Page 178 - Design of Reinforced Masonry Structures

4.42 CHAPTER FOUR

(e.g., a wall above an opening). The beam width would typically be the actual width of
the CMU (which is smaller than the nominal width) or the actual width of the brick. It is a
common practice to use Grade 60 reinforcement because most research is based on tests on
masonry using Grade 60 reinforcement. The strength of masonry, CMU or brick is specified
according the specifications of a job. With this information given, a designer encounters
two types of problems in design:

1. Determination of the amount of reinforcement when the depth of the beam is also
known.
2. Determination of both the depth of the beam and the amount of reinforcement.
In the first case, when all the other information is given and the amount of reinforcement
is to be determined, the problem is rather simple. Example 4.14 illustrates the procedure for
determining the required amount of reinforcement when everything else is known. In the
second case, when both the beam depth and the amount of reinforcement are to be deter-
mined, the problem is a bit more laborious. Examples 4.15 and 4.16 illustrate the procedure
for determining both the required depth of the beam and amount of reinforcement when
everything else is known.
In cases where the depth of the beam is unknown (as is usually the case in design), it
is necessary to guess the nominal depth (h) of the beam for the initial trial, estimate its
dead weight, and proceed with deign. Although no firm guidelines can be established to
estimate a reasonable depth of a beam, one can begin with an assumed nominal beam
depth greater than or equal to 8 in., which is the minimum nominal depth requirement
for a beam [MSJC-08 Section 3.3.4.2.5(b)]. Therefore, a nominal beam depth (h) of
16 in. (i.e., two 8-in. high CMU blocks) or 24 in. (three 8-in. high CMU blocks) can be
assumed for initial design, and the final design depth can be determined from subsequent
trial-and-error procedure. Once the initial trial nominal depth is chosen, the next step is to
select the design depth d of the beam (the distance from the extreme compression fibers
to the centroid of tension reinforcement). This depth can be determined by considering
the thickness of the bottom face of a bond beam or a lintel unit, and the grout cover
requirements. The thickness of the bottom face of the masonry unit can be assumed to
be approximately 2 in. All beams and lintels are required to be grouted solid. MSJC-08
Section 1.15.3.5 requires reinforcement embedded in grout to have a thickness of grout
between the reinforcement masonry units not less than ¼ in. for fine grout and ½ in. for
coarse grout. With a ½ in. grout cover, and assuming a No. 8 bar for flexural reinforce-
ment, the minimum distance from the bottom of the masonry unit to the centroid of the
bar works out to be 2¾ in. This can be rounded off to 3 in. Therefore, as a maximum, the
depth d (also sometimes referred to as the effective depth) can be reasonably assumed as
the nominal depth of the beam minus 3 in. See Fig. 4.8. The assumption here is that the
tensile reinforcement consists of one bar (as in most cases). In case the flexural reinforce-

ment consists of two bars (e.g., one bar above the other; bundling of bars is not permitted
in masonry (MSJC-08 Section 3.3.3.6) the depth d is to be measured from the centroid of
the bar group, and it should be verified that the strain in the lowermost reinforcing bar (i.e.,
nearest the tension face of the beam) satisfies the condition e ≥ 1.5e . Furthermore, the
s
y
variation in the size of reinforcing bras in a beam should not be greater than one bar size,
and no more than two bar sizes should be used in a beam (MSJC-05 Section 3.3.4.2.2.1).
The purpose of this restriction is to increase the depth of the compression zone of the beam
and to increase ductility. When two bars of significantly different sizes are placed in a
beam, the larger bar requires a much higher load to reach yield strain. Note that MSJC-08
Section 3.3.3.1 does not permit reinforcing bars larger than No. 9 for strength design of
reinforced masonry.