Chapter 4. Experimental Study on Seismic Demand of Nonstructural
4.3. Evaluation of Peak Floor and Peak Component Acceleration
4.3.2. Effect of component ductility
criterion (0.5 ≤ Tp/Ta ≤ 1.5) given by the ASCE 7-22 commentary (ASCE/SEI 2022) (see Figure 4.14). The resonant period ratio range (0.5 ≤ Tp/Ta ≤ 1.5) given by the ASCE 7-22 commentary seems wide enough to cover the resonant region. The res- onant bands underestimated were belonged to the ranges of 0.92 ≤ Tp/Ta ≤ 1.31 and 0.98 ≤ Tp/Ta ≤ 1.28 for the 2nd and roof floors, respectively.
(a) Specimen FH300-S
(b) Specimen FH150-S
Figure 4.15 Peak steel rack responses plotted from every measured hysteretic cycle for determining yield and maximum rack displacements (sliding base)
(a) Specimen FH300-F
(b) Specimen FH150-F
Figure 4.16 Peak steel rack responses plotted from every measured hysteretic cycle for determining yield and maximum rack displacements (fixed base)
implying negligible contribution of the very stiff (rigid) access floor (fn,access150 = 27.0 Hz) to the eigen property of the steel rack. Therefore, the dynamic behavior of the steel racks in FH150-series specimens was essentially that of steel racks rigidly
(a) Transfer function of FH300-F measured at top of steel rack (mounted on flexible access floor)
(b) Transfer function of FH150-F measured at top of steel rack (mounted on rigid access floor) Figure 4.18 Effect of access floor on natural frequency of steel rack specimens
Figure 4.17 Comparison of elastic CAR between FH150- and FH300-series specimens
mounted on the concrete floor slab. However, a significant contribution of the flex- ible access floor was observed in specimen FH300-F. The specimen effectively be- came a 2-DOF system, and the 1st and 2nd mode natural frequencies were measured as 3.20 Hz and 11.00 Hz, respectively. These resulted from the flexibility of the 300mm-high access floor (fn,access300 = 6.5 Hz, see Figure 4.4) and the high mass ratio between the steel rack and the access floor (mrack/maccess300 = 2.19).
Figure 4.18 presents the elastic component acceleration amplification (CAR) which was evaluated before the specimens yielded. The PCA measured at the top of the steel rack was normalized by the PFA to calculate the elastic CAR. First, from the results of FH150-series specimens, it was observed that the base sliding in FH150-S specimen seemed to have a minor effect on the component response; the magnitude of sliding was small, approximately 4 mm. The overall CAR for FH300-series speci- mens was higher by about 40 % than that of FH150-series specimens because the fundamental period of the FH300-series specimens was closer to the 2nd mode of
Figure 4.19 2-DOF numerical model for the yielded FH300-F specimen
the 2-story steel frame (T1,FH300/T2,frame = 0.76). These results clearly indicate that possible interaction between nonstructural elements and non-rigid mounting needs to be properly considered in their seismic design.
To evaluate the relationship between CAR and component ductility (μcomp), the yield and maximum displacements of the yielded steel rack specimens were ex- tracted based on the measured hysteretic responses (Figures 4.15-16), following the same procedure utilized for the PFA analysis. CAR reduction was measured by nor- malizing inelastic CAR by elastic CAR. The low-to-moderately yielded specimens FH300-S and FH150-F (μcomp = 1.22 – 1.42) showed only minor period elongation, implying that the tuning ratio of the specimens remained almost the same. CAR re- duction of specimens FH300-S and FH150-F was calculated as the ratio of the meas- ured elastic and inelastic CAR. However, a very high level of component ductility was developed for specimen FH300-F (see Figure 4.16(a)), and the specimen became more closely tuned to the 1st mode of the test frame (Tp/Tn = 1.08), resulting in a much higher CAR (= 3.62) compared to the measured elastic CAR (= 1.88). In order to obtain the elastic CAR corresponding to the yielded FH300-F specimen, a linear time- history analysis of 2-DOF system corresponding to the yielded FH300-F specimen
Table 4.3 Verification of numerical 2-DOF model based on dynamic proper- ties measured from yielded FH300-F specimen
Access floor-mounted steel rack
1st mode 2nd mode
f1 (Hz) ζ1 (%) f2 (Hz) ζ2 (%)
Shake table test 1.63 1.18 5.30 0.56
Numerical analysis 1.66 1.08 5.84 0.21
was conducted. The equation of motion for the 2-DOF model can be defined as fol- lows.
[
rack]
access access access access access access access g rack
access
m u c u k u m u m u
+ + = − +m
(4.1)
rack r rack r rack r rack access
m u +c u +k u = −m u
where ür = ürack – üaccess; ur = urack – uaccess
The 2-DOF model was established by referring to the dynamic properties of the steel rack and the yielded access floor that were individually measured after the test- ing (Figure 4.19). The time-history analysis was implemented by MATLAB based on Newmark’s method. The constructed 2-DOF numerical model was verified by comparing the analyzed dynamic properties with those measured from the yielded FH300-F specimen. As can be seen in Table 4.3, the numerical results correlated well with the measured properties of the test specimen.
Figure 4.20 shows the measured CAR and the corresponding component ductility levels. The relationship between CAR and component ductility given by ASCE 7-22 is also plotted. Overall, the measured CAR is less than that predicted by ASCE 7-22.
The CAR underestimation made by ASCE 7-22 may be related to the difference be- tween the component hysteretic model (bilinear hysteresis model with 3 % strain hardening) assumed by ASCE 7-22 (ASCE/SEI 2022) and the pinching hysteretic behavior generally exhibit inferior energy-dissipating capacities. Considering that many of the floor-mounted nonstructural elements such as steel racks (Jovanović et
al 2019; Dai et al. 2020) and partition walls (Petrone et al. 2016; Rahmanishamsi et al. 2017) frequently involve pinched hysteretic behavior of tabbed or hooked joints, further investigation including the pinching model is warranted to establish a more realistic relationship between the component ductility and CAR.