Response Evaluation - Fundamentals of Earthquake Engineering - page 249

Table 4.13 Local and global limit states relative to the response curve in Figure 4.41 of the sample SPEAR
frame.

Local limit states Top displacement Global limit states Top displacement

(mm) % of Height (mm) % of height

Yield 1st Beam Yielding 62 0.69 Yield Global yield 54 0.60

1st Column Yielding 45 0.50

Collapse 1st Column Failure 65 0.72 Collapse 2.5% ID ratio 106 1.18

10% strength drop 109 1.21

Key : ID = inter - storey drift.

as corresponding to the extreme fi bre of core concrete reaching its crushing strain, i.e. ε cu = 0.003. The
above LSs monitored for the sample frame are consistent with the framework provided in Figure 4.40
and with the ' engineering limit states ' in Table 4.11. The value of inter-storey drift of ID = 2.5% cor-
responds to the LS of ' collapse prevention ' in Table 4.12. Since the yield point is not clear in the plot
of base shear- versus - top displacement of Figure 4.41, the proposal by Park (1988), presented in Section
2.3.3, is utilized to detect the ' global yield ' . An idealized elastic -plastic system is used to defi ne the
yield point in the global response of the structure. The yield displacement is therefore based on the
idealized elastic-plastic system with reduced stiffness, which is evaluated as the secant stiffness at 75%
of the ultimate strength. Lateral displacements of the top of the frame corresponding to local and global
LSs are summarized in Table 4.13 .
The values in Table 4.13 may be employed to compute the frame global ductility μ by using equation
(2.16) of Chapter 2. In so doing, it is observed that the sample structure has low ductility, i.e. 1.0 ≤ μ
≤ 2.0. Values of μ may be, however, overestimated if only global limit states are considered. For the
sample frame, local limit states result in reliable damage quantifi cation. It is, therefore, essential, when
performing seismic structural assessment to compute LSs as both local and global response quantities.
Exact damage assessment of the irregular SPEAR frame can be achieved only by using dynamic
response history analysis, since pushover curves cannot refl ect the effects of soft storey and torsion on
member level damage using conventional damage assessment. Nevertheless, the LSs presented in Table
4.13 alongside the response curve in Figure 4.41 are useful guidelines for a quick and brief assessment
of the capacity of the structure.

4.8 Output for Assessment
Previous sections of this chapter have focused on the defi nition of the load input, modelling issues,
methods of structural analysis and limit states that may be used to assess the earthquake response of
structures. The evaluation of seismic performance requires the selection of appropriate output quantities
or response indicators. Commonly used indicators are summarized in Figure 4.42 . Output quantities
are subdivided into actions (stresses and their resultants) and deformations (strains and their resultants).
Local and global indicators are used for accurate and reliable assessment of seismic response. In general,
local output parameters are required primarily to detect potential damage localization and to evaluate
the attainment of threshold values of stress and strain in fi bres at different performance levels, such as
yielding, cracking, crushing and buckling, as shown in Tables 4.11 and 4.13. On the other hand, global
response indicators are used to estimate the fundamental structural response characteristics presented
in Section 2.3. The evaluation of local and global parameters depends upon assumptions made regarding
the level of discretization adopted for the structure. Substitute and stick models illustrated in Section