An analysis of five different building models created with five different column sections under the influence of earthquakes was made, and the analysis results were evaluated by showing separate tables, graphs, and figures for each model and each floor. The earthquake analysis parameters were taken from the Turkish 2018 Earthquake Regulation and analysed with the Sta4Cad program, and the results were given in a table for the five building models (Table 1).
Table 1. Earthquake Analysis parameters for building models.
Earthquake Standard
|
TBDY2018 CODE
|
Earthquake Analysis
|
MOD Superposition Method Linear Analysis
|
Earthquake Ground Motion
|
10% probability of exceeding DD2 in 50 years
|
Ground Class
|
ZC
|
Building Coordinate (Latitude/Longitude)
|
40.84184° / 31.15039°
|
Local Spectral Acceleration Coefficient Ss/Sı
|
1.321 / 0.358
|
Design Spectral Acceleration Coefficient Sds/Sdi
|
1.585 / 0.537 DD2
|
Building Behaviour Coefficient R: 3.78 received
|
Structures with Limited Ductility (SS) Frames
|
System Strength Excess Coefficient D
|
2,5 - A31
|
Earthquake Design Class “EDC”
|
1
|
Building Height Class “BHC”
|
6 Hn=16.0m
|
Building Utilization Class “BUC”
|
3 I=1.0
|
Modal Analysis Minimum Seismic Load Ratio ß
|
0.8
|
Earthquake Load Eccentricity
|
0.050
|
Performance Goals Normal Performance Target Evaluation/Design
|
DD2 KH (Controlled Damage), DGT (Design by Strength)
|
As a result of the analyses made, the earthquake loads affecting the floors of the buildings, the displacements on the floors, the maximum earthquake displacements, and the minimum earthquake joints for each building model are calculated separately for the "x" and "y" directions and given in tables.
3.1. Analysis of the Model Created by Columns with 35x35 cm Sections (Reference Model)
As a result of the dynamic analysis of the building model created with 35x35 cm section columns shows the graphs of the horizontal and vertical elastic design spectrum and acceleration values below (Figure2). Analysis results were given below (Table 2 and Table 3).
Table 2. Modal Analysis, Equivalent earthquake method, Earthquake loads and floor type
Floor
|
X DIRECTION
|
Y DIRECTION
|
Modal Analysis
|
Equivalent Earthquake Method
|
Earthquake Load
|
Floor Type
|
Modal Analysis
|
Equivalent Earthquake Method
|
Earthquake Load
|
Floor Type
|
5
|
71.318
|
110,850
|
85,842
|
Upstairs
|
70.293
|
110.850
|
85.290
|
Upstairs
|
4
|
66.227
|
103,046
|
79,715
|
Normal
|
65.756
|
103.046
|
79.784
|
Normal
|
3
|
45.185
|
79,266
|
54,387
|
Normal
|
45.013
|
79.266
|
54.617
|
Normal
|
2
|
36.498
|
55,486
|
43,931
|
Normal
|
36.341
|
55.486
|
44.094
|
Normal
|
1
|
33.939
|
32,258
|
40,851
|
Normal
|
33.743
|
32.258
|
40.942
|
Normal
|
Ʃ
|
253.166
|
380.908
|
304.726
|
General
|
251.146
|
380.908
|
304.726
|
General
|
Vtx= 253.166 > 0.04*I*Sds.W= 133.27 Vtx= 251.15 > 0.04*I*Sds.W= 133.27
X Earthquake control: 0.80x380.908 =304.726 >>>253.166
Y Earthquake control: 0.80x380.908 =304.726 >>>251.146
Table 3. Floor Earthquake displacements, Max. seismic displacement and min. seismic joint (mm), α=0.5 (R/I) 1.890
Floor
|
Hi (m)
|
Install
|
Install
|
Earthquake displacements
|
Earthquake joints
|
δx (m)
|
θz (rad)
|
δy (m)
|
θz (rad)
|
uiX
|
uiY
|
min. diX
|
min. diY
|
5
|
16.0
|
0,0609205
|
0,0002181
|
-0,059519
|
-0,001057
|
60.9
|
59.5
|
162.8
|
159.1
|
4
|
13.0
|
0,0564608
|
0,0002038
|
-0,055209
|
-0,000980
|
56.5
|
55.2
|
150.9
|
147.6
|
3
|
10.0
|
0,0483625
|
0,0001759
|
-0,047354
|
-0,000839
|
48.4
|
47.4
|
129.3
|
126.6
|
2
|
7.0
|
0,0375561
|
0,0001376
|
-0,036863
|
-0,000651
|
37.6
|
36.9
|
100.4
|
98.5
|
1
|
4.0
|
0,0242233
|
0,0000897
|
-0,023914
|
-0,000418
|
24.2
|
23.9
|
64.7
|
63.9
|
TBDY 3.6.2.1 A1 torsional irregularity; nbi=1.194<1.2 solved by modal analysis. "Controlled Damage Performance" could not be achieved in this model building, whose Performance Analysis was performed at 36.7%>20%. The ratio of plasticized column Vc was calculated as 100%>30%.
