Chapter 5. Seismic Performance Evaluation of Ceiling Systems Based on
5.2. Shake-Table Test of Non-Seismic Ceiling Systems
5.2.1. Shake table test frames
In this study, ceiling specimens were tested using 3 types of test frames which are a large-size test frame, small-size test frame, and the full-scale 2-story steel mo- ment frame. The information about the full-scale 2-story steel moment frame can be referred to Chapter 4.
A large-size test frame was specially designed and fabricated for conducting dynamic test using two isolated shake tables synchronously (see Figure 5.1). The overall dimension of the large-size test frame was 13.1 m (length) × 5.1 m (width) × 3 m (height). It was composed of three segments: 1) two identical stiff frames (5.1 m × 5.1 m) installed on two shake tables and 2) a 4.1 m × 5.1 m link segment, which connects the two frames rigidly at the roof level (see Figure 5.2).
Figures 5.3 – 5.5 present detailed information of the frame segments. Each 5.1 m × 5.1 m square frame composed of 2 side wall frames, 1 end wall frame, 1 opening frame and 1 top frame. All the wall frames were stiffly designed using diagonal braces in order to construct a rigid test frame. At the upper side of the wall frames, HSS-100×50×3.2 box beams were welded for installation of wall molding for ceiling systems. For installation of ceiling systems, HSS-50×50×3.2 box beams were densely located at the top of the square frame. As shown in Figure 00, the holes to hang ceiling systems were introduced where the intervals were determined for in- stalling the ceiling systems with 610 mm interval hanger bolts and 900 mm interval
Figure 5.1 Large-size test frame for shake table testing of suspended ceiling systems and modular segments
hanger bolts. To facilitate the assembly of the test frame, all the elements were bolt connected through the holes introduced at the sides and top of the elements.
The large-size test frame was intended to conduct uniaxial shake table test in the longitudinal direction. The test frame was designed to have a horizontal natural frequency of 24 Hz for each bare square frame and 17 Hz for the combined test frame including the mass of ceiling specimens. The natural frequency of the whole test frame was measured to be 16.8 Hz by the white noise test (see Figure 5.6). On this basis, the frame was considered to be sufficiently stiff for preventing unintended amplification of the table input motion at the test frame roof. The test frame was mounted on two 5.0 m× 5.0 m three degrees-of-freedom shake tables having a max- imum acceleration capacity of 1.0 g.
Figure 5.2 3D plan showing configuration of large-scale test frame
Figure 5.3 Top view of large-size test frame showing hanger bolt hole locations
(a) 3-dimensional veiw of square frame
(b) Plan view of the top of square frame
(c) Side view of square frame (side wall frame)
(d) Side view of square frame (opening frame) Figure 5.4 Configuration and detailed plan for square frame
(a) 3-dimensional view of link segment
(b) Plan view of the top of square link segment
(c) Side view of link segment
Figure 5.5 Configuration and detailed plan for link segment
Small-size specimen tests were also conducted to supplement the large-size uni- axial shake table testing and evaluate the multi-directional input effects. A test frame with a size of 4.1 m (length) × 4.1 m (width) × 3.2 m (height) (see Figures 5.7 -5.8) was mounted on a six degrees-of-freedom shake table (4.0 × 4.0 m) having a maxi- mum acceleration capacity of 1.5 g. The natural frequencies of the small-size test frames were measured to be 16.1 Hz in the horizontal direction and 9.0 Hz in the vertical direction (see Figure 5.9).
Figure 5.6 Transfer function measured at the top of large-size test frame
Figure 5.7 Small-size test frame for multi-directional shake-table test
(a) Plane view of the bottom of small-size test frame
(b) Plan view of the top of small-size test frame
(c) Side view of small-size test frame
Figure 5.8 Detailed configuration and plan for small-size test frame
Before conduction tests for ceiling systems, a coherence function analysis was conducted for the large-size test frame to ensure that both the top of the square frame 1 and 2 exert identical floor motions without any differential movements. The co- herence function is a statistical tool that can be used to examine the relation between two different signals. The coherence function can be determined as follows:
(a) Horizontal direction
(b) Vertical direction
Figure 5.9 Transfer function measured at the top of small-size test frame
2
2 ( )
( ) ( )
xy xy
xx yy
G f G f G f
=
(5.1)
where Gxx(f) = auto-correlation function of xth signal, Gyy(f) = auto-correlation func- tion of yth signal, Gxy(f) = cross-correlation function of xth and yth signals.
When the coherence function is equal to one, two signals are completely related, or two signals are completely identical in terms of their phase and frequency contents.
If the coherence function is far from unity, it implies that the two signals have severe differences in their frequency contents; in this experimental study, the ceiling spec- imen installed on the square frame 1 and 2 was subjected to different floor motions (top frame acceleration response) caused by the differential movements between the square frames.
Figure 5.10 Coherence function measured at the top of large-size test frame
Figure 5.10 shows the coherence function measured from the recorded signals on the top of the square frames 1 and 2. It can be observed that the coherence function maintains almost unity in the whole frequency range except for around 20 Hz, where the coherence function highly fluctuated. Such a high fluctuation, around 20 Hz, is speculated to be caused by the local vibration of the beam members at the top frame and will not affect the global response of the ceiling specimens. Therefore, it can be concluded that the large-scale test frame installed on the two isolated shake tables was perfectly synchronized, and the whole suspended ceiling specimen installed on the large-size test frame is expected to be subjected to the same floor motions.