# Seismic Response of Steel SMFs Subjected to Vertical Components of Far- and Near-Field Earthquakes with Forward Directivity Effects

Authors: Shahrokh Shahbazi; Iman Mansouri; Jong Wan Hu; Noura Sam Daliri; Armin Karami
Journal: Advances in Civil Engineering
 (2019)

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## Abstract

In the near-field earthquake, forward directivity effects cause long-period pulse with a short effective time and a large domain in the velocity time history. This issue increases the ductility needs of structures, and in recent decades, the destructive effects of these kinds of records have been evaluated in comparison with far-field earthquakes. This brings about the necessity to compare a structure’s behavior subjected to vertical components of near-field (NF) earthquakes, including forward directivity effects vs. the effects of vertical components of far-field (FF) earthquakes. The present study investigated 3-, 5-, 8-, and 20-story steel moment frames with special ductility (SMF) through which modeling effects of panel zone have been applied, subjected to vertical component of near-field (NF) earthquakes with forward directivity and the vertical component of far-field earthquakes. By investigating the results, it can be clearly seen that the average values of the maximum displacement, shear force of the stories, and the velocity of each story under the impact of the near-field earthquake are greater than the amount of that under the effect of a far-field earthquake. However, this comparison is not valid for the amount of acceleration, axial force, and moments in the columns of the structures accurately.


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## Body

## 1. Introduction

Near-fault (NF) ground motions are specified by long-period velocity and displacement pulses [1] and high values of the ratio between the peak of vertical and horizontal ground accelerations [2]. In near-fault earthquakes, the fault geometry position related to the considered place is significant besides the rupture mechanism and kind of faulting. The amplitude of this pulse depends on the directivity of rupture distribution to the site. Since the rupture diffusion velocity is almost the same as the velocity of shear wave diffusion, if the fault rupture propagates to the considered place, the waves in a short-term period will reach to the place resulted in a pulse with high amplitude and short period that is called forward-effect directivity [3, 4].Over the past thirty years, there have been leading developments in the way that characteristics of vertical ground motion are interpreted and quantified [5–9]. In comparison with other studies, these researches have determined that vertical response spectra are most susceptible to spectral period and source-to-site distance. Additionally, the vertical-to-horizontal (V/H) response spectral ratios are higher on soil than on rock, and at shorter periods than at longer periods, in general [10].In engineering design, the vertical-to-horizontal acceleration (V/H) ratios of peak ground acceleration are usually recommended as 2/3. Moreover, the shape of the vertical response spectrum is similar to that of the horizontal response spectrum. During the recent years, it was understood that the areas near the epicenter and faults exert a strong vertical ground motion. The vertical-to-horizontal V/H response spectral ratios are greater than 2/3. The ratios for long periods were smaller than the value of that for short periods. In the past studies, it has been found that the V/H response spectral ratios are potently related to the period and site-to-source distance during the 1994 Northridge earthquake [11].In the seismic design of critical structures such as nuclear power plants and dams, vertical ground motions are frequently considered. However, some researches over the previous ten years recommend that the vertical ground motion component can have a great impact on the seismic response of common highway bridges especially for the sites placed in almost 15 km of major faults, as well [12–14].Although, in recent years, nonlinear dynamic analysis has become standard practice to figure out the seismic performance of structures, applying the direct analysis to evaluate the critical demands is computationally expensive and difficult. As a result, the main goal of the present research is to perform extensive nonlinear dynamic analyses and obtain all important demands of structures for comparing the results of near-field and far-field ground motions.In particular, the seismic response of steel moment frame with special ductility is investigated under the effect of panel zone modeling subjected to vertical components of near-field earthquakes with the forward directivity effect and vertical components of far-field earthquakes. To this end, velocity, vertical acceleration, vertical displacement, column axial force, moment column, and the shear force of the stories under the impact of far- and near-field earthquakes have been compared in 3-, 5-, 8-, and 20-story structures.In previous studies, the comparison of near-field and far-field earthquakes has been mentioned repetitively. However, near-field earthquakes are divided into two subdivisions: forward directivity and filling step. This research is the first to study the effect of the vertical component of near-field and far-field earthquake with forward directivity on the behavior of steel moment frames with special ductility. In order to obtain better results of this comparison, some of the major elements for the engineers and designers, e.g., axial force in the columns, generated a moment in the columns, maximum drift, and shear force, have been applied.


