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Inelastic performance of RC buildings subjected to near-source multi-component earthquakes
Alexandria Engineering Journal (2017) xxx, xxx–xxx
H O S T E D BY
Alexandria University
Alexandria Engineering Journal www.elsevier.com/locate/aej www.sciencedirect.com
ORIGINAL ARTICLE
Inelastic performance of RC buildings subjected to near-source multi-component earthquakes Laila Elhifnawy, Hamdy Abou-Elfath *, Emad El-Hout Department of Structural Engineering, Faculty of Engineering, Alexandria University, Alexandria, Egypt Received 23 July 2016; revised 9 December 2016; accepted 4 March 2017
KEYWORDS 3-D analysis; Inelastic analysis; Multi-component earthquake; RC buildings; Vertical earthquake
Abstract The inelastic behavioral characteristics of three RC buildings having 6-, 10- and 20stories under near-source multi-component earthquake excitations are investigated. Ten earthquake records are used in the analysis to cover a wide range of vertical to horizontal spectral ratios. The performances of the buildings are evaluated through the roof displacements, the maximum story drift ratios and the maximum axial forces and strain ductility factors in the building members. Four analysis cases are considered for each earthquake including, one lateral earthquake component (X-case), two lateral earthquake components (XY-case), one lateral earthquake component accompanied with the vertical earthquake component (XZ-case) and two lateral earthquake components accompanied with the vertical earthquake component (XYZ-case). The results obtained in this study indicate that the multi-component effect of the earthquakes has a considerable effect on the axial forces and strain ductility factors of the building columns although it does not significantly affect the building lateral-deformation response. Ó 2017 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction It has been observed in recent earthquakes that several buildings have suffered extensive damage despite the fact that they had been designed based on the latest seismic design codes. One of the main reasons behind this damage is the multicomponent effect of earthquakes [1,2]. Measurements of ground motion during past earthquakes indicated that the
* Corresponding author. E-mail addresses: [email protected] (L. Elhifnawy), [email protected] (H. Abou-Elfath), [email protected] (E. ElHout). Peer review under responsibility of Faculty of Engineering, Alexandria University.
vertical spectral ordinates may be exceeding the horizontal values [3]. Many codes around the world including the Egyptian code [4] estimate the seismic design forces for each earthquake component separately and then combine the structural responses of the earthquake components by approximate combination rules such as the 30 percent (30%) rule and the square root of the sum of the squares rule. In many modern codes, the vertical response spectrum ordinates are obtained by multiplying the corresponding horizontal spectrum ordinates by a Vertical-to-Horizontal Spectral Ratio (V/H-SR), where V and H are the vertical and the horizontal spectral accelerations, respectively. The V/H-SR is usually taken as a fraction that is less than one. In the FEMA specification [5], the V/H-SR is considered constant and equals to 2/3 following the research work of Newmark et al. [6]. The
http://dx.doi.org/10.1016/j.aej.2017.03.023 1110-0168 Ó 2017 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: L. Elhifnawy et al., Inelastic performance of RC buildings subjected to near-source multi-component earthquakes, Alexandria Eng. J. (2017), http://dx.doi.org/10.1016/j.aej.2017.03.023
2
L. Elhifnawy et al.
columns 0.6
7.0 m
7.0 m
6.0 = 18.0 m 3
0.6 m 16 # 22
7.0 m
7.0 m
0.5 0.5 m 12 # 22
All beams are 0.25 0.60 m 6 # 22 3 # 22
7.0 m
(a) Floor plan
Figure 1
7.0 m
(b) Frame elevation
Six-story RC building.
All beams are 0.25 x 0.60 m
(a) Floor plan Figure 2
3.25 = 32.5 m
12 # 22 8 # 20 6.0 m
6.0 m
6.0 m
Internal External
12 # 25 8 # 25
10
8 # 22 4 # 25
4 # 20
0.45 m 0.45 0.65 m Internal
6.0 m
External
6.0 m
0.65
0.50 m 0.50
6.0 m 6.0 m
8 # 18
4#18
4#18
6.0 m
0.35
6.0 m
0.35 m
5#22 4#18
(b) Frame elevation Ten-story RC building.
Euro code [7] and the Egyptian code [4] recommend the use of two V/H-SRs of 0.45 and 0.9 depending on the expected siteto-source distance. Many analytical studies were conducted on the single degree of freedom level to improve the prediction of the V/ H-SR in order to be employed in modern seismic design codes. Research works by Ambraseys and Simpson [3], Collier and Elnashai [8] and Bozorgnia and Campbell [9], indicated that the V/H-SR is a strong function of the source to site distance and local site conditions. Moreover, some empirical models were developed for estimating the V/H-SR ratio [10–13]. Many studies both analytically and experimentally were conducted on the multi-degree of freedom level for evaluating the performance of buildings under multi-component earth-
quake excitations. Diotallevi and Landi [14] investigated the nonlinear dynamic responses of RC frames using two loading cases, the first case is excited by the horizontal component of ground motion only and the second case is excited by the horizontal and the vertical components of ground motion. The results of this investigation showed that the axial forces in the columns and the roof displacement increase due to consideration of the vertical ground motion. Faella et al. [15] investigated the nonlinear seismic responses of four-story three-dimensional RC buildings. The analysis was performed under the effect of bi-directional (two horizontal components of earthquakes) and unidirectional ground motions. The analysis showed that there was no significant difference between the two loading cases in terms
Please cite this article in press as: L. Elhifnawy et al., Inelastic performance of RC buildings subjected to near-source multi-component earthquakes, Alexandria Eng. J. (2017), http://dx.doi.org/10.1016/j.aej.2017.03.023
3
6.0 m
6.0 m
6.0 m
Inelastic performance of RC buildings
6.0 m
6.0 m
6.0 m
0.50
0.35 0.6 0.35 0.6
3.6 = 72.0 m
0.55
0.4 0.6
0.55
0.4 0.6
0.4 0.6
20
0.6
0.4 0.6
0.6
0.4 0.6
0.4 0.6
12 # 25
0.65
0.4 0.6
0.65
0.4 0.6 0.4 0.6 0.4 0.6
0.4 0.65 0.4 0.65
6.0 m
16 # 25
6.0 m
External columns
0.7
0.7
0.4 0.65
6.0 m
(a) Cross section dimensions Figure 3
12 # 25
12 # 20
0.50
0.3 0.6
16 # 25
8 # 25
0.3 0.6
4 # 20 4 # 20 6 # 20 4 # 20 8 # 20 4 # 20 8 # 20 4 # 20 10 # 20 6 # 20 10 # 20 6 # 20 12 # 20 8 # 20 12 # 20 8 # 20 8 # 25 6 # 25 8 # 25 6 # 25 8 # 25 6 # 25 8 # 25 6 # 25 8 # 25 6 # 25 8 # 25 6 # 25 8 # 25 6 # 25 8 # 25 6 # 25 8 # 25 6 # 25 8 # 25 8 # 20 8 # 25 8 # 20 8 # 25 8 # 20
Internal columns
0.25 0.5
8 # 20
0.45
0.25 0.5
0.45
0.25 0.5
8 # 25
(a) Floor plan
(c) Steel reinforcement details Twenty-story RC building.
of the global response parameters, but the damage has increased in the local level of the member sections for the bidirectional ground motion loading case. Perea and Esteva [16] also investigated the nonlinear dynamic performance of RC frames. The analysis used three cases of the input motions: the vertical ground motion only, the horizontal motion only, and both the horizontal and the vertical motions jointly. The results obtained indicated that plastic hinge rotational demands in beams and columns were increased when including the horizontal and the vertical ground motions together.
Mwafy and Elnashai [17] investigated the nonlinear dynamic responses of three different RC frames. The analysis used two cases of the input motions: the horizontal motion only and both the horizontal and the vertical motions combined. It was concluded that the axial forces and the curvature ductility in columns are increased when including the vertical ground motion. Kadid et al. [18] also considered two loading cases in the dynamic analysis of three RC buildings. The first loading case was the horizontal component of ground motion only, while the second was the horizontal and the vertical ground motions combined. The results indicated that the ver-
Please cite this article in press as: L. Elhifnawy et al., Inelastic performance of RC buildings subjected to near-source multi-component earthquakes, Alexandria Eng. J. (2017), http://dx.doi.org/10.1016/j.aej.2017.03.023
4
L. Elhifnawy et al. Table 1
Selected near-source earthquakes.
Rec. No.
Earthquake
Stations
M
Distance (Km)
H1 (g)
H2 (g)
V (g)
V/H-SR
1 2 3 4 5 6 7 8 9 10
Nahanni, 1985 Santa Cruz, 1989 Palm Springs, 1986 Northridge, 1994 Westmorland, 1983 San Fernando, 1971 Park field, 2004 El Centro, 1940 Cape Mendocino, 1992 Coalinga, 1983
Territories Capitola Desert Hot Springs Sylmar Ca – Fire Station Pacoima Dam Fault Zone 14 Imperial Valley Petrolia Transmitter hill
6.9 7.0 5.9 6.7 6.0 6.6 6.0 6.7 7.0 6.0
5.97 18.0 12.0 18.0 7.2 3.5 8.0 12.2 15.5 9.5
1.34 0.47 0.30 0.80 0.47 1.17 1.31 0.35 1.50 1.17
1.1 0.4 0.27 0.38 0.38 1.08 0.53 0.21 1.04 0.85
2.37 0.51 0.54 0.33 0.64 0.71 0.56 0.21 0.75 0.46
1.63 1.41 1.15 1.0 0.88 0.85 0.66 0.65 0.64 0.51
M: Earthquake magnitude, H1 and H2: Horizontal PGAs, V: Vertical PGA.
