Page 163 - Design of Reinforced Masonry Structures

DESIGN OF REINFORCED MASONRY BEAMS 4.27

e. Direction of flexural stress (whether parallel or normal to the bed joints). For example,
in a transversely loaded masonry beam, the flexural stresses are parallel to the bed
joints, whereas, in flexural elements subjected to in-plane loads (such as shear walls),
the flexural stresses are normal to the bed joints.
Values of modulus of rupture for hollow and solid grouted masonry are listed in MSJC-
08 Table 3.1.8.1. Values are listed for two mortar types: (1) portland cement/lime or mortar
cement and (2) masonry cement or air entrained portland cement/lime. For each category,
values of modulus of rupture are listed for Types M or S (same values for both) and Type
N mortars. Value of modulus of rupture for different masonry and mortar types are con-
siderably different, so designers should carefully choose their values corresponding to the
mortar type specified or to be used for a particular job.
Masonry beams typically are parts of masonry walls that are solid grouted. Therefore,
in the context of beams, the value of modulus of rupture for solid grouted masonry should
always be used. For partially grouted masonry, the modulus of rupture values can be
obtained from linear interpolation between grouted hollow units and ungrouted hollow
units, based on amount (percentage) of grouting.

4.6.2 Nominal Cracking Moment of Masonry Beams

The nominal cracking moment of a masonry beam is defined as its flexural strength without
reinforcement (i.e., an unreinforced masonry beam). MSJC Section 3.3.4.2.2.2 requires that
the nominal strength M of a reinforced beam be not less than 1.3 times the nominal cracking
n
moment strength of the beam (M ) calculated based on modulus of rupture (i.e., the strength
cr
of an unreinforced or plain masonry beam). This relationship can be stated as
(Strength of a reinforced masonry beam)
[1.3(strength of a plain masonry beam)] (4.49)
For design purposes, Eq. (4.49) can be restated as Eq. (4.50):

M ≥ 1.3M (4.50)
n
cr
This requirement is intended to prevent brittle failures of flexural elements. Such a pos-
sibility exists where a beam may be so lightly reinforced that bending moment required to
cause yielding of the reinforcement is less than the cracking moment (i.e., moment required
to causing cracking). See Example 4.11.
The moment strength in this case is calculated based on the section properties of an
uncracked section. Therefore, the value of nominal cracking moment can be calculated
based on the convention flexure formula for a beam of homogeneous materials as follows:
M = fy
r
(4.51)
cr
I
where M = nominal cracking moment of a masonry beam
cr
f = modulus of rupture
r
y = distance of extreme fibers in tension measured from the neutral axis
I = moment of inertia of the gross cross section
The moment of inertia of a rectangular section having width b and total depth h is given
by Eq. (4.52):
I = bh 3 (4.52)
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