve a high reliability are prohibitive. If on the other hand both acting and resisting variables have coefficients of variation smaller than 10%, like for most dead loads and well-known small resistance variability, a higher class can be achieved by very little effort and this should be done.
Quality assurance and inspections
Quality assurance (for new structures) and inspections (for existing structures) have an increasing effect on costs. This will lead to a lower reliability class. On the other hand, due to QA and inspections the uncertainty will normally decrease and a higher class becomes economically more attractive. General rules are difficult to give.
Existing structures
For existing structures the costs of achieving a higher reliability level are usually high compared to structures under design. For this reason the target level for existing structures usually should be lower.
Service life and/or obsolesce
For structures designed for short service life or otherwise rapid obsolesce (say less than 10 years) the beta-values can be lowered by one or half a class.
By definition serviceability failures are not associated with loss of human life or limb. For existing structures the demand will be more related to the actual situation in performance and use. No general rules are given in this document.
7.2.2. Serviceability Limit State¶
When setting target values for serviceability limit states (SLS) it is important to distinguish between irreversible and reversible serviceability limit states. Target values for SLS can be derived based on decision analysis methods.
For irreversible serviceability limit states tentative target values are given in Table 2. A variation from the target serviceability indexes of the order of 0.3 can be considered. For reversible serviceability limit states no general values are given.
