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Steel Designers' Manual - 6th Edition (2003)
36.3.3 Design rules
Material resistance
The design resistances of steel members and other steel components is generally
related to the yield strength of the material. However, in the case of both bolted
connections and welded connections, the design strength is related to the tensile
strength (i.e. the UTS). This is also relevant when considering net cross-section
resistance at bolt holes.
Thus generally the design resistance Rd of a cross-section needs to be related to
a characteristic value of the yield strength f y using:
R d = Af y /g M
EC3 Design of steel structures 1057
in which A is the cross-section area.
For convenience, the characteristic yield strength f y is taken as equal to the
specified ‘guaranteed’ minimum value for yield strength R eH given in the
relevant product standard for structural steel, generally EN 10025. This is not
the ‘true’ characteristic strength (based on 95% or any other statistically determined
level of probability), which clearly will be higher. More importantly, the value of g M
needs to cover the variability of the section properties represented by A as well as
that of the yield strength f y.
An ECSC funded study of the variability of section properties, yield strength and
cross-section resistance using large numbers of samples of current production at a
variety of European (including British) steel mills found that the mean value of A
is approximately equal to the nominal value, but that the mean value of f y is about
1.2 times the nominal value. In addition, the shape of the distribution curve showing
its variability is markedly skewed, being noticeably truncated on the negative side,
presumably due to the process control procedure.
Reliability analysis related to the EN 1990 target reliability b, and taking account
of the actual distribution of yield strength and section properties, leads to a value
of R d related to the EN 1990 target reliability b = 3.8 that corresponds to a required
value of g M of slightly less than 1.0.
In simplified terms, the mean yield strength is about 1.2 times the nominal value:
thus the mean resistance is also about 1.2 times the nominal resistance Af y (see Fig.
36.1). The precise value of the characteristic resistance is not important, because the
design resistance has been determined directly from the data in conformity with EN
1990. This design resistance turns out to be equal to the nominal resistance, hence
g M = 1.0.
It is important to note that this is only possible because this value of g M = 1.0 is
used exclusively with the nominal ‘guaranteed minimum’ value of the yield strength.
For steel reinforcement the yield strength used in design is a characteristic value,
and a larger value of g M is needed to obtain the design value.