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Rawnaq Hameed Zghair Hessam Aldin Meshkat Razavi DOI: 10.24412/2520-6990-2021-592-5-12 THE NUMERICAL STUDY OF X-SHAPED METALLIC DAMPERS WITH DIFFERENT GEOMETRY IN RC FRAMES UNDER NEAR-FIELD AND FAR-FIELD EARTHQUAKES
Abstract.
One of the widely applicable displacement-dependent dampers that causes energy dissipation through the material yielding is metallic yielding damper. This damper consists of metallic plates in various shapes that are parallel to each other in the number required and are fitted to the link beams and the end of the chevron braces. Meanwhile, the yielding damper with X-shaped sheets (XMD) is one of the common types of these dampers. The application of XMD has the benefits of easy replacement in the event of an earthquake, the lack ofneed to maintain, the ability to concentrate and limit the energy level in specific locations of the structure, the favorable reduction of energy loss in other elements of the structure and they are only affected by lateral loading. The energy loss in these devices is caused by the plastic deformation of the plates under bending. Based on this, when heavy earthquakes occur, large volumes of material will deform and the damper can dissipate a great deal of energy. In this study, two analytical and numerical approaches were used. The analytical approach was based on mathematical relationships and was verified using experimental findings. It was then used to verify the numerical models developed in ABA QUS. Then, six XMD models were developed by changing the parameters ofmaterials, sheet thickness and number of them, and hysteretic and skeleton curves as well as their behavioral parameters were extracted. Afterwards, the bilinear behavior of these dampers was assigned to the two RC structures of 5 and 10 stories taken from Chukka and Krishnamurthy research model to study the behavior of these dampers under near and far-field earthquakes. The findings indicated that the analytical approach is in good agreement with numerical outputs of the entire XMD models and the bilinear model fitted with the entire skeleton curves. Furthermore, the amount of dissipated energy is sensitive to the modulus of elasticity, thickness and the number of the sheets which means that increasing these parameters leads to an XMD with higher yield force, elastic stiffness, effective stiffness, effective damping ratio and more dissipated energy.
Keyword: ABAQUS, Wen plastic link element, Dynamic Nonlinear Time History analysis (DNTH), Reinforced concrete moment frames, XMD
Introduction:
In the past years, engineers were trying to make structures safe against earthquakes by increasing their strength, in order to keep structures in the elastic region. However, increasing the strength was associated with increasing the stiffness that decreases time period and elevates the earthquake force. This performance will cause the construction costs to increase. On the other hand, there is no economic justification to design structures for the largest possible earthquake. Since it is impossible to assess the characteristics of the largest earthquake, structures may experience the inelastic behavior in large earthquakes. Thus, the engineers have been sought methods and created devices to absorbed energy economically. One of these devices is metallic yielding damper that can dissipate seismic energy and thus reduce the energy entering into the structure. In addition, this type of damper does not require an external power source and does not add energy to the structure of the building. Among various types of metallic yielding damper, X-shaped metallic dampers (XMD) is a combination of multiple X-shaped plates placed parallel to one another which are typically installed between the chevron bracing and beam and dissipate energy through inelastic deformation [1]. To improve the seismic response of structures, numerous studies have been conducted in developing the earthquake-resistant systems. One of the most used earthquake-resistant systems is passive energy dissipation devices or dampers.
These dampers dissipate input earthquake energy and reduce the seismic demand on the structural members. The most effective and popular dampers are X-shaped metallic damper (XMD). This device is a combination of multiple X-shaped plates placed parallel to one another which are typically installed between the chevron bracing and beam. This device resists the horizontal forces associated with inter-story drift through the yielding of plates [2]. In the past, structures were over-designed to also resist the dynamic forces resulting from seismic loads. These structures had high stiffness and strength. Thus, under the earthquake, they absorbed energy and deformed beyond their elastic range. Today, structural maintenance systems are designed to accommodate these deformations. These new systems are divided into three categories of passive energy dampers as well as semi-active and active systems. In this study, one of the passive energy dissipation systems called metallic damper is considered. This type of damper dissipates the seismic energy and hence reduces the energy applied to the structure. In addition, this damper does not require any external power source and does not add extra weight to structure [3]. Thus far, X-shaped metallic dampers with different geometry and material properties have not been investigated in three-dimensional RC structures under different earthquakes. The findings of this study will provide comparative results of the relative performance of X-shaped metallic dampers in different RC structures. Another innovation of this study
is to present and develop an analytical approach that can predict the behavior of these dampers under cyclic loading. In addition, sensitivity analysis will be performed on different parameters of these dampers and then the seismic behavior of X-shaped metallic dampers will be evaluated in three-dimensional RC structures under near-field and far-field earthquakes. The findings of this study can ultimately help designers, executor engineers and contractors to improve the seismic performance of structures. In addition, it will provide an appropriate foundation for the development of new regulations.
