SANDWICH PLATE SYSTEM RISERS FOR STADIA Dale ... - SPS

INTRODUCTION
SANDWICH PLATE SYSTEM RISERS
FOR STADIA
Dale Braun 1 , Stephen J. Kennedy 1 ,
D.J. Laurie Kennedy 1 and David E. Allen 2
Presented to:
SSRC 2002 Annual Stability Conference
24-27 April 2002
Seattle, Washington, USA
Intelligent Engineering (IE) has developed and patented the Sandwich
Plate System (SPS), in which two metal plates are bonded to and form a
sandwich with a compact polyurethane elastomer core. The elastomer
provides continuous support to the plates and precludes local plate
buckling and the need for stiffeners. The flexural stiffness and strength
of the sandwich plate is tailored to meet particular static and dynamic
structural requirements by selecting appropriate thicknesses for the
sandwich elements.
The CANAM-MANAC Group Inc, fabricated the steel for a double-Lshaped
prototype riser section designed by Intelligent Engineering
(Canada) Limited, and shown in Figure 1, in their plant in Ville de St.
Georges, Quebec. The elastomer was injected by BASF Livonia, MI,
USA. Both static and dynamic tests were carried out in May 2001 in
the fabrication shop in Ville de St. Georges by a team with members
from Intelligent Engineering 1 , Elastogran Olching, BASF Livonia,
1 D. Braun, S.J. Kennedy and D.J.L. Kennedy, Intelligent Engineering
(Canada) Limited, 72 Chamberlain Avenue, Ottawa, Ontario, Canada,
K1S 1V9
2
David E Allen, Consultant, 1212-211 Wurtemburg Street, Ottawa,
Ontario, Canada, K1N 8R4
1

BASF Ludwigshafen and CANAM-MANAC and additional dynamic
tests were carried out at BASF Toronto in November 2001. The
relatively light SPS double riser unit proved most satisfactory exhibiting
great strength and very good dynamic performance as described herein.
Figure 1. End view of test specimen in fabrication shop
TEST SPECIMEN
As fabricated, the steel plates of the 12.2 m or 40-foot long specimen
with two treads, each 0.836 m or 2.74 feet wide, were nominally 3.8
mm thick and the core was 32 mm thick for a total sandwich thickness
of about 40 mm or 1.6 inches. The SPS designation of 4-32-4 represents
the thickness in millimetres of the components. The prototype was
divided into four longitudinal cavities of 3.05 m length into which the
elastomer, designed to swell slightly on setting and thus to provide an
optimum bond with the grit blasted steel, was injected. The injection
time per cavity was just over four minutes.
As seen in Figure 1, raker supports were also provided so that the riser
was positioned as it would be for use in a sports stadium. The figure
also shows a vertical “skirt” below the toe of the lower tread and a
horizontal “skirt” adjoining the top edge of the upper riser. These were
provided to correspond to the support that would be given to the riser
by adjacent units in the field. With the two treads and the web of the
top skirt, three horizontal surfaces are available for loading. Finite
element analyses show that the two skirt reactions amounted to 25.5%
of the total uniformly applied load or conversely that the two riser units
of the specimen supported 74.5% of the total load. The total mass of
the test specimen is estimated, based on measured dimensions and
volumes of elastomer, to be 4950 kg consisting of 1280 kg of
elastomer, 2110 kg of steel in the double–L risers, and 1560 kg in the
two skirts. This mass (equivalent to a weight of 48.56 kN or 10.92
kips) was supported as self-weight in the test. In a stadium, the skirts
would not be present, but 22 seats per row, with an estimated weight of
5.2 psf, would be. Therefore, the total dead load (excluding the weight
of the skirts) of 8620 pounds over a total horizontal projected area of
220 square feet for the two treads is 39.2 psf. (The estimated weight of
6-inch thick concrete risers with seats, as has been proposed for this
span, is about 125 psf or 3.2 times that of the 4-32-4 SPS risers).
