Journal of Structural Engineering

Intensive vibrations may occur in slender structures like footbridges and long-span floors due to movement of pedestrians. Problems are usually treated in the time domain as Fourier series models of the forcing function, but most methods have disadvantages of neglecting the stochastic character of human walking, being computationally inefficient for random vibration analysis, and overestimating responses in the case of resonance. Meanwhile, frequency-domain models of other types of structural loading are efficient while being a more acceptable approach widely adopted for dealing with stochastic response problems. Hence, an experiment-based power spectral-density (PSD) model normalized to walking frequency and order of harmonic is proposed. To construct this model, 1,528 individual walking-load time histories were collected from an experiment on a rigid floor. These records were then linked to obtain a smaller number of longer samples for a good frequency resolution in spectral analysis. Using the linked samples and for a frequency normalized to mean walking frequency, PSD models in the range $1\pm 0.05$ for the harmonic and subharmonic are suggested as a Gaussian mixture with eight model parameters. Via the stationary and nonstationary stochastic vibration theory, the proposed model is used to predict the structural response in terms of root-mean square and peak of acceleration. The framework is finally tested via field measurements demonstrating applicability in practical design work.

Eight high-strength RC columns confined by carbon fiber–reinforced polymer (CFRP) sheets and two control specimens are tested under cyclic lateral load and constant axial load. The effectiveness of the high-strength RC column strengthened by CFRP to enhance its ductility and earthquake-resistance is described at high and low axial compression ratios. Failure patterns, hysteresis curves, skeleton curves, ductility, and strain distribution analysis of the columns are studied systematically in tests. The results show that the ductility and the seismic behavior of columns are obviously improved by wrapping CFRP around the columns, and the strengthening mode of the horizontal full reinforcement can achieve better seismic performance than horizontal strap reinforcement. A new strength model for predicting the lateral ultimate capacity of rectangular concrete columns strengthened with CFRP subjected to cyclic loading is proposed. The results of the model agree well with test results in this paper and in other relevant literature.

This paper uses probabilistic models and minimization of certain risk measures to expose risk aversion and optimal retrofit strategies for an existing building portfolio. A case study is presented addressing 622 buildings on the Vancouver campus of the University of British Columbia, Canada, a location subjected to multiple sources of seismicity. An array of probabilistic models is used to predict ground-motion intensities, structural responses, and consequent cost of damage due to earthquakes in the next 50 years. A key result is the exceedance probability curve for repair costs discounted to present value. A model is also postulated for the cost of retrofit, i.e., strengthening each building. Because both costs depend on the level of retrofit, the total expected cost and other properly defined risk measures are convex functions of the retrofit level. As a result, the conducted optimization analyses yield unique optimal retrofit levels. A computer program is employed to coordinate the multimodel analyses, which consist of 281 random variables in 4,389 instances of 14 different model types. The analyses reveal substantial risk aversion in the current designs when the direct cost of damage is considered. If indirect costs eight times the direct cost of damage are included, then current designs are optimal from an expected cost perspective.

Viscoelastic coupling dampers (VCDs) are used for the seismic and wind protection of tall buildings. In the past, several tests have been carried out on VCDs under severe loading conditions for concept validation purposes and different numerical models have been used for evaluating the performance of tall buildings with VCDs. Nonetheless, for practical applications understanding the performance of VCDs over a full range of demands including extremely small amplitudes of vibration, long-duration loading, and realistic well-defined design level seismic and wind events, as well as a comparative evaluation of different numerical models are needed. To address this research gap, a systematic study was carried out to understand the performance of VCDs based on full-scale tests and to assess the suitability of different numerical models in predicting their response. A range of displacement-controlled tests was carried out on a full-scale VCD specimen. Seismic loading was derived by considering both far-fault long-period long-duration ground motions as well as near-fault pulse-like ground motions that were developed based on a site-specific study and were scaled to represent the design earthquake (DE) and the risk-targeted maximum considered earthquake (${\mathrm{MCE}}_{\mathrm{R}}$) levels for a real project. Long-duration wind loading of 6-h with $1\text{-}$, $10\text{-}$, $50\text{-}$, and 500-year mean recurrence intervals (per Canadian practice) developed based on wind tunnel testing of another real project were used. The temperature rise in the specimen during the tests was measured using high-precision thermocouples embedded in the viscoelastic (VE) layers as well as an external thermal camera. The test results indicated well-defined force-deformation hystereses of the specimen at all levels of strain amplitudes including those at extremely small deformation amplitudes up to $2.5\mathrm{\mu m}$ of deformation. The temperature rise of the specimen was less than 1°C and 4°C, respectively for the earthquake and wind loadings representative of the real projects that were considered in this study. This temperature rise was found to be lower when compared with previous generations of VE materials, which were tested under loading representative of shorter buildings with higher fundamental frequencies. Finally, the accuracy of four different macroscopic numerical models with different degrees of complexities in simulating the test results was investigated. Different numerical models were found to be suitable for different loading conditions and recommendations are provided for practical nonlinear modeling of tall buildings with VE dampers.

