Structural Maximum Response of Storey Accelerations

In document Behaviour of three dimensional concrete structures under concurrent orthogonal seismic excitations (Page 180-184)


5.3.4 F RAMEWORK OF THE IDA S TUDY Structural Maximum Response of Storey Accelerations

Maximum values of global radial storey accelerations (Ar) for the IDA of the five

prototype structures were computed and are presented in Figure 5-5. Figure 5-5 (a) and (b)

exhibit respectively the median and 90th percentile values of radial storey accelerations. Figures

5-5 (c) and (d) show the median and 90th percentile values of radial storey accelerations

normalised by their intensity measures (Ar/IM). Figures 5-5 (b) and (d) show that beyond IM =

0.4g, the 90th percentile maximum values of Ar and Ar/IM erratically increase in an explosive-

like fashion exhibiting apparent collapse behaviour. Note the maximum storey accelerations up

to MCE occur at the roof level, however at 3DBE (incipient collapse) they occur in the mid

section of the considered structures in contrast with the far-field study where maxima occurred

only in the roof levels, see Appendix A2 Figures A2-11 to A2-15 and A2-26 to A2-30. This is

Figures 5-5 (c) and (d) for Sa(T1=2s) ≤ 0.1g (elastic response) show that the values of a =

Ar/IM were almost identical, i.e., b ≈ 1. However, Ar/IM values for Sa(T1=2s) ≥ 0.15g (DBE) and ≤ 0.25g (MCE) show reducing magnitudes of storey accelerations due to structural softening, which reduces the structural Sa intake (longer periods) that consequently decreases the values of

Ar. This indicates that the coefficient b < 1. Nonetheless, the values of Ar/IM maintain the same

ratios with their overall medians, particularly up to MCE, see Table 5-8 which lists values of

Median responses (expected demands) and 90th percentile (code-maximum) demands of Ar/IM.

Regression analysis and Tables 5-8 and 5-9 show quite similar values of a and b for the

median responses of both near- and far-field studies for Sa(T1=2s) ≤ MCE and show significant

difference for Sa(T1=2s) > MCE. Figure 5-5 (c) show that the near-field median responses

almost maintain their values, i.e., b ≈ 1, up IM = 0.4g when then they rapidly increase illustrating collapse onset that is confirmed by Figure 5-5 (d). For the 90th percentile demands, values of a

and b for Sa(T1=2s) ≤ MCE are generally larger than those of the far-field study. For Sa(T1=2s) >

MCE near-field value of b is similar to that of the far-field study, while near-field a value is

markedly larger. This raised value of a illustrates enlarged response magnitude due to high

mode effects overtaking residual strengths of individual structural members after the onset of

strength degradation of the considered structures. Finally Tables 5-10 and 5-11 list the

coefficients of variation COV(a) and COV(b) where Table 5-10 show markedly large values of

COV > 0.3 in contrast with those of the far-field indicating high variability and a blow-out in the

magnitude Ar.

Tables 5-6 and 5-7 show that the overall median of A/IM and A90th/IM for the near-field study is markedly lower for Sa(T1=2s) ≤ 0.4g when the near-field values markedly exceed the

values of the far-field study. Low values of A/IM for IM ≤ 0.4g can be ascribed to the scaling down of the near-field suite by large value of Sa(T1=2s) when compared with the far-filed suite

attributed to the high content of high mode frequencies with relatively higher spectral

accelerations than those of the far-field study.

The effects of biaxial interaction on the normalised 50th and 90th percentile demands

(A/IM and A90th/IM) are studied and listed in Table 5-5. The near-field values of aAr for median

responses ascribe to value of approximately one, i.e. γbiaxial,A = 1 (no biaxial interaction effects),

in contrast with the far-field study. On the other hand the 90th percentile demands for the near-

field study have significantly less reduction in value than those of the far-field, which can be

approximated (conservatively) by 8% reduction. Hence for the 90th percentile demands the

biaxial interaction correction factor γbiaxial,A ≈ 0.92 that is suitable for medium to long period

seismic-code designed structures excited by near-field events. Thus it can be credibly

implemented in a rapid calculation of Ar of structures with Tx/Ty≤ 1.5. Completed Set of Indicative Values of Structural Performance and Demands

