Page 132 - Design of Reinforced Masonry Structures

3.26 CHAPTER THREE

humidity, the magnitude of carbonation shrinkage can be equal to the drying shrinkage,
effectively doubling the total amount of shrinkage [3.44].
Shrinkage strain is partially recoverable upon rewetting (concrete swells when it gets
soaked with water, and shrinks when it dries out again. Consequently, structures exposed to
seasonal changes in humidity undergo slight expansion and contraction caused by changes
in shrinkage strains. If these strains are prevented from occurring freely in a concrete
masonry structure, the result would be cracking due to development and build up of tensile
stresses (cracks act as a mechanism of relief from tensile stresses cause by prevention of
free movement). Typically, this problem is solved by providing expansion joints and vol-
ume change joints (discussed in Chap. 9).
The following values of moisture coefficients are specified by the MSJC-08 Code [3.2
(Secs. 1.8.4 and 1.8.5)]:
Coefficient of moisture expansion for clay masonry:
−4
k = 3 × 10 in/in (3.12)
e
The shrinkage of clay masonry is negligible. Coefficient of shrinkage for concrete
masonry:
k = 0.5s (3.13)
m
where s = total linear shrinkage of concrete masonry units determined in according to
l
ASTM C426: Test Method Linear Drying Shrinkage of Concrete Masonry Units [3.45].
−4
The maximum value of s is taken as 0.065 percent or 6.5 × 10 in./in., thus:
l
−4
−4
k = 0.5 s = 0.5 (6.5 × 10 ) = 3.25 × 10 in/in (3.14)
m max
The maximum total shrinkage of a wall can be calculated by multiplying its length with
the coefficient of shrinkage. If the shrinkage movement is prevented from occurring freely,
the resulting stress can be calculated from Hooke’s law. Example 3.2 illustrates the calcula-
tions for shrinkage deformation in a concrete masonry wall.
Example 3.2 Deformation due to shrinkage.
Calculate (a) total shrinkage in the concrete masonry wall described in Example 3.1,
and (b) the maximum stress that would be created in the wall if the movement due to
shrinkage is restrained.
Solution:
a. Total deformation due to shrinkage:
The coefficient of shrinkage for concrete masonry is
−4
−4
k = 0.5 s = 0.5 (6.5 × 10 ) = 3.25 × 10 in/in (3.14 repeated)
m max

The length of masonry wall, L = 24 ft
Total maximum shrinkage, ∆ m, max = k L = (3.25 × 10 in/in) (24 × 12) = 0.0936 in.
−4
m
b. Maximum stress caused by restraining the shrinkage movement:
Stress = (strain)( modulus of elasticity, E )
m
6
From Example 3.1, E = 1.8 × 10 lb/in. 2
m
σ max = (∆ m,max )(E ) = 3.25 × 10 )(1.8 × 10 ) = 585 lb/in. 2
6
−4
m
2
Thus, a maximum tensile stress of 585 lb/in. might be caused if the wall movement
due to shrinkage is prevented. This stress value is much higher than the allowable tensile
stress in concrete masonry.