Development of Design Code Oriented Formulas for Elastomeric Bearings Including Bulk Compressibility and Reinforcement Extensibility Niel C. Van Engelen 1 ; Michael J. Tait, M.ASCE 2 ; and Dimitrios Konstantinidis, M.ASCE 3 Abstract: The introduction of alternative reinforcement types for elastomeric bearings has rendered it necessary to consider the extensibility of the reinforcement as an additional design parameter. The extensibility of the reinforcement reduces the lateral restraint on the elastomer and, similar to the compressibility of the elastomer, influences important design parameters such as the compression modulus and bending modulus. Neglecting the compressibility of the elastomer or the extensibility of the reinforcement may result in an unconservative over- estimation of these design parameters. Existing analytical solutions, which have been developed based on the pressure solution, are usually not suitable for design purposes. In this study, the analytical solutions for infinite strip, circular, square, and annular pad geometries are expanded and simplified to form geometry-specific approximations that account for reinforcement extensibility and bulk compressibility. The derived approximations closely and conservatively follow the analytical solutions over a large range of shape factors and values of the elastomer bulk modulus and reinforcement extensibility. A similar procedure used for the compression modulus and bending modulus is applied to approximate the maximum shear strain due to compression, including bulk compressibility and reinforcement extensibility. Generalized equations are proposed that can be adapted to the elastomeric pad geometries considered. DOI: 10.1061/(ASCE)EM .1943-7889.0001015. © 2016 American Society of Civil Engineers. Introduction Fiber-reinforced elastomeric isolators (FREIs) were originally proposed as a potential low-cost alternative to conventional steel- reinforced elastomeric isolators (SREIs) (Kelly 1999). The concept was centered on the light-weight nature of the fiber reinforcement, which has comparable mechanical properties in tension to steel, and the ability to manufacture and cut FREIs to the desired size from larger pads. From an analytical perspective, the primary dif- ference between FREIs and SREIs is that the assumption of rigid reinforcement is relaxed and the extensibility and lack of flexural resistance of the fiber reinforcement must be considered. Similar to the compressibility of the elastomer, the extensibility of the reinforcement can play an important role in the design and perfor- mance of the isolator. From a design perspective, not including the compressibility of the elastomer and/or the extensibility of the reinforcement could seriously and unconservatively overestimate important properties, such as the compression modulus and bend- ing modulus, or impose unwarranted design restrictions due to substantial errors in calculated values, such as the maximum shear strain due to compression. The sensitivity of elastomeric isolators to the compressibility of the elastomer is well recognized (Kelly and Konstantinidis 2011). This sensitivity is demonstrated in Fig. 1 as a function of the shape factor, S, for an infinite strip pad where the compression modulus, E c , has been normalized by the compression modulus assuming an incompressible elastomer, E ∞ c . The compressibility of the elas- tomer is represented by the ratio of the bulk modulus, K, to the shear modulus, G. Even for a relatively low shape factor (defined as the ratio of the loaded area to unloaded area of a single layer of elastomer) of 10, and K/G = 2,000, the compressibility of the elastomer decreases E c by 19%. Similarly, elastomeric isolators are sensitive to the extensibility of the reinforcement as demonstrated in a finite element investigation by Osgooei et al. (2014). Despite this, compressibility is often ignored, accounted for in a limited capacity, or erroneously corrected for in current design codes and standards (AASHTO 2014a, b; CSA 2014; ISO 2010). The development of generalized expressions for critical design param- eters, such as the compression and bending modulus and the maximum shear strain due to compression, inclusive of the com- pressibility of the elastomer and extensibility of the reinforcement is valuable from a design perspective. Analytical solutions for the compression modulus and bending modulus, which include the compressibility of the elastomer and extensibility of the reinforcement, are available for most simple elastomeric pad geometries. These analytical solutions are often complex and unsuitable for design purposes. Alternatively, Constantinou et al. (2011) presented simplified expressions for the maximum shear strain due to compression and rotation that include tabulated correction factors to account for the bearing geometry and elastomer bulk compressibility. Van Engelen and Kelly (2015) developed a generalized expression for the compres- sion modulus and bending modulus that included bulk compress- ibility based on a Taylor series expansion and inversion of the analytical solutions. These studies assume rigid reinforcement and do not account for the extensibility of the reinforcement. 1 Ph.D. Candidate, Dept. of Civil Engineering, McMaster Univ., 1280 Main St. West, Hamilton, ON, Canada L8S 4L7 (corresponding author). E-mail: vanengn@mcmaster.ca 2 Associate Professor, Dept. of Civil Engineering, McMaster Univ., 1280 Main St. West, Hamilton, ON, Canada L8S 4L7. E-mail: taitm@ mcmaster.ca 3 Assistant Professor, Dept. of Civil Engineering, McMaster Univ., 1280 Main St. West, Hamilton, ON, Canada L8S 4L7. E-mail: konstant@ mcmaster.ca Note. This manuscript was submitted on January 26, 2015; approved on August 13, 2015; published online on February 23, 2016. Discussion period open until July 23, 2016; separate discussions must be submitted for individual papers. This paper is part of the Journal of Engineering Mechanics, © ASCE, ISSN 0733-9399. © ASCE 04016024-1 J. Eng. Mech. J. Eng. 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