Journal of Structural Engineering

Seismic isolation systems constitute an accepted and simple technique for earthquake protection of structural systems and sensitive components. This approach has considerable potential in preventing the structures and their equipment from earthquake destruction. For predicting the behavior of an isolation bearing, Haringx’s theory is usually employed. According to this theory, the mechanical properties of an elastomeric isolation bearing can be predicted and described. Many investigators have proposed a nonlinear, mechanical model for multilayer elastomeric bearings. However, in previous theoretical and experimental studies, the effects of initial rotation at the ends of the bearings have been neglected. In this study, Haringx’s theory is extended and an analytical method is presented by considering the initial rotations of the upper and lower ends of multilayer rubber bearings as new boundary conditions. Three boundary conditions have been considered for modeling the elastomeric isolation bearing: (1) equal rotation at the bottom and top end of a bearing, (2) rotation only at the bottom end, and (3) rotation only at the top end of a bearing. According to these boundary conditions, variations of the lateral displacement and interior rotation of the laminated rubber bearings are obtained. The variations of horizontal stiffness, internal bending moment, and interior shear force of the bearing have also been presented. Examples are presented to demonstrate the validity of the development method in predicting the mechanical properties of elastomeric bearings with specified geometric parameters. The results of this study have shown that initial rotation as a boundary condition will change the mechanical properties of the laminated rubber bearings.

The segmental prestressed concrete box girder of Koror-Babeldaob (KB) Bridge in Palau, which had a record span of 241 m (791 ft), presents a striking paradigm of serviceability loss because of excessive multidecade deflections. The data required for analysis have recently been released and are here exploited to show how the analysis and design could be improved. Erected segmentally in 1977, this girder developed a midspan deflection of 1.61 m (5.3 ft) compared with the design camber after 18 years, and it collapsed in 1996 as a consequence of remedial prestressing, after a 3-month delay. Compared with three-dimensional analysis, the traditional beam-type analysis of box girder deflections is found to have errors up to 20%, although greater errors are likely for bridges with higher box-width-to-span ratios than the KB Bridge. However, even three-dimensional finite-element analysis with step-by-step time integration cannot explain the observed deflections when the current American Concrete Institute, Japan Society of Civil Engineers, Comité Euro-International du Béton (or Comité Euro-International du Béton—Fédération internationale de la précontrainte), and Gardner and Lockman prediction models for creep and shrinkage are used. These models give 18-year deflection estimates that are 50–77% lower than measured and yield unrealistic shapes of the deflection history. They also predict the 18-year prestress loss to be 46–56% lower than the measured mean prestress loss, which was 50%. Model B3, which is the only theoretically based model, underestimates the 18-year deflection by 42% and gives a prestress loss of 40% when the default parameter values are used. However, in Model B3, several input parameters are adjustable and if they are adjusted according to the long-time laboratory tests of Brooks, a close fit of all the measurements is obtained. For early deflections and their extrapolation, it is important that Model B3 can capture realistically the differences in the rates of shrinkage and drying creep caused by the differences in the thickness of the walls of the cross section. The differences in temperature and possible cracking of the top slab also need to be taken into account. Other paradigms on which data have recently been released are four bridges in Japan and one in the Czech Republic. Their excessive deflections can also be explained. The detailed method of analysis and the lessons learned are presented in Part II.

As a sequel to Part I, which clarified the causes of the unexpectedly large deflections of the Koror-Babeldaob Bridge in the Pacific island nation of Palau, Part II presents the numerical procedure and reviews the lessons learned. The box girder represents a thick shell that is discretized by eight-node, three-dimensional (3D) finite elements. Except for corrections due to cracking, concrete creep is assumed to follow aging linear viscoelasticity and is modeled by a rate-type law based on the Kelvin chain, the properties of which are adjusted for humidity conditions and temperature. In each time step and at each integration point, Widder’s formula is used to convert the aging compliance function to a continuous retardation spectrum for the current age of concrete, and discretization of the spectrum yields the current elastic moduli of the Kelvin units. The shrinkage strains depend on the environmental humidity and the thickness of each plate in the cross section. The computations proceed according to Bažant’s exponential algorithm, which is unconditionally stable and reduces the problem to a sequence of elasticity problems with an orthotropic effective stiffness of material and nonisotropic inelastic strains, different for each integration point in each time step. These problems are solved by commercial software ABAQUS. The segmental construction sequence is also modeled. The computer results reported in Part I explain the excessive deflections and compare the performance of various material models for creep and shrinkage. Part II formulates the lessons learned and makes recommendations for implementation.