## 2. Characteristics of Modeled Buildings

In the present paper, 3-, 5-, 8-, and 20-story buildings were selected for the analysis. All modeled structures are shown in Figure1. Also, the 20-story building is represented from reference [15]. According to the classification of the HAZUS-MH MR5 [16] instruction, 3-, 5-, 8-, and 20-story buildings are categorized as low-, middle-, and high-rise buildings.Figure 1
Topology of 20-, 8-, 5-, and 3-story buildings.The lateral resisting systems are the special moment resisting frame inX and Y directions. They were used in order to examine the seismic behavior of four models constructed in very high-risk zones on soil type III. ETABS software and Iranian national building code [17] were used for the seismic design of these four models.According to the European standard profiles, different types of profiles were considered for beams and columns. As a result, profile we were used for the beams, and the box-shaped section was considered for columns (Table1).Table 1
Sections of 3-, 5-, and 8-story structures.
No.
Column
Beam
3-story
1
Tube 200 × 200 × 20
IPE 300
2
Tube 200 × 200 × 20
IPE 300
3
Tube 200 × 200 × 20
IPE 270
4
Tube 280 × 280 × 20
IPE 400
5
Tube 280 × 280 × 20
IPE 300
6
Tube 280 × 280 × 20
IPE 270
5-story
1
Tube 240 × 240 × 20
IPE 330
2
Tube 240 × 240 × 20
IPE 360
3
Tube 180 × 180 × 20
IPE 240
4
Tube 300 × 300 × 20
IPE 330
5
Tube 300 × 300 × 20
IPE 360
6
Tube 240 × 240 × 20
IPE 240
8-story
1
Tube 340 × 340 × 20
IPE 450
2
Tube 340 × 340 × 20
IPE 450
3
Tube 280 × 280 × 20
IPE 450
4
Tube 200 × 200 × 20
IPE 360
5
Tube 400 × 400 × 20
IPE 450
6
Tube 400 × 400 × 20
IPE 450
7
Tube 340 × 340 × 20
IPE 450
8
Tube 280 × 280 × 20
IPE 360
The below syntax is used for the position of columns and beams in the result of analysis (Table8). Cij∗ is the code for location of columns results. i = number of stories. Bik∗ is the code for location of beams results. j = number of columns from the left of structures. k = number of spans from the left of structures.Different assumptions were made in the present study. In all stories, dead and live loads were 650 kg/m2 and 200 kg/m2, respectively. However, different loads were applied for roofs, at 540 kg/m2 and 150 kg/m2, respectively. The columns are assumed to be axially flexible. Thus, the beams should be simulated as flexible members in all directions [18]. In a real structure, the vertical flexibility (bending) of very stiff beams is larger than the axial flexibility of the columns. Elastic elements were considered for all beams and columns in OpenSees, a software application employed for modeling these structures. Bilin Material was used to describe the behavioral properties of the elements. In addition, the Krawinkler Panel Zone Model [19] was used (Figure 2).Figure 2
Schematic representation of a typical panel zone [19].The panel zone deforms primarily in shear due to the opposing moments in the columns and beams. The panel zone was explicitly modeled using the method of Gupta and Krawinkler [20] as a rectangle composed of eight very stiff elastic beam-column elements with one rotational spring to represent shear distortions in the panel zone [21] (Figure 2).The Bilin Material imitates the Modified Ibarra-Medina-Krawinkler Deterioration Model with a bilinear hysteretic response. Figure3 shows the parameters of Bilin Material. The relationships between variables were developed following Lignos and Krawinkler [22].Figure 3
The Modified Ibarra-Medina-Krawinkler Deterioration Model [22].The fundamental horizontal periods of 3-, 5-, 8-, and 20-story buildings were 0.48, 0.91, 0.78, and 3.57 seconds, respectively. Moreover, the fundamental vertical periods of 3-, 5-, 8-, and 20-story buildings were 0.065, 0.11, 0.09, and 0.36 seconds, respectively.To represent the structure’s nonlinear behavior, the studied structures were modeled with elastic beam-column elements connected by rotational springs. Based on the Modified Ibarra Krawinkler Deterioration Model, the springs follow a bilinear hysteretic response.The plastic hinge was modeled by a rotational spring placed in the middle of the reduced beam sections (RBS). An elastic beam-column element was used to connect the spring and the panel zone.Since an elastic element as a model of a frame member was connected in series with rotational springs at either end, the stiffness of these components had to be modified in order that the equivalent stiffness of this assembly was equivalent to the stiffness of the actual frame member [23].


