The Design of Modern Steel Bridges - TEDI

78 The Design of Modern Steel Bridges
(2) Level II – in this method some idealisations are introduced into the
probability analysis to reduce the numerical difficulties; thus, for each mode of
failure, a failure boundary is defined by structural theories in the space of the
variable parameters, from the probability distribution of the variables a
checking point on the failure boundary is identified where failure is most likely
to occur, and by linearising the failure boundary at the design point an
approximate reliability of the structure is estimated.
(3) Level I – this is a semi-probablistic method in which appropriate levels of
reliability are achieved for each structural element by the application of a
number of partial safety factors to a pre-defined set of characteristic values of
the variables. The characteristic value of each variable has a pre-defined low
probability of occurrence and is determined, wherever possible, from the mean
value, the standard deviation and the distribution type of the variable obtained
by tests or measurement. When statistical data are not available, nominal
values based on past practice are used. The partial safety factors may be
determined by a Level II (or III) method for the required degree of safety. Thus
the Level I method can be made identical to Level II (or III) if the partial safety
factors are expressed as continuous functions of the means, standard deviations
and distribution types of the variables. However, most structural codes drafted
in Level I format prescribe discrete values of the safety factors instead of
continuous functions, to be applied to a rationalised, i.e. reduced, number of
design variables.
The idea that the statistical variation in a parameter should be considered in
structural design is not new. For example, the design wind speeds are determined
from the distribution of the annual extreme mean hourly speeds in the
British codes and of the annual extreme fastest mile speeds in North America.
The acceptance criteria for the concrete mix are designed to ensure that the
probability of producing concrete with a cube strength less than the specified
characteristic value is less than a pre-defined target, which is 5% in the UK and
10% in the USA. Probability based limit state codes recognise that, in the
presence of uncertainties, absolute reliability cannot be achieved, but the
probability of exceeding a limit state can be ensured to be acceptably low.
In between the permissible stress codes and the limit state codes there have
been several intermediate developments. For example, the load and resistance
factor designs developed in the USA[1–3] use factored loads and factored
resistances, with different factors for different loads, reflecting their different
degrees of variability. Thus
Xðnominal
loads load factorÞ
4
resistance
resistance factor
This method does not deal with all the limit states, and the factors are based on
past experience, intuition and perception regarding the uncertainties involved.