Keywords

1 Introduction

Aseismic design of a multistory steel frame especially in case of an industrial facility like steel or power plant is very much complicated because of its process-specific requirement. In those cases, the design engineer needs to take care of not only the structural constrains but also must accommodate the equipment or facilities for which the structure is to be constructed. Many a time process requirement is such that the structural stability system cannot be planned in the desired way. For example, in case of a silo or water tank supporting Junction House, where in addition to the huge overburden load belt conveyor enters or exits the building at an angle and an elevation-difference to each other, usual bracing planning is not possible. Aseismic design of such structure may call for some amount of energy dissipation using the ductility of the constituting members. As per the philosophy of capacity design, predetermined members of the structure are expected to perform in the zone of plastic deformation while others continue to remain elastic. Energy dissipation through this process has a serious limitation because in such a situation the weak link of the structural lattice, i.e., the ones which are designed to operate in the nonlinear range undergo permanent deformation. In the post-earthquake situation, repair and rehabilitation of such structures become a difficult task because of those partially damaged members. Therefore, it is imperative from the perspective of the seismic resilience that the energy dissipation system be planned and designed in such a way so that it doesn’t impair the major load-bearing system and can perform uninterruptedly even after the seismic event. Friction damped bracing system (FDBS) is one of such solutions which has been popular for the last three to four decades. Although the usage of FDBS is not new, as of now the existing international design standards doesn’t provide with an integrated design approach where the influence of the passive energy dissipation system, i.e., FDBS in this case, is considered. One of the major reasons behind this incompleteness is the insufficient study of the structural behaviour with and without FDBS. The current article reports a numerical study of a five-storey five-bay 2D frame for different bracing configurations and compares the behaviour of FDBS with conventional braced frame and moment-resisting frames. The study also tries to identify the basic scheme for bracing placement which facilitates the maintenance without hindering the process requirements. Before the reader is introduced with the detailed working methodology a brief review of the existing state of art friction damper enabled structural analysis and design practices are presented in the next section. Subsequently, the models, ground motion input, its selection procedure and the results are discussed. The article concludes by summarizing the findings of the study and the scope of further research.

2 Friction Damped Bracing System (FDBS): Brief History and Questions Pertaining to the Design and Application

Passive energy dissipation system works as a response to the external force that is applied to the structure and is intended to be resisted [1]. Friction damper is one of the force-based passive energy dissipation devices which uses friction between two metallic and/or non-metallic surfaces to dissipate energy. The device is widely used in the automobile industry as a component of the automotive brake to dissipate kinetic energy. Avtar Pall introduced the mechanism to the structural requirements with the innovative design of Pall damper applied to the panelled structures [2]. After that, through many studies, the energy dissipation behaviour of this kind of damper including its surface attributes are studied thoroughly [3,4,5]. Over the time, different types of friction devices are invented and introduced to the structure such as Sumitomo friction damper [6], Energy dissipating restraint [7], the energy dissipator that uses slotted-bolted connection [8, 9], cylindrical friction damper [10], etc. Recently, Quaketek Inc. [11] has developed a friction damper which uses a similar principle that of the Pall damper. In terms of quantifying the behaviour of these devices, two of the important parameters are the initial slip force to storey yield force ratio and the ratio of bracing stiffness to the corresponding storey stiffness [12]. Although several attempts have been made to practice the structural design involving FDBS [13,14,15], till date no international design standard prescribes designing the structure considering active participation of the passive energy dissipation device [16]. As per the National Earthquake Hazards Reduction Program (NEHRP) recommended provisions (FEMA P-750, 2009) the design load applicable for the seismic force-resisting system without the damper can be reduced up to 75 per cent if the damper is installed [17]. Additionally, in terms of damper arrangement also available guideline is not sufficient. FEMA-356 (2000) stipulates that there should be at least four displacement activated dampers in a storey along any principal direction [18], whereas usually an undamped bracing system may comprise of only one set of vertical bracing in the storey. Therefore, the question is how to use FDBS as a replacement of conventional bracing system (CBS). Moreover, in a horizontally spread building location of the horizontal load transfer system is very important. With the understanding of these requirements in the next section working methodology of this study is described.