This paper focuses on an investigation of transverse joint details with tight bend diameter U-bars for accelerated bridge construction. It presents the testing results of potential alternate reinforcing materials and joint details in two phases. Headed bar and U-bar [stainless steel and deformed wire reinforcement (DWR)] specimens with the same joint detail configuration were tested and compared in Phase I, followed by testing of U-bars (DWR) with varied concrete strength, bar spacing, and overlap length in Phase II. Test results were evaluated based on tension capacity, cracking at service loading and failure, and steel strain. A strut-and-tie model is proposed to predict the tension capacity of a transverse joint, which is capable of identifying the most critical parameters and yields safe and consistent predictions. Based on the experimental results, a No. 5 U-bar joint detail with no less than 152 mm (6 in.) overlap length and No. 4 lacer bars was recommended.

The application of bending theory based methods and strut-and-tie models for the design of pile caps to resist shear is still a subject of debate, with the latest Eurocodes permitting both methods but not giving much guidance as to their use. The former UK design standards for concrete buildings and bridges, recently withdrawn, gave more guidance, and it is likely that these methods will continue to be used by designers. However, there is considerable discrepancy between these standards, particularly with regard to the width of cap over which shear enhancement at short spans may be applied, and how much longitudinal reinforcement to take as a tie in the strut-and-tie method. Both standards are also seen as conservative. To gain a better understanding of the problem and assess the available design methods, nonlinear finite-element analysis has been performed to investigate the shear behavior of four-pile reinforced concrete pile caps, under full-width wall loading. The models were validated against an experimental program that included an optical photogrammetric method for measuring full-field displacements. An extensive parametric study was carried out, varying shear span, cap width, and reinforcement ratio over a practical range. The conservatism of the UK design standards, and the real shear capacity of the pile caps were found to be a function of shear enhancement factor and the width of the cap over which shear enhancement is applied. Strut-and-tie behavior was observed in the models, and a commonly used strut-and-tie method was found to give fairly good predictions. A modified strut-and-tie method is suggested for this particular configuration of a four-pile cap under full-width loading, which gives more accurate predictions. This is especially so for samples with large transverse pile spacing, where a significant proportion of the longitudinal reinforcement over the width of the cap can be assumed to participate in the yielding ties.

The mechanical performance of reinforced concrete beam-thin-wall joints under out-of-plane bending moments is studied and the analytical solutions in terms of stresses and rotational stiffness of the wall are obtained. For convenience, the equivalent bending width of the shear walls is introduced and obtained based on two equivalence principles. A detailed parametric study of the equivalent bending width is carried out, including geometric parameters, boundary conditions, and reinforcement ratio of the beam-wall joint in shear wall. Some simplified formulae for the equivalent width are proposed and compared with both the analytical solutions and the experimental results. Good agreements are found.

Coating the walls with reinforced concrete layers is a conventional method of strengthening masonry structures in Iran. However, because of the lack of analytical and experimental information about the behavior of strengthened masonry walls with this method, the design of these walls is generally conducted based on empirical relations and decisions that may result in uneconomical or underdesigned strengthening details. This paper aims to develop a rational method for design and seismic evaluation of unreinforced masonry walls strengthened with reinforced concrete layers. In the proposed method, four failure modes are considered for these walls, and the strength relations and acceptance criteria for each of them are provided in accordance with FEMA 356 and ASCE 41 relations for reinforced concrete and masonry walls. The accuracy of the proposed method in predicting the nonlinear behavior and governing failure modes of the strengthened walls is validated by comparing the results with available experimental and performed numerical results.