6 20 5
18
14
Story level
Story level
16 4 3 X
2
XY
10
15
20
25
30
Mean floor displacements of the 6-story building.
Story level
8
6
4
X XY
2
XZ XYZ
0 5
10
15
20
25
30
35
40
Floor displacement (cm)
Figure 5
XZ XYZ
0 10
20
30
40
50
60
Floor displacement (cm)
10
0
XY
0
Floor displacement (cm)
Figure 4
X
2
0 5
8
4
XYZ 0
10
6
XZ
1
12
Mean floor displacements of the 10-story building.
tical component had little effect on the story drifts and base shear but it caused an increase in the column axial forces. Djarir and Abdelkrim [19] investigated the effect of combined horizontal and vertical accelerations on the seismic response of reinforced concrete frames on flexible foundations. Five and nine-story buildings were considered in the analysis. It has been found that the inclusion of the vertical ground motion with the soil-structure interaction has resulted in a reduction in the horizontal displacement compared to the case with only the horizontal earthquake component.
Figure 6
Mean floor displacements of the 20-story building.
Mwafy [20] investigated the nonlinear dynamic responses of twelve RC buildings. Different building heights and structural systems (moment-resisting frames and dual frame-wall systems) as well as structural regularity were taken into consideration. The analysis used two cases of the input motions: the horizontal motion only and both the horizontal and the vertical motions combined. The results of this investigation showed that the axial forces in the columns, base shear, and the roof displacement have increased due to consideration of the vertical ground motion. The focus of this study is on investigating the inelastic behavioral characteristics of RC buildings under the effect of near-source multi-component earthquakes. Three RC buildings having 6-, 10- and 20-story are analyzed under the effect of ten near-source earthquake records with a wide range of vertical to horizontal peak spectral ratios. The earthquakes are scaled to insure that the buildings undergo inelastic behavior with a minimum of 2% story drift ratio. The seismic response of the prototype buildings considered in this study is obtained using four earthquake loading cases including one lateral component (X-case), two lateral components (XY-case), one lateral component accompanied with the vertical component (XZ-case) and two lateral components accompanied with the vertical component (XYZ-case). A comparison is made between the building responses to the four earthquake loading cases X, XY, XZ and XYZ to evaluate the multicomponent effect of the earthquake records on the prototype buildings of this study.
Please cite this article in press as: L. Elhifnawy et al., Inelastic performance of RC buildings subjected to near-source multi-component earthquakes, Alexandria Eng. J. (2017), http://dx.doi.org/10.1016/j.aej.2017.03.023
Inelastic performance of RC buildings Table 2
5
Values of w for the roof displacements of the three buildings (%).
Record No.
6-story building
1 2 3 4 5 6 7 8 9 10 Average
10-story building
XZ
XYZ
XY
XZ
XYZ
XY
XZ
XYZ
1.15 0.47 0.16 4.39 2.91 1.81 4.61 1.75 0.42 3.12 0.67
0.44 0.71 0.24 0.01 0.10 0.46 1.10 0.09 0.72 0.58 0.055
1.76 1.24 0.41 4.55 3.07 2.14 4.11 3.03 1.18 3.59 0.93
0.53 1.53 0.21 1.53 0.13 0.13 0.48 4.23 0.36 1.16 0.67
0.06 1.05 0.52 0.29 4.58 0.03 0.02 0.15 0.59 0.04 0.23
0.55 2.46 0.85 1.49 0.02 0.15 0.52 4.08 0.89 1.14 0.88
0.60 0.07 1.22 0.94 5.29 1.88 4.85 1.03 0.13 3.96 2.0
1.98 0.17 0.71 0.05 0.034 0.80 1.16 0.70 1.73 0.33 0.15
1.26 0.20 0.61 0.83 5.37 3.0 4.95 1.38 1.53 3.76 2.04
6
Story number
5
3
XYZ XZ
2
XY
1
X
0.5
1 1.5 Story drift ratio (%)
2
2.5
Figure 7 Height-wise distribution of the mean story drift ratios for the 6-story building.
Story number
4
0
20-story building
XY
20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
XYZ XZ XY X
0 10 9 8 7 6 5 4 3 2 1
0.5
1 Story drift ratio (%)
1.5
2
Story number
Figure 9 Height-wise distribution of the mean story drift ratios for the 20-story building.
XYZ XZ XY X
0
0.5
1 1.5 Story drift ratio (%)
2
2.5
Figure 8 Height-wise distribution of the mean story drift ratios for the 10-story building.
2. Prototype buildings, computer models and earthquake selection Three RC frame buildings having 6-, 10- and 20-stories are used to evaluate the multi-component effect of the nearsource earthquake records. The 6-story building has two bays with a constant bay width of 7.0 m in each direction [21]. The building has a floor area of 196.0 m2. The story height of the 6story building is 3.0 m and the total height is 18.0 m. The structure was designed according to the Egyptian codes (ECP 2012007 and ECP 203-2007). The building was designed
symmetrically in the transverse directions using concrete strength of 30.0 MPa and reinforcing bar yielding strength of 360.0 MPa. The building dimensions and the cross-sectional details are presented in Fig. 1. The 10-story building has three bays with a constant bay width of 6.0 m in each direction [22]. The story height for the 10-story building is 3.25 m and the total height is 32.5 m. The structure was designed according to the ACI code. The building was designed symmetrically in the transverse directions using concrete strength of 25.0 MPa and reinforcing bar yielding strength of 400.0 MPa. The dead load was considered as 8.0 KN/m2, while the live load was assumed to be 2.0 KN/m2. The dimensions and cross-sectional details of the building are shown in Fig. 2. The 20-story building has three bays with a constant bay width of 6.0 m in each direction [23]. The story height for the 20-story building is 3.6 m and the total height is 72.0 m. The structure was designed according to the Canadian codes (the 1995 NBCC and the 1994 CSA). The building was assumed to be located in the city of Victoria on Canada’s west coast. The design base shear coefficient was equal to 6.4% of the total weight. The building was designed symmetrically in
Please cite this article in press as: L. Elhifnawy et al., Inelastic performance of RC buildings subjected to near-source multi-component earthquakes, Alexandria Eng. J. (2017), http://dx.doi.org/10.1016/j.aej.2017.03.023
6
L. Elhifnawy et al. Table 3
Values of w for the MSDRs of the selected buildings (%).
Record NO.
1 2 3 4 5 6 7 8 9 10 Average
6-story building
10-story building
XZ
XYZ
XY
XZ
XYZ
XY
XZ
XYZ
1.18 0.48 0.46 3.94 2.42 1.01 4.88 0.76 0.07 3.20 0.46
1.32 0.64 0.26 0.13 0.02 0.00 1.70 0.01 0.69 0.51 0.054
0.39 1.24 0.64 3.99 2.55 1.10 4.12 2.22 0.99 3.63 0.67
1.70 1.39 0.32 3.84 8.38 0.86 0.14 4.72 0.80 2.88 1.16
0.46 1.93 0.02 0.01 7.36 0.54 0.05 0.13 0.93 0.29 1.01
1.20 2.75 0.43 3.99 7.86 1.58 0.11 5.38 2.37 3.09 1.46
4.25 3.77 2.52 6.92 4.01 2.06 5.43 5.38 0.29 7.13 1.43
0.96 2.06 0.32 1.58 0.02 0.88 2.79 0.44 1.69 1.12 0.29
5.5 5.79 2.37 4.37 4.27 3.14 5.29 5.46 2.27 7.36 0.81
Series4
6
Series3 Series2 Series1
4 3
Story number
Story number
5
2 1 0
20-story building
XY
500 1000 1500 2000 2500 3000 Column maximum axial compression force (kN)
3500
Figure 10 Height-wise distribution of the mean column MACFs for the 6-story building.