Related Literature:
In the past years, engineers were trying to make structures safe against earthquakes by increasing their strength, in order to keep structures in the elastic region. However, increasing the strength was associated with increasing the stiffness that decreases time period and elevates the earthquake force. This performance will cause the construction costs to increase. On the other hand, there is no economic justification to design structures for the largest possible earthquake. Since it is impossible to assess the characteristics of the largest earthquake, structures may experience the inelastic behavior in large earthquakes. Thus, the engineers have been sought methods and created devices to absorbed energy economically. Moghaddasi and Namazi in 2016 evaluated the performance of TADAS dampers for the seismic rehabilitation of buildings. In their study, the effect of the yielding dampers on seismic behavior of structures and their application in retrofitting was studied. The obtained results indicated that the use of TADAS dampers in reinforced concrete buildings enhances the capability of the energy absorption and improves the dynamic behavior of structures, including a reduction in base shear, relative- story displacement and the internal forces of structural members [4]. Aguiar et al. in 2016 developed free software to find the seismic capacity curve of frames with ADAS or TADAS dissipators. CEINCI-LAB was a computer software developed using MATLAB for static or dynamic structural analysis, in a friendly way and simultaneously serves the user to reinforce structural knowledge. In their works, the most important aspects were presented to find the resistant seismic capacity curve of a reinforced concrete or steel plane frame, with ADAS or TADAS energy dissipators above Chevron Braces, using the Pushover technique [5]. Hernández and Colunga in 2017 modeled hysteretic energy dissipation devices in reinforced concrete structures. Results obtained from pushover and nonlinear time-history analyses are compared to evaluate orthogonally effects in reinforced concrete frames with hysteretic energy dissipation devices. Plane and three-dimensional frames were modeled using two different software. Their results were evaluated from capacity pushover curves, inelastic demands mappings, fundamental periods and hysteresis loops of the dissipation devices. Finally, comments are presented about rigorous modeling in three dimensions related to the importance of the stiffness in the beam-column joint [6].Madheswaran et al. in 2017 worked on earthquake response of reinforced concrete building retrofitted with geopolymer
concrete and X-shaped metallic damper. A three-story half-scale reinforced concrete (RC) building was fixed with an X-shaped metallic damper at the ground floor level, was designed and fabricated to study its seismic response characteristics. Experimental studies were carried out using the (4 m 9 4 m) tri-axial shake table facility to evaluate the seismic response of a retrofitted RC building with an open ground story (OGS) structure using yielding type X-shaped metallic dampers and repairing the damaged ground story columns using geo-polymer concrete composites. This work discussed the preparation of test specimens, experimental set-up, instrumentation, method of testing of RC building and the response of the structure. The metallic damper reduced the time period of the structure and displacement demands on the OGS columns of the structure. Nonlinear time history analysis was performed using the structural analysis package, SAP2000 [7].Marasco and Cimellaro in 2017 presented a new energy-based ground motion selection and modification method limiting the dynamic response dispersion and preserving the median demand. In this study, the conditional mean spectrum and the design response spectrum were used as target spectra, and the records that give an applicable and compelling contribution to the hazard were considered. The methodology has been tested showing significant effects in terms of low variability of parameters and accuracy in preserving the median demand for a given hazard scenario [8].