## 3. Near-Field Earthquakes

Near-field ground motions are more complex than the far-field records, and this difference can change the response characteristics of the structure significantly. The main characteristics of near-field ground motions are as follows: (1) permanent displacement (fling) effect induced by the permanent tectonic offset of a rupturing fault; (2) severe impulsive velocity effect observed in the velocity time histories of various strong-motion earthquakes (e.g., 2015 Nepal earthquake); and (3) hanging-wall by which earthquakes at sites placed on the hanging wall of a dip-slip fault are larger than at sites placed on the footwall at the same distance [24].In earthquakes occurring near the fault, diverse key factors, including geometry position, failure mechanism, and faulting, appear to be important. As in most cases with a high period describing a kind of excitation like a strike, ground velocity can result in pulse [25]. In addition, one of the features of near-field earthquake records including forward directivity is the existence of long-period pulses in their velocity time history. These pulses can be observed in the velocity time history of the vertical and horizontal components of these records (Figure 4).Figure 4
Velocity-time history of vertical and horizontal components of near-field earthquake with the effect of forward directivity.


## 4. Selection of Ground Motions

In the evaluation of structures in time history analyses, various factors seem to play a major role. The selection of ground motions has been made so that they all represent the Mw = 6.5 template scenario as the result of the risk segmentation in Iran’s with very high seismic zones. Furthermore, as the conditions of a site have a significant effect on the characteristics and frequency content of the strong ground motion records, the ground motions were selected to ensure that the average of the spectrum resultant closely matches the design spectrum at all periods (Figures5 and 6). Based on this, 15 earthquake records for both near- and far-field subjected to forward directivity have been considered for the evaluation of nonlinear time-history. Near- and far-field earthquakes which were calculated on type 3 soil have been recorded in the maximum from 10 to 100 km away from the fault, respectively. The magnitudes of near- and far-field earthquakes ranged from 6.53 to 6.93 moment magnitude scale and 6.4 to 7.5 moment magnitude scale, respectively. Tables 2 and 3 demonstrate the seismographs and their related characteristics.Figure 5
Elastic response spectral acceleration for far-field records.Figure 6
Elastic response spectral acceleration for near-field records.Table 2
Near-field records.
#Records
Event name
Year
Station
Mw
Vertical PGA (g)
PGA (g)
R (km)
#Record1
Erzican
1992
Erzican
6.69
0.234
0.49
2
#Record2
Imperial Valley
1979
EC country
6.53
0.244
0.23
7.31
#Record3
Imperial Valley
1979
“El Centro-Meloland Geot. Array”
6.53
0.248
0.32
0.07
#Record4
Kobe
1995
KJMA
6.9
0.338
0.83
0.94
#Record5
Kobe
1995
“Port Island (0 m)”
6.9
0.566
0.35
3.31
#Record6
Kobe
1995
Takatori
6.9
0.284
0.67
1.46
#Record7
Northridge-01
1994
Newhall-Fire Sta
6.69
0.548
0.59
3.16
#Record8
“Imperial Valley-06”
1979
“Brawley Airport”
6.53
0.1528
0.22
8.54
#Records9
Loma Prieta
1989
Saratoga-W Valley Coll
6.93
0.3957
0.33
8.48
#Records10
Northridge-01
1994
Rinaldi Receiving Sta
6.69
0.958
0.87
0
#Records11
Northridge-01
1994
Sylmar-Converter Sta
6.69
0.605
0.92
0
#Records12
“Imperial Valley-06”
1979
“El Centro Array #10”
6.5
0.109
0.14
6.2
#Records13
“Imperial Valley-06”
1979
“Holtville Post Office”
6.5
0.256
0.26
7.7
#Records14
“Loma Prieta”
1989
“Gilroy Array #2”
6.93
0.295
0.32
12.7
#Records15
“Loma Prieta”
1989
“Gilroy Array #3”
6.93
0.341
0.37
14.4
PGA: peak ground acceleration.Table 3
Far-field records.
#Records
Event name
Year
Station
Vertical PGA (g)
PGA (g)
Mw
R (km)
#Record1
Imperial Valley-06
1979
Calexico, Fire Station
0.193
0.27
6.5
10.45
#Record2
Kocaeli_ Turkey
1999
Duzce
0.206
0.36
7.5
98.2
#Record3
Landers
1992
Palm Springs, Airport
0.111
0.075
7.2
36.15
#Record4
Landers
1992
Yermo Fire station
0.1358
0.24
7.3
86
#Record5
Loma Prieta
1989
Coyote Lake Dam, downstream
0.095
0.18
7.1
20.8
#Record6
San Frenando
1971
LA-Hollywood stor
0.164
0.22
6.6
39.5
#Record7
Big Bear
1992
Desert Hot Spr
0.119
0.22
6.4
39.5
#Record8
“Imperial Valley-06”
1979
“Delta”
0.142
0.35
6.53
33.7
#Records9
“Imperial Valley-06”
1979
“El Centro Array #11”
0.143
0.38
6.5
29.4
#Records10
“Kobe_Japan”
1995
“Shin-Osaka”
0.063
0.23
6.9
46
#Records11
“Superstition Hills-02”
1987
“El Centro Imp. Co. Cent”
0.127
0.35
6.5
35.8
#Records12
Loma Prieta
1989
Gilroy Array #3
0.3416
0.56
6.9
31.4
#Records13
Chi chi
1999
Chy101
0.165
0.44
7.6
32
#Records14
Duzce
1999
Bolu
0.2
0.82
7.1
41.3
#Records15
Northridge
1994
Hollywood—Willoughby Ave
0.151
0.25
6.69
23.07


