Page 257 - Design of Reinforced Masonry Structures

4.120 CHAPTER FOUR

causes additional deflections, which would permit additional water to accumulate, caus-
ing still more deflection. This phenomenon of progressively increasing deflections and
more accumulated water may lead to a ponding failure and consequent considerable
structural damage [4.13].
In some cases, deflection limitations of flexural elements such as lintels may be nec-
essary for proper functioning of windows and doors below the opening. However, this
constitutes a serviceability problem, not structural. In general, deflections that may lead to
structural damage are several times larger than those causing serviceability problems. If a
member deflects so much that it comes in contact with another member, the load paths may
change, causing cracking.
The Code limitations for deflections of masonry beams are empirical. MSJC-08
Section 1.13 provides requirements governing beam deflections. It requires beams and
lintel to be designed to have adequate stiffness to limit deflections that adversely affect
strength or serviceability. To this effect, it is required that deflections of beams and lin-
tels due to unfactored dead plus live loads (i.e., service loads) not exceed 1/600 of clear
span when providing vertical support to unreinforced or empirically designed masonry.
These empirical requirements are intended to limit excessive deflections which may
cause damage to the supported unreinforced (plain) masonry, or reinforced masonry
with vertical reinforcement only. According to MSJC-08 Commentary [4.3], reinforced
masonry beams with span lengths of 8 times d have immediate deflections of approxi-
mately 1/600 of span lengths. Masonry beams and lintels with shorter spans should have
sufficient stiffness to prevent serviceability problems, and therefore deflections need not
be checked. Additionally, it is noted that most masonry beams have some end restraint
due to being built integrally with a wall. Tests have shown that those end support condi-
tions reduce the deflections from about 20 to 45 percent from those with simply sup-
ported specimens [4.29].

4.20 SERVICE LOAD ANALYSIS OF REINFORCED
MASONRY BEAMS

4.20.1 Concept of Transformed Section
Reinforced masonry is constructed from four dissimilar materials: masonry units (con-
crete or clay), mortar, grout, and steel reinforcement. The elastic properties of all these
materials are different from each other. Consequently, like reinforced concrete, masonry
is a non-homogeneous material. Beams made from dissimilar are referred to as composite
materials.
The conventional theory of flexure (f = My/I) is based on the fundamental principles

that (1) the material is homogeneous and that (2) the plane sections remained plane so the
strains varied directly with their distance from the neutral axis. This theory does not apply
directly to beams of nonhomogeneous materials. However, by suitable modifications, an
equivalent section can be obtained in terms of one material to which the theory can be
applied. This equivalent section is called transformed section. When applying the bending
theory to composite beams, only one assumption is retained, that is, plane sections remain
plane so that strains vary directly with their distances from the neutral axis. In general, the
concept of transformed section is applicable to any beam consisting of dissimilar materials,
and the conventional theory of flexure can be applied.
In sections of homogeneous materials such as steel or aluminum, the neutral axis is
located at the geometric centroid of the section. But because of nonhomogeneity, the neutral
axis in a reinforced masonry beam is not located at the geometric centroid of the section.