Civil Engineering Reference
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eccentricity and no confinement at all. The confined strength in between the two
extremes (
f
cc
and
f
c
) is mapped gradually as a function of the compression-zone
ratio (CR).
1
1
f
=
f
+
f
cc
1
cc
c
0.8
+
CR
(7.94)
1
+
CR
−
0.2
where
e
bh
e
bh
0.2
+
0.1
(7.95)
CR
=
The relationship in Equation (7.95) has been correlated by plotting the nor-
malized eccentricity against the compression area to cross-sectional area ratio for
rectangular cross sections having different aspect ratios at the unconfined failure
level. The aspect ratios used are 1:1, 2:1, 3:1, and 4:1, as shown in Figure 7.18,
selected as an example. Each curve in Figure 7.18 represents specific α angle (tan
α =
M
y
/
M
x
) ranging from zero to 90°. It is seen from this figure that there is an
inversely proportional relation between the normalized eccentricity and compres-
sion-zone ratio, regardless of the α angle followed. By plotting the curves from all
aspect ratios into one graph and establishing the best-fit curve, Equation (7.95) is
introduced.
Aspect ratio 1:1
120
0
10
20
30
40
50
60
70
80
90
100
80
60
40
20
0
0
5
10
15
20
25
30
35
Eccentricity/(bh)
0.5
FIGURE 7.18
Compression-zone ratio vs. normalized eccentricity in rectangular columns
(aspect ratio = 1:1).
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