20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
Series4 Series3 Series2 Series1
0
10 9 8 7 6 5 4 3 2 1
Series4 Series3
Story number
Series2 Series1
0
1000 2000 3000 4000 5000 Column maximum axial compression force (kN)
6000
Figure 11 Height-wise distribution of the mean column MACFs for the 10-story building.
the transverse directions using concrete strength of 30.0 MPa and reinforcing bar yielding strength of 360 MPa. The dimensions and cross-sectional details of the building are shown in Fig. 3. The DRAIN-3DX computer program [24,25] is used to perform the dynamic inelastic analysis. The Fiber beam-column element (type 15) is used to model the beam-column members of the buildings. A sensitivity analysis is conducted to determine the model parameters. The inelastic lengths at the member ends are taken equal to 20% of the member length. Each inelastic end is then divided into twelve segments and the
2000 4000 6000 8000 10000 Column maximum axial compression force (kN)
12000
Figure 12 Height-wise distribution of the mean column MACFs for the 20-story building.
element cross section is divided into twenty concrete fibers in each direction. The structural mass is assumed lumped at the nodes and the P-D effect has been taken into consideration. The dynamic analysis is performed using a time step increment of 0.02 s and Rayleigh damping which is defined to achieve 5% viscous damping in the first two natural modes of the building. A suite of 10 near-source multi-component earthquake records is selected in this study. The record information is presented in Table 1. The selected records have wide range of vertical to horizontal peak spectral ratios. The records are selected from COSMOS Virtual Data Center [26]. The earthquakes are scaled to insure that the buildings undergo inelastic behavior with a minimum of 2% story drift ratio. Each scale factor is applied identically to the three earthquake components. The scale factors are determined by trial and error for each building and earthquake. Each earthquake has three different scale factors for the three buildings considered in this study. 3. The floor-displacement response Figs. 4–6 show the variation of the mean floor displacements in the X-direction along the height of the 6-, 10- and 20-story
Please cite this article in press as: L. Elhifnawy et al., Inelastic performance of RC buildings subjected to near-source multi-component earthquakes, Alexandria Eng. J. (2017), http://dx.doi.org/10.1016/j.aej.2017.03.023
Inelastic performance of RC buildings Table 4
Values of w for the column MACFs of the selected buildings (%).
Record No.
1 2 3 4 5 6 7 8 9 10 Average
7
6-story building
10-story building
XZ
XYZ
XY
XZ
XYZ
XY
XZ
XYZ
1.92 0.045 0.40 0.63 0.27 0.72 0.60 0.27 0.14 0.45 0.24
61.23 35.98 56.75 12.45 47.69 29.37 37.91 25.62 19.87 8.02 33.49
64.02 35.31 56.75 12.95 45.93 29.77 39.4 26.34 19.6 8.16 33.82
1.04 0.19 0.03 2.08 1.96 0.41 0.30 1.72 0.97 0.61 0.78
116.03 60.19 60.68 12.04 51.54 24.99 38.06 14.50 22.36 2.62 40.30
116.68 59.26 60.79 13.16 52.82 25.12 38.15 14.94 21.92 3.17 40.60
17.6 2.75 0.50 3.31 3.90 0.52 1.90 5.39 1.21 0.48 3.76
59.31 57.01 57.57 27.17 13.40 57.86 86.33 20.55 7.90 12.03 39.91
64.36 56.12 57.57 27.06 16.77 57.86 82.70 20.83 9.12 12.14 40.45
Series4
6
Series3 Series2 Series1
4 3 2 1 1 2 3 4 5 6 Maximum column SSDF for the 6-story building
7
Figure 13 Height-wise distribution of the mean maximum column SSDFs of the 6-story building.
10 9 8 7 6 5 4 3 2 1
Series4
Story number
Story number
5
0
20-story building
XY
20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
Series4 Series3 Series2 Series1
0
Series3
2 4 6 Maximum column SSDF for the 20-story building
8
Story number
Series2
Figure 15 Height-wise distribution of mean maximum column SSDFs of the 20-story building.
Series1
displacement values of the XYZ-case are 0.93%, 0.88% and 2.04% higher than those of the X-case for the 6-, 10- and 20-story buildings, respectively. 0
1 2 3 4 Maximum column SSDF for the 10-story building
5
Figure 14 Height-wise distribution of mean maximum column SSDFs of the 10-story building.
buildings, respectively. The results presented for each building display little differences among the predictions of the X, XY, XZ and the XYZ loading cases. For each building, the results of the X-loading case are considered as a reference for comparing the performances of the various earthquake loading cases. A parameter w is defined to measure the percentage of change in the performance of any earthquake loading case in comparison with that of the X-loading case. Values of w for the roof displacement in the X-direction of the three buildings are summarized in Table 2. The results presented in the table indicate that, on average, the XYZ-case exhibits slightly higher levels of roof displacements in comparison with the other loading cases. The average roof
4. Story-drift response The story drift is an important parameter for evaluating seismic damage of the structural elements in any story. Figs. 7–9 show the variations of the mean story drift ratios in the Xdirection along the height of the 6-, 10- and 20-story buildings, respectively. The results presented in the figures show little differences among the predictions of the four earthquake cases for each building. The results also show that the Maximum Story Drift Ratios (MSDRs) of the earthquake loading cases occur in the third-, sixth- and eighteenth-story of the 6-, 10and 20-story buildings, respectively. Values of w for the MSDRs of the selected buildings are summarized in Table 3. For the 6- and the 10-story buildings, the results presented in the table indicate that, on average, the XYZ-case displays slightly higher levels of MSDRs than the other loading cases. The average MSDRs of the XYZ-case are 0.67% and 1.46% higher than those of the X-case for
Please cite this article in press as: L. Elhifnawy et al., Inelastic performance of RC buildings subjected to near-source multi-component earthquakes, Alexandria Eng. J. (2017), http://dx.doi.org/10.1016/j.aej.2017.03.023
8
L. Elhifnawy et al. Table 5
Values of w for the maximum SSDFs in columns of the selected buildings (%).
Record No.
1 2 3 4 5 6 7 8 9 10 Average
6-story building
10-story building
XZ
XYZ
XY
XZ
XYZ
XY
XZ
XYZ
91.47 10.3 6.06 21.96 19.32 41.91 10.08 49.28 35.75 2.8 25.67
0.66 1.65 0.32 1.75 0.17 1.02 4.51 1.6 7.96 0.31 0.86
77.91 6.60 8.07 20.05 18.40 40.61 4.00 47.57 40.25 2.90 24.22
90.71 48.59 86.41 62.43 69.63 72.14 50.05 66.32 44.21 46.33 63.68
1.76 12.39 0.15 0.61 0.45 10.83 0.51 0.39 12.31 3.20 3.73
97.41 36.68 80.16 62.64 70.13 81.77 51.58 67.54 44.28 47.41 63.96
26.43 36.95 5.28 65.94 17.81 82.62 47.00 52.15 19.72 72.22 42.61
4.92 3.03 8.33 9.96 3.30 3.03 2.19 2.47 20.42 3.73 0.29
29.82 45.90 2.14 62.43 18.80 81.15 45.66 55.24 36.61 73.63 45.14
Series4
6
Series3 Series2 Series1
4 3 2 1 1 2 3 4 5 Maximum beam SSDF for the 6-story building
6
Figure 16 Height-wise distribution of the mean maximum beam SSDFs of the 6-story building.
10 9 8 7 6 5 4 3 2 1
Series3
Story number
Series2
Series4 Series3 Series2 Series1
2 4 6 Maximum beam SSDF for the 20-story building
8
Figure 18 Height-wise distribution of the mean maximum beam SSDFs of the 20-story building.
Series1
0.5 1 1.5 2 2.5 Maximum beam SSDF for the 10-story building
20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
Series4
0
Story number
Story number
5
0
20-story building
XY
3
Figure 17 Height-wise distribution of the mean maximum beam SSDFs of the 10-story building.
the 6- and the 10-story buildings, respectively. For the 20-story building, on average, the XY-case displays the highest level of MSDRs in comparison with the other loading cases. The average maximum story drift ratio of the XY-case is 1.43% higher than those of the X-case for the 20-story building.
shown in the figures indicate that the column MACFs occur in the first-story of the three buildings under the effect of the four earthquakes’ loading cases. The results presented for the three buildings show little differences between the predictions of the X and the XY loading cases and also between the predictions of the XZ and the XYZ loading cases. This indicates that the changes in column axial forces are mainly due to the effect of the vertical ground motion component (the Z-loading case). Values of w for the column MACFs of the selected buildings are summarized in Table 4. For each building, the results presented in the table indicate that, on average, the XYZ-case displays the highest level of column MACFs in comparison with the other loading cases. The average column MACFs of the XYZ-case are 33.82%, 40.60% and 40.45% higher than those of the X-case for the 6-, 12- and the 20-story buildings, respectively.
5. Column maximum axial compression forces 6. Steel strain-ductility-factors in columns Figs. 10–12 show the variations of the mean Maximum Axial Compression Forces (MACFs) in columns along the height of the 6-, 10- and the 20-story buildings, respectively. The results
In this study, the Steel Strain-Ductility-Factor (SSDF) in a column is calculated as the maximum steel strain in the column
Please cite this article in press as: L. Elhifnawy et al., Inelastic performance of RC buildings subjected to near-source multi-component earthquakes, Alexandria Eng. J. (2017), http://dx.doi.org/10.1016/j.aej.2017.03.023
Inelastic performance of RC buildings Table 6
Values of w for the maximum SSDFs in beams of the selected buildings (%).
Record No.
