Page 190 - Dynamic Loading and Design of Structures

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Figure 4.17 Favourable and unfavourable collapse mechanisms in buildings: (a) beam mechanism
(favourable); (b) column mechanism (unfavourable).

hinge rotations is equal to the ratio of the total height to the storey height (i.e. in the four
storey structure of Figure 4.17 the plastic rotation of the columns in the mechanism of Figure
4.17b is four times that of the members in the beam mechanism (Figure 4.17a)). It is clear that
the ductility requirements, expressed here by the plastic hinge rotations, are higher in the
column sidesway mechanism, and the difference increases with the height of the frame. As
discussed in detail in the literature (for instance by Penelis and Kappos, 1997, for R/C
structures, and by Bruneau et al., 1998, for steel structures), the available ductility of
members subjected to compressive axial loading (columns) is lower than that of beams, while
)
the second order (P-Δ effects that may lead to physical collapse of the structure are also more
critical in the column sidesway mechanism. These are the main reasons why the plastic
mechanism involving mainly hinges in the beams is considered a favourable one, whereas the
mechanism involving hinges at both the top and bottom of columns is an unfavourable one. A
practical way to avoid the formation of the latter mechanism is to ensure that the beams at a
beam—column joint are stronger than the columns.
Provisions to materialize the previously described concept are included in most modern
codes and form part of the so-called capacity design of a structure subjected to seismic
loading. Capacity design is essentially a procedure for imposing on a structure the desired
member strength hierarchy and eventually achieving a failure mechanism involving inelastic
response in members that can conveniently (and reliably) be detailed to develop inelastic
deformations. Most seismic codes recognize this principle, albeit to a varying degree of clarity,
and the degree to which capacity design is incorporated in each code also varies significantly.