In keeping with Chapter 4, indicative values of interstorey drifts (θr90th), lateral storey

drifts (δr90th) and accelerations (Ar90th) at different levels of structural performance are presented

in Table 5-12. These values are evaluated by implementing the power law and 90th percentile

values of coefficients a and b from Table 5-8. Table 5-13 lists the indicative values of the far-

field study that show larger values for DBE and MCE levels than those of the near-field. Note

that the near-field values of θr90th at DBE (0.9%) and MCE (1.6%) are respectively less than IO

and LS performance levels in contrast with the far-field study. This reduction is again attributed

to lower βEQ values of the near-field suite and its down scaling by larger value of Sa(T1) when

compared with the far-field suite. Figure 5-6 provides a plot of the IM normalised overall median

values of the median and 90th percentile demands of θr, δr and Ar at different levels of IM for the

near-field study. This figure shows a large sudden increase at IM > 0.4g indicating a brittle

collapse. Figure 5-7 compares near- and far-field overall medians of θr, δr and Ar at different

far-field values of δr/IM are markedly similar up to IM = 0.35g (>MCE), while Ar/IM values of

the near-field study was significantly lower than the far-field one. Figure 5-8 displays the PGA

normalised overall medians of Ar/PGA that show marked similar 50th percentile (expected)

responses and close values for the 90th percentile demands, counteracting the scaling by different

Sa(T1). Note that Figure 5-8 shows (expectedly) that PGA levels of intensity levels (DBE and

MCE) for near-field events are higher than those of far-field events. Nonetheless, the near-field

values are predominately less than those of the far-field; which is confirmed by Figure 5-7 that

exhibits the 90th percentile values of the near-field are less than those of the far-field up to IM =

0.4g when it overtakes the far-field values in extremely large (flat) increases. Again, this can be

attributed to the large content of high mode frequencies contained in the near-field earthquakes

with relatively higher spectral acceleration magnitudes that excites the considered structures in

high modes. These high mode frequencies excite individual members particularly the severely

degraded (more flexible) ones that enlarge the formed plastic mechanism to explosion-like

failure. This finding highlights the crucial importance and need to limit the level of strength

degradation by providing higher shear reinforcement that confines the concrete cores of

members of interest to reduce their level of strength degradation, particularly in beams. This

strength upgrade would limit the deformation extent of the formed plastic mechanisms and

consequently provide higher resistance to high mode vibrations. This would result in reducing

(or ultimately eliminating) the brittle nature of failure due to high mode (vibration) effects.

Furthermore, Figure 5-6 and its data can be utilised in calculating the dispersion factors

for demand randomness (βxR) for the investigated EDP’s: θr, δr and Ar via equation (4.1). Values

of βxR are listed in Table 5-14, where median values of βθR, βδR and βAR were 0.21, 0.10 and 0.37

respectively for Sa(T1=2s) ≤ Sa(MCE). These near-field values of βθR, βδR and βAR are markedly

less than those of the far-field, see Table 5-15, due to relatively lower βEQ. Note that the

response variability increases when Sa(T1=2s) > Sa(MCE). Median values of βθR, βδR and βAR

θr, significant increase for δr and insignificant increase for Ar. Nonetheless at 3DBE (collapse),

median values of βθR and βAR increased to 1.087 and 0.685 that could be interpreted as collapse

onset starts localised in the storey of maximum θr90th, and shows marked increase in interstorey

drifts. This incipient collapse, due to excessive interstorey drifts, is accompanied with high

lateral accelerations (high force demands), as indicated by Ar and βAR values. Note that δr

follows increases in θr however with markedly smaller values. While the overall high values βAR

suggests that Ar has generally high randomness for motions both smaller and larger than MCE,

pre- and post-collapse. On inspecting Figure 5-9, near-field θr90th is always less than that of the

far-field study up to CP level at which they are equal. Beyond CP level, near-field values of

θr90th markedly increase. Consequently one can postulate that near-field events cause marked

damage that lead to faster brittle collapse as structural strength markedly degrades at CP level.

In document Behaviour of three dimensional concrete structures under concurrent orthogonal seismic excitations (Page 180-184)