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The Buckling Restrained Braced Frame (BRBF) is used in steel structures as a lateral load resisting system for seismic events. In typical design procedure the impact of gravity loads acting on BRBFs is neglected and the beams and columns of the structure are designed to resist all gravity loads. In actuality BRBFs are supporting portions of gravity loads acting on the structure which may be changing the overall performance of BRBFs. The purpose of this study is to determine the impact of large gravity loads on BRBF performance. This is done using finite element analysis to test two different structures supporting large gravity loads. The first structure is a seven story structure consisting of different BRBF configurations; the second structure is a three story structure with all BRBFs in an eccentrically braced configuration. Each structure was modeled with applied ground motion simulations with and without gravity loads, and with gravity loads but no applied ground motion simulations. Results indicate that gravity loads have no significant impact on the overall performance of BRBFs for either structure.

A typical buckling restrained brace (BRB) consists of a core segment and a buckling restraining mechanism. When compared to a conventional brace, BRBs provide nearly equal axial yield force in tension and compression. Buckling restraining mechanism can be grouped into two main categories. Buckling is inhibited either by using a concrete or mortar filled steel tube or by using steel sections only. While a large body of knowledge exists on buckling restrained braces the behavior of steel encased BRBs has not been studied in detail. Another area that needs further investigation is the detailing of the deboding material. For all types of BRBs a debonding material or a gap has to be utilized between the core brace and the restraining mechanism. The main function of the debonding material is to eliminate the transfer of shear force between the core brace and the restraining mechanism by preventing or reducing the friction. A two phase research study has been undertaken to address these research needs. In the first phase an experimental study was carried out to investigate the potential of using steel encased BRBs. In the second phase a numerical study was conducted to study the friction problem in BRBs. The experimental study revealed that steel encased braces provide stable hysteretic behavior and can be an alternative to mortar filled steel tubes. Material and geometric properties of the debonding layer for desired axial load behavior were identified and presented herein.

Στόχος της εργασίας είναι η παραμετρική μελέτη μεταλλικών τρισδιάστατων πλαισίων με συνδέσμους δυσκαμψίας, ανθεκτικούς σε λυγισμό (BRB: Buckling Restrained Braces). Τα πρώτα κεφάλαια της εργασίας αποτελούν το θεωρητικό υπόβαθρο της διατριβής και αναφέρονται στα ζητήματα που αφορούν τον αντισεισμικό σχεδιασμό των μεταλλικών κατασκευών. Στο υπόβαθρο αυτό βασίστηκε τόσο ο σχεδιασμός του δείγματος των κατασκευών όσο και η επιλογή των υπό διερεύνηση παραμέτρων. Το αντικείμενο της εργασίας καθαυτό παρουσιάζεται στα τρία τελευταία κεφάλαια όπου γίνεται η περιγραφή του σχεδιασμού των τελικών κτιρίων ώστε να επιτευχθεί φυσική μονοαξονική εκκεντρότητα και στη συνέχεια η ανάλυση των κατασκευών αυτών με μη γραμμικές αναλύσεις. Από αυτές δημιουργείται μια βάση δεδομένων από την οποία εξάγονται συμπεράσματα που αφορούν τη συσχέτιση της εκκεντρότητας με τα μεγέθη απόκρισης των κατασκευών. / The subject of this thesis is the non linear analysis of 3D steel frames with buckling restrained braces (BRB).

