F. K. Kong MA, MSc, PhD, CEng, FICE, FIStructE, R. H. Evans CBE, DSc, D ès Sc, DTech, PhD, CEng, FICE, FIMechE, FIStructE (auth.)-Reinforced and Prestressed Concrete-Springer US (1987)

16 Limit state design concepts
1:'
1~------------t
(a)
Load F or strength f
Probability density
function of If-Fl
Probability Of
failure
(b)
Strength - Load If-F I
Fig. 1.6-1 Classical structural reliability theory [12]
why, in practice, the classical reliability theory cannot be applied in its
purest form [12]. One of these is that for structures such as those covered
by BS 8110 (or ACI 318-83) [16, 17], the probabilities of failure that are
socially acceptable must be kept very low (e.g. 1 in 10 6 ). At such low
levels, the probability of failure is very sensitive to the exact shapes of the
distribution curves for strength and load. To determine these exact shapes
would require very large numbers of statistical data, and such data are not
yet available. In particular, sufficient numbers of extreme values of the
strengths of complete structures (to define accurately the shapes of the tails
of the distribution curves) may never be available. Also in the simple
example illustrated in Fig. 1.6-1, only one load and one strength variable
are considered. For a real structure, there will in general be many loads
and many modes of failure, usually with complex correlations between
them, making it very difficult to calculate the probability of failure. In limit
state design [3, 4], our engineering experience and judgement have been
used to modify, and to remedy the inadequacies of, the pure probabilistic
approach to structural design [ 15].
Further information on structural design and safety concepts may be
found in an interesting book [18] by the late Professor Lord Baker of
Cambridge University.