Page 342 - Design of Reinforced Masonry Structures

5.62 CHAPTER FIVE

The bending of the column occurs about its strong axis (axis parallel to the short side of
the cross section). The design, 5 percent damped, spectral response acceleration param-
eter at short periods, S = 1.25g. Calculate the shear strength of this column.
DS
Solution
Given: CMU column nominal 16 × 24 in., b = 15.625 in., h = 23.625 in., d = 19.825 in.,
2
d′= 3.8 in., A = 2.41 in. (four No. 7 bars), column height h′ = 24 ft, ′ f = 2000 psi,
st
m
f = 60 ksi., S = 1.25g.
y
DS
(Note: The column described in this example is the same column as described in
Example 5.11 for which interaction diagram was plotted. Based on that interaction dia-
gram, it is evident that the column can support the imposed loads. These calculations are
not repeated here. In general, for a column for which shear strength is to be determined,
a designer must also ensure that it can support the imposed loads.)
Check code compliance with respect to dimensional limits, h ′/t ratio and longitudi-
nal reinforcement.
Nominal column width = 16 in. > 8 in. OK
Nominal column depth = 24 in. < 3t = 3 × 16 = 48 in. OK
h ′/t = (24)(12)/16 = 18 < 30 OK
A = (15.625)(23.625) = 369 in. 2
n
Longitudinal reinforcement, A = 2.41 in. 2
st
.
ρ = A st = 241 = 0 0065
.
A 369 0 .
n
r = 0.04 r = 0.0025 r = 0.0065
max min provided
0.0025 < 0.0065 < 0.04 OK
Lateral ties: Tie diameter = 0.375 in. > 0.25 in. OK

s = 8 in. ≤ 16d = 16 (7/8) = 14 in. OK
b
≤ 48 tie diameter = 48(0.375) 18 in. OK
≤ 16 in. OK
Load Combinations:

1. U = 1.4D = 1.4(20) = 28 kips
2. U = 1.2D + 1.6L = 1.2 (20) + 1.6 (20) = 56 kips
r
3. U = (1.2 + 0.2S )D + rQ + L + 0.2S
DS
E
= [1.2 + 0.2(1.25)](20) = 29 kips
In Load Combination 3, the term rQ represents horizontal force effects due to
E
earthquake (= 0 for gravity load effects)
[Note: Both live load (L) and snow load (S) are zero in this problem.]
4. U = (0.9 – 0.2S ) D + rQ + 1.6H
DS
E
where H = load due to lateral pressure due to earth, ground water or bulk materials
= 0 in this problem