Analysis of X-shaped and Double X-shaped Metallic Dampers on Multistorey Frames

Metallic yielding dampers are passive energy dissipating devices that are designed to disperse earthquake energy through hysteretic behavior. This research used ETABS software to analyze the performance of two metallic yielding dampers of the type Added damping and Stiffness (ADAS); X-shaped damper and Double X-Shaped damper. The story shear response of two frames, one a low-rise building of five stories, and another high-rise building of 20 stories was analyzed. Each damper had three types of material; A992 steel, A36 steel and aluminium. The site location for both structures were in the region of California in the United States of America. The structures were analyzed by subjecting them to two earthquakes Loma Prieta and San Fernando as they were two of the major earthquakes that struck California in the nineties. The results showed that both dampers performed satisfactorily. But their performance depended on the magnitude of the earthquake and the number of stories of the structure. Dampers that were made of steel performed better than the ones made of aluminium. Both X-shaped and Double X-shaped dampers were concluded as good energy dissipating devices according to the results obtained.


Introduction
The traditional way of designing structures was to design them so that they resist dynamic forces by strength then energy absorption and finally deformation. During a seismic event these conventionally designed structures deform beyond their elastic limit. Nowadays. structural protective systems are designed to prevent this from happening. These modern structural protective systems can be divided into three parts. They are:

Seismic Isolation 2. Passive Energy Dissipation 3. Semi Active and Active Systems
This study has considered passive energy dissipation technique of metallic yielding dampers. The other types of passive energy dissipation devices are Friction dampers, Viscoelastic dampers, tuned mass dampers, Tuned liquid dampers. These devices absorb the energy from seismic activities and therefore reduce the dissipation of energy throughout the structure. They do not require an external power source and also cannot add energy to the structural system. These systems have been developed because earthquakes are one of the most unpredictable natural disasters in the world. The duration of an earthquake can vary from a few seconds to a few minutes according to its magnitude (USGS, 2014). In the USA the most affected region is California. These seismic activities are mainly due to two plates; the North American plate and Pacific plate; make contact and slide over each other. One of the worst earthquakes to hit California was the Loma Prieta earthquake in 1989 which had a magnitude of 6.9. The slip had occurred on 35 km of the San Andreas Fault at depths ranging from 7 to 20 km. It caused very severe ground shaking and liquefaction of floodplain deposits near the Pajaro and Salinas rivers and also along the San Francisco Bay (USGS, 2014).

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Journal of the University of Ruhuna, Sri Lanka 7(1), 2019 Structures that were constructed before 1960s were designed to tolerate only vertical loads. But when an earthquake hits, the structure is subjected to a horizontal load. Today, there are two methods used to prevent damage done by horizontal loads . They are: 1. For houses and low-rise buildings: increasing the strength and stiffness of the structure so that the structure is in the elastic range.
2. For multi storey and high-rise buildings: using external applications like dampers and base isolation techniques.

Hysteretic damping mechanism
Hysteresis loops are a sequence of loops in the forcedisplacement or resistance-deformation relationship created due to successive loadings and unloading on structures. These are a result of cyclic characteristics of ground motion. When a structure is affected by a severe earthquake, the deformations experienced are beyond the elastic range. These inelastic deformations depend on the magnitude of the earthquake and also the load-deformation characteristics of the structure.
Hysteresis loops are used to measure the structure's capacity to dissipate energy. The structural stiffness and yield displacement determine the shape and orientation of the loop. Hysteretic behavior is affected by factors like structural system, structural material and type of connection (Maneetes, 2007).

