Earthquake incidence angle influence on seismic performance of reinforced concrete buildings
* Author to whom correspondence should be addressed.
Sigma Journal of Engineering and Natural Sciences 2017, Vol. 35, Issue 4, pp. 609-631; doi.org/10.62051/ytu.sigma-journal-of-engineering-and-natural-sciences-earthquake-incidence-angle-influence-on-seismic-performance-of-reinforced-concre
Abstract
Keywords: Earthquake incidence angle influence; finite element method; reinforced concrete building; seismic performance.
1. Introduction
Buildings occupy the major percentage of engineering stocks. Although it is known that in case of destruction there will emerge significant life and financial losses, the last dramatic and destructive events (2004 Sumatra earthquake in Indonesia. 2011 Van earthquakes in Turkey. 2011 Sendai earthquake in Japan) showed that there was not enough attention at the design and construction phases of buildings. After the October 23 and November 9, 2011 Van/Turkey
Corresponding Author: e-mail: ahmetcan@ktu.edu.tr, tel: (462) 377 40 20 609
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earthquakes, the site investigations demonstrated that (Bayraktar et al., 2013 and 2015) nearly all of the non-engineering reinforced concrete buildings completely collapsed or damaged heavily. Most of these were not designed and constructed in accordance with the related design codes. From the past to the present day, is studied earthquake effect in engineering structures. Many studies show that the effect of earthquakes has changed with respect to incidence angle. When studies are investigated, analytical formulae develop for the determination of the critical angle of earthquake ground motion. In virtue of developed formulas, the maximum values that occur at the critical angle have been determined (Athanatopoulou 2005, Song et al. 2008). The earthquake motion at a specific point of the ground is recorded along two horizontal directions and one vertical. However, in view of some studies, vertical direction component of ground motion may be considered uncorrelated with horizontal directions components (Penzien and Watabe 1975). Nearly all design codes suggested the simultaneous implementation of two horizontal components for each earthquake excitation (FEMA 2000; Eurocode 2004; TERDC 2007). When the studies done from past to this day are examined, many different studies present on effect of earthquake angles (2-directions), in engineering constructions (Gonzalez 1992, Rigato and Medina 2007, Fujita and Takewaki 2010, Kostinakis and Athanatopoulou 2015). In study, the constructions are subjected to earthquake ground accelerations whose values range between 0 to 90 and 0 to 180 degrees, with an increment of 5, 6, 15, 20 etc. degrees (Lagaros 2010, Lucchini et al. 2011, Kostinakis et al. 2013, Kumar and Gajjar 2013, Fontara et al. 2015). In many papers, present that asymmetric-plan structures (Nguyen and Kim 2013, Van and Kim 2013), high-rise steel building (Hosseini and Salemi 2008, Tun and Htun 2014), highway tunnel (Sevim 2013), bridge (Armouti 2002, Liang and Lee 2003, Goa et al. 2004, Ateş et al. 2009, Torbol and Shinozuka 2012, Atak et al. 2014, Newton 2014, Ni et al. 2015) are analyzed and designed based on different seismic excitation angles. Quadri and Madhuri (2014) studied about critical angle of seismic incidence of RC frames. In study, four-story reinforced concrete building is subjected to earthquake ground accelerations whose values range between 0 to 90 with an increment of 10 degree. Kanya and Rao (2015) investigation effect of earthquake incidence angle on seismic performance of RC buildings. In this study, one regular and two plan irregular buildings are modelled and investigated. All the buildings are subjected to ground accelerations whose values range between 0 to 180 degrees. Magliulo et al. (2014) tried to influence of earthquake direction on the seismic response of irregular plan RC frame buildings. In the survey is carried out nonlinear static and dynamic analysis. The incidence angles taken from 0 to 330 degrees, with an increment of 30 degrees. Dynamic earthquake responses of structures are evaluated by diffent researchers (Lopez and Torres 1997, Gao et al. 2004, Fujita and Takewaki 2009, Polycarpou at al. 2015) This paper presents the effect of earthquake incidence angle on the structural dynamic behavior of reinforced concrete building. The eighteen directions whose values range between 0 to 90 degrees, with an increment of 5 degrees are taken into account for comparison. The variation of the maximum story displacements and internal forces in columns and beams are considered to determine these influence on the seismic performance.