LOADING
The prototype was loaded in two different ways. For the static load
tests, to load the risers even beyond the specified live load of 100 psf,
1800 concrete building blocks were used. A random sample of 100
blocks was weighed in 20 groups of five on a balance. The mean
weight of five blocks was 144.35 pounds. The balance was checked
against an electronic scale, taken as the standard, which gave a
calibration factor of 0.9893. Thus a block was taken to weigh
[144.35/5] x 0.9893 = 28.56 lb or to have a mass of 12.96 kg. The 1800
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locks represent an effective distributed load supported by the tread
area or riser load of 174 psf or 8.33 kPa as compared to a common
specified load of 100 psf or 4.8 kPa for sports stadia. Figure 2 shows
the fully loaded specimen with the 1800 blocks stacked six high in five
rows of sixty blocks each comprising two rows on each tread and one
row on the upper skirt. By first loading three rows only (the two of the
upper tread and the inner row on the lower tread) and then by adding
the two remaining rows, a total of 12 load steps were achieved within
the six layers. It was impractical to load the risers further.
weight of the two skirts as they would not be present in the actual
structure, is 45 530 pounds. Thus, the riser specimen was loaded to
1.02 of the total factored load level in the static test. (The National
Building Code of Canada load factors are 1.25 for dead load and 1.5 for
live load resulting in a factored load of 43 770 pounds and a prototype
load of 1.06 times the total factored load level).
The second method of loading was with three rows of 22 people each.
This basic loading was applied in two different settings. First,
CANAM-MANAC workers stood evenly spaced along the two treads
and on the top skirt as shown in Figure 3. On average, these workmen
weighed 190.7 pounds each (a mass of 86.5 kg). Allowing for the load
carried by the top and bottom skirts, as described previously, the
Figure 2. Loading with concrete building blocks
The total weight supported in the test, including the self-weight of the
risers and skirts of 10 910 pounds, was 62 320 pounds of which 74.5%
or 46 370 pounds was supported by the risers themselves. With dead
and live load factors of 1.2 and 1.6 respectively, as specified in ASCE
7-98 Minimum Design Loads for Buildings and Other Structures, the
total factored load to be supported on 220 square feet, excluding the
Figure 3. Three rows of 22 workers, 42.6 psf or 2.04 kPa
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uniformly distributed load on the risers amounted to 42.6 psf or 2.04
kPa. Second, a like number of BASF office personnel in Toronto sat on
folding chairs in two rows with a third row standing on the top skirt as
shown in Figure 4. The average weight was 177.7 pounds or the mass
was 80.6 kg equivalent to 39.7 psf or 1.90 kPa. These loadings are
respectively about 1.22 and 1.13 times heavier than the static live load
of 35 psf usually associated with full sports stadia. The loadings with
people provide a basis for the qualitative evaluation of the riser under
loads simulating field conditions as discussed later and for the
quantitative evaluation of vibration characteristics.
specimen at both tread-riser junctions and under the bottom skirt. A
limited number of strain gauges were also used to provide back-up
measurements but these data are not reported here.
Two accelerometers, provided and operated by Elastogran GmbH, were
used to measure the vibration response of the test specimen. One was
capable of measuring vertical accelerations and the second of
measuring the response in three dimensions. The accelerometers were
mounted on the unloaded face of the upper tread at mid-span. The
specimen was excited dynamically in several ways and the vibration
response recorded electronically. When loaded with blocks, the
specimen was excited by a blow of a hammer, by a person jumping
lightly, or by lifting one end of the riser from the floor with the
overhead crane and then letting it fall. When loaded with workers,
rhythmic movements of the workers, a heel drop, or one person
jumping from one level to another were used.
STATIC TESTS
Figure 4. Three rows of 22 people, 39.7 psf or 1.90 kPa
INSTRUMENTATION
In the static tests, the vertical and horizontal deflections at mid-span
were measured using mechanical dial gauges on the underside of the
When the riser prototype is loaded vertically under gravity loads, such
as with the weight of the concrete blocks, it deflects vertically
downward and horizontally towards the rear. This occurs because the
principal flexural axes are inclined to the horizontal with the major axis
(at an angle of 31.8° to the horizontal and intersecting the treads at
about their mid-width and mid-thickness). The vertical load has
components parallel to the major and minor principal axes and the
resulting bending moments cause deflections about the two axes that
are inversely proportional to the respective flexural stiffnesses.
In Figure 5 are plotted the mean vertical and horizontal mid-span
deflections against the total load supported by the risers themselves, i.e.
the total applied load multiplied by 0.745 to obtain that portion carried
by the risers and thus excluding the portion supported by the top and
bottom skirts. Under uniform loading it is anticipated that all identical
riser treads would deflect the same amount. Hence, it is valid to
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consider the mean deflections, thus eliminating any deviations from
uniformity of either the riser geometry or the loading. The deflections
plotted are the net deflections of the risers with respect to the rakers.
