Vertical Stiffness and Deformation Analysis Models of Rubber Isolators in Compression and Compression-Shear States

The vertical stiffness and deformation theories of rubber isolators in compression and compression-shear states are systemically researched in the paper, a series of basic concepts, such as origin compression stiffness, origin compression longitudinal elastic modulus, offset vertical stiffness, etc. are suggested with corresponding theoretical formula and experimental estimation method. Based on the basic concepts and newly suggested calculating theories, the deformation calculating theory related to pure compression state and compression-shear state of isolating bearing is established. The vertical stiffness, offset vertical stiffness and deformation tests are performed with nature rubber bearings and lead plug rubber bearings total 16 original specimens to verify the new concepts and computation model of rubber isolators. All test results show that the theories established in the paper are suitable for analyzing the vertical stiffness and deformation of rubber isolators.     

Tension Buckling in Multilayer Elastomeric Bearings

The compression buckling of mutilayer elastomeric bearings which are widely used as vibration mounts, bridge bearings, and seismic isolators for buildings is well understood and is governed by theoretical analysis and confirmed by extensive experimental work. What is not well known is that the theoretical analysis that predicts the compression buckling behavior also predicts that a bearing could be subject to buckling in tension with a tension buckling load that is of the same order as the compressive buckling load and a buckled shape that is the same as that in compression. The tensile buckling load will not be achievable in practice in most bearings since it will generally be much larger than the load that will induce cavitation in the elastomer, but the analysis can be very valuable in explaining the behavior of seismic isolators when loaded in tension while laterally displaced. This can occur when extreme seismic loading on an isolated building induces global overturning. Isolators at the periphery of the building can be in a state of combined tension and shear. The analysis shows that the elastomer can sustain the tension load without cavitation since rotation of the central portion converts tension to rotated shear.     

Experimental Study of the XY-Friction Pendulum Bearing for Bridge Applications

The XY-friction pendulum (XY-FP) bearing is a modified Friction Pendulum (Earthquake Protection Systems, Inc., Vallejo, Calif.) bearing that consists of two perpendicular steel rails with opposing concave surfaces and a connector. The connector resists tensile forces, provides for independent sliding in the two principal directions of the isolators, and ideally, permits unhindered rotation about its vertical axis. Experimental studies on an XY-FP seismically isolated truss-bridge model were undertaken to study response under tridirectional excitations and to evaluate the use of XY-FP bearings for bridges. A truss bridge model was tested on a pair of earthquake simulators using acceleration orbits and near-field earthquake histories. The experimental results demonstrated the effectiveness of the XY-FP bearings as an uplift-prevention isolation system: the XY-FP bearings simultaneously resisted significant tensile loads and functioned as seismic isolators. The bidirectional horizontal response of the small-scale XY-FP isolation system was coupled due to the internal construction of the small-scale connectors that joined the two rails of each XY-FP bearing and the limited free-to-rotate capacity of the XY-FP bearings due to misalignment of the isolators during installation.     

Stiffness Analysis of Fiber-Reinforced Rectangular Seismic Isolators

The reinforcing elements of multilayer elastomeric isolation bearings, which are normally steel plates, are replaced by a fiber reinforcement. The fiber-reinforced isolator is significantly lighter and could lead to a much less labor-intensive manufacturing process. In contrast to the steel reinforcement, which is assumed to be rigid, the fiber reinforcement is flexible in extension. This paper presents theoretical approaches for analyzing the compressive stiffness and bending stiffness of fiber-reinforced rectangular isolators. The influence of fiber flexibility on the stiffness of isolators is studied. In addition to theoretical stiffness solutions which are expressed in series form, simplified stiffness formulas based on the solutions of an infinitely long strip pad are also presented.     

