Page 326 - Design of Reinforced Masonry Structures

5.46 CHAPTER FIVE

TABLE E5.11 Calculations for Values of Axial Load and Bending Moment for the Interaction
Diagram for Column in Example 5.11 (Excel spreadsheet)
′ f C m C S T fP n fM n
s
Point c in. ′ ε ε ksi kips kips kips kips k-in.
T
s
1 – 0.00207 0.00207 417.6 –
2 23.625 0.00210 −0.00040 −11.7 472.5 71.4 −14.0 398.2 1412
3 19.825 0.00202 0.00000 0.1 396.0 68.7 0.1 331.6 1877
4 17.0 0.00194 0.00042 12.0 340.0 66.0 14.5 279.4 2108
5 14.0 0.00182 0.00104 30.2 280.0 61.8 36.2 218.1 2267
6 10.8 0.00162 0.00208 60.0 216.6 54.9 72.0 142.4 2368
7 10.0 0.00155 0.00246 60.0 200.0 52.3 72.0 128.7 2298
8 8.0 0.00131 0.00370 60.0 160.0 44.1 72.0 94.3 2073
9 6.5 0.00104 0.00513 60.0 130.0 34.5 72.0 66.0 1843
10 5.0 0.00060 0.00741 60.0 100.0 19.3 72.0 33.7 1540
11 4.0 0.00013 0.00989 60.0 80.0 2.8 72.0 7.7 1274
12 3.67 −0.00009 0.01100 60.0 73.4 −3.1 72.0 −1.2 1181

strains, which might be compressive or tensile depending on the position of the neutral axis
in various cases, can be calculated from strain distribution diagrams as follows:
Case 1: Zero strain on the tension face of the column, c = h (Point 2 on the interaction
diagram).
Figure 5.13 shows the column cross section and the strain distribution and force dia-
grams corresponding to zero strain on the tension face of the column. Strain is tension
reinforcement (e ) in this case would be compressive, which can be calculated from
T
similar triangles of strain distribution diagram:
ε cd ( )
−
d
T = = 1 −
ε c c
m
whence
T ( )
d
)
ε = 1 − ε (compressive (5.41)
c m
b 0.8fʹ m
ε m = 0.0025
εʹ s dʹ
C s a/2
a C m
h c = h d

ε T
C T
ε m = 0
FIGURE 5.13 Strain distribution and force diagrams for the case of zero strain on the ten-
sion face of column.