Page 164 - Design of Reinforced Masonry Structures

4.28 CHAPTER FOUR

For a rectangular section, y = h/2. Therefore, Eq. (4.51) can be expressed as

2
3
(
M = fbh /12 ) = f r ⎜ ⎛ bh ⎞ ⎟ (4.53)
r
cr ⎠
h (/ ) 2 ⎝ 6
Equation (4.53) can be expressed as
M = f S (4.54)
r
cr
2
where S = section modulus of the gross or uncracked rectangular section = bh /6.
Examples 4.9 to 4.11 illustrate the calculation of nominal cracking moments of rein-
forced masonry beams and related code applications.

Example 4.9 A nominal 10 × 40-in. concrete masonry beam built from lightweight
CMU is reinforced with two No. 6 Grade 60 bars for tension (Fig. E4.9). The centroid
of reinforcement is located 6 in. from the bottom of the beam. The grout weight is
3
140 lb/ft . ′ f = 1500 psi. Check if the beam is adequate to carry the imposed loads.
m
Calculate the nominal cracking moment of this beam. The beam consists of solid
grouted masonry in running bond laid in Type S portland cement mortar. Does the
beam satisfy the code requirement?

9.63" (10" nominal) Solution
For a nominal 10 × 40 in. concrete masonry beam,
b = 9.63 in., h = 40 in. From Eq. (4.53), the cracking
moment of the beam is
⎛ bh ⎞
2
M = f r ⎜ ⎟ (4.53 repeated)
cr
⎝ 6 ⎠
2
The modulus of rupture, f = 200 lb/in. for solid
d = 34" r
40" grouted masonry in running bond laid in Type S port-
land cement mortar (MSJC Table 3.1.8.2.1). Therefore,
M = (020. ) (963 40. )( ) 2 = 531 6 . k-in. = 42 8 . k-ft t
cr
6
1.3M = 1.3(42.8) = 55.64 k-ft
cr
The nominal strength of this beam, M , of this beam
n
2#6 was calculated to be 139.55 kip-ft in Example 4.2 (calcu-
lations not repeated here), which is greater than 1.3M .
cr
FIGURE E4.9 Therefore, the beam satisfies the Code requirements for
nominal cracking moment strength of the beam.
Example 4.10 A two-wythe 8 × 24 in. clay brick beam has an effective depth of
20 in. It is reinforced with one No. 8 Grade 60 bar for tension (Fig. E4.10). Determine
the cracking moment of this beam. ′ f = 2500 psi. Portland cement Type S mortar would
m
be used for construction. Does the beam satisfy the Code requirements?