Figure 1.
Verification algorithm proposed by Blandon and Priestley [
18].
Figure 1.
Verification algorithm proposed by Blandon and Priestley [
18].
Figure 4.
Time-history analysis/DDBD displacement average ratio using approach 1 and a set of synthetic accelerograms: (a) EPP (r = 0), (b) bilinear (r = 0.2), (c) Takeda model (“narrow” type, α = 0.5, β = 0.0, r = 0.05), (d) Takeda model (“fat” type α = 0.3, β = 0.6, r = 0.05).
Figure 4.
Time-history analysis/DDBD displacement average ratio using approach 1 and a set of synthetic accelerograms: (a) EPP (r = 0), (b) bilinear (r = 0.2), (c) Takeda model (“narrow” type, α = 0.5, β = 0.0, r = 0.05), (d) Takeda model (“fat” type α = 0.3, β = 0.6, r = 0.05).
Figure 5.
Time-history analysis/DDBD displacement average ratio using approach 2 and a set of synthetic accelerograms: (a) EPP (r = 0), (b) bilinear (r = 0.2), (c) Takeda model (“narrow” type, α = 0.5, β = 0.0, r = 0.05), (d) Takeda model (“fat” type α = 0.3, β = 0.6, r = 0.05).
Figure 5.
Time-history analysis/DDBD displacement average ratio using approach 2 and a set of synthetic accelerograms: (a) EPP (r = 0), (b) bilinear (r = 0.2), (c) Takeda model (“narrow” type, α = 0.5, β = 0.0, r = 0.05), (d) Takeda model (“fat” type α = 0.3, β = 0.6, r = 0.05).
Figure 6.
Time-history analysis/DDBD displacement average ratio using approach 1 and a set of natural accelerograms: (a,b) EPP (r = 0), (c,d) bilinear (r = 0.2), (e,f) Takeda model (“narrow” type, α = 0.5, β = 0.0, r = 0.05), (g,h) Takeda model (“fat” type α = 0.3, β = 0.6, r = 0.05).
Figure 6.
Time-history analysis/DDBD displacement average ratio using approach 1 and a set of natural accelerograms: (a,b) EPP (r = 0), (c,d) bilinear (r = 0.2), (e,f) Takeda model (“narrow” type, α = 0.5, β = 0.0, r = 0.05), (g,h) Takeda model (“fat” type α = 0.3, β = 0.6, r = 0.05).
Figure 7.
Time-history analysis/DDBD displacement average ratio using approach 2 and a set of natural accelerograms: (a,b) EPP (r = 0), (c,d) bilinear (r = 0.2), (e,f) Takeda model (“narrow” type, α = 0.5, β = 0.0, r = 0.05), (g,h) Takeda model (“fat” type α = 0.3, β = 0.6, r = 0.05).
Figure 7.
Time-history analysis/DDBD displacement average ratio using approach 2 and a set of natural accelerograms: (a,b) EPP (r = 0), (c,d) bilinear (r = 0.2), (e,f) Takeda model (“narrow” type, α = 0.5, β = 0.0, r = 0.05), (g,h) Takeda model (“fat” type α = 0.3, β = 0.6, r = 0.05).
Figure 8.
Four, eight, and twelve-storey vertically regular RC frames (dimensions in cm).
Figure 8.
Four, eight, and twelve-storey vertically regular RC frames (dimensions in cm).
Figure 9.
Linearized pushover curves (LPOC) obtained for the four-storey (a,b), eight-storey (c,d) and twelve-storey (e,f) frames designed with three different damping equations (Model Code 2009, Blandon and Priestley, proposed parameters) and approach 1 (a,c,e) or approach 2 (b,d,f).
Figure 9.
Linearized pushover curves (LPOC) obtained for the four-storey (a,b), eight-storey (c,d) and twelve-storey (e,f) frames designed with three different damping equations (Model Code 2009, Blandon and Priestley, proposed parameters) and approach 1 (a,c,e) or approach 2 (b,d,f).
Figure 10.
Displacement and inter-storey drift average envelopes obtained with NLTH for the three four-storey frames designed with different damping equations (Model Code 2009, Blandon and Priestley, proposed parameters) and approach 1 (a,b) or 2 (c,d), compared with the DDBD design profile.