Over the past two decades, plastic constraint effects have been an issue of concern in both fracture mechanics and structural integrity research, and several methods have been proposed for considering loss of plastic constraint. This paper shows the ability of a simplified model to predict brittle fracture under low plastic constraint conditions. Fracture toughness tests are performed on single-edge notched bend (SENB) steel specimens with deep and shallow notches, as well as on double-edge notched tension and center-notched tension (CNT) specimens. When compared with SENB specimens with a deep notch, the CNT specimens show high fracture toughness as a result of the loss of plastic constraint at the crack tip. Here, the Weibull stress approach and a toughness scaling model (TSM) are used to consider the effects of the loss of plastic constraint on the fracture toughness of the specimens. The corrected fracture toughness values evaluated by the TSM are found to be close to the toughness values observed in the tests and to the values predicted by the Weibull stress approach. This paper also briefly discusses the effect of ductile crack growth on brittle fracture.

To enhance the strength and constructability of rectangular (or trapezoidal) tubular compression members, reinforced or unreinforced concrete may be filled in the tube. Longitudinal stiffeners are often attached to increase the local buckling strength of the thin-walled skin. The effect of important design parameters on the minimum required stiffener moment of inertia was investigated numerically in this study by examining the residual stress distributions, initial imperfections, and elastic and inelastic buckling stresses of a number of hypothetical models. Because the thin-walled panel can only buckle (bulge) out from the concrete core, the buckling mode shape of a panel with multiple stiffeners resembles a waffle slab. A series of parametric studies was performed to characterize and quantify the analytically collected data. A new equation for the minimum required moment of inertia for the longitudinal stiffeners was derived. Through the evaluation of a few selected case studies and a design example, the validity and reliability of the proposed equation was demonstrated.

The direct strength method (DSM) recently included in the North American Specification and Australian/New Zealand Standard AS/NZS 4600:2005 gives design rules for compression and bending. No rules are presented in this standard for shear or for combined bending and shear. Two series of tests on C-section can be used to develop and calibrate rules for design in shear and for combined bending and shear. These are the University of Missouri Rolla tests of the 1970s and recent tests on high-strength C-sections at the University of Sydney. Both series of tests use a similar test rig, although different levels of tension field action have been observed. Two features researched are the effect of full-section shear buckling (as opposed to web-only shear buckling), and tension field action. Full-section buckling is a feature of the DSM but requires software that can evaluate full sections for shear. The paper proposes DSM design rules for C-sections in shear and for combined bending and shear both with and without tension field action. The test results are compared with the proposed design rules.

This paper examines the assumption implicit in Cochrane’s formula that stresses are uniformly distributed across the net section of a staggered bolted connection. The assumption was found to be overoptimistic for connections in steel having low ductility, leading to unconservative estimates for the tension capacity if the in-plane shear lag is not accounted for. The reduction factor of 0.9 specified in the North American specification for cold-formed steel structures partially, but not wholly, addresses the problems inherent in the code equations. This paper points out that the simplification of Cochrane’s original formula into the standard formula used in steel design codes worldwide can lead to additional design capacity that may not be justified. It proposes an equation that accounts for the in-plane shear lag and incorporates Cochrane’s original formula for determining the net section area. The proposed equation is demonstrated through laboratory tests on 74 staggered bolted connection specimens in 1.5 mm and 3.0 mm G450 sheet steel to be more accurate and consistent than the code equations in predicting the net section tension capacity.

The University of Maine, in conjunction with Willamette Industries, Georgia-Pacific, Strongwell, and APA—the Engineered Wood Association, tested 90 fiber-reinforced polymer (FRP)-reinforced glue-laminated wood (glulam) beams. This study showed that a FRP reinforcement ratio of 3% in tension can increase glulam-allowable bending stress ($F_b$) by more than 100%. Furthermore, this physical testing was used to verify a nonlinear probabilistic computer model for reinforced glulam, called the reinforced laminated (ReLAM) model. ReLAM uses moment-curvature ($M\mathrm{\text{-}}\Phi$) analysis and Monte Carlo simulation to predict the strength and stiffness of a population of reinforced glulams, requiring as input distributions of the lamstock long-span flatwise-bending modulus of elasticity ($E$), ultimate tensile stress, and ultimate compressive stress. ReLAM output lists the reinforced glulam modulus of elasticity (MOE) and $F_b$ in terms of the gross cross-sectional dimensions, providing beam properties in the same fashion as the current tabulated properties for unreinforced glulams. ReLAM accurately predicted the $F_b$ and MOE for the 90 reinforced glulams tested, demonstrating that it is a valuable tool for the analysis of reinforced glulams with various layups, reinforcing materials, and reinforcing levels.

