STUDY ON REHABILITATED RC BEAM-COLUMN CONNECTIONS WITH BEAM WEAK IN FLEXURE
3.5 COMPARISON OF TEST RESULTS OF CONTROL AND REHABILITATED SPECIMENS
3.5 COMPARISON OF TEST RESULTS OF CONTROL AND REHABILITATED
type-1 and type-2 can not be made because of different applied rehabilitation strategies.
Depending on the extent of damage, different rehabilitation strategies were considered.
The appropriately chosen repair strategy could retrieve back the lost capacity even for a severely damaged connections. Table 3.1 summarized load carrying capacities of all the specimens. It is seen from table 3.1 that specimens damaged under loading type-1 and type-2 could restored their load carrying capacity after rehabilitation. Thus, it may be inferred that the applied repair techniques are effective in restoring the load carrying capacity.
Fig. 3.17 Envelope curves for BWFL specimens -90
-60 -30 0 30 60 90
-80 -60 -40 -20 0 20 40 60 80
Beam tip load (kN)
Beam tip displacement (mm) BWFLRe : Type-1
BWFLC : Type-1 BWFLRe : Type-2 BWFLC : Type-2
-50 -30 -10 10 30 50
-70 -50 -30 -10 10 30 50 70
Beam tip load (kN)
BWFMRe: Type-1 BWFMC : Type-1 BWFMRe: Type-2 BWFMC : Type-2
Table 3.1 Ultimate load carrying capacity for beam weak in flexure (BWF) specimens Specimen
size
Control specimens Rehabilitated specimens +ve load
(kN)
- ve load (kN)
Avg.load (kN)
+ve load (kN)
- ve load (kN)
Avg.
load (kN) Specimens subjected to loading type-1
Full 74.55
*30, #22
72.02
*30, #22
73.285 84.39
*30, #22
83.78
*30, #22
84.085
Medium 36.95
*16.67, #16
32.74
*26.67, #25
34.845 42.13
*33.33, #34
39.86
*33.33, #34
40.995
Small 9.98
*13.33, #28
9.79
*10, #25
9.885 14.33
*23.33, #49
9.45
*13.33, #28
11.89
Specimens subjected to loading type-2
Full 72.23
*40, #10
74.98
*35, #9
73.605 72.78
*40, #10
83.35
*35, #9
78.065
Medium 36.00
*20, #8
35.99
*20, #8
35.995 39.50
*20, #8
39.00
*20, #8
39.250
Small 10.35
*25, #17
10.05
*16.67, #12
10.200 11.72
*26.67, #18
11.00
*21.67, #15
11.360
Note: * and #: displacement and cycle number corresponding to its maximum load -ve: Push direction and +ve: Pull direction
Fig. 3.19 Envelope curves for BWFS specimens -15
-10 -5 0 5 10 15
-40 -30 -20 -10 0 10 20 30 40
Beam tip load (kN)
Beam tip displacement (mm) BWFSRe : Type-1
BWFSC : Type-1 BWFSRe : Type-2 BWFSC : Type-2
(b) Stiffness degradation
Secant stiffness is evaluated as the peak-to-peak stiffness of the beam tip load- displacement relationship. The secant stiffness is an index of the response of the specimen during a cycle and its strength degradation from a cycle to the following cycle. It is calculated as the slope of the line joining the peak of positive and negative capacity at a given cycle. The procedure for calculation is shown in Fig. 3.20. Two points A and A/ in positive and negative direction of the envelope curve for a particular amplitude are joined by a straight line. The slope of this straight line is the stiffness (K) of the joint assemblage corresponding to that particular amplitude and is calculated by the following expression as recommended by Naeim and Kelly [1999].
- -
D D
D D
F F K D D
+ +
= −
− (3.1)
where DD+ and DD- in Eq. 3.1 are the X co-ordinates of A and A/ respectively, FD+andFD− are the corresponding Y co-ordinates in the envelope curve (Fig. 3.20).
Drift angle is defined as the ratio of beam tip displacement to the length of the beam. Drift obtained by horizontally displacing the beam ends are equivalent to the inter storey drift angle of a frame structure subjected to lateral loads.
The effectiveness of a rehabilitation techniques in restoring the stiffness of damaged connections may be evaluated by comparing stiffness versus drift angle plots for different cases. These plots for all the specimens under loading type-1 and type-2 are shown in Fig.
3.21-3.26. Comparing these curves (control and rehabilitated), the stiffness attained by the rehabilitated specimen at the beginning of the test was observed to be significantly lower.
However, at the end of the test, the stiffness attained in both control and rehabilitated specimens are comparable.
