Page 149 - Design of Reinforced Masonry Structures

DESIGN OF REINFORCED MASONRY BEAMS 4.13

The ratio of yield strain in Grade 40 reinforcement and the ultimate strain in concrete
masonry can be expressed as
.
c ε 0 0025
= mu = = 0 644. (4.21)
d ε + ε 0 0025 + 0 00138.
.
mu y
Equation (4.21) shows that in a concrete masonry beam, Grade 40 reinforcement would
yield when the condition given by Eq. (4.22) is satisfied:
c
≤ 0 644 (4.22)
.
d
For all values of c/d > 0.644, the strain in Grade 40 reinforcement would be less than
the yield strain of 0.00138.
b. Clay masonry: Proceeding as above, c/d ratios corresponding to yielding of tension
reinforcement can be obtained for clay masonry for which e = 0.0035. The c/d ratio
mu
corresponding to yielding of Grade 60 tension reinforcement in clay masonry can be
expressed by substituting e = 0.0035 (instead of 0.0025) and e = 0.002 in Eq. (4.18).
y
mu
Thus,
.
c ε 0 0035
= mu = = 0 636. (4.23)
.
d ε mu + ε y 0 0035 + 0 0020.
Equation (4.23) shows that in a clay masonry beam, Grade 60 reinforcement would
yield when the condition given by Eq. (4.24) is satisfied:
c
≤ 0 637 (4.24)
.
d
For all values of c/d > 0.636, the strain in Grade 60 reinforcement would be less than
the yield strain of 0.002.
Similarly, the c/d ratio corresponding to yielding of Grade 40 reinforcement in clay
masonry beams can be expressed as

.
c ε 0 0035
= my = = 0 717 (4.25)
.
d ε mu + ε y 0 0035 + 0 00138
.
.
Therefore, in a clay masonry beam, Grade 40 reinforcement would yield if the condition
given by Eq. (4.26) is satisfied:
d
.
c ≤ 0 717 (4.26)
For all values of c/d > 0.717, the strain in Grade 40 reinforcement would be less than
the yield strain of 0.00138.
Equations. (4.19), (4.22), (4.24), and (4.26) provide a check, based on strain compat-
ibility, for verifying yielding of steel reinforcement in reinforced masonry beams. It is
reiterated that the value of e for both concrete and clay masonry (0.0025 and 0.0035,
mu
respectively) is greater than e for both Grades 60 and 40 steels (0.002 and 0.00138,
y
respectively). One should intuitively recognize that because of linearity of strain distribu-
tion even at the ultimate conditions, if c = d/2, strain in tension reinforcement would be
equal to the ultimate strain in masonry, and therefore, greater than e for both Grades 60
y