LOAD AND RESISTANCE FACTOR DESIGN in .NET

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LOAD AND RESISTANCE FACTOR DESIGN
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Figure 18.1 Limit state function and pdf of basic random variables.
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LOAD AND RESISTANCE FACTOR DESIGN
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Relationship of partial factors to design point.
in which i is the partial factor for variable xi , and xi * is the value of the transformed variable xi at the design point. Considering the usual case (Figure 18.3) in which there are more than one load variables, Qi , but only a single aggregated resistance variable, R, the corresponding load and resistance factors become Q i E[Li ] R R = E[R] i = (18.22) (18.23)
in which the i are the load factors and is the resistance factor. Note, this case of multiple load variables and a single resistance variable is strongly in uenced by structural (as opposed to, geotechnical) reliability considerations, in which the uncertainties of load conditions dominate those of resistance. As the practice of geotechnical reliability continues to evolve, it is likely that geotechnical applications of LRFD will begin to differentiate resistance factors, while consolidating the multiplicity of load factors. This would be in line with Taylor s early work on separating partial safety factors for cohesion and friction components of soil strength (Taylor 1948). For the present, however, load factors for superstructure design, for practical purposes, need to harmonized with load factors for foundation design, and thus the formulation of Equations (18.22) and (18.23) remains.
Choice of reliability index
Studies by a number of workers suggest ASD methods for foundation design result in nominal probabilities of failure that range from 0.0001 to 0.01 (Meyerhof 1994). These correspond to reliability indices that range from 2.5 to 3.5 (Table 18.4). In modern foundation codes, target reliability indices ranging from 2.0 to 3.0 are common, the former for cases of non-essential designs with high redundancy, the latter for critical designs with little redundancy. Unlike the case of a unique site and facility with a known loss function
LOAD AND RESISTANCE FACTOR DESIGN
Table 18.4 Relationship between probability of failure and reliability index for lognormal distribution (after Withiam et al. 1998) Probability of failure, pf Reliability index, 2.5 3.0 3.5 4.0 4.5 5.0 5.5 Normal distribution 6.21 10 3 1.35 10 3 2.33 10 4 3.17 10 5 3.40 10 6 2.87 10 7 2.90 10 8 logNormal distribution 0.99 10 2 1.15 10 3 1.34 10 4 1.56 10 5 1.82 10 6 2.12 10 7 2.46 10 8
for failures, a code must be developed for a broad spectrum of potential conditions, and thus the optimization of reliability level against cost is more qualitative. As an approximation, the relationship between probability of failure and reliability index for Normal variables is often taken from Rosenblueth and Esteva (1972) as pf = 460e( 4.3 ) for 2 6 ln = 460 pf 4.3 for 10 1 pf 10 9 (18.24)
(18.25)
18.3 Foundation Design Based on LRFD
Two areas of geotechnical engineering where LRFD approaches have enjoyed popularity are the design of foundations and the development of codes for foundations. This has been driven in part by the desire to harmonize the design of structural elements of bridges and buildings with the design of the foundations that support those superstructures. In the United States the move to LRFD codes for both shallow and deep foundations has been fostered by AASHTO. The design of foundation systems has bene ted more from LRFD than have other areas of geotechnical engineering because it is one of the few areas to be codi ed, especially in European practice. Foundation performance is also an area for which the extensive statistical data exist for comparing observed with predicted performance that are required with which to calibrate partial factors.