Applied load on riser, kPa
10
8
6
4
2
0
horizontal
vertical
0 5 10 15 20 25 30
Mean midspan deflection, mm
Figure 5. Load midspan deflection curves
The load-deflection curves are linear to the maximum test value that is
slightly in excess of the factored load level. The slight irregularities in
the plots are attributed to the loading sequence where, in the load steps
with partial layers, the load is not quite uniformly distributed from top
to bottom across the width of the risers. The horizontal deflection is
about 0.53 times the vertical deflection. The maximum deflection, the
vector sum of the two components, at the maximum load is
approximately 30 mm or 1/400 of the span centre-to-centre of supports.
At the specified load level of 4.8 kPa or 100 psf, the deflection is only
17.0 mm or 1/700 of the span. Finite element analyses based on
measured geometry and nominal mechanical stiffness properties for the
elastomer and steel essentially confirm the measured deflections with
calculated deflections about 10% greater than the measured values.
This difference is considered to be due to a combination of two factors.
First, the calculated deflections are based on nominal values of the
flexural stiffnesses or EI. These are likely less than the actual values for
the heavily rolled thin steel used in the risers. Second, slight
inaccuracies in the testing carried out in the field could have occurred in
less than ideal laboratory conditions.
The prototype carried the factored load without any inelastic action. No
buckling of the very thin steel plates, supported laterally by the
elastomer to which they are bonded, occurred. The load that could be
carried at failure would be greater by that needed to take the riser cross
section to incipient yielding of the steel and is likely to be that to cause
full plastification of the cross section (other tests on flat SPS flexural
specimens have shown this to be the case). This latter load is the true
measure of the strength of the SPS riser prototype. The SPS riser
prototype is considered to have a strength considerably in excess of that
needed to carry the factored loads.
The maximum deflection at the specified load level of only 1/700 of the
span, more than meets common deflection criteria for building floors of
1/300 of the span.
DYNAMIC TESTS
To determine the dynamic properties of the SPS risers, vibrations were
induced by heel drop tests, by a person jumping from one tread to
another or even by dropping one end of the riser a few centimetres to
the floor. These tests were carried out with the risers loaded with
different numbers of layers of concrete blocks, or with people.
Observations were made as load was added to the specimen and again
as the load was reduced. The raw data were low-pass filtered, at 10 Hz,
to remove high frequency vibrations and noise that do not affect human
reaction to vibration.
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Figure 6 gives the measured fundamental natural frequency as a
function of the load carried by the risers. The natural frequency
decreases from about 6 Hz or more when unloaded to 2.7 Hz at an
applied load of 8.33 kPa. This trend follows the well-known
relationship that the natural frequency is inversely proportional to the
square root of the mass. At the specified load level of 4.8 kPa the
natural frequency is about 3.2 Hz and at the likely load level of 1.7 kPa
or 35 psf it is about 5 Hz or more.
10
9
8
7
6
5
4
Excitation by:
human movement
crane drop
Acceleration, g
0.08
0.06
0.04
0.02
0
-0.02
-0.04
-0.06
-0.08
0.03
1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
Time, seconds
(a) Jump on unloaded riser
3
2
1
0
Likely live
load, 1.7 kPa
Specified live
load, 4.8 kPa
0 1 2 3 4 5 6 7 8 9 10
Load on risers, kPa
Figure 6. Resonant frequency versus load on risers
Figures 7a and 7b show 10 Hz low-pass filtered vibration records of
acceleration versus time for two cases, one with two persons on the
risers producing a negligible load, and the other with 66 people
producing a load on the risers of 1.90 kPa. Excitation was caused by a
person jumping from one tread to another and by a heel drop
respectively. The damping ratio was calculated over a vibration decay
time period where the peak acceleration had decreased to about one
Acceleration, g
0.02
0.01
0
-0.01
-0.02
-0.03
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Time, seconds
(b) Heel drop on fully loaded riser
Figure 7. Acceleration–time curves
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tenth of the peak acceleration at the start of the time interval from the
relationship:
⎡ ⎛ y ⎤
0
⎞
⎢ln
⎜
⎟⎥
1 ⎢ ⎝ y1
⎠
β =
⎥
π ⎢ − ⎥
[1]
2 f
n
t
1
t
0
⎢ ⎥
⎢⎣
⎥⎦
where f n is the natural frequency and y 0 and y 1 are the peak
accelerations at the beginning and end of the vibration decay time
period t 1 -t 0 selected to give a value of y 0 /y 1 of approximately 10. The
damping ratio, taken as the average of that computed from the positive
and negative peaks in Figure 7 was determined to be 2.1% with the
seats unoccupied and 14.1% with the seats occupied. The value of
2.1% as compared to about 1% for bare steel or pre-stressed concrete
alternatives suggests superior performance for the SPS risers. This is
attributed to the inherent energy-absorption characteristics of the
elastomer itself. For the fully loaded stands, the “soft” mass of the
people increases the damping significantly as the damping ratio shows.