1 2 3 4 5 6 7 8 9 10 Average
9
6-story building
10-story building
20-story building
XY
XZ
XYZ
XY
XZ
XYZ
XY
XZ
XYZ
4.00 0.70 1.64 1.38 0.86 1.73 4.38 4.60 0.33 1.71 0.6
2.61 0.16 0.67 0.296 0.0 0.35 1.11 0.06 0.78 0.40 0.19
6.04 0.75 2.61 1.11 0.66 1.63 3.73 4.66 0.45 2.26 0.69
0.36 0.14 0.16 2.03 4.28 3.85 2.64 3.29 1.97 0.34 0.54
0.22 0.07 0.32 0.14 3.71 1.51 0.21 0.29 4.52 0.27 0.29
0.07 0.28 0.08 2.31 3.62 3.09 3.26 3.44 3.74 0.67 0.72
2.43 0.23 1.80 1.79 0.36 8.95 4.95 4.14 2.31 3.93 0.36
0.85 8.62 1.13 5.04 0.18 4.80 0.93 1.02 4.36 0.15 1.38
4.36 4.26 0.212 1.80 0.84 1.84 0.62 4.37 2.42 3.98 0.22
X-Case
XZ -Case Figure 19
XY-Case
XYZ -Case
Distributions of plastic hinges in the 6-story frame.
X-Case
XZ-Case
XY-Case
XYZ-Case
Figure 20
Distributions of plastic hinges in the 10-story frame.
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10
L. Elhifnawy et al.
X-Case
XZ-Case
XY-Case
XYZ-Case
Figure 21
Distributions of plastic hinges in the 20-story frame.
divided by the steel yield strain. Figs. 13–15 show the variations of the mean SSDFs of columns along the height of the 6-, 10- and 20-story buildings, respectively. The results shown in the figures indicate that the maximum SSDFs in columns occur in the first-, the sixth- and the eighteenth-story of the 6-, 10- and 20-story buildings, respectively. The results presented for each building show very little differences between the predictions of the X and the XZ loading cases and also between the predictions of the XY and the XYZ loading cases. This indicates that the vertical component of ground motion has little effect on the SSDFs in columns, whereas the Y-component has significant effect on the SSDFs of columns. Values of w for the maximum SSDFs in columns of the selected buildings are summarized in Table 5. For the 6-story building, the results presented in the table indicate that, on average, the XY-case displays the highest level of the maximum SSDFs in columns in comparison with the other loading cases. The average maximum SSDF in columns of the XY-case is 25.67% higher than that of the X-case for the 6-story building. For the 10- and 20-story buildings, the results presented in the table indicate that, on average, the XYZ-case displays the highest level of the maximum SSDFs in columns in comparison with the other loading cases. The average maximum
SSDF in columns of the XYZ-case is 63.96% and 45.14% higher than those of the X-case for the 10- and 20-story building, respectively. 7. Steel strain-ductility-factors in beams Figs. 16–18 show the variations of the mean SSDFs in beams along the height of the 6-, 10- and 20-story buildings, respectively. The results shown in the figures indicate that the maximum SSDFs in beams occur in the second-, third- and the seventeenth-story of the 6-, 10- and 20-story buildings, respectively. The results also display little differences among the predictions of the X, XY, XZ and the XYZ loading cases for the three buildings considered. Values of w for the maximum SSDFs in beams of the selected buildings are summarized in Table 6. For the 6-story building, the results presented in the table indicate that, on average, the XZ-case displays the highest level of the maximum SSDFs in beams in comparison with the other earthquake loading cases. For the 10-story building, the results presented in the table indicate that, on average, the XYZcase displays the highest level of the maximum SSDFs in beams in comparison with the other loading cases. The average maximum SSDF in beams of the XYZ-case is 0.28% higher
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Inelastic performance of RC buildings than that of the X-case for the 10-story building. For the 20story building, the results presented in the table indicate that, on average, the XY-case displays the highest level of the maximum SSDFs in beams in comparison with the other loading cases. The average maximum SSDF in beams of the XY-case is 0.36% higher than that of the X-case for the 20-story building. 8. Damage state of the 6-story building Fig. 19 shows the distribution of plastic hinges of the interior frame in the X-direction of the 6-story building. The distributions of plastic hinges are presented for the four loading cases of El Centro earthquake record. The plastic hinge distributions are approximately similar for the X and the XZ loading cases and for the XY and the XYZ loading cases. In the X and the XZ loading cases, plastic hinges occur at the base of the first story columns, at most of the frame beam-ends and at little number of the top-ends of the frame columns. In the XY and the XYZ loading cases, plastic hinges occur at most ends of the frame beams and columns. This indicates that the Y-component has an influence on the distribution of the frame plastic deformations. The Ycomponent causes a change in plastic hinge distribution from a desirable beam-hinging mechanism under the X and the XZ loading cases to a less desirable beam-column-hinging plastic mechanism under the XY and the XYZ loading cases. 9. Damage state of the 10-story building Fig. 20 shows the distribution of plastic hinges of the interior frame in the X-direction of the 10-story building. The distributions of plastic hinges are presented for the four loading cases of El Centro earthquake record. The number of beam plastic hinges reaches 43 for each of the four loading cases. The numbers of column plastic hinges are 19, 51, 20 and 50 for the X, XY, XZ, and the XYZ loading cases, respectively. This indicates that the Y-component has an influence on the distribution of the frame plastic deformations. The Y-component causes a significant increase in the number of plastic hinges in the frame columns. 10. Damage state of the 20-story building Fig. 21 shows the distribution of plastic hinges of the interior frame in the X-direction of the 20-story building. The distributions of plastic hinges are presented for the four loading cases of El Centro earthquake record. The plastic hinge distributions are approximately similar for the X and the XZ loading cases and for the XY and the XYZ loading cases. The numbers of beam plastic hinges reach 114, 107, 114 and 105 for the X, XY, XZ, and the XYZ loading cases, respectively. The numbers of column plastic hinges are 66, 142, 72 and 147 for the X, XY, XZ, and the XYZ loading cases, respectively. This indicates that the Y-component has an influence on the distribution of the frame plastic deformations. The Y-component causes a significant increase in the number of plastic hinges in the frame columns.
11 11. Conclusions The focus of this study is on evaluating the inelastic behavioral characteristics of RC buildings under the effect of 10 nearsource multi-component earthquake excitations. Based on the results of the analysis carried out in this study, the following conclusions are drawn: The consideration of multi-component earthquakes has very little effect on the roof drifts and the story drifts of the RC buildings. The vertical component of earthquakes causes a significant increase by up to 40% in the column maximum axial forces, unlike the second horizontal component, which had a little effect on the column maximum axial forces. The multi-component earthquake causes a very little change in the strain ductility factors of steel in the building beams. The multi-component earthquake causes a significant increase in the strain ductility factors of steel in the building columns. The results indicate that the increase in the column strain ductility factors is mainly due to the effect of the second horizontal component of the earthquake. The vertical component has a minor effect on the column strain ductility factors. The multi-component earthquakes can alter the distribution of plastic hinges in RC buildings as a result of the axialforce variation and the existing of biaxial moments in the building columns. The consideration of the multi-component earthquakes in RC building design is a crucial issue to ensure a satisfactory seismic performance of these types of structures. Evaluating the effectiveness of the design approaches considered in building codes to account for the multi-component earthquake effects is an essential topic that needs to be addressed in future research. This evaluation will require the availability of seismic performance objectives that correspond to specific seismic input levels. Based on the outcome of the current study it is recommended that the seismic performance objectives be based on the strain responses and not on the displacement quantities. This may represent a problem as most available seismic performance objectives are usually identified quantitatively in terms of story drift ratios.
References [1] A.J. Papazoglou, A.S. Elnashai, Analytical and field evidence of the damaging effect of vertical earthquake ground motion, Earthquake Eng. Struct. Dynam. 25 (10) (1996) 1109–1137. [2] Kim SJ, Elnashai AS, Seismic assessment of RC structures considering vertical ground motion, MAE center report No. 08– 03, University of Illinois at Urbana-Champaign, 2008. [3] N.N. Ambraseys, K.A. Simpson, Prediction of vertical response spectra in Europe, Earthquake Eng. Struct. Dynam. 25 (4) (1996) 401–412. [4] ECP-201: Egyptian code for calculating loads and forces in structural work and masonry, Housing and Building National Research Center, Ministry of Housing, Utilities and Urban Planning, Cairo, 2012.
