Journal of Structural Engineering

The equivalent linear system is one of the approximate methods for estimating the maximum inelastic displacement response of structures in performance-based seismic design and evaluation. Traditionally, the equivalent period and damping of such a system are defined by the ductility ratio ( $\mu =\text{maximum}$ displacement/yield displacement). However, for existing structures, the strength ratio ( $R=\text{elastic}$ lateral strength/yield lateral strength) is generally known rather than the ductility ratio. If the ductility ratio is used for defining the equivalent period and damping, the maximum inelastic displacement demand of existing structures has to be determined through an iterative procedure until the computed displacement is within an allowable tolerance to the assumed displacement. In addition, it was reported that the existing equivalent linear system may overestimate the maximum inelastic deformation of short-period structures because it is independent of periods of vibration $\left(T\right)$ . To avoid iteration and improve accuracy, this paper presents results of a comprehensive statistical investigation on the equivalent linearization in which both the equivalent period and damping are defined by strength ratios and periods of vibration. The accuracy of the developed equivalent linear system is also discussed based on a set of 72 recorded earthquake ground motions. In addition to the advantage of noniteration, the recommended equivalent linear system gives good predictions of the mean maximum inelastic displacement of structures for systems with all period ranges.

An important consideration for the design of seismic isolation systems composed of elastomeric and lead–rubber bearings is the safety of individual bearings for maximum considered earthquake shaking. One assessment of bearing safety involves the calculation of the vertical (or axial) earthquake load on the individual seismic isolation bearings. This paper investigates the influence of vertical earthquake excitation on the response of a bridge isolated with low-damping rubber and lead–rubber bearings through earthquake simulation testing. Response data collected from the experimental program are used to determine the vertical load on the isolation system due to the vertical component of excitation. A comparison of the normalized vertical load data to the vertical base acceleration showed significant amplification of the vertical response for each simulation and configuration. Disaggregation of the axial load history showed the summation of maximum values from the vertical earthquake load and overturning moment overestimates the maximum axial load because these maximum values are unlikely to occur simultaneously. Additionally, a spectral analysis procedure using the unreduced vertical stiffness of the bearings was shown to provide a reasonable estimate of the vertical earthquake load.

In regions without seismic provisions, it is common to use transfer plates as part of the structural system. In this paper, pseudodynamic tests with substructure techniques were conducted on an 1:4 scale test specimen representing the first 2 stories of a 18-story high-rise building with a transfer plate under earthquake actions. Columns of the test specimen were strengthened to prevent failure under the pseudodynamic tests. Three types of time–history records were applied, including triangular waves and a series of El-Centro Earthquakes. Based on the experimental results, it is predicted that the bottom of the transfer plate will be severely damaged when subjected to an El-Centro Earthquake with maximum acceleration at $64\%g$ .

This paper presents a computational investigation of the robustness of a typical concrete deck–steel beam composite floor system with simple shear connections in the event that a center column has been removed. The study provides insight into the behavior and failure modes of simple shear connections and composite floor systems comprised of such connections. Analyses of a connection subassemblage indicate that loads are primarily resisted by cable action of the beams after column loss resulting in increasing tensile forces in the beams and connections that could eventually precipitate failure. Simulation results show that the floor deck contributes significantly to the floor system response through: diaphragm action to prevent the exterior columns from being pulled inward and membrane action primarily through the reinforcement mesh and metal deck. The analyses indicate that the capacity of the analyzed floor system under the column removal scenario is significantly less than the load specified by the General Services Administration’s current progressive collapse guidelines. This suggests that applying these guidelines, the composite floor system studied would be vulnerable to collapse if a center column is lost.

Dual systems consisting of two shear-flexural structures are often used in high-rise buildings. This paper presents a second-order analysis of such dual systems, in which closed-form solutions are derived for the lateral flexural and shear displacements, as well as for the bending moments and shear forces in the two structures. The buckling of the dual system is also investigated. It is found that the total buckling load is a simple summation of the buckling loads of the two component structures when they act independently, and that it is independent of the distribution of the vertical loads amongst the two structures. A simple formula for the amplification factors is proposed for use in routine design. The second-order theory developed in this paper is used to investigate the amplification factors for the lateral displacements and bending moments in a typical shear-flexural structure. It is shown that the amplification factors determined from the proposed formula are in good agreement with those obtained by the more rigorous second-order analysis in most cases. It is also found that the various amplification factors are independent of the distribution of the vertical loads among the two structures.

