Page 261 - Design of Reinforced Masonry Structures

4.124 CHAPTER FOUR

Equation (4.144) locates the neutral axis of a section whose properties are completely
known (i.e., size of the beam, and the location and area of tension reinforcement, and no
compression steel present). See Example 4.32. For computational expediency, values of k
given by Eq. (4.144) are tabulated for various values of nr (Table A.15).

4.20.3 Modular Ratio, n
The modular ratio, n, was defined earlier as the ratio of modulus of elasticity of steel, E ,
s
to that of masonry, E (both were discussed in Chap. 3). Whereas the value of E is com-
s
m
monly taken as a standard 29,000 ksi (MSJC-08 Section 1.8), the value of the modulus of
elasticity of masonry, E , is based on the 28-day compressive strength of masonry prism.
m
This relationship is analogous to the modulus of elasticity of concrete which also is based
on the 28-day compressive strength of a concrete cylinder.
MSJC-08 Section 1.8 specifies the following values of E for clay and concrete masonry:
m
For clay masonry: E = 700 ′ f
m m
For concrete masonry: E = 900 ′ f
m
m
The above values of E are based on the chord modulus values determined from stress
m
values of 5 to 33 percent of the compression strength of masonry. The chord modulus is
defined as the slope of a line intersecting the stress-strain curve at two points, neither of
which is the origin of the curve. Readers are referred to the commentary to MSJC Code
[4.3] for a discussion on research that forms the basis of the specified E values.
m
Values of n corresponding to a few typical values of ′ f are given in Table A.14. Referring
m
to Fig. 4.36, the moments of inertia of the gross section (uncracked) taken about its centroi-
dal axis is given by Eq. (4.144):
I = bh 3 (4.145)
g
12
Note that the moment of inertia of the gross section, I [Eq. (4.145)], does not take into
g
account the presence of tension or compression reinforcement present in the uncracked
section. This is a conservative approach, but this is how it has been traditionally specified
in design codes. If the transformed area of reinforcement present in the beam were to be
considered for calculating the moment of inertia of the gross section, defined as gross
transformed moment of inertia I , its value would be greater than I (i.e., I > I ). However,
gt g gt g
the increase in the value of I is small.
g
The moment of inertia of the transformed cracked section taken about the centroidal

axis of the cracked section can be expressed as Eq. (4.146):
(
(
2
−
I = bkd) 3 + nA d kd) (4.146)
cr s
3
Example 4.32 illustrates the procedure for calculating I of a rectangular reinforced
cr
masonry section. Example 4.33 shows calculations for I for the same section.
gt
Example 4.32 Moment of inertia of a cracked rectangular reinforced
masonry section.
A simply supported nominal 8 × 24 in. CMU beam is reinforced with one No. 9
Grade 60 bar for tension with its centroid located at 20 in. from the compression face of