2. Ground Motion Incidence Angle
To evaluate the ground motion rotation influence, the two orthogonal (x and y) components of acceleration üxg(t) and üyg(t) are rotated by considered degree and resolved to the structural degrees of freedom (Fig. 1a). It is accepted that üxg(t) and üyg(t) are initially directed along to the X and Y directions, respectively. The rotation (θ) of ground motion components at counter clockwise can be resolved to equivalent ground motion components along the axes (ü1 (t) and ü2 (t)) of the structural degrees of freedom.
Figure 1. Rotation of ground motion acceleration (a) and structure (b)
ü s1 t cos sin 0 ü xg t t sin cos 0 t ü s 2 ü yg ü s 3 t 0 0 1 ü zg t
The transformation matrix (T) is used to perform this operation and is based solely on geometry (Cronin 2007). It should be note that the term of üzg(t) shown the vertical motion which is not affected by planar rotation. A similar approach can be used in the literature (Mohraz and Mehran 1994, Safak and Bendimerad 1998, Liang and Lee 2003) to study ground motion incidence angle is to rotate the structure and transform the original ground motion components to the rotated structural degrees of freedom (Fig. 1b).
ü s1 t cos sin 0 ü xg t t sin cos 0 t ü yg ü s 2 ü s 3 t 0 0 1 ü zg t
The transformation matrix Tt is simply the inverse of T and could also be thought of as the clockwise rotation of ground motion with respect to a stationary structure (Cronin 2007).
3. Description Of The Reinforced Concrete Building
The building is a five story reinforced concrete frame structure with shear walls. The height of each floor and total height of building are 3m and 15m, respectively. The floor area of building is about 325m2 and there is not a basement on the building. The foundation is designed and projected as a raft foundation. The fixed boundary condition is taken into account considering Z1 local site class is and A (rock) soil groups. There is a reinforced concrete shear-wall with 25cm thickness surrounding the side corners and elevator shaft. Each floor consists of 60 reinforced concrete slabs with 12cm thickness. The plan and vertical section of the building are shown in Fig. 2. Some structural and analyses properties of the selected building are given in Table 1. 611
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c) Vertical section on 4-4 grids Figure 2. Plan and sections views of the selected building 612
Table 1. Some structural and analyses properties of the selected building Structural and Analyses Properties Earthquake Zone
4. Finite Element Modelling And Modal Analysis
Finite element model of the selected five story reinforced concrete building is constituted by SAP2000 (2015) program. This program can be used to determine the linear and nonlinear static and dynamic behavior of all engineering structures. The analytical model is created by in-situ investigation on existing structure and static project drawings (Fig. 3).
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Figure 3. Some view of the finite element model of reinforced concrete school building 614
In the analytical model, the columns and beams are modelled as frame elements having six degrees of freedom in each node (translation in x. y and z directions; rotation around the x. y and z axes). The shear-wall and slab are modelled using shell elements having two degrees of freedom in each node (translation in x and z direction). Modal analysis of the building is carried out to calculate likely natural frequencies and mode shapes. The first three natural frequencies are attained in the range of 6-12Hz. The first and second mode shapes are translation mode in y and x direction, the third corresponding mode shape is torsional mode in x-y plane (Fig. 4).
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Mod-3 (f3=11.586Hz) x-y plane (68% mass par. ratio) Figure 4. The first three analytical natural frequencies and mode shapes
5. Earthquake Ground Motion
The ERZICAN/ERZ-NS and ERZICAN/ERZ-EW components of 95 Erzincan station recorded during the Erzincan Earthquake in 1992 are used as ground motions. The time-histories of accelerations and velocities of these records with earthquake response spectra considered 5% damping ratio are indicated in Fig. 5-6. The strong motion records are obtained from the PEER 616
Strong Motion Database (PEER 2016). The databases have information on the site conditions and the soil type for the instrument locations. Table 2 presents the list the parameters of the ground motion records.
