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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 5
Influence of the type of measuring device in determininging the static modulus of elasticity of concrete
1. Introduction
The use of the modulus of elasticity is frequently related to dis-
placement and deflection calculations in the design phase of a
reinforced concrete structure. The structural engineer specifies a
value for the modulus of elasticity of the concrete which he uses in
his calculations to satisfy serviceability limit states. This value for
the modulus of elasticity will be later verified during the construc-
tion phase by the construction engineer or the concrete contractor.
An incorrect verification of the modulus of elasticity can have seri-
ous consequences for the structural design, for example, exces-
sive deflections not foreseen during the design phase.
Several factors can influence the value of the concrete’s modulus of
elasticity [8,10,14] such as concrete compressive strength, concrete
specimen casting process, loading and unloading speed of the test-
ing apparatus, mortar content, type of strain measurement device,
aggregate type and size, testing machine operator, concrete speci-
men size. This research had the objective to study and evaluate the
influence of some of these variables on the static modulus of elastic-
ity: influence of measurement device (dial or digital indicator, surface
mounted strain gages, externally fixed strain gages or clip gages,
linear variable differential transformer – LVDT), concrete type (Class
C30 and Class C60) and cylindrical specimen size (100 mm x 200
mm e 150 mm x 300 mm). Tests were conducted in two different
concrete laboratories in the Goiânia, GO region.
The modulus of elasticity can be defined as a relation between the
applied stress and the measured strain below yield stress. Accord-
ing to code ABNT NBR8522:2008 [3], the static modulus of elastic-
ity for a concrete loaded in axial compression is determined by the
inclination of the stress-strain curve obtained in testing cylindrical
concrete specimens. The specimen is subjected to incrementally
increasing loads and the strain is measured at each load incre-
ment. The types of modulus of elasticity are related to different
loading stages and should be chosen based on the purpose of the
test. Figure 1 shows the different types of static modulus of elastic-
ity in concrete subjected to compression.
Briefly, the moduli of elasticity are:
n
Initial tangent modulus: is given by the inclination of a tangent
line at the origin of the stress-strain diagram. It is used to char-
acterize concrete deflections at very low stresses.
n
Tangent modulus at a given stress: is the inclination of a tan-
gent line of the stress-strain diagram at any given stress. It is
used to simulate the structure to loading or unloading at differ-
ent loading stages. Loading and unloading can be applicable,
for example, when a numerical structural analysis is needed
due to large accidental loads.
n
Secant modulus: is given by the inclination of a secant line
obtained between any two points in the stress-strain dia-
gram. Frequently the points chosen correspond to a stress of
0.5MPa and a stress at 50% of the ultimate stress. In this case,
it simulates the structure during its initial loading stage when
permanent loads prevail. The Brazilian Code for Design and
Execution of Reinforced Concrete Constructions ABNT NBR
6118:2003 [4] proposes a value for the secant modulus as 85%
of the initial tangent modulus. The secant modulus is frequently
used by structural engineers in design.
In this work, the initial tangent modulus of elasticity was deter-
mined. It was done according to code ABNT NBR 8522:2008 [3]
which prescribes, in this case, concrete strains at stress levels of
0.5 MPa and 30% of ultimate stress. This code prescribes an initial
stress of 0.5 MPa, and not a zero value, to minimize the effect
of specimen imperfections, testing machine variability and the ac-
commodation process of the top and bottom plates of the testing
machine, since these factors can generate in initial disturbance in
the stress-strain diagram near zero stress.
The value of the initial tangent modulus of elasticity, E
ci
, is given by
the equation below:
(1)
E
ci
= (
σ
b
- σ
a
) / (
ε
b
- ε
a
)
where:
σ
b
is the higher stress and it is equal to 0.3 of the rupture stress;
σ
a
is the basic stress and is equal to 0.5 MPa;
ε
b
is the average strain of the specimen under the higher stress;
ε
a
is the average strain of the specimen under the basic stress;
Contrary to strain measurements in steel rebars, strain measure-
ments in concrete are much harder to obtain. In steel, strain measur-
ing devices known as strain gages are widely used and give good
quality and reliable results. But in concrete, the same does not hap-
pen and several researchers [6,7,8,9] and laboratories in Brazil and
worldwide have search for other alternatives to obtain reliable strain
measures with less statistical variability. Among these alternatives
for measuring strains in concrete, the present research work verified
the use of four different measuring devices [15,16]: dial indicator,
surface bonded strain gages, externally fixed strain gages or clip
gages, linear variable differential transformer – LVDT.
The digital or dial indicator is a mechanical measuring device
where a small piston moves indicating the measurement. Both the
strain gage and the clip gage work based on the same principle of
changes in the electrical resistance of a coil during the deformation
of the body to which they are attached. The difference is that the
strain gage is bonded (glued) to the body surface and the clip gage
Figure 1 – Different types of modulus
of elasticity in the stress-strain curve