Page 130 - Design of Reinforced Masonry Structures

3.24 CHAPTER THREE

Expansion or contraction of masonry can be calculated based on the deviation of tem-
perature from ambient temperature at the time of construction. For example, if the variation
in the temperature is ∆T, the change in the length of a wall would be:
∆L = k L∆T (3.9)
t
where ∆L = change in the length of wall (expansion or contraction)
L = original length of wall

It should be obvious that provision should be made in constructed walls to accom-
modate the thermal movement, failing which thermal stresses would be induced in the
masonry, which could cause undesirable consequences. The thermally induced stress in the
wall can be determined from Hooke’s law as follows, provided the strain remains within
the elastic limit:
∆ L
ε = (3.10)
T
L
σ = ε E (3.11)
T T m
where ε = thermal strain
m
σ = thermal stress (stress induced due to temperature variation)
T
Thermal movements are inevitable in a structure regardless of the type of building mate-
rial used in construction. These movements can sometimes cause cracking in concrete or
masonry. Large-scale effects of expansion and contraction are relieved by volume change
joints. Various types of joints provided in masonry buildings are discussed in detail in Chap. 9
of this book.
Example 3.1 illustrates the thermal movements in a wall due to variation in the ambient
temperature.

Example 3.1 Thermal movements in a wall.
A concrete masonry wall, constructed from nominal 8 × 8 × 16-in. medium-weight
units is 24-ft long and 12-ft high. The wall is fully grouted; the grout weight being 140
3
lb/ft . The temperature in the local area varies from 70°F in the winter to 120°F in the
summer. Calculate (a) the amount of thermal movement the wall would undergo due to
temperature variation, (b) the stress that would be induced in the wall if thermal move-
2
ment is prevented. The 28-day compressive strength of masonry is 2000 lb/in. .
Solution:
a. Thermal movement.

The wall would expand when the temperature rises beyond 70°F and shorten in
length when the temperature falls below 70°F. We can calculate the elongation and
shortening of the wall separately.
1. Elongation due to rise in temperature from 70 to 120°F:
Length of wall, L = 24 ft
Change in temperature, ∆T = 120 – 70 = 50
−6
For concrete masonry: k = 4.5 × 10 in./in./°F
t
The change in the length of wall is given by Eq. (3.9):
−6
∆L = k L∆T = (4.5 × 10 )(24 × 12)(50°) = 0.0648 in.
t