Metallic yielding dampers (MYD)
Metallic yielding dampers use hysteretic behavior to dissipate energy absorbed from a seismic activity. Energy is dissipated during the plastic deformation of the metallic components of the dampers. This was first proposed by Kelly in 1972(Kelly, 2006. During a seismic activity larger amount of the energy will be absorbed by the metallic dampers than the structure itself. The dampers have to be placed at selected locations of the main structure. Since they are not embedded to the main structure, replacement of them after deformation is easier (Benavent-Climent, 2010). These damping devices must have the suitable characteristics like adequate elastic strength and stiffness so that the device does not reach inelastic region under service loads. The other characteristics include; having a good capability to dissipate energy and a resistance to low cycle fatigue. The results of numerical and analytical investigations have revealed that the key parameters involved in the design of these dampers are: the ratios of bracing stiffness to device stiffness, brace-device assemblage stiffness to device stiffness, and assemblage stiffness to that of the corresponding story

Added damping and stiffness (ADAS)
Added damping and stiffness devices were first studied by Whittaker. This device has a number of Xshaped plates. The two ADAS devices that are analyzed in this study are X-shaped metallic damper and Double X-shaped metallic damper. The X shaped structure makes sure that yielding occurs over the entire length of the device. ADAS devices improve the behavior of the main structure by increasing its stiffness, increasing its strength and its ability to dissipate energy (Whittaker, 1989).
ADAS have some advantages: they do not require sophisticated technology to get produced, they can easily be integrated into structures, and they show a stable behavior under the effect of the earthquake, as well as environmental factors (temperature, humidity) which do not affect their performance. These dampers are usually mounted in a frame of a bracing system. After the earthquake, they can easily be replaced for the reinforcement of the structure for future earthquakes (Rais, Qunis & Chebili, 2013).
The equations used to determine the required parameters are given below: The initial elastic stiffness: Where n is the number of plates which compose the ADAS system, b is the width of the plates, h the height of the plates and E the elasticity modulus of the material .

X-shaped Metallic
DamperThis has properties like large initial stiffness and high bearing capability. But experimental results have shown that stress concentrates in the center and the corner of the damper and experiments have also shown that bending deformation is less than stress deformation .

Double X-shaped Metallic Damper
This type of damper was first proposed by Li and Li in 2008. The photograph and the hysteresis curve for this damper is shown below. From the experiments they concluded that this damper has both large initial stiffness and energy dissipating capability. The double X shape makes it more resistant to buckling.

Aluminium 6061-T6; 6061-T651
The shear yielding of aluminium had been found to be very ductile and very large inelastic deformations are possible without tearing or buckling (Summers et al., 2015). The low yield strength of aluminium in shear allows the use of thicker webs which further reduces the chances of web buckling. The yielding in shear mode maximizes the material participating in plastic deformation without excessive localized strains. A992 is a high strength, low alloy steel. Its best applied where there is need for more strength per unit of weight. This structural steel alloy is typical used for wide flange and I beams. It has a high material ductility as it has a high yield to tensile strength ratio and is resistant to atmospheric corrosion (Segui, 2007).

Mild Yield Steel: A36 steel
As the dampers are passive to seismic input they should fail before any other component of the main structure does. Therefore, using a low yield steel is the best option for damping devices. For a large earthquake the device is going to undergo great repeated deformations in the plastic region. This shows that the device needs to be made of a material that has excellent elongation and low cycle fatigue characteristics.

Base frame modeling
The site location for this study was chosen as Los Angeles, California. Throughout the study 5 storey and 20 storey ordinary base frames were analyzed. Chevron bracing (inverted V-braces with vertical slotted connections) was selected. Chevron bracing has slotted connections provide only horizontal load transfer from the braces to the beam therefore the vertical components of the brace loads become equal. Thus, the brace loads are governed by the buckling resistance of the compression brace and not the member tensile strength. Also, vertical load transfers to the beam are also avoided (Bubela, 2003).
The assignment of loads along with gravity loads were done according to ASCE 7-10. The ASCE 7-10 linear static load of 1.2D ± 0.5L ±1.0E was used where D= Dead Load, L= Live Load & E=Earthquake Load. Table 4 shows the characteristics of frames that were designed.  ETABS 2013 software was used for the modelling and analysis of the above-mentioned frames. Figures 6 and  8 show the two base frames (5 storeys and 20 storeys) with section properties while Figure 7 shows load assignments, with Chevron bracing.

