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Behaviour of Glass Plates Under Pressure Loading

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1
BEHAVIOUR OF GLASS PLATES UNDER PRESSURE LOADING Eri Iizumi
, Gregory A. Kopp
†
∗
Department of Civil and Environmental Engineering, The University of Western Ontario, London, Ontario, N6A 5B9, Canada, +1-519-661-2111 ext 88144 e-mail:
ei i zumi @uwo. ca
†
Boundary Layer Wind Tunnel Labratory, The University of Western Ontario, London, Ontario, N6A 5B9, Canada, +1-519-661-3338 e-mail:
gak@bl wtl . uwo. ca
Abstract:
Glass plate breakage tests under the realistic wind pressure loading, which have not been done anywhere else, are studied, a part of which are presented in this paper. Test results are reported with results of numerical simulation based on the fracture mechanics.
1
INTRODUCTION
During strong windstorms (e.g., hurricanes), various cladding materials are often damaged. Damage to windows and glazing has generally been outstanding in both residential structures and high-rise buildings. Although windborne debris has been considered as a significant factor of window damage [1], there is a potential of window glass breakage due to fluctuating wind pressures as well. Whereas full-scale glass plate breakage tests have been conducted by several researchers ([2], [3]), the applied loads were ramp loading, step-up loading (hold the pressure for a certain time and linearly increase the pressure) and step-up cyclic loading. These loading do not accurately simulate real wind loading, which changes temporally because of turbulence. This has been mainly because of the limited technology and long experimental time. In the current glass design in North America, the glass failure prediction model (GFPM) developed by Beason [4] is being utilized. This uses two interdependent surface flaw parameters,
m
~and
k
~, which are determined by testing for each geometric shape in quite a complex approach. In addition, several faults in this method have been brought up by other researchers ([3], [5]). The primary purpose of the present study is to investigate the glass plate behavior under realistic, fluctuating wind loads, simulating windstorms. In order to understand glass plate behavior, preliminary tests with rather simple loading, ramp loading and saw-tooth loading, have been conducted in advance of fluctuating wind load. This paper presents the results of these preliminary tests, and the comparison of the test and numerical simulation results based on fracture mechanics. Full-scale glass breakage tests are conducted with an application of a sophisticated loading device, Pressure Loading Actuator (PLA), developed for the “Three Little Pigs” Project [6] at the University of Western Ontario (UWO).
2
REVIEW OF PREVIOUS WORK
The reduction of glass plate strength has been evaluated based on the concept of damage accumulation since failure does not always occur at the maximum nominal stresses under constant or variable loads of a certain time duration. This is different from many other materials. Brown [7] expressed the cumulative effect of loading on glass plate as
[ ]
=
∫
f
t n
t
0
)(
σ
const
(1)
2
where
f
t
is the time over which the glass is stressed, )(
t
σ
is the variation of stress at the critical flaw location with time, and
n
is a constant. This is called Load Duration Theory. This theory has been validated by glass plate breakage tests under static and cyclic loading, and utilized by many researchers for evaluation of the reduction of glass plate strength. Besides Brown’s method based on the Load Duration Theory, there are two well-known glass failure models. One is the Crack Growth Model by Evans and Wiederhorn [8] which is based on crack propagation controlled fracture to predict component lifetimes after proof testing. The other is the GFPM suggested by Beason [4], which uses the finite different method and is recognized as the state-of-the-art in North America. Fisher-Cripps and Collins [9] investigated all these models and concluded that none of the models can predict the failure probabilities for both short and long term stresses. In Japan, Kawabata [3] conducted numerical simulation developed by Simiu [10] and verified it by comparing the results of full-scale glass plate breakage tests. In Simiu’s simulation, fracture mechanics were utilized and the probability of glass strength was assumed to follow the Weibul distribution.
3
FINITE ELEMENT ANALYSIS
Finite element analysis on glass plates under uniform pressure is necessary to obtain input stress data used in the numerical simulation as well as for confirmation of the simply-support condition of the experimental rig. This analysis was performed using commercial software SAP 2000. Since the deflection of the glass plate becomes much larger than the thickness of the plate, this needs to be treated using non-linear plate analysis. As validation of the use of SAP 2000, the FEA results (stress and deflection) were compared with those calculated using Seaman’s theoretical equation [11] and those obtained by Fisher-Cripps and Collins [9] in Table 1. The calculation was made for the case of )(004.011
m
××
glass plate under the uniform pressure of
kPa
2.2. Material properties used in the calculation were assumed as
( )
GPa E
54.71
=
, .23.0
=
ν
Considering the uncertainty in material properties, these data correspond well, and the use of SAP 2000 is deemed adequate for this analysis.
Table 1: Comparison in stress and deflection
deflection (mm)centermaxcenter non-linear(-)24.0711.1FEAlinear37.537.522.0FEAnon-linear17.320.810.5FEAlinear37.437.422.2FEAnon-linear17.922.7510.5Presentstress (MPa)Seaman's equation [11]Fisher-Cripps & Collins [9]
4
FULL SCALE TESTING 4.1
Pressure Loading Actuator (PLA)
The PLA, which can replicate real, full-scale, temporally-varying wind pressures, was employed to apply both static and dynamic wind loads. This device uses an advanced, adaptive control system to replicate target pressure time histories. For details, refer to [6].