Bending Stiffness of Fiber-Reinforced Circular Seismic Isolators

The reinforcing elements of multilayer elastomeric isolation bearings, which are normally steel plates, are replaced by a fiber reinforcement. In contrast to the steel reinforcement which is assumed to be rigid, the fiber reinforcement is flexible in extension. This paper presents the theoretical approach to analyze the bending stiffness of the fiber-reinforced circular isolators. The elastomer is assumed to be incompressible and pressure dominant. The stiffness formula is derived. The influence of fiber flexibility on the mechanical properties of fiber-reinforced circular isolators under bending moment, such as the pressure in the elastomer, the stress in the reinforcement, and the bonding shear stress between the elstomer and the reinforcement, are presented.     

Nonlinear Model for Lead–Rubber Bearings Including Axial-Load Effects

Existing models for isolation bearings neglect certain aspects of their response behavior. For instance, rubber bearings have been observed to decrease in stiffness with increasing axial load, and soften in the vertical direction at large lateral deformations. The yield strength of lead–rubber bearings has also been observed to vary with axial load, such that a lightly loaded bearing may not achieve its theoretical strength. Models that include these axial-load effects in lead–rubber bearings are developed by extending an existing linear two-spring model to include nonlinear behavior. The nonlinearity includes an empirical equation for the experimentally observed variation of yield strength. For numerical implementation, the bearing forces are found by solving the nonlinear equilibrium and kinematic equations using Newton’s method, and the instantaneous bearing stiffness matrix is formed from the differentials of these equations. The response behavior of the models is confirmed by comparison with experimental data.     

Three-Dimensional Finite-Element Analysis of High Damping Rubber Bearings

A three-dimensional finite element modeling of high damping rubber bearings is studied. At first, the constitutive model of high damping rubber materials proposed by the writers is formulated in order to derive the constitutive tensor, which is required in the application of the finite element method. Second, a mixed finite-element method consistent with the proposed constitutive model is described. In this method, slightly compressible materials with rate form constitutive models are applied. Then, using the constitutive model and the finite-element method, a three-dimensional finite element model of high damping rubber bearings is constructed. The simulations by the model are found to be in good agreement with the experimental results of the bearing. Finally, complex deformation such as torsional or rotational deformation of the bearing are simulated by the finite-element model, and the design equations for these deformation are proposed on the basis of the simulations or experimental results.     

Effect of Friction on Unbonded Elastomeric Bearings

This paper describes a theoretical analysis of a type of thermal expansion bridge bearing which could be used as a lightweight low-cost elastomeric seismic isolator for application to housing, schools, and other public buildings in earthquake-prone areas of the developing world. The analysis covers the effect of the frictional resistance of the supports on the vertical stiffness of this type of isolator. The most important aspect of these bearings is that they do not have end plates, which reduces their weight, but also means that they are not bonded to the upper and lower support surfaces and are held in place only by friction. This at first sight might seem to be a deficiency of this design, but it has the advantage that it eliminates the presence of tensile stresses in the bearings. It is these tensile stresses and the bonding requirements that arise from them that lead to the high costs of conventional isolation bearings. A theoretical analysis of the response of these bearings to vertical load shows that slip between the unbonded surfaces and rigid supports above and below can have a significant influence on the vertical stiffness and the internal pressure distribution.     

Comparative Modeling Study of Reinforced Beam on Elastic Foundation

In this paper, governing ordinary differential equations are derived for a reinforced Timoshenko beam on an elastic foundation. An analytical solution is obtained for a point load on an infinite Timoshenko beam on elastic foundation. Special attention is drawn to the location, tension, and shear stiffness of reinforcement and its influence on settlement/deflection of the beam and reinforcement tension force. A finite element (FE) model is established for the same infinite beam problem. Results from the TB model (Timoshenko beam on elastic foundation) are compared with results from the FE model and from the PB model (the Winkler model, based on the pure bending beam theory). It is found that results from the proposed TB model are, in general, in good agreement with results from the FE model as compared with results from the PB model. The TB model is better than the PB model in considering the shear deformation of the beam. This TB model is particularly useful in modeling a reinforced beam with or without considering the reinforcement shear stiffness. The TB model has practical applications in modeling geosynthetics∕fiber-glass reinforcement of foundation soils or pavement.     