Acceleration, g
0.15
0.1
0.05
0
-0.05
-0.1
0.15
0 1 2 3 4 5
Time, seconds
(a) Excitation frequency 2.3 Hz
Figures 8(a) and 8(b) are acceleration-time records of simulated rock
concerts in which half the people sat and stamped with one foot while
the other half “jounced” in a standing position by inducing vertical
movement with forward and backward knee movements. The figures
are for two beat frequencies of 2.3 and 2.75 Hz as noted. Third and
fourth beat frequencies of 2.0 and 2.6 Hz, not reported here, gave
similar results. The peak accelerations, from all acceleration-time
records, reach 0.10 g to 0.13 g. The vibrations were clearly perceptible
to three inactive observers in the stands but were considered acceptable
by all observers for all beat frequencies. The vibrations felt similar for
all frequencies because of the high damping provided by the mass of
the spectators. The acceleration-time records show that acceleration
nearly dies out in the short time interval between excitations, such that
there is very little resonance build-up.
Acceleration, g
0.1
0.05
0
-0.05
-0.1
0 1 2 3 4 5
Time, seconds
(b) Excitation frequency 2.75 Hz
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Figure 8. Acceleration–time records of simulated rock concerts
This reduction is also seen by comparing the vibration decay time
period of approximately 0.6 seconds in Figure 7(b) with 3 seconds in
7(a). For an excitation frequency of 2.3 Hz, second harmonic resonance
build-up was expected at a frequency of 4.6 Hz, but this did not occur.
The vibration, therefore, is primarily the repeated impact responses
rather than continuous resonance vibration.
The frequency spectra in Figures 9(a) and 9(b) of the acceleration-time
records of Figures 8(a) and 8(b) respectively, show that most of the
vibration occurs at multiples (harmonics) of the beat frequency. The
broader spikes in the frequency spectrum for 2.3 Hz in Figure 9(a),
indicates that the participants were not in step and, as a result, the
vibration was more variable and less harmonic than in Figure 9(b). This
also reduced the resonance build-up that was expected to occur at the
second harmonic of 4.6 Hz.
in turn attached by springs of the requisite stiffness to the ground,
should be carried out to assess the overall dynamic performance of the
system. The effective damping ratio of the structure occupied by
people and vibrating at its natural frequency, however, would need to
be re-evaluated.
Acceleration, g
0.015
0.01
0.005
0
0 2 4 6 8 10
Frequency, Hz
In a moving “wave” test in which all persons stood up quickly, raised
their arms and then sat down, no vibrations were felt because all
persons participated and there were no passive observers.
Walking tests were conducted when there were only a few persons on
the risers when the damping was a minimum. The data for one test with
a person walking with a step frequency of 1.7 to 1.9 Hz indicated a
peak acceleration of 0.03g but was more disturbing to an observer than
the higher accelerations during the “rock concert” vibrations. However,
for a completed stadium with risers well connected to one another, the
mass to be excited would be considerably larger than for the test.
Consequently the walking acceleration would be reduced
correspondingly. This should be assessed by a finite element dynamic
analysis of a typical complete riser section.
Acceleration, g
0.03
0.02
0.01
0.00
(a) Excitation frequency 2.3 Hz
0 2 4 6 8 10
Frequency, Hz
(b) Excitation frequency 2.75 Hz
For a stadium with risers on flexible supports, dynamic analyses of riser
sections attached to a mass of the requisite weight at each support and
Figure 9. Frequency spectra
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ATTACHMENT OF SEATS
As is the case for prestressed concrete risers, the seats are attached to
the vertical face by threaded anchor rods epoxied into blind holes
drilled into the elastomer. In this case the length of embedment is
limited to the thickness of the elastomer core and one face- plate, that is
36 mm. In Figure 10 one of the two anchor rods, on the left side of the
seat as faced, is visible.