3.2. Analysis of the Model Created with 40x40 cm Section Columns
As a result of the dynamic analysis of the building model created with 40x40 cm section columns, the graphs of the horizontal and vertical elastic design spectrum and acceleration values are shown below (Figure 3). Analysis results were given below (Table 4 and Table 5).
Table 4. Modal Analysis, Equivalent earthquake method, Earthquake loads and floor type
Floor
|
X DIRECTION
|
Y DIRECTION
|
Modal Analysis
|
Equivalent Earthquake Method
|
Earthquake Load
|
Floor Type
|
Modal Analysis
|
Equivalent Earthquake Method
|
Earthquake Load
|
Floor Type
|
5
|
85,057
|
112,821
|
88,913
|
Upstairs
|
83,811
|
112,821
|
88,168
|
Upstairs
|
4
|
76,793
|
104,247
|
80,274
|
Normal
|
76,393
|
104,247
|
80,364
|
Normal
|
3
|
52,719
|
80,190
|
55,109
|
Normal
|
52,746
|
80,190
|
55,488
|
Normal
|
2
|
42,750
|
56,133
|
44,688
|
Normal
|
42,710
|
56,133
|
44,930
|
Normal
|
1
|
38,234
|
32,797
|
39,967
|
Normal
|
38,024
|
32,797
|
40,001
|
Normal
|
Ʃ
|
295,554
|
386,188
|
308,951
|
General
|
293,684
|
386,188
|
308,951
|
General
|
Vtx= 295.55 > 0.04*I*Sds*W= 135,12 Vty= 293,68 > 0.04*I*Sds*W= 135,12
X Earthquake control: 0.80x386,188 = 308,951 > 295,554
Y Earthquake control: 0.80x386,188 = 308,951 > 293,684
Table 5. Floor Earthquake displacements, Max. seismic displacement and min. seismic joint (mm), α=0.5 (R/I) 1.890
Floor
|
Hi (m)
|
Install
|
Install
|
Earthquake displacements
|
Earthquake joints
|
δx (m)
|
θz (rad)
|
δy (m)
|
θz (rad)
|
uiX
|
uiY
|
min. diX
|
min. diY
|
5
|
16.0
|
0,0459516
|
0,0001661
|
-0,044677
|
-0,000796
|
46.0
|
44.7
|
122.8
|
119.4
|
4
|
13.0
|
0,0423043
|
0,0001541
|
-0,041177
|
-0,000733
|
42.3
|
41.2
|
113.1
|
110.1
|
3
|
10.0
|
0,0358465
|
0,0001316
|
-0,034949
|
-0,000621
|
35.8
|
34.9
|
95.8
|
93.4
|
2
|
7.0
|
0,0272139
|
0,0001007
|
-0,026609
|
-0,000470
|
27.2
|
26.6
|
72.7
|
71.1
|
1
|
4.0
|
0,0166159
|
0,0000622
|
-0,016353
|
-0,000286
|
16.6
|
16.4
|
44.4
|
43.7
|
Earthquake structure release: x=0.00287, y=0.00279. "Controlled Damage Performance" could not be achieved in this model building, whose Performance Analysis was performed at 36.5%>20%. The plasticized column Vc rate was 72.2%>30%.
3.3. Analysis of the Model Created by Columns with 45x45 cm Sections
As a result of the dynamic analysis of the building model created with 45x45 cm section columns shows the graphs of the horizontal and vertical elastic design spectrum and acceleration values below (Figure4). Analysis results were given as tables (Table 6 and Table 7).