A near full-scale three-dimensional jointed precast prestressed concrete beam-to-column connection designed and constructed in accordance with an emerging damage avoidance design philosophy is tested under displacement-controlled quasistatic reverse cyclic loading. The performance of the subassembly is assessed under unidirectional loading along both orthogonal directions as well as under concurrent bidirectional loading. The specimen is shown to perform well up to a 4% column drift with only some minor flexural cracking in the precast beams, while the precast column remains uncracked and damage free. This superior performance is attributed to steel armoring of the beam ends to mitigate the potential for concrete crushing. Under bidirectional loading a tapered shear-key layout is used to effectively protect the beams against adverse torsional movements. A three-phase force–displacement relationship is proposed that gives due consideration to the prerocking flexural deformation of the beam; the rigid body kinematics during the rocking phase; and the yielding of the external dissipaters and posttensioning tendons. Good agreement is demonstrated between the proposed theoretical model and experimental observation. An equivalent viscous damping model is also proposed to represent both change in the prestress force in the subassembly and yielding of the supplemental energy dissipaters in the rocking connection.

An analytical model for the nonlinear dynamic behavior of unreinforced masonry walls subjected to out-of-plane loading is developed. The formulation is based on variational principles, dynamic equilibrium conditions, and the nonlinear constitutive behavior of the materials involved. The model focuses on one-way action through the height of the wall, which is modeled as a structural assembly of masonry units connected by mortar joints. The masonry units and the mortar joints are modeled as first-order shear deformable flexural members with large displacements, moderate rotations, and small strains. The cracking and the nonlinear behavior of the mortar material, the opening and closing of cracks, the rocking phenomenon, and the development of a time-dependent arching force are also considered. A numerical study that examines the capabilities of the proposed model and quantifies some aspects of the dynamic behavior of the masonry wall is presented. It is shown that the dynamic behavior of the wall is a nonperiodic or even chaotic one, which is influenced by the various physically and geometrically nonlinear effects. In particular, the geometrically nonlinear effect of the arching action and the critical influence of the nonlinear-cracking behavior of the mortar or its interfaces on the dynamic behavior of the wall are quantified highlighting the necessity of a nonlinear analysis approach for the assessment of the dynamic response of the wall. A comparison between the theoretical results and experimental results available in the literature reveals the degradation of the natural frequency with the increase of the amplitude of the response and demonstrates the ability of the presented modeling and analysis approaches to quantify the dynamic nonlinear response of the wall.

In this paper, the possibility of achieving a high level of ductility by flexural yielding in fully grouted reinforced concrete masonry shear walls is evaluated. Six full-scale walls were tested to failure under reversed cyclic lateral loading to investigate the effects of amount and distribution of vertical reinforcement and the level of axial compressive stress on the inelastic behavior and ductility. Results showed that yielding of the outermost vertical bars extended to a height equivalent to half the wall length. Also, the top wall displacement (drift) at the onset of yielding of the vertical reinforcement was highly dependent on the amount of reinforcement, but only minimally affected by the level of axial compressive load. However, at maximum loads, the displacements were less sensitive to either the amount of vertical reinforcement or the level of axial compression. Correspondingly, the displacement ductility was found to be very sensitive to the amount of vertical reinforcement, but was not dependent on the level of axial compression. In general, high levels of ductility and energy dissipation capabilities accompanied by relatively small strength degradation were observed for the test specimens.

A new connection for steel moment-resisting frames that incorporates posttensioning elements to provide a self-centering capacity along with friction mechanisms to dissipate energy is proposed and experimentally validated. The restoring force from the posttensioning elements in the connection makes the structure return to its undeformed state, even after experiencing large inelastic drifts. A bolt-prestressed friction mechanism with a frictional interface consisting of stainless steel and new nonasbestos organic break lining pads dissipates seismic input energy as the system undergoes lateral deformations. Cyclic tests were conducted to investigate the efficiency of the proposed friction interface and its performance under loading conditions that are expected during seismic loading. The test results showed that the frictional behavior is stable, repeatable, and predictable, although its friction coefficient is relatively low. Exterior and interior self-centering moment connections equipped with the proposed friction dampers were tested to study their structural behavior under cyclic loading. The results confirmed that friction damped posttensioned self-centering connections are capable of developing similar stiffness and strength characteristics to welded connections. They are also capable of undergoing large deformations with good energy dissipation characteristics, but without introducing inelastic deformations in the beams or the columns and without residual story drifts. Even at the ultimate stage, i.e., beyond the self-centering limit, the proposed connections can be detailed to exhibit a ductile response with the formation of flexural hinges in the beam sections, thus avoiding the sudden loss of strength and stiffness that occurs when the posttensioning elements are overloaded or when the beams buckle under excessive combined axial loads and bending moments.

In dynamic analysis, the energy dissipation in a base-isolated building is typically accounted for by allocating damping properties independently to the superstructure and to the isolation system. Rayleigh damping applied to the superstructure component alone is often used to represent the superstructure energy dissipation. At least one study has indicated that when used improperly, superstructure Rayleigh damping leads to excessive damping of the response of a base-isolated structure. As shown here, even when used as recommended for combining subsystems with disparate damping properties, Rayleigh damping results in undesirable suppression of the first mode response. To correct this behavior, stiffness-proportional damping can be used in lieu of Rayleigh damping. Stiffness-proportional damping is demonstrated to negligibly affect the first mode response, yet provide the expected energy dissipation in higher modes.