1 Introduction
2 Experimental Program
2.1 The Tested Assemblies' Description
Assembly ID | Upgrading state | Tie column dim | Tie beam dim | Long RFT | Trans RFT | ||
---|---|---|---|---|---|---|---|
B (mm) | L (mm) | B (mm) | L (mm) | ||||
S-01 | Un-strengthened | 150 | 150 | 150 | 150 | 4T10 | T6@20 cm |
S-02 | Strengthened | 150 | 150 | 150 | 150 | 4T10 | T6@20 cm |
2.2 Test Configuration
2.3 Instrumentation
3 Experimental Observations and Discussion
3.1 Un-strengthened 3D Assembly Behavior and Failure Pattern
3.2 The Failure Pattern and Behavior of a Strengthened 3D Assembly
Id | Direction | First visible cracks stage | Maximum load stage | Failure stage | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Loads | Displacement at top story | Loads | Displacement at top story | Loads | Displacement at top story | |||||||||||
Load (kN) | Var.% | Disp. (mm) | Var.% | Drift | Load (kN) | Var.% | Disp. (mm) | Var.% | Drift | Load (kN) | Var.% | Displ (mm) | Var.% | Drift | ||
S-01 | Push | + 80 | – | + 6 | – | 0.0026 | 168 | – | 25 | – | 0.01 | 136 | – | 48 | – | 0.021 |
Pull | − 80 | – | − 6 | – | 0.0026 | − 154 | – | − 25 | – | 0.01 | − 114 | – | − 43 | – | 0.018 | |
S-02 | Push | 200 | 150# | 8 | 33# | 0.0035 | 270 | 61# | 27 | 8# | 0.011 | 246 | 80# | 33 | − 31# | 0.014 |
Pull | − 220 | 175# | − 10 | 67# | 0.0043 | − 300 | 95# | − 27 | 8# | 0.011 | − 265 | 132# | − 33 | − 23# | 0.014 |
3.3 Energy Dissipation
3.4 Hysteretic Damping
3.5 Stiffness Degradation
4 Numerical Analysis
4.1 Finite Element Model
4.2 Implementation and Numerical Assessment
Assembly ID | Direction | Max. load (kN) | Displacement in relation to the maximum load (mm) | Load cracking (kN) | Max. displacement (mm) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Exp | F.E.M | \(\frac{\mathrm{Exp}.}{\mathrm{F}.\mathrm{E}.\mathrm{M}.}\) | Exp | F.E.M | \(\frac{\mathrm{Exp}.}{\mathrm{F}.\mathrm{E}.\mathrm{M}.}\) | Exp | F.E.M | \(\frac{\mathrm{Exp}.}{\mathrm{F}.\mathrm{E}.\mathrm{M}.}\) | Exp | F.E.M | \(\frac{\mathrm{Exp}.}{\mathrm{F}.\mathrm{E}.\mathrm{M}.}\) | ||
S-01 | Push | 168 | 187 | 0.89 | 25 | 34 | 0.74 | 80 | 100 | 0.80 | 48 | 34 | 1.41 |
Pull | − 154 | − 182 | 0.85 | − 25 | − 34 | 0.74 | − 80 | − 105 | 0.76 | − 43 | − 34 | 1.26 | |
S-02 | Push | 270 | 306 | 0.88 | 27 | 20 | 1.35 | 200 | 220 | 0.90 | 33 | 25 | 1.65 |
Pull | − 300 | − 306 | 0.98 | − 27 | − 20 | 1.35 | − 220 | − 230 | 0.95 | − 33 | − 25 | 1.65 |
5 Parametric Study
Parametric study | ||||||
---|---|---|---|---|---|---|
No. of stories | No. of bays | Strengthening location of different wall sides | Longitudinal rft of tie columns | Shear links of tie columns | ||
One bay | Two bay | Three bay | ||||
One story | One story | One story | One story | Un-retrofitted specimen | 4T10 | T6@200 |
Two story | Two story | Two story | Two story | Retrofitted- full coverage specimen | T124 | T8@200 |
Three story
| Three story
| Three story
| Three story
| Retrofitted- front and back only specimen
| T164 | T10@200 |
Four story | Four story | Four story | Four story | Retrofitted- side walls only specimen | ||
Five story | Five story | Five story | Five story |
Damage state | DS1 | DS2 | DS3 | DS4 | ||||||
---|---|---|---|---|---|---|---|---|---|---|
STORY | BAY | Direction | Load (kN) | Drift ratio (%) | Load (kN) | Drift ratio (%) | Load (kN) | Drift ratio (%) | Load (kN) | Drift ratio (%) |
1 Story | 1 Bay | Pull | 89 | 0.06 | 155 | 0.137 | 389 | 0.96 | 378 | 1.38 |
Push | − 90 | − 0.06 | − 159 | − 0.137 | − 355 | − 1.38 | − 355 | − 1.38 | ||
2 Bays | Pull | 207 | 0.07 | 352 | 0.16 | 825 | 0.96 | 825 | 0.96 | |
Push | − 70 | − 0.07 | − 107 | − 0.16 | − 362 | − 0.96 | − 362 | − 0.96 | ||
3 Bays | Pull | 198 | 0.06 | 346 | 0.137 | 1076 | 0.83 | 1076 | 0.83 | |
Push | − 155 | − 0.05 | − 195 | − 0.137 | − 421 | − 0.83 | − 421 | − 0.83 | ||
3 Story | 1 Bay | Pull | 20 | 0.026 | 136 | 0.426 | 182 | 0.64 | 182 | 0.64 |
Push | − 46 | − 0.026 | − 139 | − 0.426 | − 184 | − 0.64 | − 184 | − 0.64 | ||
2 Bays | Pull | 57 | 0.03 | 109 | 0.053 | 498 | 0.64 | 498 | 0.64 | |
Push | − 57 | − 0.03 | − 109 | − 0.053 | − 324 | − 0.64 | − 324 | − 0.64 | ||
3 Bays | Pull | 128 | 0.026 | 245 | 0.053 | 758 | 0.426 | 758 | 0.426 | |
Push | − 126 | − 0.026 | − 147 | − 0.106 | − 347 | − 0.426 | − 347 | − 0.426 | ||
5 Story | 1 Bay | Pull | 60 | 0.264 | 108 | 0.396 | 121 | 0.53 | 121 | 0.53 |
Push | − 78 | − 0.264 | − 92 | − 0.396 | − 112 | − 0.53 | − 112 | − 0.53 | ||
2 Bays | Pull | 87 | 0.033 | 122 | 0.066 | 287 | 0.33 | 287 | 0.33 | |
Push | − 93 | − 0.033 | − 127 | − 0.066 | − 238 | − 0.33 | − 238 | − 0.33 | ||
3 Bays | Pull | 56 | 0.017 | 115 | 0.07 | 465 | 0.264 | 465 | 0.264 | |
Push | − 48 | − 0.017 | − 94 | − 0.07 | − 218 | − 0.264 | − 218 | − 0.264 |