Reinforced concrete frame buildings designed and built prior to the enactment of modern seismic codes of the pre-1970’s era are considered seismically vulnerable, particularly when they are subjected to strong ground motions. It is the objective of this research to develop a new and innovative seismic retrofit technology for seismic upgrading of nonductile or limited ductility reinforced concrete frame buildings involving the implementation of buckling restrained braces. To achieve this objective, combined experimental and analytical research was conducted. The experimental research involved tests of large-scales reinforced concrete frames under slowly applied lateral deformation reversals, and the analytical research involved design and nonlinear analysis of laboratory specimens, as well as design and dynamic inelastic response history analysis of selected prototype buildings in eastern and western Canada. The research project started with a comprehensive review of the building code development in Canada to assess the progression of seismic design requirements over the years, and to select a representative period within which a significant number of engineered buildings were designed and constructed with seismic deficiencies. A similar review of seismic design and detailing provisions of the Canadian Standard Association (CSA) Standard A23.3 on Design of Concrete Structures was also conducted for the same purpose. Six-storey and ten-storey prototype buildings were designed for Ottawa and Vancouver, using the seismic provisions of the 1965 National Building Code of Canada, representative of buildings in eastern and western Canadian. Preliminary static and dynamic linear elastic analyses were performed to assess the effectiveness of upgrading the ten-storey reinforced concrete building designed for Ottawa. The retrofit methods studied consisted of lateral bracing by adding reinforced concrete shear walls, diagonal steel braces, or diagonal steel cable strands. The results indicated that the retrofit techniques are effective in limiting deformations in non-ductile frame elements to the elastic range. The numerical analyses were used to demonstrate the effectiveness of Buckling Restrained Braces (BRBs) as a retrofit method for seismically deficient reinforced concrete frame buildings. The experimental phase of research consisted of two, 2/3rd scale, single bay and single storey reinforced concrete frames, designed and constructed based on a prototype sixstorey moment resisting frame building located in Ottawa and Vancouver, following the requirements of the 1965 edition of the NBCC. One test specimen served as a bare control frame (BCF) that was first tested, repaired and retrofitted (RRF) to evaluate the effectiveness of the proposed retrofit methodology for buildings subjected to earthquakes in the City of Ottawa. The control frame was assessed to be seismically deficient. The second frame served as a companion non-damaged frame (RF) that was retrofitted with a similar retrofit concept but for buildings subjected to earthquakes in the City of Vancouver. A new buckling restrained brace (BRB) was conceived and developed to retrofit existing sub-standard reinforced concrete frames against seismic actions. The new BRB consists of a ductile inner steel core and an outer circular sleeve that encompasses two circular steel sections of different diameters to provide lateral restraint against buckling in compression of inner steel core. Mortar is placed between the two circular sections to provide additional buckling resistance. The inner core is connected to novel end units that allow extension and contraction during tension-compression cycles under seismic loading while providing lateral restraint against buckling within the end zones. The end units constitute an original contribution to the design of Buckling Restrained Braces (BRBs), providing continuous lateral restraint along the core bar. The new technique has been verified experimentally by testing four BRBs on the two test structures under simulated seismic loading. The test results of the BRB retrofitted frames indicate promising seismic performance, with substantial increases in the lateral load and displacement ductility capacities by factors of up to 3.9 and 2.6, respectively. In addition, the test results demonstrate that the BRB technology can provide excellent drift control, increased stiffness, and significant energy dissipation, while the reinforced concrete frames continue fulfilling their function as gravity load carrying frames. The above development was further verified by an exhaustive analytical study using SAP2000. At the onset, analyses were conducted to calibrate and verify the analytical models. Two-dimensional, one-bay, one-storey models, simulating the BCF and RRF test frames, were created. The models were subjected to incrementally increasing lateral displacement reversals in nonlinear static pushover analyses, and the results were compared with those obtained in the test program. Material nonlinearity was modeled using “Links” to incorporate all lumped linear and nonlinear properties that were defined with moment-rotation properties for flexural frame members and with force-displacement properties for the diagonal buckling restrained braces. Comparison with test data demonstrated good agreement of the frame behaviour in the elastic and post-elastic ranges, and the loading and unloading stiffness. The research program was further augmented with nonlinear dynamic time history analyses to verify the feasibility of the new retrofit technique in multi-storey reinforced concrete frame buildings located in Canada and their performances relative to the performance-based design objectives stated in current codes. Prior to conducting the analyses, 450 artificial earthquake records were studied to select the best matches to the Uniform Hazard Spectra (UHS) according to the 2010 edition of the NBCC for Ottawa and Vancouver. Furthermore, additional analyses were conducted on buildings for the City of Ottawa based on amplified Uniform Hazard Spectrum compatible earthquake records. The nonlinear time-history response analyses were conducted using a model that permits inelasticity in both the frame elements and the BRBs.The results indicated that reinforced concrete buildings built before the 1970’s in the City of Ottawa do not require seismic retrofitting; they remain within the elastic range under current code-compatible earthquake records. The structural building performance is within the Immediate Occupancy level, and all structural elements have capacities greater than the force demands. In the City of Vancouver, buildings in their virgin state experienced maximum interstorey drifts of 2.3%, which is within the Collapse Prevention structural performance level. Improved building performance was realized by retrofitting the exterior frames with multiple uses of the BRB developed in this research project. The seismic shear demands were reduced in the columns, while limiting the deformations in the non-ductile frame elements to the elastic range. The lateral interstorey drift was limited to 0.92%, which lies within the Life Safety structural performance level.

This thesis presents the development of a design procedure for buckling-restrained braced frames (BRBF's). This procedure uses nonlinear time history analysis and a formal optimization algorithm. The time history analysis includes an elasto-plastic model for the braces. The optimization algorithm is a genetic algorithm. This procedure is referred to throughout the thesis as the "Nonlinear Time History Analysis Procedure with Optimization" (NTHO). Current design specifications for BRBF's are based on inelastic design spectra and approximate formulas for the determination of natural period. These spectra are used to obtain seismic base shear, and the distribution of equivalent lateral forces. Yielding and drift criteria are then used to determine brace areas. This design procedure is referred to throughout the thesis as the "Equivalent Lateral Force Procedure" (ELF). The thesis compares results from the NTHO and ELF procedures for a variety of BRBF's and levels of seismicity. The ELF procedure is judged against the more accurate NTHO procedure, and BRBF's are identified where the ELF procedure produces unconservative and excessively conservative designs. Since the NTHO procedure is more computationally expensive than the ELF procedure, design charts are developed for quickly sizing brace areas for a variety of BRBF's based on the NTHO procedure. Among the conclusions at the end of the thesis is the surprising result that the design charts show a near linear variation of brace area from story to story.