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12 [5] Federal Emergency Management Agency, NEHRP guidelines for the seismic rehabilitation of buildings, Report No. FEMA356, Washington D.C., 2000. [6] N.M. Newmark, J.A. Blume, K.K. Kapur, Seismic design spectra for nuclear power plants, ASCE J. Power Div. 99 (2) (1973) 287–303. [7] Euro code 8, Design of structures for earthquake resistance, part 1: General rules, seismic actions, and rules for buildings, PREN 1998-1, European Committee for Standardization (CEN), 2004. [8] C.J. Collier, A.S. Elnashai, A procedure for combining vertical and horizontal seismic action effects, J. Earthquake Eng. 5 (4) (2001) 521–539. [9] Y. Bozorgnia, K.W. Campbell, The vertical-to-horizontal response spectral ratio and tentative procedures for developing simplified V/H and vertical design spectra, J. Earthquake Eng. 8 (2) (2004) 175–207. [10] N.N. Ambraseys, J. Douglas, Near-field horizontal and vertical earthquake ground motions, Soil Dynam. Earthquake Eng. 23 (2003) 1–18. [11] E. Kalkan, P. Gu¨lkan, Empirical attenuation equations for vertical ground motion in Turkey, Earthquake Spectra 20 (3) (2004) 853–882. [12] Z. Gu¨lerce, N.A. Abrahamson, Site-specific spectra for vertical ground motion, Earthquake Spectra 27 (4) (2011) 1023–1047. [13] J.J. Bommer, S. Akkar, O. Kale, A model for vertical-tohorizontal response spectral ratios for Europe and the Middle East, Bull. Seismol. Soc. Am. 101 (4) (2011) 1783–1806. [14] P.P. Diotallevi, L. Landi, Effect of the axial force and of the vertical ground motion component on the seismic response of RC frames, in: Proceedings of the 12th World Conference on Earthquake Engineering 2000, Auckland, New Zealand. [15] G. Faella, V. Kilar, G. Magliulo, Symmetric 3d RC buildings subjected to bi-directional input ground motion, in: Proceedings of the 12th World Conference on Earthquake Engineering 2000; Paper No. 1809. [16] T. Perea, L. Esteva, Effects of the vertical ground motions on the non-linear analysis of reinforced concrete frames, in:
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[26]
Proceedings of the 13th World Conference on Earthquake Engineering 2004, Vancouver, Canada; Paper No. 1853. A.M. Mwafy, A.S. Elnashai, Vulnerability of code-compliant RC buildings under multi-axial earthquake loading, in: Proceedings of the 4th International Conference on Earthquake Engineering 2006, Taipei, Taiwan; Paper No. 115. A. Kadid, D. Yahiaoui, R. Chebili, Behaviors of reinforced concrete buildings under simultaneous horizontal and vertical ground motions, Asian J. Civil Eng. 11 (4) (2010) 463–476. Y. Djarir, K. Abdelkrim, Seismic response of reinforced concrete frames on flexible foundations subjected to both horizontal and vertical ground motions, Malaysian J. Civil Eng. 24 (2) (2012) 202–214. AM. Mwafy, Effect of bidirectional excitations on seismic response of RC buildings, J. Earthquake Tsunami 6 (4) (2012). H. Salem, Computer-aided design of framed reinforced concrete structures subjected to flood scouring, J. Am. Sci. 7 (10) (2011) 191–200. E.H. Sokkary, Analytical study on upgrading the seismic performance of nominally ductile RC frame structures using different rehabilitation techniques, Ph.D. Thesis, Concordia University 2007, Montreal, Quebec, Canada. A. Ghobarah, Response of structures to near-fault ground motion, in: Proceedings of the 13th World Conference on Earthquake Engineering 2004, Vancouver, B.C., Canada; Paper No. 1031. V. Prakash, G.H. Powell, S. Campbell, Drian-3DX. Base Program Description and User Guide. Version 1.10, Department of civil engineering, University of California at Berkeley, USA, 1994. D. Marinescu, T. Benson, DRAIN-3DX Program Version 3.14, Department of civil engineering, University of California at Berkeley, USA, 2010. The Consortium of Organizations for Strong-Motion Observation systems, COSMOS (available at website:).
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H O S T E D BY
Alexandria University
Alexandria Engineering Journal www.elsevier.com/locate/aej www.sciencedirect.com
ORIGINAL ARTICLE
Inelastic performance of RC buildings subjected to near-source multi-component earthquakes Laila Elhifnawy, Hamdy Abou-Elfath *, Emad El-Hout Department of Structural Engineering, Faculty of Engineering, Alexandria University, Alexandria, Egypt Received 23 July 2016; revised 9 December 2016; accepted 4 March 2017
KEYWORDS 3-D analysis; Inelastic analysis; Multi-component earthquake; RC buildings; Vertical earthquake
Abstract The inelastic behavioral characteristics of three RC buildings having 6-, 10- and 20stories under near-source multi-component earthquake excitations are investigated. Ten earthquake records are used in the analysis to cover a wide range of vertical to horizontal spectral ratios. The performances of the buildings are evaluated through the roof displacements, the maximum story drift ratios and the maximum axial forces and strain ductility factors in the building members. Four analysis cases are considered for each earthquake including, one lateral earthquake component (X-case), two lateral earthquake components (XY-case), one lateral earthquake component accompanied with the vertical earthquake component (XZ-case) and two lateral earthquake components accompanied with the vertical earthquake component (XYZ-case). The results obtained in this study indicate that the multi-component effect of the earthquakes has a considerable effect on the axial forces and strain ductility factors of the building columns although it does not significantly affect the building lateral-deformation response. Ó 2017 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction It has been observed in recent earthquakes that several buildings have suffered extensive damage despite the fact that they had been designed based on the latest seismic design codes. One of the main reasons behind this damage is the multicomponent effect of earthquakes [1,2]. Measurements of ground motion during past earthquakes indicated that the
* Corresponding author. E-mail addresses: [email protected] (L. Elhifnawy), [email protected] (H. Abou-Elfath), [email protected] (E. ElHout). Peer review under responsibility of Faculty of Engineering, Alexandria University.
vertical spectral ordinates may be exceeding the horizontal values [3]. Many codes around the world including the Egyptian code [4] estimate the seismic design forces for each earthquake component separately and then combine the structural responses of the earthquake components by approximate combination rules such as the 30 percent (30%) rule and the square root of the sum of the squares rule. In many modern codes, the vertical response spectrum ordinates are obtained by multiplying the corresponding horizontal spectrum ordinates by a Vertical-to-Horizontal Spectral Ratio (V/H-SR), where V and H are the vertical and the horizontal spectral accelerations, respectively. The V/H-SR is usually taken as a fraction that is less than one. In the FEMA specification [5], the V/H-SR is considered constant and equals to 2/3 following the research work of Newmark et al. [6]. The
http://dx.doi.org/10.1016/j.aej.2017.03.023 1110-0168 Ó 2017 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: L. Elhifnawy et al., Inelastic performance of RC buildings subjected to near-source multi-component earthquakes, Alexandria Eng. J. (2017), http://dx.doi.org/10.1016/j.aej.2017.03.023
2
L. Elhifnawy et al.
columns 0.6
7.0 m
7.0 m
6.0 = 18.0 m 3
0.6 m 16 # 22
7.0 m
7.0 m
0.5 0.5 m 12 # 22
All beams are 0.25 0.60 m 6 # 22 3 # 22
7.0 m
(a) Floor plan
Figure 1
7.0 m
(b) Frame elevation
Six-story RC building.
All beams are 0.25 x 0.60 m
(a) Floor plan Figure 2
3.25 = 32.5 m
12 # 22 8 # 20 6.0 m
6.0 m
6.0 m
Internal External
12 # 25 8 # 25
10
8 # 22 4 # 25
4 # 20
0.45 m 0.45 0.65 m Internal
6.0 m
External
6.0 m
0.65
0.50 m 0.50
6.0 m 6.0 m
8 # 18
4#18
4#18
6.0 m
0.35
6.0 m
0.35 m
5#22 4#18
(b) Frame elevation Ten-story RC building.
Euro code [7] and the Egyptian code [4] recommend the use of two V/H-SRs of 0.45 and 0.9 depending on the expected siteto-source distance. Many analytical studies were conducted on the single degree of freedom level to improve the prediction of the V/ H-SR in order to be employed in modern seismic design codes. Research works by Ambraseys and Simpson [3], Collier and Elnashai [8] and Bozorgnia and Campbell [9], indicated that the V/H-SR is a strong function of the source to site distance and local site conditions. Moreover, some empirical models were developed for estimating the V/H-SR ratio [10–13]. Many studies both analytically and experimentally were conducted on the multi-degree of freedom level for evaluating the performance of buildings under multi-component earth-
quake excitations. Diotallevi and Landi [14] investigated the nonlinear dynamic responses of RC frames using two loading cases, the first case is excited by the horizontal component of ground motion only and the second case is excited by the horizontal and the vertical components of ground motion. The results of this investigation showed that the axial forces in the columns and the roof displacement increase due to consideration of the vertical ground motion. Faella et al. [15] investigated the nonlinear seismic responses of four-story three-dimensional RC buildings. The analysis was performed under the effect of bi-directional (two horizontal components of earthquakes) and unidirectional ground motions. The analysis showed that there was no significant difference between the two loading cases in terms
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3
6.0 m
6.0 m
6.0 m
Inelastic performance of RC buildings
6.0 m
6.0 m
6.0 m
0.50
0.35 0.6 0.35 0.6
3.6 = 72.0 m
0.55
0.4 0.6
0.55
0.4 0.6
0.4 0.6
20
0.6
0.4 0.6
0.6
0.4 0.6
0.4 0.6
12 # 25
0.65
0.4 0.6
0.65
0.4 0.6 0.4 0.6 0.4 0.6
0.4 0.65 0.4 0.65
6.0 m
16 # 25
6.0 m
External columns
0.7
0.7
0.4 0.65
6.0 m
(a) Cross section dimensions Figure 3
12 # 25
12 # 20
0.50
0.3 0.6
16 # 25
8 # 25
0.3 0.6
4 # 20 4 # 20 6 # 20 4 # 20 8 # 20 4 # 20 8 # 20 4 # 20 10 # 20 6 # 20 10 # 20 6 # 20 12 # 20 8 # 20 12 # 20 8 # 20 8 # 25 6 # 25 8 # 25 6 # 25 8 # 25 6 # 25 8 # 25 6 # 25 8 # 25 6 # 25 8 # 25 6 # 25 8 # 25 6 # 25 8 # 25 6 # 25 8 # 25 6 # 25 8 # 25 8 # 20 8 # 25 8 # 20 8 # 25 8 # 20
Internal columns
0.25 0.5
8 # 20
0.45
0.25 0.5
0.45
0.25 0.5
8 # 25
(a) Floor plan
(c) Steel reinforcement details Twenty-story RC building.
of the global response parameters, but the damage has increased in the local level of the member sections for the bidirectional ground motion loading case. Perea and Esteva [16] also investigated the nonlinear dynamic performance of RC frames. The analysis used three cases of the input motions: the vertical ground motion only, the horizontal motion only, and both the horizontal and the vertical motions jointly. The results obtained indicated that plastic hinge rotational demands in beams and columns were increased when including the horizontal and the vertical ground motions together.