Numerical Analysis of Geosynthetic-Reinforced and Pile-Supported Earth Platforms over Soft Soil

Geotechnical engineers face several challenges when designing structures over soft soils. These include potential bearing failure, intolerable settlement, large lateral pressures and movement, and global or local instability. Geosynthetic-reinforced and pile-supported earth platforms provide an economic and effective solution for embankments, retaining walls, and storage tanks, etc. constructed on soft soils; especially when rapid construction and/or strict deformation of the structure are required. The inclusion of geosynthetic(s) in the fill enhances the efficiency of load transfer, minimizes yielding of the soil above the pile head, and potentially reduces total and differential settlements. A numerical study has been conducted to investigate pile-soil-geosynthetic(s) interactions by considering three major influence factors: the height of the fill, the tensile stiffness of geosynthetic, and the elastic modulus of pile material. While current methods have not fully addressed important effects of the geosynthetic stiffness and pile modulus on the soil arching ratio, numerical results suggested that the stress concentration ratio and the maximum tension in geosynthetic increase with the height of the embankment fill, the tensile stiffness of geosynthetic, and the elastic modulus of the pile material. The distribution of tension force in the geosynthetic reinforcement indicated that the maximum tension occurs near the edge of the pile.     

Strain Rate Sensitivity of Epoxy Resin in Tensile and Shear Loading

The mechanical response of E-862 and PR-520 resins is investigated in tensile and shear loadings. At both types of loading the resins are tested at strain rates of about 5×10?5, 2, and 450–700?s?1. In addition, dynamic shear modulus tests are carried out at various frequencies and temperatures, and tensile stress relaxation tests are conducted at room temperature. The results show that the toughened PR-520 resin can carry higher stresses than the untoughened E-862 resin. Strain rate has a significant effect on the response of both resins. In shear, both resins show a ductile response with maximum stress that is increasing with strain rate. In tension, a ductile response is observed at low strain rate ( ～ 5×10?5?s?1), and brittle response is observed at the medium and high strain rates (2 and 700?s?1). The hydrostatic component of the stress in the tensile tests causes premature failure in the E-862 resin. Localized deformation develops in the PR-520 resin when loaded in shear. An internal state variable constitutive model is proposed for modeling the response of the resins. The model includes a state variable that accounts for the effect of the hydrostatic component of the stress on the deformation.     

Advanced Joining Concepts for Passive Vibration Control

Passively damped joints, in which the conventional adhesives are replaced by high damping viscoelastic materials, have the potential of being effective practical means for passive vibration control of dynamically loaded civil and aerospace structures. However, this potential cannot be realized unless the associated structural penalties are reduced to acceptable limits. This paper describes a rational methodology for the development of advanced joining concepts for structural systems capable of providing enhanced dissipation of vibrational energy without serious penalties in strength, stiffness, or weight characteristics. One such configuration is that of a rhombic‐type joint, which provides a beneficial deformation coupling between the direction of load transfer and less critical offset directions. A comprehensive parametric study has been carried out in order to establish design guidelines for favorable trade‐offs between damping benefits and the associated stiffness, strength, and weight penalties in a rhombic joint. The results are compared with the corresponding trade‐offs for a double‐lap joint made of the same materials.     

Prediction of Aging Characteristics in Natural Rubber Bearings Used in Bridges

Rubber bearings used in bridges are exposed to the air and easily attacked by oxygen, even at room temperature, and heat, light, dynamic strain, and liquids. It is usually known that the degradation of polymers often occurs as a nonuniform or heterogeneous process because aged rubber will prevent deterioration from progressing into the inner rubber bearing. Thermal oxidation tests were carried out on natural rubber (NR) blocks at different elevated temperatures using the modulus profiling method. The development of the heterogeneous property profiles in aged rubber bearings is revealed. The NR blocks display the features of a diffusion-limited oxidation and the properties change most significantly at the surface. However, in the interior region beyond the critical depth, NR does not change. The property variations at the block surface and the interior are quantitatively examined, based on which, the relations are clarified among property variation, temperature, aging time, and relative position inside a rubber bearing. An appropriate aging model is established, which is able to predict the aging characteristics in NR bearing.     

