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7/2 Elasticity, shrinkage, creep and thermal movement

under a sustained load. Since that time, there have been many hundreds of research
publications and design documents, dealing with the subject, such as ACI (1973), BS
1881: Part 2 (1985), CEB-FIP (1990) and RILEM (1995).

When concrete is subjected to external stress, there is an initial (elastic) strain followed
by a slow time-dependent increase in strain (creep). There can be other time-dependent
moisture movement strains that are not associated with external stress. For example,
drying shrinkage occurs in most structural elements stored at usual temperature and
relative humidity. To calculate the deformation and deflection of structural members in
order to check their serviceability, we need to know the relation between stress and strain.
Too much long-term deflection or cracking due to induced tensile stress should be avoided
in order to provide adequate durability.

Although this chapter concentrates on creep and drying shrinkage, there are other
types of movement that contribute to the total deformation or stress induced by restraint
to movement. Thermal movement can be significant on a daily as well as a seasonal basis.
It is equal to the product of the coefficient of thermal expansion (approx. 10 × 10–6 per
°C) and the change in temperature in °C. Autogenous shrinkage is small for normal
strength concrete but not for high-strength or high-performance concrete. Swelling occurs
for saturated concrete and can be significant for lightweight concrete.

7.3 Elasticity

The definition of pure elasticity is that strains appear and disappear immediately on
application and removal of load. Examples of materials behaving in that manner are steel
(linear) and timber (non-linear). Other materials behave in a non-elastic manner, e.g.
glass (linear) and concrete (non-linear). It should be emphasized the concrete only behaves
that way when it is young or loaded for the first time; as seen in Figure 7.1, there are
possible ways of obtaining a modulus of elasticity. The shape of the stress–strain curve
depends to some extent on the rate of application of stress, application of load quickly
reducing the curvature. The deviation from linearity is also due to microcracking at the
interface of aggregate and cement paste (transition zone). Because of these effects, the
distinction between elasticity and creep is not clearly defined and, for practical purposes,
the deformation during application is considered elastic and the subsequent increases are
regarded as creep. The slope of the stress–strain curve at the stress considered is the
secant modulus of elasticity.

For estimating the total deformation in design calculations, the static modulus of
elasticity is often used as an approximation to the secant modulus, its method of determination
being specified in BS 1881: Part 121: 1983. Here, the effects of creep are reduced by
loading the specimen three times, the static modulus being determined from the slope of
the now-linear stress–strain curve. Generally, the stronger the concrete the greater the
static modulus of elasticity. However, it is usual to estimate the modulus from one of the
several empirical relationships between static modulus (Ec in GPa) and compressive strength
( fcu in MPa), e.g. BS 8110: Part 2: 1985:

Ec = 9.1 f 0.33 (7.1)
cu

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