Mwafy and Elnashai [17] investigated the nonlinear dynamic responses of three different RC frames. The analysis used two cases of the input motions: the horizontal motion only and both the horizontal and the vertical motions combined. It was concluded that the axial forces and the curvature ductility in columns are increased when including the vertical ground motion. Kadid et al. [18] also considered two loading cases in the dynamic analysis of three RC buildings. The first loading case was the horizontal component of ground motion only, while the second was the horizontal and the vertical ground motions combined. The results indicated that the ver-
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L. Elhifnawy et al. Table 1
Selected near-source earthquakes.
Rec. No.
Earthquake
Stations
M
Distance (Km)
H1 (g)
H2 (g)
V (g)
V/H-SR
1 2 3 4 5 6 7 8 9 10
Nahanni, 1985 Santa Cruz, 1989 Palm Springs, 1986 Northridge, 1994 Westmorland, 1983 San Fernando, 1971 Park field, 2004 El Centro, 1940 Cape Mendocino, 1992 Coalinga, 1983
Territories Capitola Desert Hot Springs Sylmar Ca – Fire Station Pacoima Dam Fault Zone 14 Imperial Valley Petrolia Transmitter hill
6.9 7.0 5.9 6.7 6.0 6.6 6.0 6.7 7.0 6.0
5.97 18.0 12.0 18.0 7.2 3.5 8.0 12.2 15.5 9.5
1.34 0.47 0.30 0.80 0.47 1.17 1.31 0.35 1.50 1.17
1.1 0.4 0.27 0.38 0.38 1.08 0.53 0.21 1.04 0.85
2.37 0.51 0.54 0.33 0.64 0.71 0.56 0.21 0.75 0.46
1.63 1.41 1.15 1.0 0.88 0.85 0.66 0.65 0.64 0.51
M: Earthquake magnitude, H1 and H2: Horizontal PGAs, V: Vertical PGA.
6 20 5
18
14
Story level
Story level
16 4 3 X
2
XY
10
15
20
25
30
Mean floor displacements of the 6-story building.
Story level
8
6
4
X XY
2
XZ XYZ
0 5
10
15
20
25
30
35
40
Floor displacement (cm)
Figure 5
XZ XYZ
0 10
20
30
40
50
60
Floor displacement (cm)
10
0
XY
0
Floor displacement (cm)
Figure 4
X
2
0 5
8
4
XYZ 0
10
6
XZ
1
12
Mean floor displacements of the 10-story building.
tical component had little effect on the story drifts and base shear but it caused an increase in the column axial forces. Djarir and Abdelkrim [19] investigated the effect of combined horizontal and vertical accelerations on the seismic response of reinforced concrete frames on flexible foundations. Five and nine-story buildings were considered in the analysis. It has been found that the inclusion of the vertical ground motion with the soil-structure interaction has resulted in a reduction in the horizontal displacement compared to the case with only the horizontal earthquake component.
Figure 6
Mean floor displacements of the 20-story building.
Mwafy [20] investigated the nonlinear dynamic responses of twelve RC buildings. Different building heights and structural systems (moment-resisting frames and dual frame-wall systems) as well as structural regularity were taken into consideration. The analysis used two cases of the input motions: the horizontal motion only and both the horizontal and the vertical motions combined. The results of this investigation showed that the axial forces in the columns, base shear, and the roof displacement have increased due to consideration of the vertical ground motion. The focus of this study is on investigating the inelastic behavioral characteristics of RC buildings under the effect of near-source multi-component earthquakes. Three RC buildings having 6-, 10- and 20-story are analyzed under the effect of ten near-source earthquake records with a wide range of vertical to horizontal peak spectral ratios. The earthquakes are scaled to insure that the buildings undergo inelastic behavior with a minimum of 2% story drift ratio. The seismic response of the prototype buildings considered in this study is obtained using four earthquake loading cases including one lateral component (X-case), two lateral components (XY-case), one lateral component accompanied with the vertical component (XZ-case) and two lateral components accompanied with the vertical component (XYZ-case). A comparison is made between the building responses to the four earthquake loading cases X, XY, XZ and XYZ to evaluate the multicomponent effect of the earthquake records on the prototype buildings of this study.
Please cite this article in press as: L. Elhifnawy et al., Inelastic performance of RC buildings subjected to near-source multi-component earthquakes, Alexandria Eng. J. (2017), http://dx.doi.org/10.1016/j.aej.2017.03.023
Inelastic performance of RC buildings Table 2
5
Values of w for the roof displacements of the three buildings (%).
Record No.
6-story building
1 2 3 4 5 6 7 8 9 10 Average
10-story building
XZ
XYZ
XY
XZ
XYZ
XY
XZ
XYZ
1.15 0.47 0.16 4.39 2.91 1.81 4.61 1.75 0.42 3.12 0.67
0.44 0.71 0.24 0.01 0.10 0.46 1.10 0.09 0.72 0.58 0.055
1.76 1.24 0.41 4.55 3.07 2.14 4.11 3.03 1.18 3.59 0.93
0.53 1.53 0.21 1.53 0.13 0.13 0.48 4.23 0.36 1.16 0.67
0.06 1.05 0.52 0.29 4.58 0.03 0.02 0.15 0.59 0.04 0.23
0.55 2.46 0.85 1.49 0.02 0.15 0.52 4.08 0.89 1.14 0.88
0.60 0.07 1.22 0.94 5.29 1.88 4.85 1.03 0.13 3.96 2.0
1.98 0.17 0.71 0.05 0.034 0.80 1.16 0.70 1.73 0.33 0.15
1.26 0.20 0.61 0.83 5.37 3.0 4.95 1.38 1.53 3.76 2.04
6
Story number
5
3
XYZ XZ
2
XY
1
X
0.5
1 1.5 Story drift ratio (%)
2
2.5
Figure 7 Height-wise distribution of the mean story drift ratios for the 6-story building.
Story number
4
0
20-story building
XY
20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
XYZ XZ XY X
0 10 9 8 7 6 5 4 3 2 1
0.5
1 Story drift ratio (%)
1.5
2
Story number
Figure 9 Height-wise distribution of the mean story drift ratios for the 20-story building.
XYZ XZ XY X
0
0.5
1 1.5 Story drift ratio (%)
2
2.5
Figure 8 Height-wise distribution of the mean story drift ratios for the 10-story building.
2. Prototype buildings, computer models and earthquake selection Three RC frame buildings having 6-, 10- and 20-stories are used to evaluate the multi-component effect of the nearsource earthquake records. The 6-story building has two bays with a constant bay width of 7.0 m in each direction [21]. The building has a floor area of 196.0 m2. The story height of the 6story building is 3.0 m and the total height is 18.0 m. The structure was designed according to the Egyptian codes (ECP 2012007 and ECP 203-2007). The building was designed
symmetrically in the transverse directions using concrete strength of 30.0 MPa and reinforcing bar yielding strength of 360.0 MPa. The building dimensions and the cross-sectional details are presented in Fig. 1. The 10-story building has three bays with a constant bay width of 6.0 m in each direction [22]. The story height for the 10-story building is 3.25 m and the total height is 32.5 m. The structure was designed according to the ACI code. The building was designed symmetrically in the transverse directions using concrete strength of 25.0 MPa and reinforcing bar yielding strength of 400.0 MPa. The dead load was considered as 8.0 KN/m2, while the live load was assumed to be 2.0 KN/m2. The dimensions and cross-sectional details of the building are shown in Fig. 2. The 20-story building has three bays with a constant bay width of 6.0 m in each direction [23]. The story height for the 20-story building is 3.6 m and the total height is 72.0 m. The structure was designed according to the Canadian codes (the 1995 NBCC and the 1994 CSA). The building was assumed to be located in the city of Victoria on Canada’s west coast. The design base shear coefficient was equal to 6.4% of the total weight. The building was designed symmetrically in
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6
L. Elhifnawy et al. Table 3
Values of w for the MSDRs of the selected buildings (%).
Record NO.