Force-Deformation Behavior of Isolation Bearings

The isolation bearings are widely used in earthquake prone areas to protect the structure from seismic forces. The isolation bearing consists of an isolator to increase the natural period of the structure away from the high-energy periods of the earthquake, and a damper to absorb energy in order to reduce the seismic force. The most common isolation bearings used are lead–rubber bearings. They combine the function of isolation and energy dissipation in a single compact unit, giving structural support, horizontal flexibility, damping, and a centering force in a single unit. The relation between the horizontal force and horizontal displacement of the isolation bearings is nonlinear; to calculate the stiffness and the damping constant, which correspond to effective design displacement, the nonlinear behavior is expressed by bilinear behavior. This technical note presents new relations to calculate yield force, horizontal displacement, and damping.     

Yielding behavior of prestrained interstitial-free steel and 70/30 brass

The yielding behavior of interstitial-free (IF) steel and 70/30 brass prestrained in plane strain tension and subsequently strained in uniaxial tension has been investigated experimentally. Upon reloading in uniaxial tension, brass exhibited a negative transient (decrease in flow stress) and steel exhibited a positive transient (increase in flow stress). When the yield stress is defined by the offset method, the positive transient is difficult to model using conventional yield theories as elastic deformation is thought to occur outside the original yield or loading surface. In this work, the yield point was defined using the axial strainvs transverse strain curve as measured with biaxial resistance strain gages. The curve has an initially linear elastic portion; the slope then gradually changes until the linear plastic slope is reached. The intersection of the elastic and plastic slopes is defined as the yield point. Using this alternate definition, the yielding behavior of the prestrained metals was investigated. The yield stress for both prestrained brass and steel was found to be lower than the expected monotonic stress. Compared to previous research based on a traditional definition of yield point, this result is unexpected in prestrained steel and shows that yielding does occur inside the loading surface. The positive transient may, therefore, be modeled using conventional yield theories provided that the yield surface is defined using this alternate technique.     

基于压力弹塑性变形中性层偏移模型的构建与验证

大截面棒材矫直过程中性层偏移明显,对二辊矫直辊辊型及棒材直线度的影响较大.依据三点弯曲理论建立了棒材矫直过程中基于压力弹塑性变形的中性层偏移量理论计算模型,结合室温拉伸和弯曲试验,研究了棒材矫直过程中性层偏移规律.结果表明:反弯半径和棒材力学性能对中性层偏移值的影响显著,反弯半径越小,则中性层偏移量越大;强度较低、塑性较强的材料,中性层偏移量较大.通过弯曲试验,验证了该模型的可靠性及其适用范围.      

Micromechanical Modeling of Filament Wound Cement-Based Composites

A theoretical model to predict the response of laminated cement-based composites is developed. The micromechanical model simulates the mechanical response of a multilayer cement-based composite laminate under uniaxial, biaxial, and flexural loading modes. Tsai-Wu Criterion is used for each lamina and the stacking sequence is utilized to obtain the overall stiffness matrix. The effect of distributed cracking on the stiffness degradation of the cross ply layers under tensile loading is measured using a scalar damage parameter that is empirically related to the apparent strain. The model is calibrated by predicting the load versus deformation response of unidirectional, cross ply, and angle ply laminates under tensile and flexural loading. Results are then compared to the experimental results cross ply and angle composites with various stacking sequences.     

如何正确地提高轧机工作机座的刚度

本文着重分析和讨论了提高轧机工作机座刚度的三种途径：　合理提高零部件刚度、短应力线机座、预应力机座。指出某些错误概念与问题，阐述了如何正确地提高轧机工作座的刚度。