Page 41 - Design of Reinforced Masonry Structures

1.10 CHAPTER ONE

strength of steel reinforcement) used in design. The structure is so proportioned that actual
(i.e., calculated) stresses do not exceed the allowable stresses. Following the trend in design
methodology being used for concrete structures, design codes such as 2009 IBC and MSJC-
08 Code now permit design of masonry structures based on the strength design concept.
The basic premise of the strength method is that it results in more economical structures
and provides more realistic consideration of safety.
In the strength design method, the code-specified service loads (such as dead load,
live load, wind load, earth pressure, fluid pressure, etc.) assumed to act on a structure are
augmented by multiplying with certain factors called load factors (which are different for
different loads, also called g factors in some design codes), resulting in what are called fac-
tored loads. The structure is then so proportioned that its design strength, fR , is equal to
n
or greater than the required strength (i.e., effects of factored loads, also sometimes referred
to as demand). This simple relationship can be expressed by Eq. (1.1):
Design strength ≥ required strength
fR ≥ U (1.1)
n
where f = strength reduction factor
R = resistance offered by structure (or nominal strength)
n
U = the required strength (i.e., effects of factored loads on the structure)
Equation (1.1) is a generic equation that represents the relationship between the design
strength of a structure and the required strength (load effects). On the right-hand side of
this equation, U represents the required strength or the effects due to loads, such as bending
moment, shear force, axial force, etc., obtained from structural analysis. In specific terms
of member strengths, such as moments (M), shear (V), and axial load (P), Eq. (1.1) can be
written as follows:

fM ≥ M (1.2)
n
u
fV ≥ V (1.3)
n
u
fP ≥ P (1.4)
n u
In Eqs. (1.2) to (1.4), subscripts n and u denote, respectively, nominal strength and the
factored load effects (or demand). The strength reduction factor f associated with different
types of nominal strengths (moment, shear, axial load, etc.) is specified for each type of
loading condition (see Chap. 4). Nominal strengths are calculated from principles of applied
mechanics using factored loads, which are based on code-specified service loads. There are
many good reasons for applying strength reduction factors to nominal strengths:

1. Actual loads might be different from those assumed in design calculations.
2. Actual load distribution in a structure might be different from that assumed in design.
3. Actual member dimensions might be different than assumed in design calculations.
4. Actual material strengths might be different from those assumed/specified in design.
5. The assumptions and simplifications assumed in design might result in load effects
(moment, shear, axial loads, etc.) different from those actually acting on the structure.
6. Actual structural behavior might be different (usually is) owing to the presence of
redundancies (influence of rigidity provided by nonstructural members is ignored in
structural analysis).
7. Reinforcement might not be in the same exact position as specified by the designer.