1 2 3 4 5 6 7 8 9 10 Average
6-story building
10-story building
XZ
XYZ
XY
XZ
XYZ
XY
XZ
XYZ
1.18 0.48 0.46 3.94 2.42 1.01 4.88 0.76 0.07 3.20 0.46
1.32 0.64 0.26 0.13 0.02 0.00 1.70 0.01 0.69 0.51 0.054
0.39 1.24 0.64 3.99 2.55 1.10 4.12 2.22 0.99 3.63 0.67
1.70 1.39 0.32 3.84 8.38 0.86 0.14 4.72 0.80 2.88 1.16
0.46 1.93 0.02 0.01 7.36 0.54 0.05 0.13 0.93 0.29 1.01
1.20 2.75 0.43 3.99 7.86 1.58 0.11 5.38 2.37 3.09 1.46
4.25 3.77 2.52 6.92 4.01 2.06 5.43 5.38 0.29 7.13 1.43
0.96 2.06 0.32 1.58 0.02 0.88 2.79 0.44 1.69 1.12 0.29
5.5 5.79 2.37 4.37 4.27 3.14 5.29 5.46 2.27 7.36 0.81
Series4
6
Series3 Series2 Series1
4 3
Story number
Story number
5
2 1 0
20-story building
XY
500 1000 1500 2000 2500 3000 Column maximum axial compression force (kN)
3500
Figure 10 Height-wise distribution of the mean column MACFs for the 6-story building.
20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
Series4 Series3 Series2 Series1
0
10 9 8 7 6 5 4 3 2 1
Series4 Series3
Story number
Series2 Series1
0
1000 2000 3000 4000 5000 Column maximum axial compression force (kN)
6000
Figure 11 Height-wise distribution of the mean column MACFs for the 10-story building.
the transverse directions using concrete strength of 30.0 MPa and reinforcing bar yielding strength of 360 MPa. The dimensions and cross-sectional details of the building are shown in Fig. 3. The DRAIN-3DX computer program [24,25] is used to perform the dynamic inelastic analysis. The Fiber beam-column element (type 15) is used to model the beam-column members of the buildings. A sensitivity analysis is conducted to determine the model parameters. The inelastic lengths at the member ends are taken equal to 20% of the member length. Each inelastic end is then divided into twelve segments and the
2000 4000 6000 8000 10000 Column maximum axial compression force (kN)
12000
Figure 12 Height-wise distribution of the mean column MACFs for the 20-story building.
element cross section is divided into twenty concrete fibers in each direction. The structural mass is assumed lumped at the nodes and the P-D effect has been taken into consideration. The dynamic analysis is performed using a time step increment of 0.02 s and Rayleigh damping which is defined to achieve 5% viscous damping in the first two natural modes of the building. A suite of 10 near-source multi-component earthquake records is selected in this study. The record information is presented in Table 1. The selected records have wide range of vertical to horizontal peak spectral ratios. The records are selected from COSMOS Virtual Data Center [26]. The earthquakes are scaled to insure that the buildings undergo inelastic behavior with a minimum of 2% story drift ratio. Each scale factor is applied identically to the three earthquake components. The scale factors are determined by trial and error for each building and earthquake. Each earthquake has three different scale factors for the three buildings considered in this study. 3. The floor-displacement response Figs. 4–6 show the variation of the mean floor displacements in the X-direction along the height of the 6-, 10- and 20-story
Please cite this article in press as: L. Elhifnawy et al., Inelastic performance of RC buildings subjected to near-source multi-component earthquakes, Alexandria Eng. J. (2017), http://dx.doi.org/10.1016/j.aej.2017.03.023
Inelastic performance of RC buildings Table 4
Values of w for the column MACFs of the selected buildings (%).
Record No.
1 2 3 4 5 6 7 8 9 10 Average
7
6-story building
10-story building
XZ
XYZ
XY
XZ
XYZ
XY
XZ
XYZ
1.92 0.045 0.40 0.63 0.27 0.72 0.60 0.27 0.14 0.45 0.24
61.23 35.98 56.75 12.45 47.69 29.37 37.91 25.62 19.87 8.02 33.49
64.02 35.31 56.75 12.95 45.93 29.77 39.4 26.34 19.6 8.16 33.82
1.04 0.19 0.03 2.08 1.96 0.41 0.30 1.72 0.97 0.61 0.78
116.03 60.19 60.68 12.04 51.54 24.99 38.06 14.50 22.36 2.62 40.30
116.68 59.26 60.79 13.16 52.82 25.12 38.15 14.94 21.92 3.17 40.60
17.6 2.75 0.50 3.31 3.90 0.52 1.90 5.39 1.21 0.48 3.76
59.31 57.01 57.57 27.17 13.40 57.86 86.33 20.55 7.90 12.03 39.91
64.36 56.12 57.57 27.06 16.77 57.86 82.70 20.83 9.12 12.14 40.45
Series4
6
Series3 Series2 Series1
4 3 2 1 1 2 3 4 5 6 Maximum column SSDF for the 6-story building
7
Figure 13 Height-wise distribution of the mean maximum column SSDFs of the 6-story building.
10 9 8 7 6 5 4 3 2 1
Series4
Story number
Story number
5
0
20-story building
XY
20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
Series4 Series3 Series2 Series1
0
Series3
2 4 6 Maximum column SSDF for the 20-story building
8
Story number
Series2
Figure 15 Height-wise distribution of mean maximum column SSDFs of the 20-story building.
Series1
displacement values of the XYZ-case are 0.93%, 0.88% and 2.04% higher than those of the X-case for the 6-, 10- and 20-story buildings, respectively. 0
1 2 3 4 Maximum column SSDF for the 10-story building
5
Figure 14 Height-wise distribution of mean maximum column SSDFs of the 10-story building.
buildings, respectively. The results presented for each building display little differences among the predictions of the X, XY, XZ and the XYZ loading cases. For each building, the results of the X-loading case are considered as a reference for comparing the performances of the various earthquake loading cases. A parameter w is defined to measure the percentage of change in the performance of any earthquake loading case in comparison with that of the X-loading case. Values of w for the roof displacement in the X-direction of the three buildings are summarized in Table 2. The results presented in the table indicate that, on average, the XYZ-case exhibits slightly higher levels of roof displacements in comparison with the other loading cases. The average roof
4. Story-drift response The story drift is an important parameter for evaluating seismic damage of the structural elements in any story. Figs. 7–9 show the variations of the mean story drift ratios in the Xdirection along the height of the 6-, 10- and 20-story buildings, respectively. The results presented in the figures show little differences among the predictions of the four earthquake cases for each building. The results also show that the Maximum Story Drift Ratios (MSDRs) of the earthquake loading cases occur in the third-, sixth- and eighteenth-story of the 6-, 10and 20-story buildings, respectively. Values of w for the MSDRs of the selected buildings are summarized in Table 3. For the 6- and the 10-story buildings, the results presented in the table indicate that, on average, the XYZ-case displays slightly higher levels of MSDRs than the other loading cases. The average MSDRs of the XYZ-case are 0.67% and 1.46% higher than those of the X-case for
Please cite this article in press as: L. Elhifnawy et al., Inelastic performance of RC buildings subjected to near-source multi-component earthquakes, Alexandria Eng. J. (2017), http://dx.doi.org/10.1016/j.aej.2017.03.023
8
L. Elhifnawy et al. Table 5
Values of w for the maximum SSDFs in columns of the selected buildings (%).
Record No.
1 2 3 4 5 6 7 8 9 10 Average
6-story building
10-story building
XZ
XYZ
XY
XZ
XYZ
XY
XZ
XYZ
91.47 10.3 6.06 21.96 19.32 41.91 10.08 49.28 35.75 2.8 25.67
0.66 1.65 0.32 1.75 0.17 1.02 4.51 1.6 7.96 0.31 0.86
77.91 6.60 8.07 20.05 18.40 40.61 4.00 47.57 40.25 2.90 24.22
90.71 48.59 86.41 62.43 69.63 72.14 50.05 66.32 44.21 46.33 63.68
1.76 12.39 0.15 0.61 0.45 10.83 0.51 0.39 12.31 3.20 3.73
97.41 36.68 80.16 62.64 70.13 81.77 51.58 67.54 44.28 47.41 63.96
26.43 36.95 5.28 65.94 17.81 82.62 47.00 52.15 19.72 72.22 42.61
4.92 3.03 8.33 9.96 3.30 3.03 2.19 2.47 20.42 3.73 0.29
29.82 45.90 2.14 62.43 18.80 81.15 45.66 55.24 36.61 73.63 45.14
Series4
6
Series3 Series2 Series1
4 3 2 1 1 2 3 4 5 Maximum beam SSDF for the 6-story building
6
Figure 16 Height-wise distribution of the mean maximum beam SSDFs of the 6-story building.
10 9 8 7 6 5 4 3 2 1
Series3
Story number
Series2
Series4 Series3 Series2 Series1
2 4 6 Maximum beam SSDF for the 20-story building
8
Figure 18 Height-wise distribution of the mean maximum beam SSDFs of the 20-story building.
Series1
0.5 1 1.5 2 2.5 Maximum beam SSDF for the 10-story building
20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
Series4
0
Story number
Story number
5
0
20-story building
XY
3
Figure 17 Height-wise distribution of the mean maximum beam SSDFs of the 10-story building.
the 6- and the 10-story buildings, respectively. For the 20-story building, on average, the XY-case displays the highest level of MSDRs in comparison with the other loading cases. The average maximum story drift ratio of the XY-case is 1.43% higher than those of the X-case for the 20-story building.
shown in the figures indicate that the column MACFs occur in the first-story of the three buildings under the effect of the four earthquakes’ loading cases. The results presented for the three buildings show little differences between the predictions of the X and the XY loading cases and also between the predictions of the XZ and the XYZ loading cases. This indicates that the changes in column axial forces are mainly due to the effect of the vertical ground motion component (the Z-loading case). Values of w for the column MACFs of the selected buildings are summarized in Table 4. For each building, the results presented in the table indicate that, on average, the XYZ-case displays the highest level of column MACFs in comparison with the other loading cases. The average column MACFs of the XYZ-case are 33.82%, 40.60% and 40.45% higher than those of the X-case for the 6-, 12- and the 20-story buildings, respectively.
