To reduce seismic vulnerability and the economic impact of seismic structural damage, it is important to protect structures using supplemental energy dissipation devices. Several types of supplemental damping systems can limit loads transferred to structures and absorb significant response energy without sacrificial structural damage. Lead extrusion dampers are one type of supplemental energy dissipation devices. A smaller volumetric size with high force capacities, called high force to volume (HF2V) devices, have been employed in a large series of scaled and full-scaled experiments, as well as in three new structures in Christchurch and San Francisco. HF2V devices have previously been designed using very simple models with limited precision. They are then manufactured, and tested to ensure force capacities match design goals, potentially necessitating reassembly or redesign if there is large error. In particular, devices with a force capacity well above or below a design range can require more testing and redesign, leading to increased economic and time cost. Thus, there is a major need for a modelling methodology to accurately estimate the range of possible device force capacity values in the design phase – upper and lower bounds. Upper and lower bound force capacity estimates are developed from equations in the metal extrusion literature. These equations consider both friction and extrusion forces between the lead and the bulged shaft in HF2V devices. The equations for the lower and upper bounds are strictly functions of device design parameters ensuring easy use in the design phase. Two different sets of estimates are created, leading to estimates for the lower and upper bounds denoted FLB,1, FUB,1, FUB,2, respectively. The models are validated by comparing the bounds with experimental force capacity data from 15 experimental HF2V device tests. All lower bound estimates are below or almost equal to the experimental device forces, and all upper bound estimates are above. Per the derivation, the (FLB,1, FUB,1) pair provide narrower bounds. The (FLB,1, FUB,1) pair also had a mean lower bound gap of -34%, meaning the lower bound was 74% of device force on average, while the mean upper bound gap for FUB,1 was +23%. These are relatively tight bounds, within ~±2 SE of device manufacture, and can be used as a guide to ensure device forces are in range for the actual design use when manufactured. Therefore, they provide a useful design tool.
Supplemental energy dissipation devices are increasingly used to protect structures, limit loads transferred to structural elements and absorbing significant response energy without sacrificial structural damage. Lead extrusion dampers are supplemental energy dissipation devices, where recent development of smaller volumetric size with high force capacities, called high force to volume (HF2V) devices, has seen deployment in a large series of scaled and full-scaled experiments, as well as in three new structures in Christchurch, NZ and San Francisco, USA. HF2V devices have previously been designed using limited precision models, so there is variation in force prediction capability. Further, while the overall resistive force is predicted, the knowledge of the relative contributions of the different internal reaction mechanisms to these overall resistive forces is lacking, limiting insight and predictive accuracy in device design. There is thus a major need for detailed design models to better understand force generation, and to aid precision device design. These outcomes would speed the overall design and implementation process for uptake and use, reducing the need for iterative experimental testing. Design parameters from 17 experimental HF2V device tests are used to create finite element models using ABAQUS. The analysis is run using ABAQUS Explicit, in multiple step times of 1 second with automatic increments, to balance higher accuracy and computational time. The output is obtained from the time- history output of the contact pressure forces including the normal and friction forces on the lead along the shaft. These values are used to calculate the resistive force on the shaft as it moves through the lead, and thus the device force. Results of these highly nonlinear, high strain analyses are compared to experimental device force results. Model errors compared to experimental results for all 17 devices ranged from 0% to 20% with a mean absolute error of 6.4%, indicating most errors were small. In particular, the standard error in manufacturing is SE = ±14%. In this case, 15 of 17 devices (88%) are within ±1SE (±14%) and 2 of 17 devices (12%) are within ±2SE (±28). These results show low errors and a distribution of errors compared to experimental results that are within experimental device construction variability. The overall modelling methodology is objective and repeatable, and thus generalizable. The exact same modelling approach is applied to all devices with only the device geometry changing. The results validate the overall approach with relatively low error, providing a general modelling methodology for accurate design of HF2V devices.
