Page 325 - Design of Reinforced Masonry Structures

COLUMNS 5.45

face) and tensile strain on the opposite face of the column (hereinafter referred to as the
tension face), essentially the column behaving as a vertical beam. The net result of the
combined axial load and bending moment is increased compressive strain on the com-
pression face, and reduced compressive strain on the tension face of the column. Because
the maximum compressive strain in masonry is limited to e , the combination of axial
mu
load and moment must be such that the sum of compressive strains on the compression
face due to these two loads does not exceed e . Thus, an increase in bending moment is
mu
accompanied by a decrease in the axial load. At the same time, with increasing moment, the
tension face of the column experiences increased tensile strain, so that strain on this face,
which was initially compressive, transitions gradually to tensile. As the moment on the
column increases, the position of the neutral axis in the column cross section also changes.
Forces in reinforcement near the compression face and the tension face of the column are
calculated from the strain distribution consistent with the position of the neutral axis. It
is important to recognize that, depending on the position of the neutral axis, the strain in
reinforcement near the opposite faces of the column could be tensile or compressive. In all
cases, the maximum strain in the reinforcement, compressive, or tensile, is assumed limited
to the yield strain.
Interaction diagrams involve time-consuming calculations; as such they are best gener-
ated by a computer. For illustrative purposes, Example 5.11 presents hand calculations for
interaction diagram of a column. Complete calculations are presented for four points in
the diagram (three points discussed above: Points 1, 12, and 6), and one randomly selected
point on the curve (Point 8). Calculations for other points were performed on Excel spread-
sheet. A summary of all calculations is presented in Table E5.11 and the corresponding
interaction diagram shown in Fig. E5.11f. Various points in Table E5.11 were selected on
the basis of assumed strain distribution as follows:
Point 1: Pure axial load case, zero moment
Point 2: Zero strain on tension side (c = h, the depth of the column cross section)
Point 3: Zero strain in tension steel (c = d)
Points 4 and 5, 7 to 11: Various values of c selected arbitrarily, decreasing gradually
from c = h (point 2) to a position close to compression face of the column (Point 11),
as listed in Table E5.11.
Point 6: Balanced conditions
Point 12: Pure bending case, zero axial load
For an arbitrarily selected point on the interaction diagram (Points 4, 5, and 7 to 11), the
location of neutral axis may be such that the strain in the compression reinforcement might
be compressive (when c > d′) or tensile (when c < d′). In general, the neutral axis can have
positions corresponding to the following strain distribution across the column cross section:

1. Zero strain on the tension face of the column, c = h (Point 2, strain in tensile reinforce-
ment is compressive)
2. Zero strain in tension reinforcement, c = d (Point 3)
3. Neutral axis location such that d′ < c < d (strain in compression reinforcement is com-
pressive, Points 4 to 6, and 7 to 11)
4. Neutral axis close to the compression face such that c < d′ (strain in compressive rein-
forcement is tensile)

For each of the neutral axis positions, forces in both compression and tension rein-
forcement, consistent with the strain in those reinforcements, need to be calculated. These