Table 6. Modal Analysis, Equivalent earthquake method, Earthquake loads and floor type
Floor
|
X DIRECTION
|
Y DIRECTION
|
Modal Analysis
|
Equivalent Earthquake Method
|
Modal Analysis
|
Equivalent Earthquake Method
|
Modal Analysis
|
Equivalent Earthquake Method
|
Modal Analysis
|
Equivalent Earthquake Method
|
5
|
96.932
|
114,888
|
96.932
|
Upstairs
|
95.900
|
114.888
|
95.900
|
Upstairs
|
4
|
84.763
|
105,531
|
84.763
|
Normal
|
85.048
|
105.531
|
85.048
|
Normal
|
3
|
58.830
|
81,177
|
58.830
|
Normal
|
59.452
|
81.177
|
59.452
|
Normal
|
2
|
47.724
|
56,824
|
47.724
|
Normal
|
48.093
|
56.824
|
48.093
|
Normal
|
1
|
40.875
|
33,421
|
40.875
|
Normal
|
40.960
|
33.421
|
40.960
|
Normal
|
Ʃ
|
329.124
|
391.841
|
329.124
|
General
|
319.452
|
391.841
|
329.452
|
General
|
Vtx= 363.26 > 0.04*I*Sds*W= 139.67 Vty= 362.69 > 0.04*I*Sds*W= 139.67
X Earthquake control: 0.80x401.254 = 321.003 >>>363.259
Y Earthquake control: 0.80x408.279 = 362.694 >>>326.623
Table 7. Floor Earthquake displacements, Max. seismic displacement and min. seismic joint (mm), α=0.5 (R/I) 1.890
Floor
|
Hi (m)
|
Install
|
Install
|
Earthquake displacements
|
Earthquake joints
|
δx (m)
|
θz (rad)
|
δy (m)
|
θz (rad)
|
uiX
|
uiY
|
min. diX
|
min. diY
|
5
|
16.0
|
0,0396922
|
0,0001224
|
-0,038185
|
-0,000688
|
39.7
|
38.2
|
106.1
|
102.1
|
4
|
13.0
|
0,0362648
|
0,0001134
|
-0,034950
|
-0,000629
|
36.3
|
35.0
|
96.9
|
93.4
|
3
|
10.0
|
0,0303646
|
0,0000979
|
-0,029335
|
-0,000526
|
30.4
|
29.3
|
81.2
|
78.4
|
2
|
7.0
|
0,0224819
|
0,0000767
|
-0,021814
|
-0,000388
|
22.5
|
21.8
|
60.1
|
58.3
|
1
|
4.0
|
0,0129390
|
0,0000497
|
-0,012676
|
-0,000221
|
12.9
|
12.7
|
34.6
|
33.9
|
Earthquake structure release: x=0.00248, y=0.00239. Controlled Damage Performance" could not be achieved because the performance analysis was 55.7%>20% in this model building. Since the Vc ratio is 0%<30%, no plasticizing column exists.
3.4. Analysis of the Model Created with 50x50 cm Section Columns
As a result of the dynamic analysis of the building model created with 50x50 cm section columns, the graphs of the horizontal and vertical elastic design spectrum and acceleration values are shown below (Figure 5). Analysis results were given as tables (Table 8 and Table 9).
Table 8. Modal Analysis, Equivalent earthquake method, Earthquake loads and floor type
Floor
|
X DIRECTION
|
Y DIRECTION
|
Modal Analysis
|
Equivalent Earthquake Method
|
Modal Analysis
|
Equivalent Earthquake Method
|
Modal Analysis
|
Equivalent Earthquake Method
|
Modal Analysis
|
Equivalent Earthquake Method
|
5
|
109.585
|
118,215
|
109.585
|
Upstairs
|
108.265
|
120.284
|
108.265
|
Upstairs
|
4
|
92.455
|
107,788
|
92.455
|
Normal
|
92.603
|
109.675
|
92.603
|
Normal
|
3
|
64.978
|
82,914
|
64.978
|
Normal
|
65.467
|
84.366
|
65.467
|
Normal
|
2
|
52.657
|
58,040
|
52.657
|
Normal
|
52.883
|
59.056
|
52.883
|
Normal
|
1
|
52.657
|
34,297
|
43.584
|
Normal
|
43.476
|
34.898
|
43.476
|
Normal
|
Ʃ
|
363.259
|
401.254
|
363.259
|
General
|
362.694
|
408.279
|
362.694
|
General
|
Vtx= 363.26 > 0.04*I*Sds*W= 139.67 Vty= 362.69 > 0.04*I*Sds*W= 139.67
X Earthquake control: 0.80x401.254 =321.003 >>>363.259
Y Earthquake control: 0.80x408.279 =362.694 >>>326.623
Table 9. Floor Earthquake displacements, Max. seismic displacement and min. seismic joint (mm), α=0.5 (R/I) 1.890
Floor
|
Hi (m)
|
Install
|
Install
|
Earthquake displacements
|
Earthquake joints
|
δx (m)
|
θz (rad)
|
δy (m)
|
θz (rad)
|
uiX
|
uiY
|
min. diX
|
min. diY
|
5
|
16.0
|
0,0368980
|
0,0001368
|
-0,035418
|
-0,000630
|
36.7
|
35.4
|
98.6
|
94.7
|
4
|
13.0
|
0,0334421
|
0,0001249
|
-0,032159
|
-0,000571
|
33.4
|
32.2
|
89.4
|
86.0
|
3
|
10.0
|
0,0277056
|
0,00001042
|
-0,026704
|
-0,000473
|
27.7
|
26.7
|
74.1
|
71.4
|
2
|
7.0
|
0,0200813
|
0,0000762
|
-0,019429
|
-0,000342
|
20.1
|
19.4
|
53.7
|
51.9
|
1
|
4.0
|
0,0110213
|
0,0000424
|
-0,010747
|
-0,000187
|
11.0
|
10.7
|
30.0
|
30.0
|
Earthquake structure release: x=0.00231, y=0.00221. "Controlled Damage Performance" could not be achieved because the performance analysis was 55.7%>20% in this model building. Since the Vc ratio is 0%<30%, no plasticizing column exists.