A buckling-restrained braced frame (BRBF) is a structural bracing system that provides lateral strength and stiffness to buildings and bridges. They were first developed in Japan in the 1970s (Watanabe et al. 1973, Kimura et al. 1976) and gained rapid acceptance in the United States after the Northridge earthquake in 1994 (Bruneau et al. 2011). However, it was not until the Canterbury earthquakes of 2010/2011, that the New Zealand construction market saw a significant uptake in the use of buckling-restrained braces (BRBs) in commercial buildings (MacRae et al. 2015). In New Zealand there is not yet any documented guidance or specific instructions in regulatory standards for the design of BRBFs. This makes it difficult for engineers to anticipate all the possible stability and strength issues within a BRBF system and actively mitigate them in each design. To help ensure BRBF designs perform as intended, a peer review with physical testing are needed to gain building compliance in New Zealand. Physical testing should check the manufacturing and design of each BRB (prequalification testing), and the global strength and stability of each BRB its frame (subassemblage testing). However, the financial pressures inherent in commercial projects has led to prequalification testing (BRB only testing) being favoured without adequate design specific subassemblage testing. This means peer reviewers have to rely on BRB suppliers for assurances. This low regulation environment allows for a variety of BRBF designs to be constructed without being tested or well understood. The concern is that there may be designs that pose risk and that issues are being overlooked in design and review. To improve the safety and design of BRBFs in New Zealand, this dissertation studies the behaviour of BRBs and how they interact with other frame components. Presented is the experimental test process and results of five commercially available BRB designs (Chapter 2). It discusses the manufacturing process, testing conditions and limitations of observable information. It also emphasises that even though subassemblage testing is impractical, uniaxial testing of the BRB only is not enough, as this does not check global strength or stability. As an alternative to physical testing, this research uses computer simulation to model BRB behaviour. To overcome the traditional challenges of detailed BRB modelling, a strategy to simulate the performance of generic BRB designs was developed (Chapter 3). The development of nonlinear material and contact models are important aspects of this strategy. The Chaboche method is employed using a minimum of six backstress curves to characterize the combined isotropic and kinematic hardening exhibited by the steel core. A simplified approach, adequate for modelling the contact interaction between the restrainer and the core was found. Models also capture important frictional dissipation as well as lateral motion and bending associated with high order constrained buckling of the core. The experimental data from Chapter 2 was used to validate this strategy. As BRBs resist high compressive loading, global stability of the BRB and gusseted connection zone need to be considered. A separate study was conducted that investigated the yielding and buckling strength of gusset plates (Chapter 4). The stress distribution through a gusset plate is complex and difficult to predict because the cross-sectional area of gusset plate is not uniform, and each gusset plate design is unique in shape and size. This has motivated design methods that approximate yielding of gusset plates. Finite element modelling was used to study the development of yielding, buckling and plastic collapse behaviour of a brace end bolted to a series of corner gusset plates. In total 184 variations of gusset plate geometries were modelled in Abaqus®. The FEA modelling applied monotonic uniaxial load with an imperfection. Upon comparing results to current gusset plate design methods, it was found that the Whitmore width method for calculating the yield load of a gusset is generally un-conservative. To improve accuracy and safety in the design of gusset plates, modifications to current design methods for calculating the yield area and compressive strength for gusset plates is proposed. Bolted connections are a popular and common connection type used in BRBF design. Global out-of-plane stability tends to govern the design for this connection type with numerous studies highlighting the risk of instability initiated by inelasticity in the gussets, neck of the BRB end and/or restrainer ends. Subassemblage testing is the traditional method for evaluating global stability. However, physical testing of every BRBF variation is cost prohibitive. As such, Japan has developed an analytical approach to evaluate out-of-plane stability of BRBFs and incorporated this in their design codes. This analytical approach evaluates the different BRB components under possible collapse mechanisms by focusing on moment transfer between the restrainer and end of the BRB. The approach have led to strict criteria for BRBF design in Japan. Structural building design codes in New Zealand, Europe and the United States do not yet provide analytical methods to assess BRB and connection stability, with prototype/subassemblage testing still required as the primary means of accreditation. Therefore it is of interest to investigate the capability of this method to evaluate stability of BRBs designs and gusset plate designs used in New Zealand (including unstiffened gusset connection zones). Chapter 5 demonstrates the capability of FEA to study to the performance of a subassemblage test under cyclic loading – resembling that of a diagonal ground storey BRBF with bolted connections. A series of detailed models were developed using the strategy presented in Chapter 3. The geometric features of BRB 6.5a (Chapter 2) were used as a basis for the BRBs modelled. To capture the different failure mechanisms identified in Takeuchi et al. (2017), models varied the length that the cruciform (non-yielding) section inserts into the restrainer. Results indicate that gusset plates designed according to New Zealand’s Steel Structures Standard (NZS 3404) limit BRBF performance. Increasing the thickness of the gusset plates according to modifications discussed in Chapter 4, improved the overall performance for all variants (except when Lin/ Bcruc = 0.5). The effect of bi-directional loading was not found to notably affect out-of-plane stability. Results were compared against predictions made by the analytical method used in Japan (Takeuchi method). This method was found to be generally conservative is predicting out-of-plane stability of each BRBF model. Recommendations to improve the accuracy of Takeuchi’s method are also provided. The outcomes from this thesis should be helpful for BRB manufacturers, researchers, and in the development of further design guidance of BRBFs.
