Page 139 - Design of Reinforced Masonry Structures

DESIGN OF REINFORCED MASONRY BEAMS 4.3

load-carrying capacity, or the maximum resistance it can offer) of the structure calculated
from material properties be greater than that required to resist or support the maximum
anticipated loads (also called the required strength or demand). For example, consider the
design of a beam, for which we define the nominal strength, M , and the moment demand
n
or the required strength, M , as follows:
u
M = nominal strength (or the moment resistance) calculated from material and cross-
n
sectional properties
M = moment due to the anticipated loads that a beam is required to resist (or moment
u
demand)
For design purposes, we require that M be slightly greater than, or at least equal to, M .
n
u
Mathematically, this requirement is stated as
M ≥ M (4.2)
n u
For practical purposes, we slightly modify Eq. (4.2) for computational purposes. To be
able to use the equal sign, we multiply M by factor f (phi) called the strength reduction
n
factor (discussed later). Accordingly, Eq. (4.2) can be written as
fM ≥ M (4.3)
n
u
Because, by definition, M > M , one should intuitively recognize that f < 1.0 in Eq. (4.3).
n
u
This f-factor has a specific numerical value to be used for moment calculations as dis-
cussed later. In general, however, f factors (resistance or capacity reduction factors) are
applicable to strength calculations for all masonry components. We purposely use the term
“factors” (plural term) rather than “factor” (singular term) because their values are different
for different limit states.
The term “maximum anticipated loads” (or the required strength) needs to be clari-
fied for use in design. Obviously, because of their probabilistic nature, these loads are not
known a priori. Therefore, we must have a way to predict (or estimate) these loads. One
way to do this is to simply increase the service loads in some proportion. This is accom-
plished by multiplying the service loads by certain factors called the “load factors” (speci-
fied as g factors in some codes), and the loads so determined are called the “factored loads.”
Thus, Eq. (4.3) can be restated as
f (Nominal strength) ≥ factored loads (4.4)
Equation (4.4) is quite general and is applicable regardless of the nature of the loads or
forces involved. This is the fundamental equation that forms the basis of strength design,
a design concept that parallels limit states design or load and resistance factor design
(LRFD). The loads referred to here can be of any kind: bending moment, shear, axial loads,

torsion, etc. We now see that the term “M ” in Eq. (4.2), which is applicable to beams, is
u
simply the design moment based on factored loads.
In this chapter, the terms “nominal strength” and “moment resistance” (both are denoted
as M ), which are determined from material strengths, would be used synonymously.
n
Likewise, the terms “design moment” and “moment demand” (both are denoted as M ),
u
which are determined from the imposed loads, would be used synonymously.
4.3.2 Strength Reduction Factors and Load Factors
The load factors and the strength reduction factors (the f-factors) alluded to in the preced-
ing paragraph form the foundation of the strength design philosophy. Several consider-
ations made in arriving at the values of these factors are discussed in this section.