Fig. 3.21 shows the variation of stiffness with drift angle for both control and the rehabilitated large size specimens under loading type-1. The stiffness attained by the control specimen corresponding to the first displacement amplitude of ±1.4 mm (drift angle of 0.103 %) is 11.56 kN/mm, while that for rehabilitated is 8.02 kN/mm. Thus, after repairing there was a reduction in stiffness of about 30.62 %. At the second amplitude of
±5.0 mm (drift angle of 0.37 %), the stiffness of control specimen got reduced by 32.45
%. At the same drift angle of 0.37 %, the reduction in stiffness for the rehabilitated specimen was found to be 20.60 %.
Similarly, variation of stiffness with drift angle for both control and the rehabilitated large size specimens under loading type-2 is shown in Fig. 3.22. The stiffness of the rehabilitated specimen is 9.00 kN/mm, while that for control specimen is 11.54 kN/mm.
A reduction in stiffness of 22.01 % after repairing was observed. The reduction in stiffness corresponding to a displacement amplitude of ±5.0 mm were calculated in both control and rehabilitated specimens. The degradation of stiffness is little slow for the repaired specimen at the same displacement level.
The variation of stiffness with drift angle for BWFMC and BWFMRe specimens under loading type-1 is shown in Fig. 3.23. It can be observed that the stiffness attained by the rehabilitated specimen is more than that of control except at the initial stage. The stiffness
for rehabilitated specimen is 8.65 kN/mm, while the same for control specimen is 11.00 kN/mm. Thus, repaired specimen exhibited a reduction in stiffness by 21.36 %.
Fig. 3.24 shows the plot of stiffness against drift angles for both control and the rehabilitated medium size specimens subjected to loading type-2. The stiffness of the rehabilitated specimen is 8.95 kN/mm, while that for control specimen is 11.30 kN/mm.
A reduction of stiffness about 20.80 % after repairing was observed. The stiffness of control specimen got reduced by 54.34 % at drift angle of 0.37 % while the reduction in stiffness for rehabilitated specimen was found to be 44.29 % at the same drift angle.
The stiffness degradation for both control and the rehabilitated small size specimens with loading type-1 and type-2 are shown in Fig. 3.25 and Fig. 3.26 respectively. The plot also showed similar trend of degradation in stiffness as that of full and medium size specimens.
Fig. 3.21 Stiffness versus drift angle for BWFL specimens under loading type-1 0
3 6 9 12
0 1 2 3 4 5 6
Stiffness (kN/mm)
Drift Angle (%)
BWFLC: Type-1 BWFLRe
Fig. 3.22 Stiffness versus drift angle for BWFL specimens under loading type-2
Fig. 3.23 Stiffness versus drift angle for BWFM specimens under loading type-1
Fig. 3.24 Stiffness versus drift angle for BWFM specimens under loading type-2 0
3 6 9 12
0 1 2 3 4 5 6
Stiffness (kN/mm)
Drift angle (%)
BWFLC: Type-2 BWFLRe
0 3 6 9 12
0 1 2 3 4 5 6 7 8
Stiffness (kN/m)
Drift angle (%)
BWFMC: Type-1 BWFMRe
0 3 6 9 12
0 1 2 3 4 5 6 7 8
Stiffness (kN/mm)
Drift angle (%)
BWFMC: Type-2 BWFMRe
Fig. 3.25 Stiffness versus drift angle for BWFS specimens under loading type-1
Fig. 3.26 Stiffness versus drift angle for BWFS specimens under loading type-2
Thus, comparing all these curves irrespective of loading types, a similar degradations trend was observed. Further, it is also observed that the degradation in stiffness for damaged specimens after rehabilitation is little slow with increase in lateral movement as compared to the control specimens. This behaviour may be attributed to the ductile properties introduced by the repairing materials. The lower degradation is a desirable property in earthquake like situations. It was observed during the past earthquake that
0 1 2 3 4
0 1 2 3 4 5 6 7 8 9
Stiffness (kN/mm)
Drift angle (%)
BWFSC: Type-1 BWFSRe
0 1 2 3 4
0 1 2 3 4 5 6 7 8 9
Stiffness (kN/mm)
Drift angle (%)
BWFSC: Type-2 BWFSRe
movement. Therefore, from these comparisons it can be concluded that all rehabilitated specimens satisfactorily achieved stiffness level which is well comparable to the control specimens.
(c) Energy dissipation
The ability of a structural element to resist an earthquake load depends to a large extent on its capacity to dissipate its energy. The area of hysteresis loop is a measure of the energy dissipated. The cumulative energy dissipated at a particular amplitude was calculated by summing up the energy dissipated in all the preceding cycles including that amplitude. The plots of cumulative energy dissipation versus drift angle for control as well as rehabilitated specimens are shown in Fig. 3.27-3.29. It may be noted that though the energy dissipation for loading type-1 and type-2 have been presented in the same figure, comparison between these two can not be made due to different loading characteristic.