Figure 10.
Displacement and inter-storey drift average envelopes obtained with NLTH for the three four-storey frames designed with different damping equations (Model Code 2009, Blandon and Priestley, proposed parameters) and approach 1 (a,b) or 2 (c,d), compared with the DDBD design profile.
Figure 11.
Displacement and inter-storey drift average envelopes obtained with NLTH for the three eight-storey frames designed with different damping equations (Model Code 2009, Blandon and Priestley, proposed parameters) and approach 1 (a,b) or 2 (c,d), compared with the DDBD design profile.
Figure 11.
Displacement and inter-storey drift average envelopes obtained with NLTH for the three eight-storey frames designed with different damping equations (Model Code 2009, Blandon and Priestley, proposed parameters) and approach 1 (a,b) or 2 (c,d), compared with the DDBD design profile.
Figure 12.
Displacement and inter-storey drift average envelopes obtained with NLTH for the three twelve-storey frames designed with different damping equations (Model Code 2009, Blandon and Priestley, proposed parameters) and approach 1 (a,b) or 2 (c,d), compared with the DDBD design profile.
Figure 12.
Displacement and inter-storey drift average envelopes obtained with NLTH for the three twelve-storey frames designed with different damping equations (Model Code 2009, Blandon and Priestley, proposed parameters) and approach 1 (a,b) or 2 (c,d), compared with the DDBD design profile.
Table 1.
Literature equivalent viscous damping equations.
Table 1.
Literature equivalent viscous damping equations.
Structural System | Formulation |
---|
Bilinear elasto-plastic system [31] | |
Takeda model [32] | |
Iwan model [33] | |
Takeda model, α = 0.5 e β = 0, [34] | |
Steel members [3] | |
Concrete frame structures [3] | |
Prestressed concrete frame or cantilever structures [3] | |
Table 2.
Parameters for the computation of elastic response spectra.
Table 2.
Parameters for the computation of elastic response spectra.
Limit State | | | |
---|
OP | | | |
DL | | | |
LS | | | |
NC | | | |
Table 3.
Sets of parameters a and d in Equation (4) for each hysteretic model.
Table 3.
Sets of parameters a and d in Equation (4) for each hysteretic model.
| | Elastic P. Plastic | Bilinear | Takeda “Narrow” | Takeda “Fat” |
---|
Literature set by Blandon and Priestley [18] | a | 140 | 160 | 95 | 130 |
d | 2 | 4 | 4 | 4 |
Set 1 (Approach 1) | a | 59 | 113 | 68 | 100 |
d | 1.1 | 1 | 1 | 1.1 |
Set 2 (Approach 2) | a | 80 | 142 | 81 | 120 |
d | 1.1 | 1 | 1 | 1.1 |
Table 4.
Natural ground motions considered in the study.
Table 4.
Natural ground motions considered in the study.
Location | Year | Station | Name | PGA [g] | Arias Intensity | Significant Duration | Near/Far Field |
---|
San Fernando | 1971 | Hollywood, LA | NGA68 | 0.21 | 62.57 | 10.49 | far |
Friuli | 1976 | Tolmezzo | NGA125 | 0.35 | 150.17 | 8.48 | far |
Imperial Valley | 1940 | El Centro | NGA174 | 0.36 | 188.43 | 8.7 | far |
Superstition Hills | 1987 | Poe Road | NGA725 | 0.45 | 201.44 | 13.81 | far |
Landers | 1992 | Cool water | NGA848 | 0.28 | 116.89 | 10.43 | far |
Duzce | 1999 | Bolu | NGA602 | 0.73 | 358.23 | 8.51 | far |
Koacaeli | 1999 | Arcelik00 | NGA1148 | 0.22 | 27.81 | 11.01 | far |
Chi-Chi | 1999 | CHY101 | NGA1244 | 0.35 | 223.20 | 30.38 | far |
Imperial Valley | 1940 | Chiuahua 282 | NGA165 | 0.25 | 114.19 | 22.05 | near |
Irpinia | 1980 | Sturno 00 | NGA292 | 0.25 | 114.78 | 15.05 | near |
Nahanni | 1985 | Site2 | NGA495 | 0.49 | 82.11 | 9.87 | near |
Loma Prieta | 1989 | Bran | NGA741 | 0.48 | 515.92 | 8.97 | near |
Denali | 2002 | TAPS pump station | NGA2114 | 0.39 | 190.30 | 21.55 | near |
Chi-Chi | 1999 | TCU102 | NGA1529 | 0.17 | 164.94 | 19.93 | near |
Duzce | 1999 | Duzce | NGA1605 | 0.35 | 259.31 | 10.95 | near |
Table 5.
