Upper and lower bounds of device force capacity in high force to volume (HF2V) device design
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.