Reinforced Concrete Design To Sans 10100 Pdf
Akinlolu Bellotti
The application of Eurocode EN 1992-1-1 in revising the South African standard for structural concrete design SABS 0100-1:1992 will require the determination of partial factors in accordance with the reliability requirements of the revised South African loading code SANS 10160:2010. The partial material factors γs for steel and γc for concrete are proposed in analysing the reliability of reinforced concrete slabs and short centrically loaded columns. It appears that the partial factors γs = 1,10 and γc = 1,40 are a suitable set of factors to be considered in the foreseen revision of the code. 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.
The South African Code of Practice for the design of reinforced concrete structures SABS 0100-1:1992 was initially formulated by using as reference document the British Code of Practice for the Structural use of Concrete BS 8110: Part 1: 1985. Apart from small corrections issued in subsequent amendments (1994 and 2000) no major revision of the Code has been done. The British Code (BS 8110) has recently been replaced by Eurocode EN 1992-1-1, which is an indication that a revision of the South African code is much needed.
A process therefore commenced in 2007 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 0100-1:1992. A decision was made in principle that Eurocode EN 1992-1-1:2004 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. Furthermore, the revised South African Loading Code (SANS 10160:2010), which is presently in the final stages of being published, has been formulated using Eurocode EN 1990:2002 and the relevant parts of EN 1991 as reference standards.
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.
With the publication of SABS 0160:1989 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. The South African National Conference on Loading (SAICE 1998) made it clear that such development for concrete design was not done (Retief et al 2002). One of the objectives of the revision of SABS 0100-1:1992 should therefore be to provide an appropriate reliability basis for the stipulated design procedures.
SANS 10160:2010 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 1990:2002, the wealth of reliability investigations and procedures done against the background of the development of the Eurocode (e.g. Holick & Markov 2003; Holick & Holick 2004) could assist in providing useful guidance also for South African conditions and requirements.
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 10160-1:2010 is therefore an essential component of the reliability assessment of the revision of SABS 0100-1:1992.
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.
In Eq (2) Φ() denotes the distribution function of the standardised normal distribution. It follows from Eq (2) that the appropriate limit state function to be used in reliability analysis can be written in the form:
In the following, Eq (2) and the limit state function, Eq (3), are applied to analyse the resistance of reinforced concrete structural members. Well-established methods of structural reliability are used (probability integration and approximate analytical First Order Reliability Method (FORM)).
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.
It is also well known that in general the model uncertainties may significantly affect the resulting reliability. Although the working material from JCSS (2002) 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. Note that the characteristic values of the model uncertainties θR are 1 and are consequently not explicitly considered in design formulae.
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.
The GRF for slabs and columns as a function of the reinforcement ratio (ρ) are shown in Figure 8. Both the mean GRF (graph (a)) and characteristic GRF (graph (b)) values are shown. The differences in the attributes of the reliability behaviour of the two structural elements should be noted in terms of the magnitude of the required GRF, trends as a function of ρ and the change in GRF from mean to characteristic value.
Note that the difference between the mean and characteristic GRF derives only from the differences between the mean and characteristic values for fy and fc. The difference between graph (a) and graph (b) represents the contribution towards achieving sufficient reliability through the specification of the characteristic material properties fyk and fck. The difference between graph (b) and a value of 1,0 represents the contribution required from the partial factors γy and γc. From the results shown in Figure 8 it is clear that the specification of characteristic material properties fyk and fck, plays a more prominent role than the values of the partial factors in achieving sufficient reliability for both slabs and columns.
The source of differences in trends of behaviour for the two types of element is also apparent from Figure 10. 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 fc. Lower values for fc result in a smaller lever arm, and thus a lower resistance moment; this effect becomes more prominent as ρ increases. Lower values for fy have a counterbalancing effect on the resistance moment by decreasing the force but increasing the lever arm, with the effect again becoming more prominent with increasing ρ.
In the case of columns, the relative importance of fy and fc simply changes with the relative contribution of steel and concrete to the resistance, although modelling uncertainty is generally the dominating factor.
This paper presents the results of a reliabilitybased approach to defining the values of partial factors γs and γc for reinforced concrete slabs and short centrically loaded columns. Target reliability levels as expressed by the resistance index βR are set in accordance with South African practice. The reinforcement ratio ρ, which is considered as the main design parameter, was investigated across the range of practical values. The objective was to determine economic values for the partial factors that would ensure sufficient reliability across the range of design conditions.
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