Introduction - The Behaviour and Design of Steel Structures to EC3 - page 28

structurewithareserveofstrength.Thevaluesofthefactorsshoulddependonthe
load type and combination, and also on the risk of failure that could be expected
and the consequences of failure.Asimplified approach often employed (perhaps
illogically)wastouseasingleloadfactoronthemostadversecombinationofthe
working loads.
A previous code [48] allowed the use of the plastic method of ultimate load
design when stability effects were unimportant. These have used load factors of
1.70 approximately. However, this ultimate load method has also been replaced
by the limit states design method in EC3, and will not be discussed further.

1.7.3.4 Limit states design

ItwaspointedoutinSection1.5.6thatdifferenttypesofloadhavedifferentproba-
bilitiesofoccurrenceanddifferentdegreesofvariability,andthattheprobabilities
associated with these loads change in different ways as the degree of overload
consideredincreases.Becauseofthis,differentloadfactorsshouldbeusedforthe
different load types.
Thus for limit states design, the structure is deemed to be satisfactory if its
design load effect does not exceed its design resistance . The design load effect
is an appropriate bending moment, torque, axial force, or shear force, and is
calculated from the sum of the effects of the specified (or characteristic) loads
F k multiplied by partial factors γ G , Q which allow for the variabilities of the loads
and the structural behaviour. The design resistance R k /γ M is calculated from the
specified (or characteristic) resistance R k divided by the partial factor γ M which
allows for the variability of the resistance.Thus

Design load effect ≤ Design resistance (1.8a)

or

γ g , Q × ( effect of specified loads ) ≤ ( specified resistance /γ M ) (1.8b)

Although the limit states design method is presented in deterministic form
in equations 1.8, the partial factors involved are usually obtained by using
probabilistic models based on statistical distributions of the loads and the
capacities. Typical statistical distributions of the total load and the structural
capacity are shown in Figure 1.16. The probability of failure p F is indicated
by the region for which the load distribution exceeds that for the structural
capacity.
In the development of limit state codes, the probability of failure p F is usually
related to a parameter β , called the safety index, by the transformation

Φ( − β) = p F , (1.9)

wherethefunction Φ isthecumulativefrequencydistributionofastandardnormal
variate [35]. The relationship between β and p F shown in Figure 1.17 indicates