Page 148 - Design of Reinforced Masonry Structures

4.12 CHAPTER FOUR

From the strain distribution diagram, using Eq. (4.15):
−
5
ε = dc ε ( ) = 34 − .71 (.0025 ) = .0124
0
0
s c mu . 571
It is noted that a strain of 0.0124 in the tension reinforcement is considerably larger than
the yield strain value of 0.002 for Grade 60 reinforcement (therefore, the reinforcement
is assumed to have yielded). The ratio of actual strain to yield strain is
ε 0 0124
.
s = = 62
.
ε 0 002
.
y
The strain in tension reinforcement is 6.2 times its yield strain value.
4.5.2 Conditions for Yielding of Tension Reinforcement Based on
Strain Compatibility

4.5.2.1 Conditions for Yielding of Tension Reinforcement in Beams at Balanced
Conditions Fundamental relationships for yielding of steel reinforcement can be derived
from compatibility of strains in a reinforced masonry beam. Figure 4.4 shows strain dis-
tribution across in a reinforced masonry beam at the balanced conditions. Under these
conditions, the ultimate strain in masonry is assumed to be equal to e and the strain in the
mu
tension reinforcement is assumed to be equal to the yield strain e .
y
From similar triangles of the strain distribution diagram, we observe that
c ε
= mu (4.17)
d ε + ε
mu y
The value of c/d ratio that would result in yielding of tension reinforcement can be obtained
from Eq. (4.17) by substituting appropriate values of the ultimate strains in masonry and
reinforcement.
a. Concrete masonry: Substitution of e = 0.0025 for concrete masonry and e = 0.002 for
mu
y
Grade 60 reinforcement in Eq. (4.17) yields
c ε 0 0025
.
= mu = = 0 555 (4.18)
.
.
d ε mu + ε y 0 0025 + 0 0020
.
Equation (4.18) shows that in a concrete masonry beam, Grade 60 reinforcement would

yield when the condition given by Eq. 4.19 is satisfied:
c
≤ 0 555 (4.19)
.
d
For all values of c/d > 0.555, the strain in steel would be less than the yield strain of
0.002.
An expression similar to Eq. (4.19) can be derived for Grade 40 reinforcement for which
the yield strain is
f 40
ε = y = = 0 00138 (4.20)
.
y
,
E s 29 000