Figure 5. The ERZICAN/ERZ-NS component of 1992 Erzincan earthquake
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Figure 6. The ERZICAN/ERZ-EW component of 1992 Erzincan earthquake These records are assigned in x and y directions simultaneously during analyses. In the first analysis for 00 degree, NS component is applied along to the x direction and EW component is applied along to the y direction, respectively. Table 2. Strong motion records selected for consideration No 1 2
Near-Fault Strong Ground Motions Component M D. km Site (*) NS 6.7 4.38 C-D EW
5.1. Displacements
The changing of absolute values of the peak horizontal displacements of building for Erzincan 1992 earthquake considered nineteen directions whose values ranges between 0 to 90 degrees with an increment of 5 degrees to determine the earthquake incidence angle influence are denoted in Fig. 7. It is clearly seen that displacements increase by height of the building for all analyses. The maximum and minimum top displacements are obtained in X direction as 6.8mm and 4.4mm for 90o and 0o, respectively (Fig. 7a). Also, the maximum and minimum top displacements are obtained in Y direction as 7.0mm and 3.9mm for 0o and 80o, respectively (Fig. 7b). It can be said that the displacements are changed considerably with the different earthquake incidence angle. The maximum differences are calculated as 54.54% and 37.14% for X and Y directions, respectively. Table 3 presents the maximum differences in each angle and total differences values to evaluate the earthquake incidence angle influence more accurately. The differences, calculated as a percentage increase of the next angle change relative to the previous angle change. The time histories of horizontal displacements in X and Y directions at the top of building obtained from the linear time-history analysis are presented Fig. 8(a-b).
Figure 7. The changing of maximum horizontal displacements by the height of building
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Figure 8. The time histories of maximum horizontal displacements at the top of building Table 3. The maximum differences in displacements for each earthquake incidence angle Earthquake Incidence Angle 0o 5o 10o 15o 20o 25o 30o 35o 40o 45o 50o 55o 60o 65o 70o 75o 80o 85o 90o
4.40 4.60 4.80 5.00 5.20 5.30 5.40 5.40 5.40 5.40 5.30 5.60 5.90 6.10 6.40 6.60 6.70 6.80 6.80 Max. Diff. (%)
7.00 6.90 6.90 6.70 6.60 6.30 6.10 5.70 5.40 5.00 4.70 4.50 4.30 4.00 3.90 3.90 3.90 4.10 4.40 Max. Diff. (%)
The maximum relative drifts in X and Y directions for each floor are given in Fig. 9 (a-b). It is seen that the maximum drifts in X direction are obtained as 0.00053 at 70o.75o.80o.85o. 90o and the minimum drifts are obtained as 0.00037 at 0o and 5o. In addition, the maximum drifts in Y direction are obtained as 0.00057 at 0o.5o.10o.15o and the minimum drifts are obtained as 0.0003 at 70o. These values are well below the maximum allowable code limits as 0.02. 620
Figure 9. The maximum relative drifts in X and Y directions for each floor
5.2. Internal forces
To determine the earthquake incidence angle effect on the internal forces of building structural elements, two columns and beams are selected at the side and interval. The changing of axial forces by the height of building for Erzincan 1992 earthquake considered nineteen directions whose values range between 0 to 90 degrees with an increment of 5 degrees to determine the earthquake incidence angle influence are denoted in Fig. 10. It is seen that the axial forces have a decreasing trend by height of the building for all analyses. The maximum and minimum values are attained at the base point for S1 column (side column) as 96.55kN and 53.87kN at 0o and 80o, respectively (Fig. 10a). In addition, these values are attained at the same point for S2 column (interval column) as 65.55kN and 38.21kN at 0o and 80o, respectively (Fig. 10b). These results show that the axial forces are changed significantly as 44.21% and 41.71% for S1 and S2 columns, respectively. Table 4 presents the maximum differences in each angle and total differences values to evaluate the earthquake incidence angle influence more accurately. The differences, calculated as a percentage increase of the next angle change relative to the previous angle change. The time histories of axial forces for S1 and S2 columns are presented Fig. 11(a-b).