5. Column maximum axial compression forces 6. Steel strain-ductility-factors in columns Figs. 10–12 show the variations of the mean Maximum Axial Compression Forces (MACFs) in columns along the height of the 6-, 10- and the 20-story buildings, respectively. The results
In this study, the Steel Strain-Ductility-Factor (SSDF) in a column is calculated as the maximum steel strain in the column
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Inelastic performance of RC buildings Table 6
Values of w for the maximum SSDFs in beams of the selected buildings (%).
Record No.
1 2 3 4 5 6 7 8 9 10 Average
9
6-story building
10-story building
20-story building
XY
XZ
XYZ
XY
XZ
XYZ
XY
XZ
XYZ
4.00 0.70 1.64 1.38 0.86 1.73 4.38 4.60 0.33 1.71 0.6
2.61 0.16 0.67 0.296 0.0 0.35 1.11 0.06 0.78 0.40 0.19
6.04 0.75 2.61 1.11 0.66 1.63 3.73 4.66 0.45 2.26 0.69
0.36 0.14 0.16 2.03 4.28 3.85 2.64 3.29 1.97 0.34 0.54
0.22 0.07 0.32 0.14 3.71 1.51 0.21 0.29 4.52 0.27 0.29
0.07 0.28 0.08 2.31 3.62 3.09 3.26 3.44 3.74 0.67 0.72
2.43 0.23 1.80 1.79 0.36 8.95 4.95 4.14 2.31 3.93 0.36
0.85 8.62 1.13 5.04 0.18 4.80 0.93 1.02 4.36 0.15 1.38
4.36 4.26 0.212 1.80 0.84 1.84 0.62 4.37 2.42 3.98 0.22
X-Case
XZ -Case Figure 19
XY-Case
XYZ -Case
Distributions of plastic hinges in the 6-story frame.
X-Case
XZ-Case
XY-Case
XYZ-Case
Figure 20
Distributions of plastic hinges in the 10-story frame.
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10
L. Elhifnawy et al.
X-Case
XZ-Case
XY-Case
XYZ-Case
Figure 21
Distributions of plastic hinges in the 20-story frame.
divided by the steel yield strain. Figs. 13–15 show the variations of the mean SSDFs of columns along the height of the 6-, 10- and 20-story buildings, respectively. The results shown in the figures indicate that the maximum SSDFs in columns occur in the first-, the sixth- and the eighteenth-story of the 6-, 10- and 20-story buildings, respectively. The results presented for each building show very little differences between the predictions of the X and the XZ loading cases and also between the predictions of the XY and the XYZ loading cases. This indicates that the vertical component of ground motion has little effect on the SSDFs in columns, whereas the Y-component has significant effect on the SSDFs of columns. Values of w for the maximum SSDFs in columns of the selected buildings are summarized in Table 5. For the 6-story building, the results presented in the table indicate that, on average, the XY-case displays the highest level of the maximum SSDFs in columns in comparison with the other loading cases. The average maximum SSDF in columns of the XY-case is 25.67% higher than that of the X-case for the 6-story building. For the 10- and 20-story buildings, the results presented in the table indicate that, on average, the XYZ-case displays the highest level of the maximum SSDFs in columns in comparison with the other loading cases. The average maximum
SSDF in columns of the XYZ-case is 63.96% and 45.14% higher than those of the X-case for the 10- and 20-story building, respectively. 7. Steel strain-ductility-factors in beams Figs. 16–18 show the variations of the mean SSDFs in beams along the height of the 6-, 10- and 20-story buildings, respectively. The results shown in the figures indicate that the maximum SSDFs in beams occur in the second-, third- and the seventeenth-story of the 6-, 10- and 20-story buildings, respectively. The results also display little differences among the predictions of the X, XY, XZ and the XYZ loading cases for the three buildings considered. Values of w for the maximum SSDFs in beams of the selected buildings are summarized in Table 6. For the 6-story building, the results presented in the table indicate that, on average, the XZ-case displays the highest level of the maximum SSDFs in beams in comparison with the other earthquake loading cases. For the 10-story building, the results presented in the table indicate that, on average, the XYZcase displays the highest level of the maximum SSDFs in beams in comparison with the other loading cases. The average maximum SSDF in beams of the XYZ-case is 0.28% higher
Please cite this article in press as: L. Elhifnawy et al., Inelastic performance of RC buildings subjected to near-source multi-component earthquakes, Alexandria Eng. J. (2017), http://dx.doi.org/10.1016/j.aej.2017.03.023
Inelastic performance of RC buildings than that of the X-case for the 10-story building. For the 20story building, the results presented in the table indicate that, on average, the XY-case displays the highest level of the maximum SSDFs in beams in comparison with the other loading cases. The average maximum SSDF in beams of the XY-case is 0.36% higher than that of the X-case for the 20-story building. 8. Damage state of the 6-story building Fig. 19 shows the distribution of plastic hinges of the interior frame in the X-direction of the 6-story building. The distributions of plastic hinges are presented for the four loading cases of El Centro earthquake record. The plastic hinge distributions are approximately similar for the X and the XZ loading cases and for the XY and the XYZ loading cases. In the X and the XZ loading cases, plastic hinges occur at the base of the first story columns, at most of the frame beam-ends and at little number of the top-ends of the frame columns. In the XY and the XYZ loading cases, plastic hinges occur at most ends of the frame beams and columns. This indicates that the Y-component has an influence on the distribution of the frame plastic deformations. The Ycomponent causes a change in plastic hinge distribution from a desirable beam-hinging mechanism under the X and the XZ loading cases to a less desirable beam-column-hinging plastic mechanism under the XY and the XYZ loading cases. 9. Damage state of the 10-story building Fig. 20 shows the distribution of plastic hinges of the interior frame in the X-direction of the 10-story building. The distributions of plastic hinges are presented for the four loading cases of El Centro earthquake record. The number of beam plastic hinges reaches 43 for each of the four loading cases. The numbers of column plastic hinges are 19, 51, 20 and 50 for the X, XY, XZ, and the XYZ loading cases, respectively. This indicates that the Y-component has an influence on the distribution of the frame plastic deformations. The Y-component causes a significant increase in the number of plastic hinges in the frame columns. 10. Damage state of the 20-story building Fig. 21 shows the distribution of plastic hinges of the interior frame in the X-direction of the 20-story building. The distributions of plastic hinges are presented for the four loading cases of El Centro earthquake record. The plastic hinge distributions are approximately similar for the X and the XZ loading cases and for the XY and the XYZ loading cases. The numbers of beam plastic hinges reach 114, 107, 114 and 105 for the X, XY, XZ, and the XYZ loading cases, respectively. The numbers of column plastic hinges are 66, 142, 72 and 147 for the X, XY, XZ, and the XYZ loading cases, respectively. This indicates that the Y-component has an influence on the distribution of the frame plastic deformations. The Y-component causes a significant increase in the number of plastic hinges in the frame columns.
11 11. Conclusions The focus of this study is on evaluating the inelastic behavioral characteristics of RC buildings under the effect of 10 nearsource multi-component earthquake excitations. Based on the results of the analysis carried out in this study, the following conclusions are drawn: The consideration of multi-component earthquakes has very little effect on the roof drifts and the story drifts of the RC buildings. The vertical component of earthquakes causes a significant increase by up to 40% in the column maximum axial forces, unlike the second horizontal component, which had a little effect on the column maximum axial forces. The multi-component earthquake causes a very little change in the strain ductility factors of steel in the building beams. The multi-component earthquake causes a significant increase in the strain ductility factors of steel in the building columns. The results indicate that the increase in the column strain ductility factors is mainly due to the effect of the second horizontal component of the earthquake. The vertical component has a minor effect on the column strain ductility factors. The multi-component earthquakes can alter the distribution of plastic hinges in RC buildings as a result of the axialforce variation and the existing of biaxial moments in the building columns. The consideration of the multi-component earthquakes in RC building design is a crucial issue to ensure a satisfactory seismic performance of these types of structures. Evaluating the effectiveness of the design approaches considered in building codes to account for the multi-component earthquake effects is an essential topic that needs to be addressed in future research. This evaluation will require the availability of seismic performance objectives that correspond to specific seismic input levels. Based on the outcome of the current study it is recommended that the seismic performance objectives be based on the strain responses and not on the displacement quantities. This may represent a problem as most available seismic performance objectives are usually identified quantitatively in terms of story drift ratios.
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Please cite this article in press as: L. Elhifnawy et al., Inelastic performance of RC buildings subjected to near-source multi-component earthquakes, Alexandria Eng. J. (2017), http://dx.doi.org/10.1016/j.aej.2017.03.023