Methodology:
The current study consists of three main steps. In the first step, two base models will be reproduced, one in ABAQUS and the other in SAP2000. The former is a finite element model of X-shaped metallic damper which will be designed and simulated in ABAQUS and then it will be verified using analytical approach. Then, it will be developed by changing the geometric and material parameters to create 6 XMDs. The latter are two reinforced concrete frames from the study of Chukka and Krishnamurthy that will be reproduced in SAP2000 and then the X-shaped metallic damper behavior (parameters) extracted from ABAQUS will be later assigned to these two structures. The second step is devoted to verification in which the X-shaped metallic damper model, the analytical approach and SAP2000 RC models will be verified. The details of this step will be discussed in the verification section. Model developed in ABAQUS will be introduced to RC structures in SAP2000 to study their behavior under near and far-field earthquakes.
X-shaped metallic dampers in ABAQUS:
To provide a comprehensive understanding of the X-shaped metallic damper's behavior with different parameters, a robust finite element model using ABAQUS is proposed. For this purpose, an XMD adopted from Wu et al. experimental study is modeled. To simulate the model, 5 X-shape sheets with the thickness of 14 mm and two connection plates with the thickness of 20 mm as the top and bottom plates is created. The outline dimension of the X-damper is 1350 x180 x220mm. The dimensions of the X-shaped edge are 180x150mm. The connection plates have a size of 180 x440mm. All the parts of the XMD model is
proximate global size of the meshes is 10 and the structures mesh control with minimize mesh transition is selected. The mesh is also standard linear quad element (S4R) which made of 4-node doubly curved thin or thick shell, reduced integration, hourglass control, and finite membrane strains [9, 10].
Model development:
After verifying the algorithm, 6 XMDs adopted from Wu et al. study were developed and their parameters which are the number of the sheets, thickness of the sheets and the material of the XMD were changed to investigate the effect of changing in geometric and material parameters on the behavior of XMD. The developed dampers were named as presented in Table 1. Table 2 also presents the material parameters of XMDs which are soft steel and aluminum. Figure 2 and Figure 3 represent the details of 5 and10-sheet XMD with 14 and 21 mm thickness.
Table 1
Specimen Description Material
5Sheat-14t XMD with 5 sheets with the thickness of 14 mm soft steel
5Sheat-21t XMD with 5 sheets with the thickness of 21 mm soft steel
5Sheat-14t-AL XMD with 5 sheets with the thickness of 14 mm Aluminum
10Sheat-14t XMD with 10 sheets with the thickness of 14 mm soft steel
10Sheat-21t XMD with 10 sheets with the thickness of 21 mm soft steel
10Sheat-14t-AL XMD with 10 sheets with the thickness of 14 mm Aluminum
Table 2
Parameters of the Modulus of Poisson Ratio Yield Strength Ultimate Strength
materials Elasticity (E) (v) (°y) (°y)
Material Mpa Mpa Mpa
soft steel 211000 0.3 173.3 253.3
Aluminum (6061T6) 69637.05 0.33 276 310
180.00
made of deformable shell whose thickness is assigned in the property module. The modulus of elasticity and yield strength of the material used for the entire parts of XMD are 211000 and 173.3 Mpa respectively. The perfect elastoplastic constitutive model is used to simulate the behavior of XMD. Each upper and lower connection plate is coupled to a reference point and the sheets are tied to these plates. For boundary condition and loading, the reference point of the lower connection plate is restrained in all translational and rotational DOFs while the reference point of the upper plate is free only in the loading direction. The XMD then undergoes a loading program consisting of increasing amplitude elastic and post yield cycles of displacement presented in Wu et al. study. The displacement loading history represented in Figure 1 is applied to the reference point of the upper plate in the Z-direction. The ap-
Figure 1
Figure 2
The developed models through changing the parameters that are n which denotes the number of XMD's plates, t which is the plate thickness, E which is the modulus of elasticity of materials, and ay which is the yield stress of XMD will be studied in ABAQUS and the hysteretic and skeleton curves will be obtained, compared with analytical approach and presented to
SAP2000 to the two RC structures to investigate the effect of each change on the behavior of XMDs under near-field and far-field earthquakes. These two types of earthquakes will be the near and far-field earthquakes of Imperial Valley, Northridge, and Kobe. The flowchart of the study is presented in Figure 2.