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Figure 10. The changing of maximum axial forces by the height of building
Figure 11. The time histories of maximum axial forces at the base of building S1 and S2 columns have 25x60cm section area and 1875kN load carrying capacity. It can be seen that these values (given in Table 4) are well below the maximum capacity. There is a decreasing trend up to 80oand after increasing trend at last two steps (Fig. 12).
Table 4. The maximum differences in axial forces for each earthquake incidence angle Earthquake Incidence Angle o
0 5o 10o 15o 20o 25o 30o 35o 40o 45o 50o 55o 60o 65o 70o 75o 80o 85o 90o
S1 Column Max. Axial Force (kN) 96.55 96.30 95.31 93.60 91.17 88.06 84.27 79.84 74.90 69.70 66.30 63.46 60.10 56.36 54.83 54.39 53.87 57.79 61.66 Max. Diff. (%)
Diff. (%) 0.26 1.02 1.80 2.59 3.42 4.30 5.26 6.19 6.95 4.87 4.28 5.24 6.29 2.71 0.80 0.97 7.28 6.70 -----44.21
Max. Axial Force (kN) 65.55 65.46 64.88 63.80 62.23 60.20 57.7 54.76 51.41 48.54 46.23 43.92 41.44 39.11 38.98 38.61 38.21 40.99 43.61 Max. Diff. (%)
Diff. (%) 0.14 0.89 1.66 2.46 3.26 4.15 5.10 6.12 5.58 4.76 5.00 5.65 5.62 0.33 0.95 1.04 7.28 6.39 -----41.71
Figure 12. Changing of axial forces distribution in each columns The changing of absolute values of maximum bending moments (M33) by the height of building is denoted in Fig. 13. It is seen that the bending moments have a decreasing trend by height of the building for all analyses. The maximum and minimum values are attained at the base point for S1 column (side column) as 68.31kNm and 38.21kNm at 0o and 80o, respectively (Fig. 13a). 623
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In addition, these values are attained at the same point for S2 column (interval column) as 99.57kNm and 55.87kNm at 0o and 80o, respectively (Fig. 13b). These results show that the bending moments are changed significantly as 44.06% and 43.89% for S1 and S2 columns, respectively. Table 5 presents the maximum differences in each angle and total differences values to evaluate the earthquake incidence angle influence more accurately. The differences, calculated as a percentage increase of the next angle change relative to the previous angle change. The time histories bending moments for S1 and S2 columns are presented Fig. 14(a-b).
Figure 13. The changing of maximum bending moments by the height of building
Figure 14. The time histories of maximum bending moments at the base of building 624
Table 5. The maximum differences in bending moments for each earthquake incidence angle Earthquake Incidence Angle o
0 5o 10o 15o 20o 25o 30o 35o 40o 45o 50o 55o 60o 65o 70o 75o 80o 85o 90o
68.31 68.11 67.40 66.17 64.43 62.21 59.51 56.37 52.90 49.11 46.55 44.70 42.42 39.80 38.47 38.47 38.21 40.52 43.29 Max. Diff. (%)
99.57 99.26 98.18 96.37 94.07 90.54 86.58 81.96 76.95 71.40 67.69 64.91 61.62 57.87 56.21 56.26 55.87 58.49 62.55 Max. Diff. (%)
To determine the beam response, B1 and B2 beams (Fig. 2a) are selected to represent the side and interval beams. The support and spans values are calculated for both beams in each earthquake directions. The changing of bending moments are given in Fig. 15. The maximum and minimum values are attained for B1 beam (side beam) as 34.31kNm and 24.70kNm at 30o and 75o, respectively. These values are attained for B2 beam (interval beam) as 40.96kNm and 29.03kNm at 80o and 0o, respectively. These results show that the beam response are changed significantly as 28.01% and 41.10% for B1 and B2 beams, respectively. Table 6 presents the maximum differences in each angle and total differences. The time histories of bending moments for B1 and B2 beams are presented Fig. 16 (a-b).