3 Working Methodology

In order to understand the behaviour of FDBS over the moment-resisting frame and the conventional braced frame, two sets of frames with both types of bracing configuration are studied through nonlinear time history analysis along with additional two moment-resisting frames. Frames of various bracing configurations (both with FDBS and CBS) are studied and compared to achieve a quantitative inference.

3.1 The Numerical Model of the Structure

The structure is modelled numerically using ETABS commercial software [19]. In one of the sets, the vertical bracing system (with and without FD) is located at the central bay of the 5 bay 2D frame and in the other sets the same is located at the corner bay. Apart from these, another two structures with moment-resisting frame (MRF) are studied. In these cases, also the location of the MRF is either at the central bay or the corner bay. Frames with the lateral load transfer system located at the central bay and the corner bay are presented in the Figs. 1 and 2, respectively. Figure 3 shows a typical frame with a soft storey; in the presented case it is shown to be in the 2nd storey. Loads are applied as per the recommendations of the National Building Code of Canada, 2015 (NBCC 2015) [20].

Fig. 1
figure 1

Frames with the lateral load transfer system located at the central bay; a Moment-resisting frame, b Frame with FDBS, c Frame with CBS

Full size image
Fig. 2
figure 2

Frames with the lateral load transfer system located at the corner bay; a Moment-resisting frame, b Frame with FDBS, c Frame with CBS

Full size image
Fig. 3
figure 3

Typical frames with a soft storey (at the 2nd level); a Frame with FDBS at the central bay, b Frame with CBS at the central bay, c Frame with FDBS at the corner bay, d Frame with CBS at the corner bay

Full size image

3.2 Modelling the Friction Damped Bracing System (FDBS)

Passive energy dissipation using friction damper (FD) involves nonlinear hysteresis energy dissipation technique where nearly rectangular hysteresis loop of the FD characterizes the damper behaviour. In this case, the slip load of a specific damper is considered as the yield load of the member which connects the device. The current numerical study considers Pall type friction damper in the model [21]. Here the FD modelling guidelines provided by Pall Dynamics Inc. and Quaketek Inc. [11] are considered. As stipulated in by the Pall Dynamics, for tension only cross bracing when the damper in the tension brace slips, the compression brace is shortened suitably to avoid the buckling. This feature enables the compression brace to remain perfectly elastic and therefore, during the next cycle of loading when this brace takes the load in tension, it remains ready to take tension in the similar way. The friction damper is idealized as an ideal elasto-plastic link (Wen) as per the procedure provided by Quaketek Inc. The mass of the damper enabled bracing is taken as the sum of the bracing mass and the mass of the damper provided in the catalogue for 450 kN friction damper. The rotational inertia of the damper is not considered because of its strictly axial behaviour.

3.3 Ground Motion Selection

The Selection and scaling of time history records is an important part of the procedure of performance evaluation of structures by time history analysis. There are several methods used in the scaling of earthquake time histories. Scaling makes the selected time histories compatible with a target design spectrum at the fundamental period of the structure so that the results of time history analysis are comparable to the results of response spectrum analysis. In general, the target design spectra for scaling is the Uniform Hazard Spectra (UHS) provided in the design codes for a particular country. However, research has suggested that the UHS is an envelope curve and not suitable as a target spectrum for scaling procedures. Baker developed the concept of Conditional Mean Spectra (CMS) to be used as a suitable response spectrum for scaling procedures, which is not an envelope curve and matches the spectral amplitude of the UHS at the period of interest, i.e., the fundamental period of the structure but has much lower spectral ordinates at other time period values, using the concept of conditional probability [22]. In this article, scaling has been done using the CMS method provided by Baker. Selection of time history is also important; the chosen time history records should satisfy the seismic parameters of the site for which the structure is designed. In this case, as the building is designed for the city of Vancouver, tentime history records are selected which has a ratio of peak ground acceleration and peak ground velocity as 1, which matches the seismic parameter of Vancouver [23]. For all these ten records, the corresponding response spectrum is developed by MATLAB [24] coding. For the CMS method, the sum of squared errors, over the entire period range, is calculated between the developed CMS for Vancouver and the spectra developed by MATLAB codes corresponding to the time histories selected. Only those time histories which give the minimum values of the sum of squared errors are chosen for scaling by CMS method. Finally, the ratio of spectral ordinates of the CMS and the response spectra of the chosen time histories are calculated to be the scale factor and the time histories are multiplied by that factor to obtain the scaled records, used as the input motions for time history analysis. The input acceleration time histories are shown in Fig. 4.

