r - The Hong Kong Polytechnic University

ocking can be fully developed, the moment capacity of the column governed the overall response behavior and
the difference observed between specimen A with a fixed base and specimen B with a rocking base became
insignificant. On the other hand, for the retrofitted case of specimen C, because the purpose of its retrofit was to
enhance its ductility but not its moment strength, the increased moment strength of the column was not great
enough to let the overturning moment at the foundation base completely govern the response. Hence, the
hysteresis curves in Fig. 4 show that some plastic deformation still occurred in the column. From this
observation, it is recognized that even thought there is a good potential for a spread footing foundation to
dissipate a large amount of energy through the rocking mechanism, thereby reducing the ductility demand on the
column, the column still has to possess a certain level of strength and ductility in order to allow the rocking
mechanism to become effective.
For the second series of experiment, the test results for cyclic loading of CD40xx-x (specimens with 18-D19 main
reinforcements) and CD30xx-x (specimens with 12-D19 main reinforcements) are given Fig. 5 and 6,
respectively. In the above figures, (a) show the lateral force-displacement curves and (b) show the
moment-rotation curves. Among these specimens, CD40FS-F and CD30FS-F are the benchmark test,
representing the fixed base case or case with a footing of very large size. they can also signify the capacity of
columns with 18 main steels and 12 main steel, respectively. By comparing the results of CD40FS-F, CD40FB-R
and CD40FS-R, it is noted that the rocking behavior becomes more pronounced as the dimension of footing
decreases. Also, the maximum value of lateral forces that the column sustained decreases with the decrease in
footing size. Besides, the maximum value of the bending moment that the column sustained decreases with the
decrease in footing size, too. Because the maximum values of moment sustained by these two rocking case are less
than the moment capacity of columns indicated by CD40FS-F, the moment-rotation curves for both cases are
almost linear, implying that not much plastic deformation occurred in columns.
drift (%)
-8 -6 -4 -2 0 2 4 6 8
drift (%)
-8 -6 -4 -2 0 2 4 6 8
drift (%)
-8 -6 -4 -2 0 2 4 6 8
Lateral force (kN)
200
100
0
-100
CD40FS-F
Lateral force (kN)
200
100
0
-100
CD40FB-R
Lateral force (kN)
200
100
0
-100
CD40FS-R
-200
-200
-200
Moment (kN-m)
600
500
400
300
200
100
0
-100
-200
-300
-400
-500
-600
-200 -100 0 100 200
lateral displacement (mm)
CD40FS-F
-0.08-0.06-0.04-0.02 0 0.02 0.04 0.06 0.08
Rotation (radian)
Moment (kN-m)
-200 -100 0 100 200
lateral displacement (mm)
(a) Lateral force-displacement curves
600
500
400
300
200
100
0
-100
-200
-300
-400
-500
-600
CD40FB-R
-0.08-0.06-0.04-0.02 0 0.02 0.04 0.06 0.08
Rotation (radian)
Moment (kN-m)
600
500
400
300
200
100
0
-100
-200
-300
-400
-500
-600
-200 -100 0 100 200
lateral displacement (mm)
CD40FS-R
-0.08-0.06-0.04-0.02 0 0.02 0.04 0.06 0.08
Rotation (radian)
(b) Moment-rotation curves
Figure 5 Experimental results for the cyclic loading test of specimens CD40xx-x
Next, by comparing the results of CD30FS-F, CD30FB-R and CD30FS-R, it is also observed that with the
decrease in footing size, the nonlinear rocking behavior becomes more pronounced. And consequently the
plastic deformation occurred in column base became minor. For instance, the moment-rotation curve for the case
with a smaller footing (CD30FS-R) is almost linear, while some plastic deformation was formed in the case with
a larger footing (CD30FB-R). For CD30FB-R, the upper limit value of moment corresponding to the base
moment limitation sustained by the foundation was higher than the moment capacity of column indicated by
CD30FB-F. Therefore, before the base moment of the footing could reach its limit value, the column already
yielded. On the other hand, for specimen CD30FS-R, the upper limit value of the bending moment sustained by
column was lower than the moment capacity indicated in CD30FB-F. Thus, the column can still remain in
elastic state. These experiments showed that if the footing of the column is allowed to rock, the moment that the
column has to sustain can be limited to a certain value. This upper limit value can be calculated based on a
simple equation only related to the footing size and the total vertical force of gravity (Hung et al. 2010a). If this
limit value for moment is lower than bending moment strength of the column, the plastic deformation will not
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