Figure 3:Flowchart
Results:
An experimental model which is an XMD consisted of 15 X-shape sheets with the thickness of 14 mm and two connection plates with the thickness of 20 mm as the top and bottom plates were selected from Wu et al. study. The outline dimension of the X-damper is 1350x180x220mm. The dimensions of the X-shaped edge are 180 x150mm. The modulus of elasticity and yield strength of the material used for the XMD are 211000 and 173.3 Mpa respectively. The XMD then
underwent the loading protocol presented in chapter 3. The force-displacement hysteretic curves for specimen 1 of this study was used to verify the algorithm. Table 3 and Figure 4 presented the geometric, material and output parameters of the 15-sheet XMD experimentally investigated by Wu et al. and their comparison with the output of the algorithm as well as experimental hyster-etic curve of the damper and the bilinear curve of it which is predicted by the algorithm.
Table 3
Parameters Description Dimension Wu et al (2012) Algorithm Error Percentage
n Number of sheets — 15.00 15.00 —
B Width mm 150.00 150.00 —
H Height mm 180.00 180.00 —
t Thickness mm 14.00 14.00 —
E Elastic modulus Mpa 210000 210000 —
Yield strength Mpa 160 160 —
Q Intercept kN — 186.20 —
Fy Yield force kN 181.50 196.00 -7.40
Fu Ultimate force kN 300.00 314.825 -4.71
dy Yield displacement mm 1.44 1.32 8.89
du Ultimate displacement mm 18.00 17.357 3.70
r Post yield stiffness ratio — — 0.05 —
Ke Elastic stiffness kN/mm 126.10 148.21 -14.92
Kd Plastic stiffness kN/mm — 7.41 —
Keff Effective stiffness kN/mm — 18.138 —
Wd Energy consumed per cycle kN.mm — 11942.64 —
ßeff Effective damping ratio — — 0.348 —
Model development results: This section includes the outputs of the six XMD models developed in ABAQUS and their behavior under cyclic loading as well as their performance in the two RC structures under near and far-field earthquakes. XMDs Results from ABAQUS In this section, stress distribution contours as well as numerical hysteretic and analytical bilinear curves.
the comparison of hysteretic curves extracted form ABAQUS with bilinear curves calculated by the algorithm, skeleton curves, and the comparison of skeleton curves with the bilinear curves are presented for each model from Figure 5 to Figure 6. Table 4 also summaries the numerical and analytic outputs of the XMDs.
Figure 5
(c)
Figure 6
Figure 5 shows the stress distribution of 5Sheat-14t XMD. It can be seen that the maximum amount of stress which is 253.3 Mpa is applied to the middle part of XMD sheets which means that the sheets experienced plastic deformation and reached their ultimate strength under the cyclic loading. Furthermore, it is also observed that the maximum stress capacity of the XMD depends only on the ultimate strength of the material used for the damper. Figure 6 also indicates that the analytical approach is in good agreement with numerical
outputs and the bilinear model fitted with the skeleton curve. For 5Sheat-14t XMD, the intercept (Q), yield (Fy) and ultimate force (Fu) are 65.10, 70.76 and 134.03 kN respectively. Yield (dy) and ultimate (du) displacement are 1.43 and 17.36 mm while elastic (Ke), plastic (Kd) and effective stiffness (Keff) are 49.64, 3.97 and 7.72 kN/mm respectively. The effective damping ratio (Peff) and the amount of dissipated energy are also 0.28 and 24556.9 kN.mm respectively.
Figure 7
<C)
Figure 8
Figure 7 shows the stress distribution of 5Sheat-21t XMD. It can be seen that the maximum amount of stress which is 253.3 Mpa is applied to the middle part of XMD sheets which means that the sheets experienced plastic deformation and reached their ultimate strength under the cyclic loading. Furthermore, the 50 percent increase in the thickness of the XMD has no effect on the maximum bearing stress at the end of the cyclic loading and the maximum stress capacity of the XMD depends only on the ultimate strength of the material used for the damper.
