Page 324 - Design of Reinforced Masonry Structures

5.44 CHAPTER FIVE

With the known value of the strain in compression steel, the force in compression
steel is determined from Eq. (5.27).
We can now write the equation for equilibrium by taking into account all vertical
forces acting on the column, viz., the imposed axial load P, the compressive force in
masonry C [Eq. (5.21)], the compressive force in steel C [Eqs. (5.22) and (5.28)], and
m
s
the tensile force in steel T [Eq. (5.28)]. Thus,
∑
F = 0 (5.38)
y
C + C – T – P = 0 (5.39)
s
m
whence
P = C + C – T (5.40)
m
s
Note that Eq. (5.40) is different from Eq. (5.29) because of the presence of axial
load P on the column. This same equation was used in Examples 5.9 and 5.10. Once
this equation is solved, the value of M can be determined by summing up moments
n
due to all forces about the centroidal axis of the column as illustrated in Examples 5.9
and 5.10.
4. Other points in the interaction diagram
Generating a complete interaction diagram requires calculations for at least the
aforedescribed three points and several other points on the curve. Values of P and M for
other points in the interaction diagram may be calculated by varying strain distribution
across the column cross section as suggested in the following step-by-step procedure.
For any point on the interaction curve:
a) Set compressive strain in masonry e (= 0.0025 for concrete masonry and 0.0035
mu
for clay masonry).
b) Assume a strain distribution in the column cross section (i.e., assume a value of c,
the distance of neutral axis from the face of the column).
c) Calculate the compression forces in masonry (C ) from Eq. (5.21), and forces in
m
compression and tension steel (C , and T, respectively) based on strain distribution
s
across the column cross section, as discussed earlier.
d) Calculate the value of the axial force P from equation of equilibrium [Eq. (5.40)].
e) Calculate the value of moment M by taking moments of all forces (C , C , and T) about
m
s
the centroidal axis of column cross section (i.e., about the line of action of P).
In regard to item 2 above, it is often convenient to assume strain distribution by posi-
tioning neutral axis at several arbitrarily selected distances in the cross section and calcu-

late the corresponding values of P and M. This procedure is illustrated in Example 5.11.
It is instructive to understand the variations in the strain distribution in the cross section
of an axially loaded column subjected to bending. The influence of the two simultaneous
loading conditions for a column—axial load and bending—can be determined from the
principle of superposition. When under axial load only, the column experiences uniform
compressive strain across its entire cross section. The maximum value of this axial load cor-
responds to the nominal strength (P ) of the column, and it is assumed that the compressive
n
strain in masonry is equal to e and the compressive strain in steel reinforcement equal to
mu
its yield strain.
When an axially loaded column experiences a bending moment, the latter introduces
compressive strain on one face of the column (herein after referred to as the compression