Significant evidence based on experimental research exists to give designers confidence in the use of theoretical equations to evaluate the pullout strength of threaded steel rods glued into timber. However, the mechanism of load transfer through a timber frame moment joint utilizing glued-in steel rods requires more than simply understanding the tension performance of a glued-in rod. A method of evaluating joint strength for moment and axial forces based on traditional mechanics theory adapted for use with timber is presented. Formulas were derived from first principles for joint configurations, with extended columns or with extended beams and with various types of construction (i.e., with rods fully glued along their entire length or only glued in one of the two members connected and then tensioned). The design method also considers the effects of time-dependent deformation in timber at bearing interfaces and the effects of stress concentrations imposed by the steel rods on the timber. Some open questions that deserve further investigations are highlighted, as well as some possible details to optimize joint performance while retaining ease of assembly. The approach provides a methodology for joint design that has been successfully used in many projects.

The pull-out performance of steel rods glued into timber is well-documented, and short-term tests by many researchers have demonstrated reliable strength. The behavior of glued-in steel rods in moment-resisting beam-column joints is much more complex because of anisotropy of wood in the connection region, discontinuity of material at the interface, and the possible effects of creep of timber and stress concentrations on the joint performance. This paper describes the results of a series of long-term load tests on moment-resisting joints between glulam members and separate load tests on the various joint components, including the epoxy itself and the timber stressed perpendicular to the grain. Different types of knee joints, with rods fully epoxied along their length or epoxied only in one member and tensioned in the other, and with different geometries (with the beam extended over the column or with the column extended past the beam) were tested. Measurements were recorded to identify time-dependent stress redistribution within the test joints, creep of the joint as a whole, and possible crushing of the timber-to-timber bearing surfaces. Local deformation of timber loaded in compression perpendicular to the grain was found to contribute to excessive joint deformations in tests in which the steel rods were not glued over their full length. The test results confirm the possibility to use the transformed section method in design as presented in the first companion paper, and address a number of issues pointed out in the same paper.

Performance control (PC) is the ability to design a structure in such a way as to expect predetermined modes of response at certain stages of loading, extents of damage, and/or drift ratios. The primary purpose of this paper is to complement the existing literature on performance-based plastic design of moment frames. PC is, in fact, a new analytic performance-based elastic-plastic design method for ductile structures under seismic loading. It empowers the engineer to control the design rather than investigate design-related numerical output. Failure mechanisms and stability conditions are enforced rather than tested. Unlike traditional closed-form procedures, PC enables the designer to control the response of the structure at preselected performance stages such as before and at first yield, any fraction of the failure load, or specified drift ratios up to and including incipient collapse. It offers a simple design solution to a rather complex problem.

The finite-element (FE) method is widely recognized as a powerful tool in modeling structural and geotechnical systems and simulating their response to static and dynamic loads. In addition, numerical optimization is commonly used in many engineering applications, such as structural reliability analysis, FE model updating, structural identification, and structural optimization. This paper focuses on the extension of Open System for Earthquake Engineering Simulation (OpenSees, an existing software framework for nonlinear FE analysis) using Sparse Nonlinear Optimization (SNOPT, a state-of-the-art numerical optimization software). The extended OpenSees-SNOPT framework is general and flexible and can be used to solve a wide range of FE-based optimization problems in structural and geotechnical engineering. It has several distinguishing features: (1) advanced capabilities in solving optimization problems involving complex structural/geotechnical engineering systems; (2) versatility in modeling a very wide range of structural and/or geotechnical systems; (3) computational efficiency; (4) flexibility to easily accommodate and benefit from new developments in FE structural modeling and analysis, computational optimization, and probabilistic modeling and analysis; and (5) capabilities of exploring new optimization-based problems and solution methods. The use of this coupled framework is illustrated through three representative application examples, i.e., a FE reliability analysis of a reinforced concrete frame, a FE structural optimization problem of an electrical transmission steel tower, and a FE model updating the problem of a geotechnical system.