Page 404 - Design of Reinforced Masonry Structures

WALLS UNDER GRAVITY AND TRANSVERSE LOADS 6.55

(a) When the moment due to service loads is less than the cracking moment (i.e.,
M < M )
ser
cr
ser
δ = 5Mh 2 (6.22, MSJC-08/3-31)
ser
48EI
mg
(b) When the service load moment is greater than the cracking moment but less than the
nominal moment strength M (i.e., M < M < M )
n cr ser n
5Mh 2 5 M( − M ) h 2
δ ser = cr + ser cr (6.23, MSJC-08/3-32)
48EI 48EI cr
mg
m
Note that the cracking moment M is to be determined based on the modulus of
cr
rupture, f , as discussed in Chap. 4. Values of modulus of rupture are listed in MSJC-08
r
Table 3.1.8.2. Note that the moment of inertia of the cracked section would be based on the
effective area of steel, A , given by Eq. (6.25). The expression for the moment of inertia of
se
the cracked section can be expressed as
−
(
I = bc 3 + nA d c) 2 (6.24)
cr
se
3
where b = 12 in. (unit width of wall)
c = depth of neutral axis from the compression face of the wall
d = depth of the centroid of tensile reinforcement
n = modular ratio, and
P + A f
A = u s y (6.20 repeated)
se
f
y
Examples 6.2 and 6.3 illustrate, respectively, analysis and design of reinforced masonry
walls subjected to out-of-plane loads as discussed above. It would be noted that the basic
procedure in both cases is identical. Typically, an analysis problem involves checking the
adequacy of a wall for its capacity to carry gravity and lateral loads, and for deflection, all
design details of the wall being known. In the case of a typical design problem, all loads
(gravity and lateral) and eccentricity of gravity load would be known, and the wall thickness
and its compressive strength dimensions would have been preselected, for example, an 8-in.
2
nominal thick concrete masonry wall and the compressive strength ( ′ f ) of 2000 lb/in. . The
m
only unknown to be determined would be the size and spacing of vertical reinforcing bars.
One can proceed with design by assuming a vertical bar size (e.g., No. 5 or No. 6) and hori-
zontal spacing of these bars (assuming that the wall is spanning vertically). The calculations
then would be similar to those in Example 6.2. If the selected bar size and spacing do not
prove to be adequate, one should try a larger or smaller bar at the same or different spacing

as necessary. This step should be repeated until a satisfactory design is obtained.
Example 6.2 A 20-ft-high, 8-in.-nominal, solidly grouted, concrete masonry wall is
centrally reinforced with No. 6 vertical bars (Grade 60) spaced horizontally at 24 in. on
2
center. The wall weighs 84 lb/ft per linear foot of the wall. It carries a superimposed
dead roof load of 160 lb/ft and a roof live load of 60 lb/ft length of the wall. The roof is
supported on a ledger beam attached to the wall, which creates an eccentricity of 4 in.
2
from the center line of the wall (Fig. E6.2). The lateral load due to wind is 20 lb/ft and
2
due to earthquake 42 lb/ft . Check the adequacy of the wall to carry gravity and lateral
2
loads, and deflection ′ f = 2000 lb/in. .
m