## 5. Evaluation of Seismic Response of Structures

The ground motions were scaled so that the average value of their square root of the sum of the squares (SRSS) spectra did not fall below 1.4 times the Standard Design-Spectra for periods of 0.2T second to 1.5T seconds, where T is the fundamental period of vibration [17]. Figure 7 shows the elastic response spectra for 5% damping of these selected near-field ground motions, as well as the process of scaling for the 8-story building. In OpenSees, three types of stiffness matrix can be considered for the Rayleigh damping command: current stiffness matrix, initial stiffness matrix, and committed stiffness matrix. In the inelastic analysis, the “committed stiffness matrix” should be employed.Figure 7
Process of scaling for the 8-story building.Totally, in the present research, 120 nonlinear time history analyses were performed according to the 30 selected records and the number of considered buildings.In this study, the total acceleration response has been evaluated. By comparing the peak floor amplifications under the influence of near-field (NF) and far-field (FF) earthquakes, it was determined that, in the NF shocks with forward directivity in the 3-story building, peak floor amplifications was 0.106 g, under the #Record11 record; in the 5-story building, it was 0.067 g, which is the location on the fifth floor under the #Record10 record; for the 8-story building, it was 0.506 g, which is located on the seventh floor under the #Record11 record; finally, in the 20-story building, it was 1.818, which is located on the third floor under the #Record10. On the other hand, in each of the four structures under the influence of FF earthquakes, the peak floor amplification values of the floors amounted to 0.067 g, 0.068 g, 0.669 g, and 0.557 g. For a more accurate evaluation, a comparison of the average value of the peak floor amplifications of stories was made (Table4).Table 4
Comparison of the average value of the peak floor amplification of stories and roof displacement subjected to near- and far-field earthquakes.
Story
FF
NF
NF/FF
Acceleration (g)
3
0.029
0.038
1.310
5
0.026
0.025
0.961
8
0.189
0.198
1.047
20
0.304
0.705
2.319
Displacement (mm)
3
0.23
0.33
1.43
5
0.25
0.35
1.40
8
0.38
0.48
1.26
20
0.26
0.35
1.35By investigating the maximum roof displacement subjected to far- and near-field earthquakes, we found that near-field earthquakes including forward directivity in the 3-story building resulted in the maximum displacement in the roof (0.74 mm). In the 5-story building, near-field earthquakes caused a 0.80 mm displacement, which is 1.73 times greater than the displacement subjected to the vertical component of far-field earthquakes. This parameter can also be seen in 8-story building with the corresponding values of 0.96 mm for near-field and 0.62 mm for far-field earthquakes. At the end, the maximum roof displacement in the 20-story building with the corresponding values of 0.817 mm for near-field and 0.556 mm for far-field earthquakes.Table4 shows a comparison of the maximum roof displacements by the influence of far- and near-field earthquakes. Figure 8 shows the graphs related to the maximum displacement of the stories under the effect of near- and far-field earthquakes. Furthermore, for a more accurate investigation, the results of a comparison of the average roof displacements are given in Table 4.Figure 8
Maximum displacement in 3-, 5-, 8-, and 20-story building subjected to near- (a, c, e, g) and far-field (b, d, f, h) earthquakes.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)From the results of the analysis shown in Table5, the maximum axial forces in the 3-story structure subjected to near-field earthquakes were by 13% greater than those same forces subjected to far-field earthquakes. In the 5-story structure, the axial forces in the columns in both records of far- and near-field earthquakes were almost equal. In addition, the maximum axial force produced in the 8-story structure under the effect of near-field earthquakes was by 22% lower than that subjected to far-field earthquakes. Furthermore, in the 20-story structure, the maximum axial force subjected to near-field earthquakes was by 26% higher than that subjected to far-field earthquakes.Table 5