Figure 15. Changing of bending moments distribution in each beams 625
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Figure 16. The time histories of maximum bending moments for B1 and B2 beams Table 6. The maximum differences in bending moments for B1 and B2 beams Earthquake Incidence Angle 0o 5o 10o 15o 20o 25o 30o 35o 40o 45o 50o 55o 60o 65o 70o 75o 80o 85o 90o
Side Beam Support kNm 30.03 31.35 32.45 33.30 33.89 34.23 34.31 34.13 33.68 32.98 32.03 30.84 29.45 27.89 26.07 24.70 25.47 26.05 26.42 Max. Diff. (%)
Diff. (%) 4.40 3.50 2.62 1.79 1.00 0.23 0.54 1.30 2.08 2.88 3.73 4.48 5.30 6.53 5.24 3.11 2.25 1.44 ----28.01
Span kNm 6.67 6.85 6.97 5.93 7.07 7.04 6.97 6.84 6.66 6.4 6.14 5.82 5.45 5.16 4.89 4.96 5.20 5.40 5.58 Max. Diff. (%)
Interval Beam Diff. (%) 2.68 1.85 15.02 19.25 0.34 1.08 1.86 2.65 3.49 4.37 5.33 6.36 5.25 5.27 1.57 4.80 3.82 3.24 ----30.83
Support kNm 29.03 30.20 31.15 31.87 32.35 32.58 32.60 32.42 32.45 33.53 35.45 37.10 38.48 39.55 40.33 40.80 40.96 40.81 40.35 Max. Diff. (%)
Diff. (%) 4.03 3.17 2.31 1.50 0.71 0.06 0.56 0.10 3.31 5.74 4.67 3.70 2.80 1.97 1.17 0.39 0.37 1.13 ----41.10
Span kNm 4.11 4.33 4.53 4.70 4.83 4.93 4.99 5.01 4.99 4.93 4.84 4.71 4.54 4.34 4.12 3.87 3.85 3.90 3.93 Max. Diff. (%)
Diff. (%) 5.49 4.51 3.72 2.82 1.98 1.19 0.41 0.35 1.11 1.89 2.68 3.52 4.41 5.11 6.11 0.54 1.38 0.60 ----23.15
5.3. Principal stresses
The maximum compressive and tensile principal stresses contours attained from the shear walls for all earthquake incidence angles are given in Fig. 17. These stresses contours represent the distribution of the peak values reached by the maximum stresses at each point within the section. The maximum and minimum tensile stresses are attained at the corner of shear walls as 12.88MPa and 11.29MPa at 20o and 45o, respectively (Fig. 17a). In addition, these values are 626
attained at the same point for compressive stresses as 12.88MPa and 11.29MPa at 20o and 45o, respectively (Fig. 17b). These results show that the principal stresses are changed as 12.34%. Table 7 presents the maximum principal stresses (tension and compressive) in each angle and total differences values to evaluate the earthquake incidence angle influence more accurately. Table 7. The maximum principal stresses in shear walls for each earthquake incidence angle Earthquake Incidence Angle o
0 5o 10o 15o 20o 25o 30o 35o 40o 45o 50o 55o 60o 65o 70o 75o 80o 85o 90o
Shear Walls Tensile Stress (MPa) 12.71 12.77 12.75 12.83 12.88 12.69 12.48 12.18 11.78 11.29 11.54 11.93 12.24 12.46 12.58 12.61 12.53 12.54 12.47 Max. Diff. (%)
Diff. (%) 0.52 0.17 0.62 0.41 1.44 1.67 2.46 3.29 4.16 2.21 3.46 2.59 1.76 0.97 0.20 0.56 0.02 0.57 ---12.34
Compressive Stress (MPa) 12.71 12.77 12.75 12.83 12.88 12.69 12.48 12.18 11.78 11.29 11.54 11.93 12.24 12.46 12.58 12.61 12.53 12.54 12.47 Max. Diff. (%)
Diff. (%) 0.52 0.17 0.62 0.41 1.44 1.67 2.46 3.29 4.16 2.21 3.46 2.59 1.76 0.97 0.20 0.56 0.02 0.57 ---12.34
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Figure 17. The maximum compressive and tensile principal stresses contours for shear walls
6. Conclusion
