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Partial factors for selected reinforced concrete members: background to a revisionof SANS Contact details. The application of Eurocode EN in revising the South African standard for structural concrete design SABS will require the determination of partial factors in accordance with the reliability requirements of the revised South African loading code SANS Further research is required on the model uncertainty for different structural members flexural members, shear, columns, walls and the theoretical models of basic resistance variables related to quality control.
Keywords: concrete reliability, partial factors, concrete design, flexural resistance, column resistance. Apart from small corrections issued in subsequent amendments and no major revision of the Code has been done. A process therefore commenced in when a working group was established under the initiative of the Cement and Concrete Institute to consider the actions needed for a revision of SABS A decision was made in principle that Eurocode EN would be used as reference document.
The decision was based on the fact that this code contains the most recent research and developments in the field of reinforced concrete design, and it forms part of a much larger suite of harmonised codes. This large suite of codes enables an integrated approach across different materials and includes a well-formulated part on the basis of design and loadings. This paper presents the results of a reliability-based approach to define values for steel and concrete resistance variables material factors which can be used in the revised concrete design code.
The approach which is followed assumes that the partial factors of resistance variables are limited to material strengths alone, while other basic variables related to resistance, such as geometry, are not explicitly factored.
Theoretical models are used in the study based on assumed uncertainty for basic variables which include geometry values. These assumptions should be linked to production quality and need to be verified for the South African market. Although results show that different partial factors could be used for different structural member types, this would not be a practical design approach. Values are therefore proposed that would be valid for any structural member type albeit on the conservative side for some cases.
The reliability basis of structural design formulated in ISO General principles on reliability for structures also issued as SABS is developed into operational procedures for the determination of partial factors for actions and resistance in Eurocode EN Basis of structural design.
General guidelines for reliability analysis procedures are provided in EN Annex C Informative Basis for partial factor design and reliability analysis. Additional information on EN is also given by Gulvanessian et al , including background on its reliability basis. Reliability basis for South African structural standards. With the publication of SABS it was envisaged that the application of the principles of reliability to derive proper specifications for the treatment of loads or actions on structures should be followed by similar treatment of structural resistance by the following versions of the materials design codes.
One of the objectives of the revision of SABS should therefore be to provide an appropriate reliability basis for the stipulated design procedures. SANS Part 1 Basis of structural design provides the requirements not only for the actions on structures as stipulated in subsequent Parts, but also for structural resistance.
Since these requirements were largely derived from Eurocode EN , the wealth of reliability investigations and procedures done against the background of the development of the Eurocode e. A critical reliability feature of the Eurocode is that allowance is made for the national selection of reliability performance levels, typically as expressed by target reliability levels in calibration studies.
Provision for the appropriate performance levels required by SANS is therefore an essential component of the reliability assessment of the revision of SABS Reliability calibration. Reliability calibration for partial factor limit states design consists of the derivation of a set of partial factors that would ensure sufficient reliability of structural performance across the scope of application. Structural performance can be expressed in terms of a reliability model g X as a function of probabilistic or basic variables X.
Reliability requirements for resistance. The aim of the submitted study is to analyse partial factors for resistance variables of reinforced concrete structural members.
Consequently, suitable combinations of the partial factors may be identified by the reliability analysis of the resistance part without simultaneous consideration of the load effects. It follows from Eq 2 that the appropriate limit state function to be used in reliability analysis can be written in the form:.
Reliability of structural concrete resistance. In the following, Eq 2 and the limit state function, Eq 3 , are applied to analyse the resistance of reinforced concrete structural members. The resistance can be determined using common design formulae given for example in SANS and EN A slab was chosen as the representative bending member rather than a beam in view of the fact that the resistance of a slab is less reliable than that of a beam due to the important influence of concrete cover versus element depth for a slab.
However, in the case of the resistance of reinforced concrete structural members, the sensitivity factors of steel and concrete strength may be in the case of flexural members considerably less significant than the sensitivity factors of other variables for example resistance uncertainty and some geometric data. Consequently the theoretical partial factors, derived from the design point determined using the FORM method , generally differ from the partial factors applied to steel and concrete strength in design.
Thus from the theoretical point of view, this oversimplification of using two partial factors only is somewhat simplistic and may lead to conservative design values. Two different approaches to the analysis of the resistance of reinforced concrete structural members based on Eq 2 and 3 are applied in the following analysis:.
Commercially available software e. Both approaches are incorporated in specialpurpose software tools based on probability integration methods developed using the mathematical software MATHCAD.
Conventional models of basic variables provided in working documents of JCSS are mostly accepted. In general, however, theoretical models of basic variables including model uncertainty should be linked to production quality and available data.
European steel characteristics were used in the study. It can be shown that using local South African steel characteristics will have a negligible effect on the results see Figures 9 and 10 and the related discussion below. This is a common consequence of the sample inspection of the strengths. It is also well known that in general the model uncertainties may significantly affect the resulting reliability.
