Page 290 - Design of Reinforced Masonry Structures

5.10 CHAPTER FIVE

Similarly, for a 16 × 16 in. (actual dimensions) column,
r = 0.289t = 0.289(16) = 4.625 in.

h
For = 99 and r = 4.625 in., h = (99)(4.625)/12 ≈ 38 ft
r
Both effective column heights are unusually tall for a practical structure if the columns are
not laterally supported at some points between their ends.
It is noted that determination of nominal strength of a masonry column requires deter-
mining the value of the axial stress reduction coefficient C from Eqs. (5.12) and (5.13). It
P
is possible to simplify these computations if C can be expressed as a function of h/t ratio.
P
The derivation follows:
Case 1: h/r ≤ 99
The radius of gyration, r, for a rectangular section is given by r = t/12 [Eq. (5.16)],
which when substituted in Eq. (5.13) yields
⎛ h ⎞ 2
C =− ⎜ ⎟
1
P ⎠
⎝140( t/ 12)
( ) 2
h
1
.
=− 0 000612244 (5.17)
t
Note that for h/t = 28.577, Eq. (5.17) gives C = 0.5. Consequently, Eq. (5.17) applies
P
for h/t ≤ 28.577, which corresponds to h/r ≤ 99.
Case 2: h/r > 99
A similar expression for C can be derived in terms for h/t ratio corresponding to h/r ≥
P
99 by substituting r = t/12 in Eq. (5.13). Thus,
P ( ) 2 ⎛ 70( t ( / 12) ⎞ 2 408 33
r
70
.
C = = ⎜ ⎟ = (5.18)
h ⎝ h ⎠ ( h t) / 2
Note that for h/t = 28.577, Eq. (5.18) gives C = 0.5. Consequently, Eq. (5.18) applies
P
for h/t > 28.577, which corresponds to h/r > 99. For all values of h/t ratios greater than
28.577, C < 0.5.
P
The values of C for a practical range of h/t ratios are given in Table A.16. For intermedi-
P
ate values of h/t ratios, C can be calculated by interpolation without any appreciable error
P
as illustrated in several examples that follow.

5.4 MSJC CODE PROVISIONS FOR REINFORCED
MASONRY COLUMNS
All masonry columns and pilasters are required to be fully grouted. Columns should comply
with the code requirements governing their sizes (cross-sectional dimensions), and height–
to–least cross-sectional dimension ratio (h/t ratio), and configuration of reinforcement pre-
sented in this section. In general, these requirements, some being prescriptive, are based on
successful past construction practices, experience from historical performance of as-built
structures in earthquakes and windstorms (hurricanes and tornadoes), and to some extent, on