ABSTRACT
Two basically and conceptually different approaches for the seismic analysis and design of bridges: Traditional Strength Based Design (SBD) and the Direct Displacement Based Design (DDBD) have been compared. The main sources of differences between these two methods were identified. They are: (a) the strong correlation between the equivalent pre-yielding stiffness and strength is typically neglected in SBD, b) the equal displacement rule is not taken into account in DDBD. When these differences are eliminated the methods provide exactly the same results.
It has been demonstrated that the equivalent preyielding stiffness of SDOF systems can be estimated based on the known mass of the structure, the peak ground acceleration, the displacement ductility, and the yield displacement, before the reinforcement and the strength of the structure is determined. The yield displacement can be estimated in the same manner as is proposed in the original DDBD method, based on the yield curvature.
The yield curvature is independent of the strength of the structure. It depends only on the quality of the steel and the geometry of the cross-sections. Taking this into account, and considering the correlation between the yield displacement and curvature, it can be concluded that the equivalent pre-yield stiffness is directly proportional to the strength.
The equal displacement rule is discussed, including two different interpretations. It is demonstrated that this rule can be used for the analysis of a structure having different strengths. However, in this case its presentation and interpretation should be different from the traditional interpretation.
In the original DDBD the equal displacement rule is not applied. The required strength is defined based on the equivalent secant stiffness of the structure and the seismic displacement. The equivalent secant stiffness is estimated based on the inelastic displacement spectra, derived from the elastic displacement spectrum taking into account viscous and equivalent hysteretic damping. This damping is estimated based on empirical formulae, which are as approximate as the equal displacement rule itself. Taking this into account, the DDBD was modified using the equal displacement rule. It has been demonstrated that in such case the DDBD and SBD give the same results.
The strength determined by using original DDBD was compared with that defined by modified DDBD/modified SBD (where the pre-yield stiffness and the strength were adequately correlated). It was found that these differences can be expressed numerically using a coefficient which is the function of the displacement ductility μ and the type of structure. Using this coefficient it was found that the modified methods were more conservative in the case of a relatively small displacement ductility demand μ (i.e. if μ has a value of less than about 3). In other cases the larger required strength was calculated using original DDBD. This conclusion was obtained supposing that the same material safety factors are used in both methods.
Typically the pre-yield stiffness and the strength are not strictly correlated when the SBD is applied. In such cases the required strength can be larger as well as smaller than that estimated using DDBD, depending on that how accurately the pre-yield stiffness is defined.
Using the typical assumptions (e.g. a 50% reduction in Igross) the equivalent stiffness is often overestimated. This may lead to the larger required strength. Thus, some researchers characterize SBD as being “less economical”. However the overstrength which is provided in this way can be considered to act as an additional measure of safety, which is useful for two reasons: (a) the seismic forces defined based on the design spectrum can be exceeded; and (b) the numerical models that are used for the design are only an approximation of the real structure. This can be particularly important in irregular structures.