The objective of this investigation is to develop design rules for gypsum-sheathed cold-formed steel (CFS) members subjected to bending (out-of-plane). The parameters studied include the slenderness of the CFS stud and different sheathing configurations (sheathing thickness and fastener spacing). A comprehensive analytical study on the stiffnesses offered by the sheathing to the CFS panel was conducted for use in design equations. Three different combinations of stiffnesses offered by the sheathing were examined based on the failure modes and ultimate moment capacities obtained from the experimental results. The experimental results were compared with the predicted design strengths using the current design approach available from the American Iron and Steel Institute (AISI). The deficiency of the current design approach is highlighted, and a modified approach for incorporating the stiffnesses offered by the sheathing in the elastic buckling analysis is presented. The design strengths predicted using the modified approach on stiffness selection showed good agreement with the ultimate moments obtained from the experiments. A performed reliability analysis indicated that the modified design approach presented in this work can be used for the design of gypsum-sheathed cold-formed steel members subjected to bending (out-of-plane). A detailed design example for the sheathed CFS panel based on each design approach used in this work has been presented in the form of a table for more clarity.

This paper presents a set of deployable origami tube structures that can create smooth functional surfaces while simultaneously maintaining a high out-of-plane stiffness both during and after deployment. First, a generalized geometric definition for these tubes is presented such that they can globally have straight, curved, or segmented profiles, while the tubes can locally have skewed and reconfigurable cross sections. Multiple tubes can be stacked to form continuous and smooth assemblies in order to enable applications, including driving surfaces, roofs, walls, and structural hulls. Three-point bending analyses and physical prototypes were used to explore how the orthogonal stiffness of the tubular structures depends on the geometric design parameters. The coupled tube structures typically had their highest out-of-plane stiffness when near to a fully deployed state. Tubes with skewed cross sections and more longitudinal variation (i.e., that had more zigzags) typically had a higher stiffness during deployment than tubes that were generally straight.

A new method for the analysis of the dynamic properties of structures with viscoelastic (VE) dampers is proposed in this paper. For the first time, the proposed method enables analyses that take into account the influence of temperature on the dynamic characteristics of systems with VE dampers. The frequency-temperature correspondence principle is adopted (i.e., a thermorheologically simple material of dampers is assumed). The problem is reduced to an appropriately formulated nonlinear eigenvalue problem with parameters. The eigenvalue problem is solved using the homotopy method and the incremental-iterative procedure. The results of several examples are presented and discussed in detail.

A new type of composite steel slab system called TUBEDECK (TD) has been proposed, which combines a cast-in-situ RC slab with circular tube voids and profiled steel decks. In order to investigate the detailed flexural performance of the proposed system, monotonic loading tests were carried out on 14 specimens with variables of the presence or absence of voids and/or steel deck, slab thickness, tension reinforcement ratio ($\rho$), and load direction. Experimental results demonstrated that full composite action could be achieved in TD slabs designed with normal $\rho$, with only the chemical adhesion provided through the shape of the steel deck itself, specifically T-shaped ribs and embossments. On the other hand, if TD slabs had high $\rho$ or an inadequate void arrangement, the expected flexural strength could not be reached, failing prematurely. Based on analysis of the results, design recommendations for the proposed system are provided.

This paper presents an experimental investigation of the shear behavior of steel beam-to-column connections with unequal depth of outer annular stiffener. The depth-to-thickness ratio ($D:t$) of the hollow structural section (HSS) column, the beam depth ratio ($D_{b2}:D_{b1}$), and two sizes of outer annular stiffener are considered. This test involves seven cruciform connections subjected to lateral cyclic loading with vertical displacements imposed at the end of beams. The failure modes, hysteretic performance, strength and stiffness degradation, shear deformation, and energy dissipation of panel zone are estimated. The experimental results indicated that the whole panel exhibited large hysteretic loops, excellent ductility, and energy dissipating capacity. Due to the effect of the beam depth ratio, the tested specimens formed two types of failure modes: shear buckling of the whole panel and shear buckling of the primary panel at the column web between two beams.

External installation of steel braces has been proved an effective seismic strengthening or retrofitting scheme to upgrade the lateral load-resisting capacity of reinforced concrete (RC) frames. However, the effectiveness of steel bracing in improving the progressive collapse resistance potential of RC frames is vague. To fill the gap, five one-quarter-scaled specimens (one bare frame and four braced frames) were tested subject to a pushdown loading regime. The RC frames were nonseismically detailed for reference. Four braced frames with different bracing configurations were tested to evaluate the efficiency of braces for upgrading the load-resisting capacity of RC frames. A rational design method was implemented for designing the braced frames, including the connections between the braces and RC frames. Experimental results proved that steel bracing could increase the first peak load and initial stiffness of the frames significantly. Before mobilization of catenary action in RC frames, the tensile braces were fractured, but the compressive braces experienced severe buckling. Consequently, the braced specimens performed similarly to the bare frame in the catenary action stage.