The normal configuration is that each side has two anchor rods which
are arranged horizontally for interior supports and vertically for end
supports. The anchor rods are subject to tension when the seats are
loaded and the standard test is to determine the pull-out strength of the
connection by pulling on extended threaded anchor rods. Failure occurs
when the epoxy shears off at the crests of the threads. Thus it was not
unexpected that failure loads for anchors epoxied into elastomer where
about the same as those epoxied into the same depth of concrete. Fortyfour
tests done on either pairs of anchor rods or some special tests on
single rods gave test strengths per anchor bolt ranging from 2000 to
6000 pounds with a mean of 4630 pounds and a rather large coefficient
of variation of 0.244. Taking seat dimensions of 3.5 inches from the
lower extremity to the centre line of the anchor rods in the horizontal
configuration and 19.75 inches from the lip of the seat to the riser face,
the load applied on the lip of a seat to cause pull-out of a pair of
anchors would have minimum and mean values of 700 pounds and
1640 pounds respectively. Using limit states design principles, based
on a reliability index of 3.5 and taking the nominal strength as 4500
pounds, a resistance factor of 0.62 is established to give a factored pullout
resistance per rod of 2800 pounds. The specified load per seat,
applied at the lip, using a live load factor of 1.6, is thus 620 pounds or
several times the weight of a large man, more than ample to allow for
the dynamic effect of a person stepping down from one row to another.
SUMMARY
Figure 10. Seat attachment to vertical face of riser
In the static tests, the prototype displayed considerably more strength
than required as exemplified by the linearly elastic behaviour to slightly
above the factored load level. No buckling of the thin steel faceplates,
which are supported laterally by the elastomer, occurred. There is
reserve strength beyond this that could be considerable, but was not
determined in the field tests where testing procedures were limited.
Further inelastic finite element analyses are planned. The mid-span
deflection at the full specified load level of 4.8 kPa or 100 psf was a
meagre 1/700 of the span as compared with a deflection limit of 1/300
commonly specified for building floors.
The observed dynamic performance was very good as compared to that
expected of all-steel or pre-stressed concrete alternatives. The natural
frequency of the risers with a. span of 40 feet on stiff supports,
decreases with increasing load from a value of 6 Hz or more when
unloaded to approximately 5 Hz at the likely live load of 1.7 kPa and
just over 3 Hz at the full specified load level of 4.8 kPa. The damping
9

atio was established at about 2% of critical for the bare stands and
about 14% when fully occupied. The damping ratio for the bare stands
compares favourably with that of about 1% for steel or prestressed
concrete structures of like span. The soft mass of spectators increases
the damping ratio considerably.
basis, some further weight savings may be achieved while still meeting
the required strength and dynamic performance. Both the static and
dynamic performance are considered more than acceptable and at least
comparable to that of all-steel or precast concrete alternatives. Seats can
be anchored adequately by epoxy to the vertical riser face.
In simulated rock concerts it was not possible to induce resonance
build-up because the induced vibrations nearly died out between
impacts due to high damping provided by the occupants. The vibration
therefore, is primarily the repeated impact responses rather than
continuous resonance vibration. The vibrations were clearly perceptible
to three inactive observers in the stands but were considered acceptable
by all observers at the simulated rock concert for all beat frequencies.
Walking tests on the bare stands when the damping was a minimum
indicated a peak acceleration of 0.03g and was more disturbing to an
observer than the “rock concert” vibrations. However, risers well
connected to one another in a completed stadium would have
considerably reduced accelerations because of the increased mass to be
accelerated.. This could be assessed by a finite element dynamic
analysis of a typical complete riser section.
ACKNOWLEDGEMENTS
The risers were fabricated by CANAM-MANAC Group, Inc in St.
Georges QC, Canada and the elastomer injected there by BASF Corp,
Livonia MI, USA. The dynamic measurements were made by Daniel
Francke of BASF Ludwigshafen, Germany. David Allen was
responsible overall for the dynamic testing, supervised the testing,
provided advice and interpreted the test results. The assistance of all
participants is gratefully acknowledged.
For a stadium with risers on flexible supports, dynamic analyses of riser
sections attached to a mass of the requisite weight at each support and
in turn attached by springs of the requisite stiffness to the ground,
should be carried out to assess the overall dynamic performance of the
system. This, however, would require a re-evaluation of the effective
damping ratio of the occupied structure vibrating at its natural
frequencies.
The 4-32-4 SPS prototype riser as tested provides a viable lightweight
alternative to pre-stressed concrete risers weighing, including the fixed
seats, only 39.2 psf or about 30% of the latter. In a production line
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