Fig. 4
figure 4

Scaled ground motion records for Vancouver obtained using conditional mean spectra [25, 26]

Full size image

4 Results and Discussion

As elaborated in the previous section, 2D numerical models of four sets of braced frame steel structures and two moment-resisting frame structures are analyzed against three scaled realistic ground motion acceleration time histories for the site at Vancouver city to comprehend the influence of FDBS and its arrangement in the structural response. In this section, the hysteresis plot of the FDs and different response parameters of the frames such as Base shear, Horizontal displacement, Pseudo spectral acceleration (PSA), etc. are presented.

4.1 Hysteresis Behavior

The Hysteresis behaviour shown in Fig. 5 represents the nonlinear behaviour of the friction dampers for the five storeys of the central FDBS against the GMR—1. It is evident that the damper in the top storey doesn’t operate under enough load to be predominantly in the nonlinear range. Thus, the hysteresis loop for the fifth storey is not that prominent.

Fig. 5
figure 5

Hysteresis behaviour of the plastic links at different storey levels; a Fifth (Top) storey, b Fourth storey, c Third storey, d Second storey, e First (Ground) storey

Full size image

4.2 Base Shear (Vb)

Base shear time histories for the three types of frames with no soft storey are presented in Figs. 6, 7, 8, 9, 10, and 11. It is evident that for all the cases the base shear is lesser with FDBS in comparison to the conventional frame and in some cases, it is lesser than the rigid frame system. Moreover, FDBS slightly reduces the shake duration of the frame.

Fig. 6
figure 6

Base Shear time histories of the steel frame with the central rigid frame system, a GMR—1, b GMR—2, c GMR—3

Full size image
Fig. 7
figure 7

Base Shear time histories of the steel frame with the central FDBS, a GMR—1, b GMR—2, c GMR—3

Full size image
Fig. 8
figure 8

Base Shear time histories of the steel frame with the central CBS, a GMR—1, b GMR—2, c GMR—3

Full size image
Fig. 9
figure 9

Base Shear time histories of the steel frame with corner rigid frame system, a GMR—1, b GMR—2, c GMR—3

Full size image
Fig. 10
figure 10

Base Shear time histories of the steel frame with corner FD brace system, a GMR—1, b GMR—2, c GMR—3

Full size image
Fig. 11
figure 11

Base Shear time histories of the steel frame with the corner brace system, a GMR—1, b GMR—2, c GMR—3

Full size image
Fig. 12
figure 12

Envelope of the storey responses of the steel frame with the rigid frame system located at the corner bay of the frame

Full size image

4.3 Storey Response

Figure 12 shows the storey responses for the moment-resisting rigid frame system located at one corner bay of the frame. Displacement mode shape for both the types of bracing systems are found to be similar but the magnitude of the displacement usually increases significantly if FDBS is used. However, corresponding storey shear decreases. Figures 13 and 14 show storey responses for different soft storey locations in the frames with FDBS and CBS, respectively. As expected, with the upward shift of the soft storey deflection increases and base shear decreases but the trend is not true for the ground storey and the 4th storey.