Comparison of the maximum axial force of columns in 3-, 5-, 8-, and 20-story buildings subjected to near- and far-field earthquakes.
No. of stories
Field
Axial column force (kN)
No. of columns
Record
Near/far
3-story
1
Near
61.750
C14
#Records11
1.129
Far
54.67
C11
#Record12
2
Near
42.224
C14
#Records11
1.031
Far
40.92
C11
#Record12
3
Near
27.819
C14
#Records11
1.058
Far
26.29
C11
#Record12
5-story
1
Near
105.099
C14
#Records10
0.999
Far
105.13
C14
#Record8
2
Near
96.120
C14
#Records10
0.991
Far
96.95
C14
#Record8
3
Near
75.586
C14
#Records10
0.983
Far
76.91
C14
#Record8
4
Near
54.298
C14
#Records10
0.984
Far
55.20
C14
#Record8
5
Near
26.702
C14
#Records10
0.963
Far
27.73
C14
#Record8
8-story
1
Near
357.76
C14
#Records11
0.780
Far
458.40
C14
#Record12
2
Near
337.45
C14
#Records11
0.775
Far
435.56
C14
#Record12
3
Near
301.11
C14
#Records11
0.776
Far
388.22
C14
#Record12
4
Near
261.27
C14
#Records11
0.778
Far
335.63
C14
#Record12
5
Near
209.32
C14
#Records11
0.765
Far
273.72
C14
#Record12
6
Near
165.23
C14
#Records11
0.763
Far
216.69
C14
#Record12
7
Near
120.52
C14
#Records11
0.766
Far
157.30
C14
#Record12
8
Near
71.40
C14
#Records15
0.742
Far
96.28
C14
#Record12
20-story
1
Near
14330.09
C14
#Records5
1.267
Far
11312.26
C14
#Records13
2
Near
13563.66
C14
#Records5
1.283
Far
10569.36
C14
#Records13
3
Near
12707.71
C14
#Records5
1.299
Far
9780.81
C14
#Records13
4
Near
12707.71
C14
#Records5
1.402
Far
9060.82
C14
#Records13
5
Near
11016.25
C14
#Records5
1.318
Far
8356.13
C14
#Records13
6
Near
10155.81
C14
#Records5
1.324
Far
7667.54
C14
#Records13
7
Near
9348.77
C14
#Records5
1.337
Far
6988.96
C14
#Records13
8
Near
8556.42
C14
#Records5
1.354
Far
6320.06
C14
#Records13
9
Near
7744.19
C14
#Records5
1.363
Far
5680.05
C14
#Records13
10
Near
6917.78
C14
#Records5
1.365
Far
5068.28
C14
#Records13
11
Near
6084.43
C14
#Records5
1.364
Far
4461.07
C14
#Records13
12
Near
5227.68
C14
#Records5
1.313
Far
3979.52
C14
#Records13
13
Near
4342.26
C14
#Records5
1.245
Far
3488.41
C14
#Records13
14
Near
3558.95
C13
#Records4
1.203
Far
2958.85
C14
#Records13
15
Near
2929.68
C13
#Records4
1.215
Far
2410.56
C14
#Records13
16
Near
2303.32
C13
#Records4
1.230
Far
1871.98
C14
#Records13
17
Near
1733.34
C13
#Records4
1.287
Far
1347.13
C14
#Records13
18
Near
1181.83
C13
#Records4
1.348
Far
876.72
C14
#Records13
19
Near
726.91
C13
#Records10
1.506
Far
482.47
C14
#Records13
20
Near
312.53
C13
#Records10
1.766
Far
176.97
C14
#Records13As can be seen from the results shown in Table6, the ratio of the maximum moment subjected to vertical component of near-field earthquakes to the maximum moment generated under the effect of vertical component of far-field earthquakes in all four structures (3-, 5-, 8-, and 20-story) was 1.07, 0.96, 0.77, and 1.08, respectively.Table 6
Comparison of the maximum moment of columns in 3-, 5-, 8-, and 20-story buildings subjected to near- and far-field earthquakes.
No. of story
Field
Moment (kN·M)
No. of columns
Record
Near/far
3-story
1
Near
34.817
C14
#Records11
1.513
Far
23.00
C14
#Record12
2
Near
32.990
C14
#Records11
1.189
Far
27.75
C14
#Record12
3
Near
47.073
C14
#Records11
1.069
Far
44.05
C11
#Record12
5-story
1
Near
16.428
C14
#Records10
1.043
Far
15.74
C14
#Record12
2
Near
29.077
C14
#Records10
1.028
Far
28.27
C14
#Record8
3
Near
30.849
C14
#Records10
0.986
Far
31.29
C14
#Record8
4
Near
40.865
C14
#Records10
1.002
Far
40.78
C14
#Record8
5
Near
45.906
C14
#Records10
0.958
Far
47.93
C14
#Record8
8-story
1
Near
44.23
C12
#Records11
0.867
Far
51.00
C12
#Record12
2
Near
55.70
C14
#Records11
0.780
Far
71.42
C14
#Record12
3
Near
61.36
C14
#Records15
0.749
Far
81.89
C14
#Record12
4
Near
78.98
C14
#Records11
0.836
Far
94.48
C11
#Record12
5
Near
63.21
C14
