Experimental determination of the dynamic Modulus of Elasticity of
masonry units
J.M. Nichols
Department of Civil, Surveying and Environmental Engineering, University of Newcastle,
Callaghan, NSW, Australia.
Y.Z. Totoev
Department of Civil, Surveying and Environmental Engineering, University of Newcastle,
Callaghan, NSW, Australia
ABSTRACT: One of the parameters that has been identified as influencing the structural response of buildings is the dynamic Modulus of Elasticity of masonry units. The first aim of this
paper is to experimentally investigate the use of high frequency sinusoidal loading to determine
the dynamic Modulus of Elasticity of masonry units. The Longitudinal Vibration and the Ultrasonic Pulse methods were originally developed for the dynamic testing of concrete specimens.
These testing procedures are appropriate as each applies only a minimum stress to the masonry
units. This procedure provides results for the masonry units within the elastic range. The second
aim is to compare the dynamic Modulus of Elasticity results to the Modulus of Elasticity obtained
using quasi- static methods from the same population of masonry units. A test rig has been developed for measuring the elastic properties of masonry units under uniaxial loading.
1 INTRODUCTION
Seismicity within Australian is now recognized as a design issue, as a result of several major
earthquakes within the last 40 years in NSW, SA and WA. One of the common building materials used over the last century in Australia is masonry. There has been a growth in the use of
unreinforced masonry(URM) in the last 50 years, particularly in light commercial, housing and as
infill panels to steel and concrete framed buildings. These types of buildings can pose a significant hazard during seismic events. The main reasons for this performance problem are the relative mass to strength ratio, ductility issues and poor workmanship (Melchers & Page,1992). Unreinforced masonry can however under some circumstances withstand an interplate earthquake
and perform well within its design limitations, when constructed to accepted sta ndards.(TenaColunga & Abrams, 1992). A reasonable proportion of the larger masonry buildings and dwellings built within in Australia and elsewhere in intraplate regions would have been designed on the
basis of static loading design rules and assuming zero or low seismic loads. The design of buildings within Australian must now consider the minimum loading from the Australian Standard(AS)
Earthquake Loading Code (AS 1170.4) using either an equivalent static loading, frequency domain or time domain analysis. Material properties are required for these methods of analysis,
irrespective of the numerical method.
The first objective of this paper is to experimentally determine the dynamic Modulus of Elasticity for masonry units using two non-destructive techniques. The second objective is to measure the Young’s Modulus and Poisson’s Ratio using quasi-static methods. The third objective is
to compare the quasi-static and dynamic results. The dynamic results are based on the assumption that Poisson’s Ratio is invariant and can be measured using the quasi-static procedures.
1
Three pressed clay bricks designated by colour (red, brown, biscuit), one calcium silicate and one
concrete brick were used in the experimental work.
2 BACKGROUND
Young’s Modulus is an intrinsic property constant for a material. It can be estimated using the
15 to 85 % stress levels in the elastic range from a quasi- static test procedure on a previously
untested population sample (Krajcinovic 1996, LeMaitre 1992). Hookes’ law is defined as :
σ= E ε
(1)
where σ defines the stress (MPa), ε is defined by the natural (rather than the engineering) strain
formula (Strains) and E is Young’s Modulus (MPa). Young’s Modulus and Poisson’s Ratio
have been previously measured for a number of Australian brick types. These results were
within the range of 7,000 to 12,000 MPa and 0.12 to 0.29 respectively (Dhanasekar 1985).
Two distinct failure mechanisms can be identified for a “macroscopically homogeneous body
of brittle material”. The failure mechanism of the first kind is “quasi-static or stress wave loading of low intensity” when a single failure plane predominates activated by a “flaw in the material being stressed to a critical condition”. The failure mechanism of the second kind for masonry
or dynamic failure mode occurs “during impulsive loading where multiple fractures on different
planes can be nucleated and they grow to a significant size without arresting each other.” Ceramics and other brittle material have been shown to have a greater fracture resistance to loading that causes the failure mechanism of the second kind (Freund, 1990).
These distinct mechanisms have been observed in masonry testing (Tercelj et.al,1969, Klopp
1996). The first or quasi-static mechanism is the basis for the development of key static masonry
design rules (Page, 1979). The results form part of the dynamic test program on masonry panels
being undertaken at Newcastle. This research on the two failure mechanisms would suggest
that at an equivalent time the following inequality holds, (where ~ denotes dynamic and - denotes
static Modulus of Elasticity):
~
Et ≥ Et
(2)
This qualitative observation can be attributed of Tercelj et.al.,(1969). The dynamic Modulus of
Elasticity can be determined from Equation (3) for the Longitudinal Dynamic Test Method
(LDTM) and from Equation (4) for the Ultrasonic Pulse Method (UPM). The LDTM uses a
small audio striker to provide pulses along the longitudonal axis of the brick. The UPM uses the
measurement of the travel time of ultrasonic pulses in the transverse and longitudonal axes.
f =
~
E
2
4L ρ
(3)
V=
~
E
(1 − υ)
ρ (1+ υ )(1 − 2υ)
(4)
where f (Hz) is the fundamental natural frequency, L (m) is the length of the specimen,
ρ (kg/m3) is the density, V (m/s) is the pulse velocity and υ is Poisson’s Ratio.