Fig. 13
figure 13

Envelope of the storey responses of the steel frame with FDBS located at the corner bay of the frame for different soft storey locations

Full size image
Fig. 14
figure 14

Envelope of the storey responses of the steel frame with CBS located at the corner bay of the frame for different soft storey locations

Full size image

It is observed that if the bays adjacent to the soft storey are braced using FDBS an optimized combination of the deflection and base hear can be achieved. Figures 15 and 16 present the storey responses for such an arrangement where both base shear and horizontal deflection of the top storey (5th storey) for FDBS are lesser than the corresponding values for CBS. The horizontal deflection at the top storey, i.e., cumulative elastic maximum drift at the top of the building is 65 mm which is well within the prescribed limit of 2.5 per cent of the height. Corresponding base shear is ~457.34 kN which is less than the corresponding base hear value for the CBS system (~777.83 kN).

Fig. 15
figure 15

Storey response of the frame with FDBS and a soft storey at the 3rd level

Full size image
Fig. 16
figure 16

Storey response of the frame with CBS and a soft storey at the 3rd level

Full size image

4.4 Pseudo Spectral Acceleration (PSA)

Pseudo spectral acceleration (PSA) noted at the top floor for different locations of the soft storey in the FDBS are presented in Fig. 17. It shows that the presence of the soft storey increases the value of PSA at the top floor. As the location of the soft storey moves upward, there is a slight reduction in the spectral quantity.

Fig. 17
figure 17

Pseudo Spectral Acceleration (PSA) at the 5th storey (St.) of the steel frame with the corner FDBS, a No soft storey, b soft storey at St. 1, c soft storey at St. 2, d soft storey at St. 3, e soft storey at St. 4, f soft storey at St. 5

Full size image

5 Conclusions

The prime objective of the current study is to identify the suitable scheme and the corresponding parameters to quantify the influence of the FDBS in a steel building frame. It is well known that for the same ground motion force in a particular structure is dependent on its fundamental natural period of vibration (Tf), which in turn is a signature of its flexibility. Hence, in order to capture the actual frame response depending on the structure-specific Tf, period-specific conditional mean spectra is used in this study, i.e., eventually, each of the structures is analyzed against a unique input ground motion tailor-made for that specific frame.

It is observed that the frames with corner bracing system are flexible in comparison to the frames with the central bracing system. However, as expected, the deference is comparatively less in the case of FDBS. Another important observation is the arrangement of the FDBS has very minimum influence on the variation of Tf values.

Usage of FDBS reduces the base shear for all the cases in comparison to CBS. Usually, as the flexibility of the frame increases, base shear reduces. On the other hand, as the location of the soft storey elevates, base shear usually increases but for a rigid base frame with a soft storey at the 2nd level also increases the base shear significantly. The trend is true for both FDBS and CBS. Additionally, FDBS slightly reduces the shake duration also. The study concludes that it is possible to optimize the base shear value and the corresponding elastic cumulative maximum top storey drift using FDBS.

PSA values are found to be more if the soft storey is introduced in the structure. The important inference is that the spectral location of the amplification has a weak but direct relation with the Tf value of the structure. For the frames with a soft storey at the 4th or 5th storey, reduction in the spectral quantity may be attributed to the reduction in the overburden load, not to any structural attribute.

5.1 Contribution, Limitation, and Further Scope

Summarizing the inferences drawn in this article it is possible to say that FDBS can emerge as a reliable solution to handle the dynamic response of the framed structure. The major take-aways from the current study are as follows.

Contribution: The article reports the first-ever quantitative study of steel structural frame with FDBS against Tf specific acceleration time history. It tries to identify the possible parameters, necessary to formulate the basic member arrangement scheme, which may be important for a process plant structure where bracing arrangement may be random to meet the process requirements. Once identified, the exercise is helpful for structural maintenance also. The learnings can as well be applied for the regular frames. Nevertheless, the study confirms that if possible, the regular arrangement of bracing is beneficial.

Limitations: Two-dimensional model of the study is its major limitation. A 3D model will be able to capture the real behaviour of the structure including the influence of the torsional modes. Additionally, the current study doesn’t report the velocity response.

Further scope: The preliminary results obtained in this study opens the scope for further detail study of the frames with regular as well as irregular configurations in the temporal and spectral domains. Storey wise transfer functions for displacement, velocity, and acceleration need to be studied for 3D frames with various configurations.