#Records11
0.768
Far
82.27
C14
#Record12
6
Near
63.77
C14
#Records11
0.755
Far
84.51
C14
#Record12
7
Near
91.31
C14
#Records11
0.803
Far
113.78
C14
#Record12
8
Near
111.68
C14
#Records11
0.773
Far
144.50
C14
#Record12
20-story
1
Near
3815.19
C13
#Records5
1.082
Far
3526.56
C13
#Record13
2
Near
2140.55
C13
#Records5
1.183
Far
1809.33
C13
#Record13
3
Near
1971.99
C13
#Records5
1.179
Far
1672.12
C13
#Record13
4
Near
1862.47
C13
#Records5
1.109
Far
1679.10
C13
#Record13
5
Near
2102.03
C13
#Records5
1.224
Far
1717.44
C13
#Record13
6
Near
2107.63
C13
#Records5
1.379
Far
1528.38
C13
#Record13
7
Near
1968.57
C13
#Records5
1.312
Far
1499.84
C13
#Record13
8
Near
1735.88
C13
#Records5
1.190
Far
1457.93
C13
#Record13
9
Near
1743.19
C13
#Records5
1.275
Far
1367.14
C13
#Record13
10
Near
1788.47
C13
#Records5
1.418
Far
1261.23
C13
#Record13
11
Near
2040.55
C13
#Records5
1.630
Far
1251.65
C13
#Record13
12
Near
1884.31
C13
#Records5
1.605
Far
1173.92
C13
#Record13
13
Near
2049.72
C13
#Records4
1.768
Far
1159.12
C13
#Record12
14
Near
1819.52
C13
#Records4
1.585
Far
1148.11
C13
#Record12
15
Near
1326.48
C13
#Records4
1.230
Far
1078.67
C13
#Record12
16
Near
1282.13
C13
#Records4
1.197
Far
1071.34
C13
#Record12
17
Near
1350.00
C13
#Records4
1.395
Far
967.94
C13
#Record12
18
Near
1114.58
C13
#Records4
1.317
Far
846.47
C13
#Record12
19
Near
1040.41
C13
#Records10
1.657
Far
627.72
C13
#Record12
20
Near
730.75
C13
#Records10
1.817
Far
402.19
C13
#Record12From the results shown in Figure9 and Table 7, it can be clearly observed that the maximum shear force generated in 3- and 8-story buildings subjected to the vertical component of near-field earthquakes was by 6% and 24% lower than far-field earthquakes, respectively, and in 5- and 20-story buildings subjected to the vertical component of near-field earthquakes was by 7% and 31% higher than far-field earthquakes, respectively. In the end, the moment of beams has investigated, and the result is shown in Table 8.Figure 9
Shear force in 3-, 5-, 8-, and 20-story building subjected to near- (a, c, e, g) and far-field (b, d, f, h) earthquakes.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)Table 7
Comparison of shear force in 3-, 5-, 8-, and 20-story buildings subjected to near- and far-field earthquakes.
No. of story
Field
Shear force (kN)
Record
Near/far
3-story
1
Near
5690.151
#Record10
0.936
Far
6079.894
#Record12
2
Near
2951.553
#Record10
0.916
Far
3221.74
#Record12
3
Near
1010.715
#Record10
0.906
Far
1115.286
#Record12
5-story
1
Near
23330.8
#Record10
1.071
Far
21790.943
#Record12
2
Near
16292.44
#Record10
1.057
Far
15411.848
#Record12
3
Near
10167.194
#Record10
1.045
Far
9730.468
#Record12
4
Near
5240.218
#Record10
1.034
Far
5065.902
#Record12
5
Near
1786.496
#Record10
1.027
Far
1738.721
#Record12
8-story
1
Near
72626.839
#Record11
0.764
Far
95117.604
#Record12
2
Near
58892.989
#Record11
0.760
Far
77460.474
#Record12
3
Near
45891.719
#Record11
0.756
Far
60714.82
#Record12
4
Near
33941.519
#Record11
0.749
Far
45295.754
#Record12
5
Near
23344.349
#Record11
0.743
Far
31422.154
#Record12
6
Near
14372.579
#Record11
0.737
Far
19498.604
#Record12
7
Near
7332.913
#Record11
0.731
Far
10026.224
#Record12
8
Near
2464.752
#Record11
0.726
Far
3393.249
#Record12
20-story
1
Near
176111.944
#Records5
1.314
Far
134012.37
#Record13
2
Near
158690.158
#Records5
1.322
Far
119991.66
#Record13
3
Near
141820.68
#Records5
1.328
Far
106734.41
#Record13
4
Near
125671.188
#Records5
1.332
Far
94277.84
#Record13
5
Near
110374.086
#Records5
1.334
Far
82682.23
#Record13
6
Near
96007.611
#Records5
1.337
Far
71795.98
#Record13
7
Near
82719.533
#Records5
1.343
Far
61547.56
#Record13
8
Near
70536.314
#Records5
1.355
Far
52049.92
#Record13
9
Near
59358.197
#Records5
1.331
Far
44592.80
#Record13
10
Near
49175.739
#Records5
1.315
Far
37395.97
#Record13
11
Near
40072.416
#Records5
1.309
Far
30598.87
#Record13
12
Near
32366.182
#Records5
1.331
Far
24306.65
#Record13
13
Near
25906.607
#Records5
1.393
Far
18592.41
#Record13
14
Near
20058.394
#Records5