Cross section dimensions of columns (dimensions in cm).
Table 5.
Cross section dimensions of columns (dimensions in cm).
| 4 Storeys | 8 Storeys | 12 Storeys |
---|
| Inner Columns | Outer Columns | Inner Columns | Outer Columns | Inner Columns | Outer Columns |
---|
12 | | | | | 30 × 40 | 30 × 40 |
11 | | | | | 30 × 45 | 30 × 40 |
10 | | | | | 30 × 50 | 30 × 40 |
9 | | | | | 30 × 55 | 30 × 45 |
8 | | | 30 × 40 | 30 × 40 | 40 × 60 | 30 × 50 |
7 | | | 30 × 45 | 30 × 40 | 40 × 60 | 40 × 50 |
6 | | | 30 × 50 | 30 × 40 | 40 × 65 | 40 × 55 |
5 | | | 30 × 55 | 30 × 45 | 40 × 70 | 40 × 60 |
4 | 30 × 40 | 30 × 40 | 40 × 60 | 30 × 50 | 45 × 70 | 40 × 65 |
3 | 30 × 45 | 30 × 40 | 40 × 60 | 40 × 50 | 50 × 70 | 40 × 70 |
2 | 30 × 50 | 30 × 45 | 40 × 65 | 40 × 55 | 55 × 70 | 45 × 70 |
1 | 30 × 55 | 30 × 50 | 40 × 70 | 40 × 60 | 60 × 70 | 50 × 70 |
Table 6.
DDBD parameters of frames designed with approach 1 and different equivalent viscous damping formulations.
Table 6.
DDBD parameters of frames designed with approach 1 and different equivalent viscous damping formulations.
| Storeys | |
|
|
| % |
|
|
|
---|
Model Code 09 formulation | 4 | | | | | | | | |
8 | | | | | | | | |
12 | | | | | | | | |
Formulation and parameter set proposed by Blandon and Priestley [18] | 4 | | | | | | | | |
8 | | | | | | | | |
12 | | | | | | | | |
Formulation proposed by Blandon and Priestley [18] and calibrated parameter set 1 | 4 | | | | | | | | |
8 | | | | | | | | |
12 | | | | | | | | |
Table 7.
DDBD parameters of frames designed with approach 2 and different equivalent viscous damping formulations.
Table 7.
DDBD parameters of frames designed with approach 2 and different equivalent viscous damping formulations.
| Storeys | |
|
|
| % |
|
|
|
---|
Model Code 09 formulation | 4 | | | | | | | | |
8 | | | | | | | | |
12 | | | | | | | | |
Formulation and parameter set proposed by Blandon and Priestley [18] | 4 | | | | | | | | |
8 | | | | | | | | |
12 | | | | | | | | |
Formulation proposed by Blandon and Priestley [18] and calibrated parameter set 2 | 4 | | | | | | | | |
8 | | | | | | | | |
12 | | | | | | | | |
Table 8.
Maximum inter-storey drift ratios (in percentage) obtained from nonlinear time-history analyses.
Table 8.
Maximum inter-storey drift ratios (in percentage) obtained from nonlinear time-history analyses.
| DDBD | Approach 1 | Approach 2 |
---|
| | Model Code | Blandon and Priestley | Modified Parameters | Model Code | Blandon and Priestley | Modified Parameters |
---|
4 storeys | 2.5 | 2.45 | 2.42 | 2.11 | 2.4 | 2.29 | 2.13 |
8 storeys | 2.5 | 2.32 | 2.28 | 2.12 | 2.31 | 2.26 | 2.16 |
12 storeys | 2.5 | 2.4 | 2.32 | 2.19 | 2.34 | 2.32 | 2.27 |