3
4.2
Pressure box
The glass specimen is mounted on a pressure box ()(16.07.12
m
××
) made from steel. On the front face of this box, a plywood panel is fastened with several bolts, and the glass specimen is placed on the plywood panel with aluminum frames. The glass specimen is supported by rubber tubes in order to create the simply-support condition. The hose from the PLA is connected to the pressure box, and positive and negative (suction) pressures are applied inside the pressure box. Note only negative pressures were applied in the current tests for safety reasons. All the broken glass pieces cannot be sucked into the Pressure Box and some of them are reflected at the back side of the Pressure Box and come out in front. For this reason, the Pressure Box was covered by the Safety Guard (three layers tarp, Figure 1(b)).
PLA
PLAPressure boxGlass plateSafety Guard
(a) Set up without Safety Guard(b) Set up with Safety Guard
Screen
PLA
PLAPressure boxGlass plateSafety Guard
Safety Guard
(a) Set up without Safety Guard(b) Set up with Safety Guard
Screen
Figure 1: Test set up
5
GLASS FAILURE PREDICTION SIMULATION
The numerical simulation conducted by Kawabata [3] was replicated and its results were compared with full-scale test results. The failure is defined as the shortest time until the nominal stress of the crack on glass panel )(
t
n
σ
becomes larger than the glass strength)(
t S
: )()(
t S t
n
≥
σ
(2) The time varying glass strength )(
t S
is expressed as [3]
2102212
)(22)(
−−−
⎥⎥⎦⎤⎢⎢⎣⎡ −−=
∫
nt nnn IC ni
f
dt t K Y A
nS t S
σ
(3) where
i
S
is the initial glass strength induced by the Monte Carlo simulation with concentric ring-on-ring tests results,
IC
K Y An
,,),16(
1
=
are coefficients and
f
t
is the failure time. Note that this simulation has been verified only with ramp loading full-scale test results by Kawabata.
6
RESULTS AND DISCUSSION
In all the testing shown in this paper, single annealed glass plates of size )(006.011
m
××
were utilized. A minimum of fifteen glass plates were broken in each test configuration in order to have statistically significant data. After breaking fifteen glass plates, the data were analyzed and
4
additional trials were conducted if the results were skewed. Although the applied pressures were negative (suction), the pressures described below are positive.
6.1 RAMP LOADING TEST
Two different rates of ramp loading (16.4sec
Pa
, 6.5sec
kPa
) were conducted. The first ramp rate was chosen to compare with the results as Kawabata to ensure the appropriateness of the experimental rig. The second ramp rate was chosen in order to break within a short time, considering the limitations of the PLAs. Figure 2 shows the comparison of failure pressure test data on the same glass geometry and same loading test by Kawabata. In the figure, “
F
” stands for the failure probability. Both test results are fit to Weibul distributions, which is generally regarded as the best model for failure pressure. Although the number of trials was small in the present test, the data corresponded quite well, implying that the present test data and the testing setup are appropriate. Figure 3 shows the probability density function of failure pressure approximated by a Weibul distribution. The variations of the both test results are small (the standard deviations of both test results are 1.92 and 2.81, respectively). Based on these results, it is concluded that the test results are statistically appropriate.
00.050.10.150.20.25051015202530P
f
(kPa) P
f
:failure pressure (kPa)
P D F
16.4Pa/sec_estimate16.4Pa/sec_test6.5Pa/sec_estimate6.5Pa/sec_test
-4-3-2-10121.522.53ln(P
f
) P
f
:failure pressure (kPa)
l n ( - l n ( 1 - F ) )
Kawabata resultPresent result
Figure 2: Comparison with Kawabata resultsFigure 3: PDF of failure pressure
00.050.10.150.20.25051015202530P
f
(kPa) P
f
:failure pressure (kPa)
P D F
16.4Pa/sec_estimate16.4Pa/sec_test6.5Pa/sec_estimate6.5Pa/sec_test
-4-3-2-10121.522.53ln(P
f
) P
f
:failure pressure (kPa)
l n ( - l n ( 1 - F ) )
Kawabata resultPresent result
Figure 2: Comparison with Kawabata resultsFigure 3: PDF of failure pressure
The two ramp loading cases were replicated in the numerical simulations. The comparison with test results is shown in Figure 4. The simulation results for both failure pressure and failure time correspond well with test results.
-8-7-6-5-4-3-2-101235.566.57ln(t
f
) t
f
:failure time (sec)
l n ( - l n ( 1 - F ) )
simulationtest-8-7-6-5-4-3-2-1012311.522.53ln(P
f
) P
f
:failure pressure (kPa)
l n ( - l n ( 1 - F ) )
simulationtest
(a) Failure pressure(b) Failure time
-8-7-6-5-4-3-2-101235.566.57ln(t
f
) t
f
:failure time (sec)
l n ( - l n ( 1 - F ) )
simulationtest-8-7-6-5-4-3-2-1012311.522.53ln(P
f
) P
f
:failure pressure (kPa)
l n ( - l n ( 1 - F ) )
simulationtest
(a) Failure pressure(b) Failure time
Figure 4: Comparison between test results and simulation results (ramp loading 16.4Pa/sec)

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