1.471
Far
13630.37
#Record13
15
Near
14676.233
#Records5
1.542
Far
9515.60
#Record13
16
Near
9936.677
#Records5
1.595
Far
6228.99
#Record13
17
Near
6069.935
#Records5
1.628
Far
3727.37
#Record13
18
Near
3293.378
#Records5
1.668
Far
1973.30
#Record13
19
Near
1371.00
#Records5
1.690
Far
811.22
#Record13
20
Near
409.456
#Records5
1.866
Far
219.42
#Record13Table 8
Comparison of beam moment in 3-, 5-, 8-, and 20-story buildings subjected to near- and far-field earthquakes.
Story
NF
Loc.
Record
FF
Loc.
Record
NF/FF
Beam moment (kN·m)
3
5.088
B32
#Record10
3.986
B35
#Record6
1.28
5
6.789
B42
#Record10
5.810
B45
#Record6
1.17
8
12.390
B42
#Record15
14.320
B45
#Record12
0.87
20
1593.300
B52
#Records5
1373.670
B55
#Record13
1.16Finally, the results of this paper are summarized based on the comparison methodology in references [26, 27]. Tables 9 and 10 show that the peak vertical floor acceleration (named as PFAv) may exceed the peak vertical ground acceleration (named as PGAv). The results demonstrate that the ratio of PFAv/PGAv in 3-, 5-, 8-, and 20-story buildings under near-field records is 1.79, 1.27, 3.17, and 24.68, respectively. Moreover, this ratio for those buildings subjected to far-field records is 3.30, 4.69, 25.88, and 25.26.Table 9
Ratios of PFAv/PGAv for the near-field earthquakes.
Records no.
Records name
PFAv (m/s2)
Ratio of PFAv/PGAv
3-storey
5-storey
8-storey
20-storey
3-storey
5-storey
8-storey
20-storey
#Record1
Erzican
0.248
0.129
0.638
4.262
1.060
0.552
2.727
18.212
#Record2
Imperial Valley-EC-country
0.360
0.154
1.328
4.584
1.476
0.630
5.441
18.788
#Record3
Imperial Valley-Meloland
0.147
0.192
1.346
4.867
0.592
0.775
5.427
19.625
#Record4
Kobe-KJMA
0.201
0.153
0.296
8.344
0.596
0.454
0.875
24.687
#Record5
Kobe-PortIsland
0.300
0.238
2.562
10.877
0.530
0.420
4.527
19.217
#Record6
Kobe-Takatori
0.326
0.134
1.244
5.081
1.147
0.472
4.381
17.891
#Record7
Northridge-Newhall-fire st
0.269
0.250
0.814
11.327
0.490
0.457
1.485
20.669
#Record8
Imperial-BrawleyAirport
0.254
0.151
0.931
2.801
1.662
0.987
6.095
18.332
#Record9
Loma-Prieta-Valley
0.684
0.448
1.911
6.362
1.727
1.133
4.830
16.077
#Record10
Northridge-Rinaldi
0.639
0.663
4.108
17.840
0.667
0.693
4.288
18.622
#Record11
Northridge-Sylmar
1.046
0.332
4.964
10.117
1.728
0.548
8.206
16.722
#Record12
Imperial ElCentro10
0.144
0.107
0.664
2.386
1.321
0.986
6.088
21.889
#Record13
Imperial HoltvillePost
0.459
0.215
2.759
4.399
1.795
0.839
10.778
17.183
#Record14
LomaPieta GiloryArrar2
0.208
0.159
1.232
5.052
0.706
0.540
4.176
17.125
#Record15
LomaPieta GiloryArrar3
0.457
0.433
4.494
5.463
1.340
1.271
13.179
16.021Table 10
Ratios of PFAv/PGAv for the far-field earthquakes.
Records no.
Records name
PFAv (m/s2)
Ratio PFAv/PGAV
3-storey
5-storey
8-storey
20-storey
3-storey
5-storey
8-storey
20-storey
#Record1
Imperial Valley-CalexicoFireStation
0.637
0.304
1.751
3.255
3.302
1.577
9.075
16.866
#Record2
KocaeliTurkey-Duzce
0.481
0.230
2.268
4.558
2.334
1.117
11.009
22.126
#Record3
Landers-NorthPalmSprings
0.188
0.255
2.874
2.327
1.694
2.297
25.888
20.963
#Record4
Landers-YermoFireStation
0.174
0.131
1.230
2.725
1.281
0.965
9.057
20.067
#Record5
Loma Prieta-CoyoteLakeDam
0.109
0.045
0.457
1.928
1.149
0.470
4.812
20.292
#Record6
SanFernando-LA
0.294
0.308
2.417
2.457
1.794
1.877
14.738
14.981
#Record7
DesertHotSpr
0.107
0.116
0.675
2.619
0.902
0.977
5.673
22.009
#Record8
Imperial Valley-Delta
0.305
0.667
1.555
2.554
2.145
4.696
10.952
17.989
#Record9
Imperial Valley-El Centro Array
0.219
0.236
2.421
2.544
1.530
1.652
16.932
17.791
#Record10
Kobe-Shin-Osaka
0.049
0.026
0.088
1.591
0.771
0.411
1.392
25.260
#Record11
SuperstitionHills
0.336
0.098
0.630
2.870
2.644
0.775
4.958
22.595
#Record12
Loma Prieta-GilroyArray3
0.668
0.676
6.556
5.463
1.955
1.979
19.191
15.993
#Record13
Chi Chi Chy101
0.233
0.148
1.388
3.567
1.414
0.896
8.410
21.617
#Record14
Duzce Bolu
0.363
0.413
2.440
3.706
1.817
2.064
12.202
18.529
#Record15
Northridge Hollywood
0.258
0.205
1.123
2.576
1.707
1.358
7.439
17.061