This paper presents an investigation about the earthquake incidence angle influence on the seismic performance of buildings. The five-story reinforced concrete building with moment resisting frame and square plan has been selected and analyzed using finite element methods. The building is subjected to 1992 Erzincan earthquake ground accelerations in nineteen directions whose values ranges between 0 to 90 degrees, with an increment of 5 degrees. The first three natural frequencies are attained in the range of 6-12Hz. The first and second mode shapes are translation mode in x and y direction, the third corresponding mode shape is torsional mode in x-y plane. The displacements increase by height of the building for all analyses. The maximum and minimum top displacements are obtained in X direction as 6.8mm and 4.4mm for 90o and 0o. Also, the maximum and minimum top displacements are obtained in Y direction as 7.0mm and 3.9mm for 0o and 80o. It can be said that the displacements are changed considerably with the different earthquake incidence angle. The maximum differences are calculated as 54.54% and 37.14% for X and Y directions. The maximum drifts in X direction are obtained as 0.00053 at 70o.75o.80o.85o. 90o and the minimum drifts are obtained as 0.00037 at 0o and 5o. In addition, the maximum drifts in Y direction are obtained as 0.00057 at 0o.5o.10o.15o and the minimum drifts are obtained as 0.0003 at 70o. These values are well below the maximum allowable code limits as 0.02. The axial forces have a decreasing trend by height of the building for all analyses. 628
The maximum and minimum values are attained at the base point for S1 column (side column) as 96.55kN and 53.87kN at 0o and 80o. In addition, these values are attained at the same point for S2 column (interval column) as 65.55kN and 38.21kN at 0o and 80o. These results show that the axial forces are changed significantly as 44.21% and 41.71% for S1 and S2 columns. S1 and S2 columns have 25x60cm section area and 1875kN load carrying capacity. It can be seen that these values are well below the maximum capacity. The bending moments have a decreasing trend by height of the building for all analyses. The maximum and minimum values are attained at the base point for S1 column (side column) as 68.31kNm and 38.21kNm at 0o and 80o. In addition, these values are attained at the same point for S2 column (interval column) as 99.57kNm and 55.87kNm at 0o and 80o. These results show that the bending moments are changed significantly as 44.06% and 43.89% for S1 and S2 columns. The maximum and minimum values are attained for B1 beam (side beam) as 34.31kNm and 24.70kNm at 30o and 75o. These values are attained for B2 beam (interval beam) as 40.96kNm and 29.03kNm at 80o and 0o. These results show that the beam response are changed significantly as 28.01% and 41.10% for B1 and B2 beams, respectively. The maximum and minimum tensile stresses are attained at the corner of shear walls as 12.88MPa and 11.29MPa at 20o and 45o. In addition, these values are attained at the same point for compressive stresses as 12.88MPa and 11.29MPa at 20o and 45o. These results show that the principal stresses are changed as 12.34%. At the end of the study, it is concluded that reinforced concrete buildings have shown considerable increase in displacements and internal forces when the earthquake ground motion acceleration is subjected at various incidence angles. There is no unique specific angle of incidence for each building which increases the value of internal forces of all structural members together; each member gets its maximum value of internal forces by a specific angle of incidence.
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ALTUNIŞIK, A.C.; KALKAN, E. Earthquake incidence angle influence on seismic performance of reinforced concrete buildings. Sigma Journal of Engineering and Natural Sciences 2017, Vol. 35, pp. 609-631. https://doi.org/10.62051/ytu.sigma-journal-of-engineering-and-natural-sciences-earthquake-incidence-angle-influence-on-seismic-performance-of-reinforced-concre