of 10
Supplemental Material
for
Shake to the beat: Exploring the seismic signals and structural response of
concerts and music fans
G. Tepp, I. Stubailo, M. Kohler, R. Guy, and Y. Bozorgnia
Description of supplemental material
This document provides further details about the technical design of SoFi stadium and the
speaker experiment, additional figures, and captions for the supplemental data tables. The data
tables are provided as individual sheets in the Excel file labeled sup
plemental_tables.xlsx. We
also include SAC data files from the speaker experiment in the zip folder labeled
experiment_data.zip.
Supplemental Text
S1: Technical design of SoFi Stadium
The main structural engineering elements of SoFi stadium bowl consist of a steel frame and
concrete deck system for lateral and gravity support. The frame is made up of 1100 buckling
restrained braces for lateral support. It also has thermal expansion conn
ectors to allow for strain
associated with large temperature changes. The decks are composite (concrete) and the seats,
stairs, and curbs are pre
-
cast concrete. The floor level decks consist of corrugated steel overlain
by smooth concrete, resulting in a t
otal thickness of several inches. Structural concrete was
used to install the slab
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on
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grade and slab
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on
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metal deck work.
The stadium roof consists of a canopy supported by 37 reinforced
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concrete columns. The roof
canopy is made up of a structural steel shell including a compression ring, a cable net system,
and over 300 fluorine
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based plastic panels covering 1.2 million squa
re feet. Each blade column
contains a triple pendulum seismic isolator at the top where the roof meets the column,
seismically isolating the roof and shifting the vibration periods to longer periods (e.g., 5 s or
longer). The blade columns themselves are e
xpected to have a relatively short period of
vibration in the vertical direction (e.g. approximately 0.1 s). While the roof
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canopy
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column
system should not be relevant to this study (as it’s separate from the bowl and concert vibration
source), it will pla
y an important role in stadium response to future earthquake motions.
Details on structural engineering elements can be found in AISC’s Continuing Education series
session “Structural Analysis and Design of SoFi Stadium (U3)” presented by R. Sabelli and M.
Waggoner, publicly viewable at https://www.aisc.org/education/continuingeducation/education
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archives/structural
-
analysis
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and
-
design
-
of
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sofi
-
stadium
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u3/.
S2: Detailed description of the speaker experiment
We conducted an experiment to test whether a speaker could feasibly produce the observed
low
-
frequency (1
-
10 Hz) seismic signals. Two Basalt data loggers with epi
-
sensors (strong
motion accelerometers) were placed 1 m from a speaker system, one
in front (CIT
-
E) and one
behind (CIT
-
T), with the north component parallel to the speaker system (Figure ST1). The front
sensor was the same one temporarily deployed during the Swift concerts. Data were recorded
at 100 and 200 samples per second. The speak
er system was a portable public announcement
system (Pyle PWMA1050BT) with 3 built
-
in speakers (10 inch subwoofer, 4 inch mid range, & 4
inch tweeter), an amplifier with a frequency response down to 35 Hz, and a maximum power
output of 800 W (RMS output 40
0 W, sound pressure level 94 dB re 1 W/m). We performed the
experiment in a basement hallway with tile floors. The sensors and speakers were placed on the
floor with nothing additional to improve coupling. We initially tested the sensors at a distance of
2
m; however, the signal was too weak to work with, so we moved the sensors closer and
successfully made changes to increase the input volume of the music (e.g., switching from an
MP3 player to a laptop).
For the music tests, we plugged a laptop into the speaker system and played the song “Love
Story” at maximum volume with the Apple Music application (test 1) and at an amplified volume
with the Audacity application (test 2), which was loud enough to cause
noticeable distortion in
the sound. We clearly felt vibrations while standing near the speaker. For both tests, during the
last chorus of the song, one person jumped along with the beat in the same way as would be
done during a concert. The jumping occurre
d next to and slightly in front of the speaker (i.e.,
closer to CIT
-
E; white X in Figure ST1). For the bass beat test, a bass guitar with active
electronics was plugged into the speaker system and played at maximum volume. The bassist
finger
-
picked a low E
(lowest note on a typically tuned bass) at 120 beats per minute, first with a
metronome and then without. For the last part of the test, the bassist alternated between a low
E and the next octave E at a slightly faster pace.
Figure ST1: Experimental setup with two sensors placed on either side of the portable speaker
system. Sensors are shown at 2 m distance (center of speaker system to center of blue tape).
Yellow arrows visible on the bottom corner of the front sensor indica
te north (pointing left) &
east directions. The white X approximates the location of the jumping tests.
Supplemental Figures
Figure S1: Spectrograms for all six nights recorded by station ZY.CIT
-
E (02:30
-
07:00 UTC).
Swift concerts occurred every night except 7 August, which was a break in the 6 concert/7 night
schedule.
Figure S2: Particle motion on station ZY.CIT
-
E for song 34 with all harmonics together (top) and
each harmonic (frequency peak +/
-
0.2 Hz) individually for more detail (rows 2
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5).