3.5. Analysis of the Model Created with 55x55 cm Section Columns
As a result of the dynamic analysis of the building model created with 55x55 cm section columns, the graphs of the horizontal and vertical elastic design spectrum and acceleration values are shown below (Figure 6). Analysis results were given as tables (Table 10 and Table 11).
Table 10. Modal Analysis, Equivalent earthquake method, Earthquake loads and floor type
Floor
|
X DIRECTION
|
Y DIRECTION
|
Modal Analysis
|
Equivalent Earthquake Method
|
Earthquake Load
|
Floor Type
|
Modal Analysis
|
Equivalent Earthquake Method
|
Earthquake Load
|
Floor Type
|
5
|
121.160
|
129,253
|
121,160
|
Upstairs
|
119.861
|
131.638
|
119.861
|
Upstairs
|
4
|
98.463
|
117,080
|
98,463
|
Normal
|
98.897
|
119.241
|
98.897
|
Normal
|
3
|
69.750
|
90,062
|
69,750
|
Normal
|
70.448
|
91.724
|
70.448
|
Normal
|
2
|
56.453
|
63,043
|
56,453
|
Normal
|
56.783
|
64.207
|
56.783
|
Normal
|
1
|
45.618
|
37,487
|
45,618
|
Normal
|
45.520
|
38.179
|
45.520
|
Normal
|
Ʃ
|
391.444
|
436.926
|
391,444
|
General
|
391.508
|
444.987
|
391.508
|
General
|
Vtx= 391.44 > 0.04*I*Sds*W= 142.43 Vty= 391.51 > 0.04*I*Sds*W= 142.43
X Earthquake control: 0.80x436.926 = 349.541 >>>391.444
Y Earthquake control: 0.80x444.987 = 355.990 >>>391.508
Table 11. Floor Earthquake displacements, Max. seismic displacement and min. seismic joint (mm), α=0.5 (R/I) 1.890
Floor
|
Hi (m)
|
Install
|
Install
|
Earthquake displacements
|
Earthquake joints
|
δx (m)
|
θz (rad)
|
δy (m)
|
θz (rad)
|
uiX
|
uiY
|
min. diX
|
min. diY
|
5
|
16.0
|
0,0349540
|
0,0001318
|
-0,033504
|
-0,000593
|
35.0
|
33.5
|
93.4
|
89.6
|
4
|
13.0
|
0,0313859
|
0,0001191
|
-0,030149
|
-0,000532
|
31.4
|
30.1
|
83.9
|
80.6
|
3
|
10.0
|
0,0256931
|
0,0000983
|
-0,024744
|
-0,000435
|
25.7
|
24.7
|
68.7
|
66.1
|
2
|
7.0
|
0,0182144
|
0,0000703
|
0,0176612
|
-0,000308
|
18.2
|
17.6
|
48.7
|
47.1
|
1
|
4.0
|
0,0095430
|
0,0000373
|
-0,009299
|
-0,000161
|
9.5
|
9.3
|
30.04
|
30.0
|
Earthquake structure release: x=0.00231, y=0.00221. "Controlled Damage Performance" could not be achieved because the performance analysis was 24.4%>20% in this model building. Since the Vc ratio is 0%<30%, there is no plasticizing column.