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PRACTICAL METHOD TO DETERMINE LOAD AND RESISTANCE
FACTORS
USED IN LIMIT STATE DESIGN
Authors: Yasuhiro MORI, Dept. of Architecture, Nagoya University
Hideki IDOTA, Dept. of Architecture, Nagoya Institute of Technology
Tsuyoshi TAKADA, Graduate School of Engineering, the University of Tokyo
ABSTRACT
The safety problem in structural engineering can be treated more rationally with probabilistic
methods. These methods provide basic tools for evaluating structural safety quantitatively.
Uncertainties in loads, material properties, and construction practice, which have been
traditionally dealt with by empirical safety factors, can be taken into account explicitly and
consistently in probabilistic safety assessment. Based on such methods, a first-generation of
limit state design codes were developed; the safety checks are associated with a specified
limit state probability or reliability.
The design format in these codes is given with load and resistance factors or partial safety
factors with which structural design can be carried out semi-deterministically in practice. In
most cases, only single set of the factors is provided in the code. Conceptually, the structural
performance level can be controlled by differentiating the factors, which makes reliabilitybased design an ideal tool for performance based design. However, intensive knowledge in
the theory of probability and statistics is required to determine the appropriate factors for a
target reliability level. In order to implement fully the advantage of reliability-based design, a
practical method is developed for use in practice to determine load and resistance factors for
an arbitrary target reliability level. This method will be introduced in Recommendation for Limit
State Design that will be published by Architectural Institute of Japan in 2002.
It is well known that load and resistance factors for Safety Margin R- S=0, where resistance,
R, and load intensity, S, are lognormal random variates, can be determined by a closed form
as,
1
. exp (x.t.x)
=
 1+Vx2
in which VX and ζ X are the coefficient of variation of X and standard deviation of ln X,
respectively, α X is the separation factor, and β T is the target reliability index. The practical
method uses the same form for load and resistance factors for safety Margin R-( S1 + S2 +...
Sn )=0. Separation factors are determined based on the variability in each random variable. In
the course of the analysis, it was found that the achieved reliability level of a structural
component designed based on the load and resistance factors determined by the closed
expression is fairly close if all of the random variables are lognormally distributed and if their
statistics are realistic. For the case that some of the random variables are not logormally
distributed, an approximation method is proposed to treat them as lognormal random variates.
Turkstra’s rule is used to consider the temporal variability in load intensity. The accuracy of
the factors, i.e. the error of the achieved reliability level from the target level is investigated
using numerical examples. It is shown that the achieved level is close enough in practice to
the target level when the principal load is fairly dominant.