Page 287 - Design of Reinforced Masonry Structures

COLUMNS 5.7

5.3 AXIAL STRENGTH OF REINFORCED
MASONRY COLUMNS

Load-carrying capacity of unreinforced masonry columns is limited by the compressive
strength of masonry units. This limited capacity can be augmented by providing longitu-
dinal reinforcement to carry additional compressive loads. The presence of reinforcement
also adds ductility to column behavior, an important requirement for their performance.
Philosophically, the nominal axial strength P of a short reinforced masonry column is
n
taken as the sum of the separate nominal axial strengths of masonry, (P ) , and the rein-
n m
forcement, (P ) . Theoretically, these two strength components can be expressed as
n s
() = 080 f ′ (A − A st ) (5.5)
P
.
m
n
nm
(P ) = f A st (5.6)
y
n s
where ′ f = specified compressive strength of masonry
m
A = net cross-sectional area of masonry
n
A = area of longitudinal reinforcement
st
f = yield stress of steel in compression
y
Again, theoretically, the nominal strength of an axially loaded reinforced masonry column
can be expressed as the sum of two strength components given by Eqs. (5.5) and (5.5):
P = () + P () = .080 f ′( A − A + f A (5.7)
)
P
n n m n s m n st y s
Equation (5.7) gives the nominal strength of a perfectly straight, short, axially loaded rein-
forced masonry column. For practical columns, Eq. (5.7) is modified for two important reasons:
1. There is always some unintentional (or accidental) eccentricity present in columns,
which would cause some bending with consequent loss in axial load capacity. To
account for this eventuality, the nominal strength given by Eq. (5.7) is multiplied by a
factor of 0.8, which is different from the 0.8 multiplier applied to compressive strength of
masonry (as in 0.8 ′ f ) in Eq. (5.7). It is noted that columns designed under the allowable
m
stress design (ASD) provisions of the MSJC Code [5.1] are required to be designed, as
a minimum, for an eccentricity of 0.1 times each side dimension, independently about
each axis (MSJC Code Section 2.1.6.2). This minimum eccentricity of axial loads results
from construction imperfections not otherwise anticipated in analysis [5.2]. There is no
such requirement under the strength design provisions of the code; the 0.8-factor is used
in lieu of that requirement.
2. To account for slenderness of the columns, the nominal axial strength given by Eq. (5.7)
is multiplied by yet another reduction factor, which is a function of the slenderness ratio
h/r of the column.
Masonry columns, like concrete columns, behave differently when their slenderness
increases beyond certain limits. Accordingly, Eq. (5.7) is expressed as two separate equa-
tions applicable to two different ranges of slenderness ratios:
For h/r ≤ 99
⎡ h 2 ⎤
]
.
P = 080[ P′ + P′ 1 − 140 r ⎦
⎢
s ( ) ⎥
n
⎣
m
⎡ h 2 ⎤
= 080 080 f f ′ A( − A ) + f A ] − (5.8)
1
.
[ .
st ( ) ⎥
⎢
m n st y ⎣ 140 r ⎦