Applied Loads and Stability of Steel and Steel-Concrete Composite Bridges - Finite Element Analysis and Design of Steel and Steel-Concrete Composite Bridges - page 162

order to verify that calculated effects due to the actions do not exceed the
design strength/deformation limits. The reliability approach is achieved
through the use of limit state design principles adopted nowadays in most
current codes of practice.
The design rules specified in the Eurocode are based on the limit state
design approach. According to EC0 [ 3.4 ] , the design verification of the ulti-
mate limit states is governed by the following equation:

26 Þ
where E d is the design value of the effects of actions (internal moment, axial
force, etc.) and R d is the design value of the corresponding resistance. At
ultimate limit states, actions (i.e., the internal bending moments and axial
forces due to the applied loadings and displacements) are expressed in terms
of combinations of actions that can occur simultaneously. The basic expres-
sion is expressed as follows:

E d R d ð 3 :

!

E X g G , j G k , j + g p P + g Q , 1 Q k , 1 + X
i

g Q , i c 0 , i Q k , i ð 3 : 27 Þ

> 1

where G k , j is the characteristic value of the j th permanent action, P is the per-
manent action caused by controlled forces or deformation (prestressing), Q k ,1 is
the characteristic value of the “leading” variable action, and Q k , i are the accom-
panying variable actions. The E () denotes “the effect of” and the “+” signs
denote the combination of effects due to the separate actions. Permanent
actions are self-weight (typically the weight of steel, concrete, and superim-
posed load such as surfacing and parapets); the partial factors g G applied to each
type of permanent action may be different, hence the summation term and the
j index subscript. The g p factor is related to prestressing actions and may be
ignored. The variable actions are either direct (the weight of traffic, the wind
pressure, etc.) or indirect (expansion/contraction due to temperature). The
partial factors g Q depend on the type of action and its predictability. It is
unlikely that the most adverse loading from one action will occur simulta-
neously with that due to a different action. In recognition of this, EC refers
to one action as a “leading action” and the other actions as “accompanying”;
a reduction factor c is applied to accompanying actions. In principle, each dif-
ferent action should in turn be considered as the leading action, to determine
which combination of leading and accompanying actions is the most onerous,
but for simplified highway bridge design, it may be assumed that the traffic
loading is the leading action. There are similar expressions for combinations