Figure 8 also indicates that the analytical approach is in good agreement with numerical outputs and the bilinear model fitted with the skeleton curve. For 5Sheat-21t XMD, the intercept (Q), yield (Fy) and ulti-
mate force (Fu) are 152.85, 159.22 and 256.24 kN respectively. Yield (dy) and ultimate (du) displacement are 0.95 and 15.43 mm while elastic (Ke), plastic (Kd) and effective stiffness (Keff) are 167.53, 6.70 and 16.61 kN/mm respectively. The effective damping ratio (Peff) and the amount of dissipated energy are also 0.36 and 57239.4 kN.mm respectively. It can be seen that the 50 percent increase in the thickness of the XMD increases the amount of dissipated energy up to 133.09 percent.
According to Figure 7 to Figure 9, for the amount of energy consumed per total hysteresis curves, the XMD with 10 sheets with the thickness of 21 mm has the highest amount of consumed energy and the rest that are 5Sheat-21t, 10Sheat-14t, 10Sheat-14t-AL, 5Sheat-14t, and 5Sheat-14t-AL are in the next order respectively. For the effective damping ratio, the XMD with 10 sheets with the thickness of 21 mm and the
XMD with 5 sheets with the thickness of 21 mm have the highest amount of consumed energy and the rest that are 10Sheat-14t, 5Sheat-14t, 10Sheat-14t-AL, and 5Sheat-14t-AL are in the next order respectively. It can be concluded that changing the sheet thickness has the highest effect on the amount of energy dissipated by XMD and its effective damping ratio. The order is different for the three other parameters so that for the yield force, the XMD with 10 sheets with the thickness of 21 mm has the highest amount and the rest that are 10Sheat-14t-AL, 5Sheat-21t, 10Sheat-14t, 5Sheat-14t-AL, and 5Sheat-14t are in the next order respectively. It can be concluded that changing the sheet thickness and the strength parameters of the employed material
140000
0
o g
.1 0
c
w
0
E E
RC structures results from SAP2000: For modeling XMDs in SAP2000, Wen's plastic element was used. For this purpose, two groups of par-aments that are material parameters to define the mate-
have the highest effect on the amount of yield force. Furthermore, for elastic stiffness, the XMD with 10 sheets with the thickness of 21 mm has the highest amount and the rest that are 5Sheat-21t, 10Sheat-14t, 5Sheat-14t, 10Sheat-14t-AL, and 5Sheat-14t-AL are in the next order respectively while for effective stiffness, the XMD with 10 sheets with the thickness of 21 mm has the highest amount and the rest that are 10Sheat-14t-AL, 5Sheat-21t, 10Sheat-14t, 5Sheat-14t-AL, and 5Sheat-14t are in the next order respectively. It can be concluded that elastic stiffness mostly depends to the sheet thickness while effective stiffness is mostly affected by the sheet thickness and the strength parameters of the employed material.
rial of XMD and the bilinear force-displacement diagram parameters of XMD to assign to this link element were used. The latter was obtained from the skeleton curves of the XMDs. Table 4 represents these parameters for simulating the XMDs in SAP2000.
120000 100000 | 80000 g 60000 40000 20000
57239.42
24556.93
12944.60
I-1
Energy consumed per total hysteresis curves I 5Sheat-14t ■ 5Sheat-21t □lOSheat-Mt ■ lG5heat-21t □ 5Sheat-14t-AL □ lOSheat-Mt-AL
Figure 9
Figure 10
Figure 11
Table 4
Parameter s Descriptio n Dimensio n 5Sheat -14t 5Sheat -21t 10Sheat -14t 10Sheat -21t 5Sheat-14t-AL 10Sheat -14t-AL
E Elastic modulus Mpa 211000 211000 211000 211000 69637.0 5 69637.0 5
ay Yield strength Mpa 173.3 173.3 173.3 173.3 276 276
Fy Yield force kN 70.76 159.22 141.53 318.44 112.70 225.40
r Post yield stiffness ratio _ 0.08 0.04 0.08 0.04 0.25 0.25
Ke Elastic stiffness kN/mm 49.64 167.53 99.28 335.06 16.38 32.76
Conclusion:
The main conclusions of this study are as follows:
• The analytical approach is in good agreement with numerical outputs of the entire XMD models and the bilinear model fitted with the entire skeleton curves. Moreover, the analytical approach can be used to verify the finite element models and the proposed algorithm can effectively predict the hysteretic curve of XMD, its performance under cyclic loading, and yield the behavioral parameters.