## 6. Conclusions

The present study has evaluated the seismic behavior of special steel moment frames of 3-, 5-, 8-, and 20-story buildings subjected to the vertical components of far- and near-field earthquakes. According to the classification of the HAZUS-MH MR5 [16] instruction, 3-, 5-, 8-, and 20-story buildings are categorized as low-, middle-, and high-rise buildings. From the results of the nonlinear time history analysis for the models studied, the following conclusions can be drawn:(i)
One of the major elements in evaluating the seismic behavior of structures is known as displacement. This study shows that the amount of forced displacement to the structure under the effect of the near-field earthquake is greater than the amount if that under the effect of the far-field earthquake.(ii)
By investigating the structures analysis results, it can be observed that the average value of the maximum axial force in the columns of 3-, 8-, and 20-story structures under the effect of the near-field earthquake is 5%, 4%, and 38% greater than their values under the effect of the far-field earthquake, respectively. However, this value for the 5-story structure is almost the same in both situations.(iii)
The ratios of the average value of the maximum moments in the columns subjected to near- and far-field earthquakes in 3-, 5-, 8-, and 20-story structures were 1.03, 0.98, 1.03, and 1.33 respectively.(iv)
Regarding the assessment of the generated shear force on the buildings, it would be valid to claim that the average of maximum created shear force in all structures (3-, 5-, 8-, and 20-story) subjected to the near-field earthquake was higher than the far-field one with the results of 10%, 5%, 14%, and 38%, respectively.



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*Source: 2647387-2019-04-03.xml*