The ultrasonic pulse method can be used to determine if the masonry unit samples show any
pattern of anisotrophy, such as may be exhibited as a result of the process of manufacture.
2
3 EXPERIMENTAL METHOD
The LVTM uses a dynamic test rig that is a modified version of the Electrodynamic’s Standard Material Tester EMFCO SCT/5 (EMFCO, n.d.) This test rig is noted in the specification
as to complying with British Standard (BS) 1881: 52 ( Longitudinal Vibration ). Specimens were
saw-cut from a standard range of bricks supplied by local manufacturers. Each specimen was
microwave dried and then tested in the rig. Each was then allowed to stabilize at room temperature before being retested. A Tektronix Function Generator FG501 with controlled frequency
was used to generate the applied sinusoidal loading function. This signal was amplified using a
Peavey Electronics Corp. XR400 Amplifier to feed the 3 Ohm coil on the test rig. Each specimen was clamped on the test rig using an 11 mm rad. jaw clamp at the midpoint of the cut brick.
A piezoelectric crystal pick-up detects the signal which was monitored on an Tektronix Oscilloscope 7603 for peak amplitude. The frequencies used were in the range from 5 to 9 kHz. A
schematic arrangement of the equipment is shown in Figure 1.
Figure 1 Layout of the dynamic test rig for the Longitudonal Vibration Test Procedure.
The second dynamic method UPM uses a standard measurement system. This method uses
the CNS Portable Ultrasonic non destructive tester (CNS 1978). A calibrating specimen is provided with the rig. Testing was at 50 kHz about the longitudonal and transverse axes of the
specimen. A schematic arrangement of the Ultrasonic Puls Method is shown in Figure 2.
Figure 2 Layout of the dynamic test rig for the Ultrasonic Puls Test Procedure
3
The quasi- static Test Method uses uniaxial compression applied to the smaller end faces of the
brick samples with a Tinius Ols en 1800 kN Universal Testing Machine(UTM). A pressure cell
in the UTM generates an analog output signal. Initially this signal was converted to a digital signal using a Gedge Systems(Aus) GS1650P Peak Indicator . The analog to digital signal generator proved to be too coarse (± 2.5kN) for this testing and caused a substantial component of the
error in the measurement. Final testing had the analog signal being fed directly into the data logger. Calibration of the signal was undertaken using the UTM dial scale.
Each brick was tested for Young’s Modulus about the longest axis to provide a reasonable
gauge length for the measurements, to protect the Linear Velocity Displacement Transducers
(LVDTs) and to partially negate end effects. The test method was based on the relevant Australian Standard for testing masonry units. Bricks were immersed for a minimum of two hours
before being tested, except for the few that were used in both the dynamic and quasi- static testing. Plywood capping was used between the solid platens and the brick.
A rectangular test rig capable of measuring the relative displacements about two axes was
designed to provide a repeatable measurement protocol. The rig is similar to the standard cylindrical concrete test rig, except that it is modified to measure Poisson’s Ratio. Vertical or longitudinal displacement was measured using two LVDTs Type RDP Electronics D2-200A. These
have a total movement of 11 mm. Horizontal displacement was measured using two LVDTs
Type Solartron DFG 5.0. These have a total movement of 12 mm. Each of the LVDTs was
calibrated using a Mitutoyo gauge with a range of 0 - 25 ± 0.005 mm and the sensitivity tested
using a Mitutoyo gauge with range of 0 - 1 ± 0.0002 mm. . The vertical gauge length was 100
mm and the horizontal gauge length was 90 mm. The final test protocol measured both displacements at the same time.
Signals were fed into a Data Electronics Datataker 600. The signals were logged and converted to an ASCII format using DASYLab 3. The results were analysed using a regression
macro written for MINITAB 10.2.
4 RESULTS
These series of experiments were undertaken to determine the Young’s Modulus, Poisson’s
Ratio and dynamic Modulus of Elasticity of masonry units. Five masonry units were tested,
three pressed clay bricks, a concrete and a calcium silicate bricks. All bricks were of local State
manufacture and the three pressed bricks were tagged by colour red, brown and biscuit.