Although the working material from JCSS gives values as high as 1,2 for the mean value of modelling uncertainty, the theoretical models given in Table 1 have means equal to unity in order to avoid biased results and differ only in the coefficients of variability 0,05 for slabs and 0,10 for columns. However, the models indicated in Table 1 should be modified whenever convincing data are available.
In the case of a reinforced concrete flexural member a beam or slab exposed to a bending moment, this probability can be analysed considering the limit state function 1 and given as:. The characteristic values of the basic variables are used together with the partial factors. The remaining variables A s , h, a and b are considered by their mean nominal values, that is, they are not factored. A short reinforced concrete column exposed to a centric load may be described by the general limit state function 1 in the following form:.
An analysis of a short reinforced column exposed to a centric load is graphically depicted in Figures 3 and 4. This is exactly the opposite trend to the case of a reinforced concrete slab. Reinforced concrete column with increased uncertainty.
It may be a consequence of insufficient quality control and poor workmanship. In order to assess the sensitivity of the reliability of columns to the variability of model uncertainty, the coefficient of variation is increased from 0,10 to 0, Figure 5 indicates that the reliability level considerably decreases compared with Figure 3. This limitation is, however, acceptable in most practical cases. The opposing reliability trends in the reinforcement of slabs and columns indicate some oversimplification of the design functions as expressed by Eq 5 and 7 respectively.
This implies that the contribution of the respective partial factors to structural performance may not be a simple linear process in terms of factored material properties as indicated by these design functions. The results also demonstrate the difficulty of selecting partial factors based on judgement due to the counter-intuitive behaviour of the design functions. More insight into the contributions of partial factors to the reliability performance of a design function can be gained through further analysis of the reliability performance functions.
Extended reliability analysis. Various techniques are available to provide additional information on the reliability performance of slabs and columns, and the influence of the respective basic variables.
Global resistance factor. The characteristic GRF can be obtained in a similar manner by using unfactored characteristic basic variables X k in the design function. Note that the difference between the mean and characteristic GRF derives only from the differences between the mean and characteristic values for f y and f c.
The difference between graph a and graph b represents the contribution towards achieving sufficient reliability through the specification of the characteristic material properties f yk and f ck. From the results shown in Figure 8 it is clear that the specification of characteristic material properties f yk and f ck , plays a more prominent role than the values of the partial factors in achieving sufficient reliability for both slabs and columns.
Theoretical partial safety factors. The partial factor which applies to the characteristic value X k is obtained by direct conversion, i. The implication is that the characteristic bias for steel and concrete is sufficient with regard to the theoretical values. Sensitivity factors. The source of differences in trends of behaviour for the two types of element is also apparent from Figure In the case of slabs the reliability is dominated by basic variables which have a negative influence reducing reliability on the contribution of the lever arm to the resisting moment, viz a and f c.
In the case of columns, the relative importance of f y and f c simply changes with the relative contribution of steel and concrete to the resistance, although modelling uncertainty is generally the dominating factor. The objective was to determine economic values for the partial factors that would ensure sufficient reliability across the range of design conditions.
The following conclusions may be drawn, and some recommendations are made for using the results and further investigations:. These differences can be ascribed to the respective mechanisms of resistance, and their sensitivities to the effects of the basic variables, as shown in Figure The resistance reliability of slabs is dominated by basic variables related to the lever arm of the resistance moment.
Concrete strength only plays a role through its effect on the lever arm, and therefore only becomes significant at high reinforcement ratios Figure This explains the counter-intuitive effect of reduced reliability with increasing reinforcement for slabs. While the variability of the steel strength reduces the reliability through the moment force, its effect on the lever arm causes an increase, with a net effect of reduced sensitivity with increasing reinforcement.
The resistance reliability of columns is dominated by model uncertainty, except in the case of low reinforcement ratios where concrete strength is also important Figure The specified characteristic material strengths f yk and f ck play an important role in achieving sufficient reliability, as indicated by Figure 8.
This effect is further enhanced by the fact that strengths are systematically exceeded in practice. Since credit is taken for this effect, it is important to verify that the models for steel and concrete strengths are valid for South African conditions, and that they are realised in the application of quality control in individual projects. It is also clear, however, that the partial factors not only reflect the effects of material strengths, but also provide for other sources of uncertainty which are applied at unfactored nominal values in design expressions.
A more refined but more elaborate scheme of providing a model factor in addition to the material factors could also be considered. Further research is required on the following topics for which available information provided by the JCSS model code is incomplete and rather general, particularly when applied to the derivation of design procedures under South African conditions:. Probability Concepts in Engineering Planning and Design.
New York: Wiley. BS Part 1: British Standard Structural Use of Concrete. Part 1.
Copying and network storage prohibited. Amendment No. Amdt 2, March NOTE 1 In terms of the Standards Act, Act 29 of , no person shall claim or declare that he or any other person complied with an SABS standard unless a such claim or declaration is true and accurate in all material respects, and b the identity of the person on whose authority such claim or declaration is made, is clear. Construction works.
Design of Reinforced Concrete Structural Elements to Sabs 0100:1 1992