Most structural optimization procedures focus on minimizing the total volume of steel in an attempt to reduce overall costs. However, many other factors can have an effect on the overall cost of a structure. Base column demands in particular, can affect base plate sizes, anchorage, and foundation design. Researchers have found that present methods for estimating column demands are too conservative. Nonlinear time history analyzes were conducted on buckling-restrained braced frames of six heights. Optimized results were found considering three ductility constraints and two optimization objectives. The two optimization objectives were minimized total brace area and minimized base column demands. The results show that designs created by using a minimized column demand objective led to column demands that ranged from 2 to 6% lower than column demands in designs generated by a total brace area minimizing objective. The average brace areas of the designs produced by the total brace area minimizing objective were 25 to 80% less than the designs produced by the column demand minimizing objective. Results showed that large braces in the top stories did not have an effect on column demands in the ground level story. The results indicate that base column demands can be minimized by minimizing braces areas. However, braces areas cannot be minimized by minimizing base column demands.

Severe earthquakes cause damage to buildings. One measure of damage is the residual drift. Large residual drifts suggest expensive repairs and could lead to complete loss of the building. As such, research has been conducted on how to reduce the residual drift. Recent research has focused on self-centering frames and dual systems, both of which increase the post-yield stiffness of the building during and after an earthquake. Self-centering systems have yet to be adopted into standard practice but dual systems are used regularly. Dual systems in steel buildings typically combine two types of traditional lateral force resisting systems such as bucking restrained braced frames (BRBFs) and moment resisting frames (MRFs). However, the cost of making the moment connections for the MRFs can make dual systems costly. An alternative to MRFs is to use gravity columns as the secondary system in a dual system. The gravity columns can be used to help resist the lateral loads and limit the residual drifts if the lateral stiffness of the gravity columns can be activated. By restraining the displacement of the gravity columns, the stiffness of the columns adds to the stiffness of the brace frame, thus engaging the lateral stiffness of the gravity columns. Three methods of engaging the stiffness of the gravity columns are investigated in this thesis; one, fixed ground connections, two, a heavy elastic brace in the top story, and three, a heavy elastic brace in the middle bay. Single and multiple degree of freedom models were analyzed to determine if gravity columns can be effective in reducing residual drift. In the single degree of freedom system (SDOF) models, the brace size was varied to get a range of periods. The column size was varied based on a predetermined range of post-yield stiffness to determine if the residual drift decreased with higher post-yield stiffness. Three and five story models were analyzed with a variety of brace and column sizes and with three different configurations to activate the gravity columns. Using gravity columns as part of a dual system decreases the residual drift in buildings. The results from the SDOF system show that the residual drift decreased with increased post-yield stiffness. The three and five story models showed similar results with less residual drift when larger columns were used. Further, the models with a heavy gravity column in the top story had the best results.

It is possible to reduce residual and maximum drifts in buildings by adding “elastic stories” that engage gravity columns in seismic response. An elastic story is a story wherein the buckling restrained brace frame (BRBF) size is increased to prevent yielding when an earthquake occurs. Buildings ranging from 4–16 stories were designed with various elastic story brace sizes and locations to determine the optimal combination to best reduce drifts. Gravity column stiffnesses were also varied in elastic story buildings to determine the effects on drifts. Computer models were used to analyze these buildings under a suite of earthquakes. Adding elastic stories reduce residual drifts 34% to 65% in 4- to 16-story BRBF buildings. General recommendations are made to achieve optimal reductions in drifts. For buildings with six or more stories, drifts were generally reduced most when an elastic story was added to every 4th story starting at level 1 (the bottom story). The most effective size for the braces in the elastic story appears to be three times the original brace size. For buildings with less than six stories, adding a three times elastic story to the bottom level was observed to reduce drifts the most. Further research is also recommended to confirm the optimal location and size of elastic stories for buildings with differing number of stories. Increasing gravity column stiffnesses in buildings with elastic stories helps to further reduce drifts, however it may not be economical. Residual drifts were observed to decrease significantly more than maximum drifts when elastic stories were added to buildings. Maximum drifts generally decreased at some levels, but also increased at others when elastic stories were used.

This paper provides an assessment of the seismic performance of a code-designed buckling restrained braced frame building using the performance-based analysis procedures prescribed in ASCE 41-06. The building was designed based on the standards of the ASCE 7-05 for a typical office building located in San Francisco, CA. Nonlinear modeling parameters and acceptance criteria for buckling restrained brace components were developed to match ASCE 41-06 design standards for structural steel components, since buckling restrained braces are not currently included in ASCE 41-06. The building was evaluated using linear static, linear dynamic, nonlinear static and nonlinear dynamic analysis procedures. This study showed that the linear procedures produced more conservative results, with the building performing within the intended Life Safety limit, while the nonlinear procedures predicted that the building performed closer to the Immediate Occupancy limit for the 2/3 maximum considered earthquake hazard. These results apply to the full maximum considered earthquake hazard as well, under which the building performed within the Collapse Prevention limit in the linear analysis results and within the Life Safety limit in the nonlinear analysis results. The results of this paper will provide data for the engineering profession on the behavior of buckling restrained braced frames as well as performance based engineering as it continues to evolve.