On examination of these plots, it may be seen that the cumulative energy dissipated by the rehabilitated specimens are relatively lower during the initial stages of loading. On the contrary, in subsequent loading cycles, the energy dissipated by the damage specimen after rehabilitation are observed to be at par with those of the corresponding control specimens. The increase in stiffness at end of imposed displacement history attracted more load corresponding to any drift angle for the rehabilitated specimens in comparison to that of the control specimen. Thus, the total area enclosed by the plot of beam tip load versus beam tip displacement was more for rehabilitated specimens than those of the control specimen. This was perhaps the reason for improvement in cumulative energy dissipation in the subsequent loading cycles. Corresponding to the drift level upto which the control specimens were tested, the energy dissipated by the rehabilitated specimens
are slightly higher than the respective control specimens (Table 3.2). Thus, it may be observed that by adopting an appropriate rehabilitation methodology, even a severely damaged structure can successfully restore the energy dissipation capacity which is comparable to those of control specimens.
Fig. 3.27 Cumulative energy dissipation for BWFL specimens
Fig. 3.28 Cumulative energy dissipation for BWFM specimens 0
20 40 60 80
0 1 2 3 4 5 6
Cumulative energy dissipated (kN-m)
Drift angle (%) BWFLRe : Type-1
BWFLC : Type-1 BWFLRe : Type-2 BWFLC : Type-2
0 10 20 30 40
0 1 2 3 4 5 6 7 8
Cumulative energy dissipated (kN-m)
Drift angle (%) BWFMRe : Type-1
BWFMC : Type-1 BWFMRe : Type-2 BWFMC : Type-2
Fig. 3.29 Cumulative energy dissipation for BWFS specimens
Table 3.2 Energy dissipation (kN-m) for beam weak in flexure (BWF) specimens Specimens
sizes
Loading type-1 Loading type-2
Control Rehabilitated Control Rehabilitated
Large 47.18 53.91 18.18 19.29
Medium 32.02 35.53 12.72 14.38
Small 3.32 3.62 2.02 2.31
(d) Displacement ductility
Displacement ductility for all specimens were calculated from the respective envelope curves as per the procedure proposed by Shannag et al. [2005] which has been explained in Fig. 3.30. As shown in the figure, the yield displacement is calculated as the point of intersection between two straight lines drawn in the envelope curve. The first line was obtained by extending the line joining the origin and 50 % of ultimate load capacity point on positive and negative sides of the envelope curve, while the second line was obtained by drawing a horizontal line through the 80 % of ultimate load capacity point on either side. In the figure, dy1and dy2represent the yield displacement in positive and negative
0 1 2 3 4 5
0 1 2 3 4 5 6 7 8 9
Cumulative energy dissipated (kN-m)
Drift angle (%) BWFSRe : Type-1
BWFSC : Type-1 BWFSRe : Type-2 BWFSC : Type-2
direction on the envelope curve respectively. The average value of yield displacement obtained from both positive and negative direction was calculated. Horizontal lines drawn through the 80% of ultimate load capacity point on positive and negative side intersect the envelope curve at far end at points x1and x2. The average of abscissa of these two points (denoted by du1 and du2 in figure) was taken as maximum displacement. The displacement ductility was calculated as the ratio of maximum displacement to the yield displacement. The calculated values are listed in Table 3.3. It may be noted that the yield displacement for rehabilitated specimens was taken same as respective values of control specimens (Alsayed et al., 2010). The displacement ductility attained by the damaged control specimens after rehabilitation are found to be marginally higher than those of the control specimens. Further, the ductility attained by the specimens (control and rehabilitated) are found to be least for largest specimens and highest for small specimen in both loading type-1 and type-2.
Fig. 3.30 Procedures for ductility calculation
Table 3.3 Displacement ductility of beam weak in flexure (BWF) specimens Loading
type Specimens
Control Rehabilitated
∆y ∆20 ∆20/∆y ∆y ∆20 ∆20/∆y
Type-1
Large 8.25 58 7.03 8.25 60 7.27
Medium 5.5 40.5 7.36 5.5 42.5 7.73
Small 3.25 26 8 3.25 32 9.85
Type-2
Large 8 58.5 7.31 8 62.5 7.81
Medium 5 47 9.4 5 52 10.4
Small 3 31 10.33 3 36 12
∆y and ∆20 : Displacement at first yield and at 20 % drop of peak load (mm)