Engineering Know-How: Lessons from Earthquakes and Rules for Seismic Design - Dynamic Behavior of Concrete and Seismic Engineering - page 342

(a) (b)

Figure 9.15. Undesirable plastifying modes

The maximum acceleration a structure can counterbalance is limited by the
resistant moment of the hinges, but their energy dissipation capacity allows the
elastic energy to counterbalance the energy injected by the earthquake.

Eurocode 8 recommends a design and dimensioning method called capacity
design . In this, the plastic hinges should arise in pre-determined areas called critical
areas , to allow the structure to reach a mechanism condition whenever energy is
dissipated by ductile rotation of the plastic hinges. The plastic moments inside the
hinges are determined by the resistant moments of individual sections. It is good
practice to arrange for resistant moments to be higher than design moments (by
about 20 to 30%), as the accelerations to which the structure is subject are
determined by resistant moments and not design moments.

This frame example allows the method to be illustrated: to ensure that the plastic
hinges will form where designers want them to, so that energy is dissipated
according to the planned mechanism, the areas outside the hinges must be designed
to stay elastic when the zones in which the hinges should appear (critical areas)
become plasticized. Inside the hinges, the maximum moment possible is the resistant
moment, derived from the design moment by multiplying it with an over-capacity
coefficient. The coefficient takes into account strain-hardening effects, such as the
reinforcements of bending strength in a reinforced concrete section. Because these
maximum moments are known in the critical areas, the other areas are deliberately
over-dimensioned with regard to them. This is supposed to prevent plastic hinges
forming in areas where they are not desired, for example, within the columns, for if
the latter are too numerous here, the risk of instability becomes greater (Figure
9.15b). The goal is to ensure hinging will mainly take place inside the beams during
an earthquake (Figure 9.16).

To ensure engineers grade the appearance of plastic hinges correctly and to
prevent them forming inside the columns, they have to dimension the post-potential