Page 283 - Design of Reinforced Masonry Structures

5.4 CHAPTER FIVE

to hereinafter as Specification. Frequent references in this discussion are made to two docu-
ments supporting the Code and the Specification, viz., the Commentary on Building Code
Requirements [5.3], and Commentary on Specification [5.4]. It is noted that Ref. 5.1 is the
reference document for design requirements (with few exceptions) for strength design of
masonry columns specified in 2009 International Building Code (2009 IBC) [5.5]. Analysis
and design of columns according to the ASD are presented in several references and are not
discussed in this book [5.6–5.8].

5.2 BEHAVIOR OF AXIALLY LOADED COLUMNS

5.2.1 Buckling Strength of Columns
Behavior of long columns of elastic and homogeneous materials that follow Hooke’s law is
well documented in texts on strength of materials. Long columns are those that fail due to
instability, commonly described as buckling failure. Because this type of failure occurs before
the material reaches its yield strength, it is referred to as the elastic buckling failure. The critical
or buckling load, also known as Euler’s load for columns is given by Eq. (5.1):
π 2 EI
P = (5.1)
cr 2
h
where P = critical or buckling load
cr
E = modulus of elasticity
I = moment of inertia of column cross-section
h = effective height of the column
2
Noting that I = Ar , where A and r, respectively, are the cross-sectional area and the
radius of gyration of the column cross section, Eq. (5.1) can be rewritten as Eq. (5.2):
π 2 EA
P = (5.2)
cr 2
( hr / )
From the standpoint of failure, columns made from elastic, homogenous materials that
follow Hooke’s law are classified as short, intermediate, and long. Short columns are char-
acterized by failure by crushing or yielding of material. The failure of both the intermediate
and the long columns is controlled by the stability of column cross section. The failure of
intermediate columns is initiated by crushing or yielding of material in some portion of
the cross section, followed by buckling. Long columns are characterized by pure buckling
failure.
Failure modes of columns made from an ideal material such as steel can be well defined
or predicted easily as described above. However, such is not the case for columns made
from nonhomogeneous material such as reinforced masonry, since no well-defined limiting
stress, such as yield stress, occurs in these columns. To date, not enough research on full-
size reinforced masonry columns has been conducted to define their behavior under failure
loads, and no rational expressions have been developed to form a basis for design.
For reinforced masonry, Eq. (5.2) can be expressed as Eq. (5.3) wherein E (modulus of
m
elasticity of masonry) has been substituted for E:
π 2 EA
P = m (5.3)
cr 2
( hr / )