Application of time history to the modeling frame
Time history data was applied after finishing the base modeling process. The time history data was obtained from Pacific Earthquake Engineering Research (PEER) database. These data were then converted to response spectrum curves by Fast Fourier transformation. This conversion was done using PRISM computer software. Then time histories were scaled to meet the requirement of the design spectrum according to ASCE 7-10.    The table below shows the scale factors used for each earthquake; Loma Prieta and San Fernando

Application of dampers to the base frame
Each damper; X-shaped and Double X-shaped, was applied to each of the designed brace frames. To do this ETABS was provided with stiffness and yielding parameters of each damper type. Firstly, link elements (nonlinear dynamic properties) were defined. Then to assign dampers, panel zones were used. The time history functions were applied to each case and analyzed by ETABS.
Damper properties like effective stiffness and yield force for each material; A992 steel, A36 steel and aluminium were calculated and input in ETABS when the link elements were defined. Each property was calculated for different number of plates. This information is given in the following tables.

Calculated non-linear damper properties
Effective stiffness and yield force for each damper type for three types of material was calculated according to the equations mentioned. The number of plates for each damper was varied in order to observe its effect to the performance of the damper.

Five Storey Analysis
The story shear graphs obtained for the 5 storey frame for Loma Prieta and San Fernando earthquakes respectively for X-shaped damperand DX-shaped damper are shown below. The 5 storey frame without any dampers was also analyzed under the time histories to understand how the dampers work. This is shown from the dotted line in the graph.
Legend for the graphs

Twenty Storey Analysis
Same as the 5 storey analysis the same time histories were applied to a 20 storey frame. Story shear graphs were obtained for X-shaped damper and DX-shaped damper. Here too, a 20 storey frame without any dampers was analyzed under the time histories to understand how the dampers work.

Discussion
From the story shear values obtained from the graphs shown in the section above, the results of the analysis are discussed as follows.
The results from the five storey analysis showed that both the dampers performed poorly when subjected to a low frequency earthquake, like the Loma Prieta earthquake. According to the phenomenon known as resonance, previous studies have shown that low rise buildings are not greatly affected by low frequency earthquakes. Therefore, the reason for both dampers to show reduced performance, when subjected to the Loma Prieta excitation, is due to the insignificant motion of the building failing to activate the dampers. The displacement graphs above clearly show the dampers responding very well to San Fernando excitation in contrast to Loma Preita. The storey shear values of the frames with the dampers have a lesser value compared to the storey shear values of the frame without any dampers. When discussing the results from the three types of materials; both type dampers made from aluminium show better performance than dampers made from A992 and A36 steel. ADAS dampers with higher number of plates have a better performance.
The results for twenty storey analysis compliment the results obtained from the five storey analysis. Here, it can be seen that the dampers do not perform well under San Fernando excitation. This is because high frequency earthquakes do not affect high rise buildings severely. High rise buildings are most affected by low frequency earthquakes since the frame's motion is sufficient to activate the dampers. Both damper types show better performance under Loma Prieta excitation, which has a low frequency. The storey shear values shown in the above graphs confirm this statement. Same as in the five storey analysis ADAS dampers with 10 and 8 plates shows better performance than the dampers with 5 plates. The performance of ADAS dampers made of steel; A992 and A36, showed better performance than dampers made of aluminium.

Conclusion
The analysis done for 5 storey and 20 storey frames show that both dampers perform well when subjected to both high frequency and low frequency earthquakes. ADAS dampers made from steel performed better than the other ADAS dampers. The performance level was high for higher number of plates in both X-shaped and Double X-shaped dampers.
From this research it was established that both dampers work efficiently under seismic activity. As from the previous researches done for ADAS, this research too proves its efficiency. Coupled with its manufacturing easiness, ADAS dampers can be further researched to achieve higher performance levels.
Overall conclusion is that both dampers are efficient and shows great promise in making structures safer from seismic activity in the future.