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Visvesvaraya Technological University Regional Center
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B.Tech
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VTU EDUSAT Programme 16
Lecture Notes
Elasticity, Shrinkage and Creep
Concrete Technology – 10 CV 42
(Common to CV/TR/CT)
Subject Expert
Dr. M. C. Natarara
Professor, Civil Engineering Department,
Sri Jayachamarajendra College of Engineering,
Mysore - 570 006
Contact: 9880 447742 / 0821 2343521
nataraja96@yahoo.com

Here the following three main types of deformations in hardened concrete subjected to
external load and environment are discussed.
Elastic strains
These are the instantaneous deformations that occur when an external stress is first
applied
Shrinkage strains
These deformations occur either on loss of moisture from the concrete on cooling of
concrete
Creep
It is the time-dependent deformation that occurs on the prolonged application of
stress
Deformation Effect
Any one or combinations of the above types of deformations in a hardened concrete
leads to cracking.
1. Elastic Strains
Elastic strain in concrete, as defined above, depends on the externally applied stress and
the modulus of elasticity of concrete:
Elastic strain
= Externally applied stress/Modulus of elasticity of concrete
Modulus of Elasticity of Concrete
Typical Stress-Strain Plot of Concrete
(1) At stress below 30% of ultimate strength, the transition zone cracks remain stable. The
stress-strain plot remains linear.
(2) At stress between 30% and 50% of ultimate strength, the transition zone microcracks
begin to increase in length, width and numbers. The stress-strain plot becomes non-linear.
(3) At 50 to 60% of the ultimate stress, cracks begin to form in the matrix. With further
increase to about 75% of the ultimate stress, the cracks in the transition become unstable,
and crack propagation in the matrix will increase. The stress-strain curve bends towards
the horizontal.
(4) At 75 to 80% of the ultimate stress, the stress reaches a critical stress level for
spontaneous crack growth under a sustained stress. Cracks propagate rapidly in both the
matrix and the transition zone. Failure occurs when the cracks join together and become
continuous.
2

•
Concrete is not a truly elastic material, as evident from the nonlinear stress-strain
curve for concrete, shown in the following Fig.:
fo
Stress
ff
ε0
εu
Strain
•
Since the stress-strain curve for concrete is nonlinear, following methods for
computing the modulus of elasticity of concrete are used yielding various types of
modulus of elasticity for concrete:
1. The “initial tangent modulus”
It is given by the slope of a line drawn tangent to the stress-strain curve at the
origin
2. The “tangent modulus”
It is given by the slope of a line drawn tangent to the stress-strain curve at any
point on the curve
3. The “secant modulus”
It is given by the slope of a line drawn from the origin to a point on the curve
corresponding to a 40% stress of the failure stress
4. The “chord modulus”
It is given by the slope of a line drawn between two points on the stress-strain
curve
Calculation of the above four types of moduli of elasticity for concrete has been
explained below using a typical stress-strain curve, as shown in the following Fig.:
Initial tangent
fo
Tangent
IT
ff
Stress
•
Chord
Secant
ε0
3
Strain
εu

•
Modulus of elasticity for concrete determined from an experimental stress-strain
relation curve, as described above, is generally termed as static modulus of
elasticity (Ec) whereas the modulus of elasticity determined through the
longitudinal vibration test is termed as dynamic modulus of elasticity (Ed)
Static modulus of elasticity (Ec)for concrete
•
Static modulus of elasticity of concrete has been related to its compressive
strength by the various Standards
Relationship between modulus of elasticity of concrete and compressive strength
•
BS 8110:Part 2:1985 has recommended the following expression for 28-day Ec in
terms of 28-day cube compressive strength (fcu), for normal weight concrete (i.e.
concrete with density, ρ ≈ 2400 kg/m3):
Ec28 = 20 + 0.2 fcu28 (where Ec28 is in GPa and fcu28 is in MPa)
Note: For lightweight concrete the above values of Ec28 should be multiplied by
the factors (ρ/2400)2 and (ρ/150)2 respectively.
•
ACI Building Code 318-89 recommends the following expression for (Ec) in terms
of cylinder compressive strength (fcyl), for normal weight concrete (i.e. concrete
with density, ρ ≈ 2400 kg/m3):
Ec = 4.7 (fcyl)0.5 (where Ec is in GPa and fcyl is in MPa)
Ec, 28 = 9.1fcu0.33 - for normal weight concrete of density = 2400 kg/m3,
and
Ec, 28= 1.7ρ2 fcu0.33 x10-6 for lightweight concrete - (ρ) =1400–2400 kg/m3
•
CEB - FIP Model Code (Euro-International)
E = 2.15 X 104 (fcm/10)1/3, E in MPa and fcm in MPa.
Static modulus of elasticity (Ed) for concrete
•
Experimental stress-strain relation curve, as described above, is generally termed
as static modulus of elasticity (Ec) and is short term modulus.
• If creep effect is considered at a given load, the modulus determined is referred to
as long term modulus of elasticity.
ELong = EShort/(1+θ),
4

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