Young’s Modulus and Poisson’s Ratio were measured using the quasi-static test method. The
test results are based on the gross area of the cross section of each unit. No allowance has
been made for the frog. The quasi-static test results for each set of the five brick types are
shown in Table 1.
Table 1. Young’s Modulus, Poisson’s Ratio and typical dimensions for the five brick types.
Brick Type
Number Tested
Pressed Clay Red
Pressed Clay Biscuit
Pressed Clay Brown
Calcium Silicate
Concrete
6
4
5
3
4
Young’s
Modulus
MPa
14,000
10,000
7,000
6,000
14,000
Poisson’s Ratio
0.22
0.29
0.21
0.17
0.33
Length : Width
:Depth
mm
226:111:75
230:110:76
227:108:74
229:108:78
232:109:77
The range of Young’s Modulus was from 1 GPa for a pressed clay red brick to 56 GPa for a
concrete brick. The stress-strain curves in compression were generally linearly elastic over the
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range used to measure Young’s Modulus(15 to 85 % of the peak stress), with a regression coefficient of R 2 ~ 0.95 being a typical value.
A few of the pressed bricks exhibited stress-strain curves that would suggest that there is a
variation of density within the brick. This variation can probably be attributed to the compaction
associated with the creation of the frog. Initial results would point to a greater material density
on the frog side of the brick. The non-symmetric shape of the pressed brick requires the use of
averaged results between the two sets of displacement for the measurement of Young’s
Modulus for some bricks. Poisson’s Ratio results ranged from 0.1 to 0.4.
The specimens used for the Longitudinal Vibration Test Method were cut from full bricks.
Three different specimen sizes were used in the experiments . Typical dimensions for each of
the specimen sizes, presented as Length (mm),:Cross Sectional area (mm2 ) and the density
(kg/m 3 ) are presented in Table 2.
Table 2. Typical Brick Properties for the specimens for the Longitudinal Vibration Test Method.
Brick Type
Pressed Clay Red
Pressed Clay Biscuit
Pressed Clay
Brown
Calcium Silicate
Concret e
Description
Specimen Type 1
Specimen Type 2
Specimen Type 3
Typical Length mm
Typical Cross
section area mm 2
3
Density kg/m
Density
180
1100
200
1 8 0 0-2020
230
2250-2 5 0 0
2170
2220
2070
2230
2320
2270
Density
2130
2180
2130
Density
Density
1810
2010
1740
2100
1760
2190
Three full size brick specimens for each of the five brick types were tested using the Ultrasonic
Pulse Method. The Longitudinal Vibration Test Method uses Equation (4) and the results of the
frequency measurements, the dimensions and the density results. The Ultrasonic Pulse Method
uses Equation (5), Poisson’s ratio from the quasi-static testing, the transit time results, the dimensions and the density results. The results for the quasi-static and dynamic testing are shown in
Figure 3. The calcium silicate and the concrete bricks exhibit isotropic behaviour in the Longitudonal Vibration Test as can be seen in Figure 3. The remaining bricks exhibit slight anistrophy
probably attributable to the method of manufacture.
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Figure 3 Modulus of Elasticity Results for the three different test procedures.
5 CONCLUSION
This study was designed to compare the quasi-statically measured Young’s Modulus to the dynamically measured Modulus of Elasticity. The work forms part of a research program into the
response of masonry panels subjected to seismic frequency and intensity of loading. The quantification of the Young’s Modulus and Poisson’s Ratio was made with three test methods. The
first method was quasi- statically in a Universal testing Machine and the second two methods
were variations on standard techniques used extensively in concrete research. A set of protocols and a test rig were developed to quasi-statically measure the Young’s Modulus of masonry
units. This test rig is based on the rig used to test concrete cylindrical specimens.
Two dynamic methods are used to measure the Modulus of Elasticity of concrete cylindrical
specimens. These two methods are the Longitudonal Vibration and Ultrasonic Pulse Velocity
Test Methods. The limitation for these procedures is the frequency dependence of the results.
The results for the quasi-static measurement of the Young’s Modulus and Poisson’s ratio for
the masonry units is presented in Table 1. The results for the dynamic measurement of the
Modulus of Elasticity for the two dynamic methods are shown on Figure 3. These results are
within the range of Young’s Modulus normally expected for these types of masonry units.
Dynamic measurement of the Modulus of Elasticity is a practicable alternative to quasi-static
destructive testing for clay masonry units. There is no evidence of frequency dependence for
the clay masonry units within the range of frequencies available with these two methods. There
appears to be a strong frequency dependence for the sand based masonry units.
Testing is required using many specimens to quantify the relationship. The frequency de pendence of the stiffness of masonry walls was noted by others at lower frequencies than used with
these two test methods. Further research is suggested on masonry units in the non elastic range.
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