• For the entire models, the sheets experienced plastic deformation and reached their ultimate strength under the cyclic loading. Furthermore, the 50 percent increase in the thickness of the XMD, doubling the number of the XMD sheet and changing the material used for the XMD have no effect on the maximum bearing stress at the end of the cyclic loading and the maximum stress capacity of the XMD depends only on the ultimate strength of the material used for the damper.
• The 50 percent increase in the thickness of the XMD increases the amount of dissipated energy up to 133.09 percent. Using material with lower modulus of elasticity and higher yield and ultimate strength (increasing the yield and ultimate strength up to 59.26 and 22.38 percent) for the XMD decreases the amount of dissipated energy down to -47.29 percent. Doubling the number of the XMD sheet increases the amount of dissipated energy up to 100.01 percent. The 50 percent increase in the thickness of the XMD and doubling the number of the sheet increases the amount of dissipated energy up to 366.21 percent which is the highest amount of energy dissipated among the six models. Using material with lower modulus of elasticity (decreasing the modulus of elasticity down to -67 percent) and higher yield and ultimate strength (increasing the yield and ultimate strength up to 59.26 and 22.38 percent) as well as doubling the number of the sheet increases the amount of dissipated energy only up to 5.46 percent.
• It can be concluded that changing the sheet thickness has the highest effect on the amount of energy dissipated by XMD and its effective damping ratio. Furthermore, changing the sheet thickness and the strength parameters of the employed material have the highest effect on the amount of yield force. Moreover, elastic stiffness mostly depends to the sheet thickness while effective stiffness is mostly affected by the sheet thickness and the strength parameters of the employed material.
Reference:
1. A. Li, Vibration Control for Building Structures: Theory and Applications: Springer Nature, 2020.
2. N. D. K. R. Chukka and M. Krishnamurthy, "Comparison of X-shaped metallic dampers with fluid viscous dampers and influence of their placement on seismic response of the building," Asian Journal of Civil Engineering, vol. 20, pp. 869-882, 2019.
3. U. Liyanage, T. Perera, and H. Maneetes, "Seismic Analysis of Low and High Rise Building Frames Incorporating Metallic Yielding Dampers," 2018.
4. M. Moghaddasi and A. Namazi, "Assessment of Performance of TADAS Dampers for the Seismic Rehabilitation of Buildings," International Journal of Applied Engineering Research, vol. 11, pp. 1051610523, 2016.
5. R. Aguiar, D. Mora, and M. Rodríguez, "CEINCI-LAB un software libre para hallar la curva de capacidad sísmica de pórticos con disipadores ADAS o TADAS," Revista ingeniería de construcción, vol. 31, pp. 37-53, 2016.
6. H. de Jesús Nangullasmú and A. Tena, "MODELADO DE DISIPADORES HISTERÉTICOS DE ENERGÍA EN ESTRUCTURAS DE CONCRETO REFORZADO. DIFERENCIAS ENTRE ANÁLISIS EN EL PLANO Y EN TRES DIMENSIONES," Revista Internacional de Ingeniería de Estructuras, vol. 22, 2018.
7. C. Madheswaran, K. Sathishkumar, and G. R. Rao, "Earthquake Response of Reinforced Concrete Building Retrofitted with Geopolymer Concrete and X-shaped Metallic Damper," Journal of The Institution of Engineers (India): Series A, vol. 98, pp. 41-52, 2017.
8. S. Marasco and G. Cimellaro, "A new energy-based ground motion selection and modification method limiting the dynamic response dispersion and preserving the median demand," Bulletin of Earthquake Engineering, vol. 16, pp. 561-581, 2018.
9. C. Zhou and J. Han, "Study on the seismic performance of X-added damping and stiffness energy dissipation device," in 15 th World Conference on Earthquake Engineering, Lisbon, Portugal, 2012, pp. 24-28.
10. T. Yang, T. Li, L. Tobber, and X. Pan, "Experimental and numerical study of honeycomb structural fuses," Engineering Structures, vol. 204, p. 109814, 2020.
