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length of an element is well known and can be calculated from
the following relationship:

Time of installation Temperature

increase ( º C)

Temperature
decrease ( º C)

Δ L = α · L · Δ T
where Δ L is the change in member length, Δ T is the change in
temperature, L the original length and α is the coefficient of
thermal expansion for the material under consideration. For
concrete, the coefficient can vary considerably depending on
the concrete mix and, in particular, the type of aggregate used.
A selection of typical ranges for coefficients of thermal expan-
sion is shown in Table 10.2 .
As can be seen, the coefficients for concrete and steel are
similar and any difference is typically ignored when analysing
reinforced concrete elements and a single factor is assumed.
As has been discussed already, the two major components
of self-straining forces due to temperature are the restraint of
the expansion or contraction, and the temperature range an
element is subjected to. Common forms of restraint and their
impact on structural forces will be discussed in a separate sec-
tion, but the practical derivation of temperature ranges will be
discussed briefly here.
The starting point for the temperature range is the ambient
temperature at the time of locking in a structural element to a
restraint; for concrete members, this is typically assumed to
be the time of casting of the concrete and the ambient 24 hour
average temperature is assumed for the time of year the elem-
ent is cast. The other extreme of the range is then assumed as
the maximum and minimum temperature that element is likely
to be subjected to. This extreme temperature value depends
on a number of factors such as the exposure of the element
(whether internal or external) and the possibility of direct solar
radiation, the degree of insulation of the member, and the size
and thickness of the member itself. Derivation of practical
ranges is subjective and relies on statistical analyses to deter-
mine likely temperatures for a geographical location according
to a specified return period (a similar risk approach is used to
determine wind and seismic forces) and a certain amount of
'engineering judgement'. A practical approach, with particu-
lar relevance to the UK is presented by the Concrete Society
(Alexander et al ., 2008).
Rules of thumb:

Winter +30 (+25*) 0

Spring/autumn +15 - 15

Summer 0

- 30

*Temperature increase from winter is taken as +25 due to a minimum
temperature of +5 ° C typically specified as minimum ambient tempera-
ture in concrete specifications for casting concrete.

Table 10.3 50 year return temperature ranges

10.9.1.2 Internal temperature
The impact of internal temperature is principally relevant
for concrete structures. When a concrete element is cast, the
chemical reaction causes relatively high temperatures to de-
velop as the water in the mix reacts with the cement during the
hydration process. The maximum temperature reached during
the reaction depends upon the materials and their proportions
in the mix, the ambient temperature, the size and depth of the
pour, and on the presence of any insulation (including form-
work). As the temperature begins to cool, and the concrete
begins to set, contraction of the concrete will occur in a similar
manner as outlined above; if this contraction is restrained,
stress will be induced. This is known as early thermal con-
traction and cracking of the concrete is a typical concern in
such situations when contraction of the concrete occurs and
is compounded by the relatively low tensile strength of the
young concrete.

Rule of thumb:

The temperature drop from the peak temperature of the concrete

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during hydration, to the ambient air temperature can be as high
as 60ºC and higher depending on the concrete mix, the tempera-
ture of the concrete at casting and the thickness of the section
being cast. A reasonable initial estimate for temperature drop in
a 300 mm deep suspended slab cast on 18 mm plywood form-
work and containing 300 kgm -3 cementitious material would be
of the order 20ºC.

As a general rule of thumb, the 50 year return temperature ranges 10.9.2 Shrinkage

Shrinkage is a mechanism which affects materials that contain
water within their matrix at the time of their installation and
which can be lost due to chemical reactions and environmental
effects. Concrete, timber and masonry are the three materials
principally affected by this mechanism and the overall effect
is to reduce the physical size of the member, principally its
length, as moisture is lost.
For concrete there are two different mechanisms that fall
under the label of shrinkage: autogenous shrinkage, which is
particular to concrete, and long-term drying shrinkage which
is a similar mechanism in concrete, timber and masonry.

■

shown in Table 10.3 would be reasonable in the UK for initial
design prior to more detailed analysis.
Appropriate factors of safety would apply to the resultant forces

■

for combination with forces due to other applied loads.

Material

Coefficient (Units: 10 - 6 / º C)

Concrete 6 to 14

Mild steel 11 to 13

Timber 3 to 30

Table 10.2 Typical ranges for coefficients of thermal expansion