For existing buildings in low and moderate seismic zones, various nonseismic ties not conforming to special seismic requirements have been used in columns for convenience in reinforcing bar placement. This study investigates the failure mode and deformation capacity of such columns. First, cyclic loading tests of 12 columns with different section geometries, tie details, and axial load ratios are performed. The test results show that postyield shear failure occurs in the columns with nonseismic ties as the inelastic deformation increases, and the ductility of the columns is affected by the spacings and anchorage details of ties. Then, to estimate the deformation capacity of the columns, a postyield shear strength degradation model depending on displacement ductility and tie details is proposed. The proposed method is applied to 80 existing column specimens with a wide range of design parameters. The postyield strength degradation and deformation capacity predicted by the proposed method agree well with the test results.

This paper examines the validity of the Whitmore net section tension capacity for the design of bolted gusset plates. Using simple algebra, this paper first shows that the Whitmore criterion and the correct block shear criterion would give similar results for a standard connection having approximately seven rows of bolts. It then shows that the Whitmore criterion severely underestimates the actual capacities of connections having two or three bolt rows tested by independent researchers. Conversely, it also shows that the same criterion overestimates the capacities of connections having nine bolt rows that were believed by the testing researchers to fail in the Whitmore section. Using finite-element analysis incorporating fracture simulation, this paper shows that the apparent Whitmore tensile fractures only took place because the tests were continued long after the ultimate limit state of block shear. This paper proposes that the Whitmore section check be made redundant in light of the block shear check, which accurately predicted the ultimate test loads of all the specimens.

Fatigue cracking is considered the most prevalent damage for welded steel structures like bridges and ships. Inspections are normally planned in the service life to assess fatigue damages in order to ensure structural safety and serviceability. Whether or not cracks are found, the inspection results provide value for fatigue damage assessment and risk mitigation. This paper aims to emphasize the value of inspection based on the information gained for fatigue crack prognosis. The probabilistic inspection results are used to update the prior distribution to a posterior distribution of fatigue damage. The change from prior to posterior distribution is quantified as the information gained from inspection. The time-variant inspection information metrics are further analyzed with utility theory to consider the attitude and preference of the decision maker toward the inspection outcome at a certain point in time. This paper presents an integrated decision-making framework for inspection planning, addressing the information perspective of inspection choice and schedule. The recommended optimum inspection plan is expected to provide the highest utility to the decision maker in the life-cycle management of aging structures. The proposed framework is applied to a fatigue-critical detail of a ship structure.

Steel-plate composite (SC) structures may be subjected to combination of in-plane and out-of-plane forces for extreme loading combinations (e.g., seismic and accident thermal). This paper presents the results from behavioral and experimental investigations conducted to evaluate the interaction of in-plane and out-of-plane forces on SC wall piers (without boundary elements). Experimental results indicate that the effect of out-of-plane forces on the in-plane behavior of SC wall piers depends on the location and magnitude of the out-of-plane loading. Wall piers subjected to out-of-plane shear equal to their nominal shear strength (per US codes) develop flexural yielding and failure due to interaction between the in-plane and out-of-plane moments. Shear failure does not occur in these wall piers. Wall piers subjected to out-of-plane shear forces significantly greater than the nominal shear strength (per US codes) are forced into a shear failure mode by the interaction of in-plane shear and out-of-plane shear. An interaction equation for in-plane and out-of-plane moments is developed to characterize the flexure-controlled behavior of wall piers. This interaction equation can be used to design and to evaluate the behavior of SC wall piers subjected to combination of in-plane and out-of-plane moments.

A simplified mechanistic model is developed in this study to predict the lateral load resistance of coupled rocking walls made from cross-laminated timber (CLT) panels as an alternative to finite-element modeling. The model is derived in an incremental format in order to capture the nonlinear behavior of the rocking wall, including crushing of the corners and inelastic response of interpanel connectors. The backbone curve and limit states generated using the proposed model are verified through a detailed finite-element model. Following the validation of the backbone curve, a spectrum-based maximum displacement prediction method is proposed for the rocking wall system under an arbitrary earthquake input. This simplified prediction method is validated using full-scale shake table test data of a two-story wood building with coupled CLT rocking walls. The model and the dynamic response prediction approach are found to be reasonably accurate for preliminary seismic design and evaluation of CLT rocking wall systems, so that detailed finite-element modeling and nonlinear time history analysis may not be necessary.

The aim of this study was to present the use of detachable laminated high-yield metal plates for precast concrete column splices. The structural behavior of precast concrete column connections with detachable high-yield-strength (650-MPa) plates with 1,000-MPa high-strength bolts was performed experimentally and numerically. A nonlinear numerical model based on concrete damaged plasticity was developed to evaluate the structural performance of the novel joint for precast concrete columns with fully restrained and partially restrained moment connections. The behavior of the proposed joint obtained numerically was in good agreement with the full-scale test data, offering accurate prediction of stresses and strains for the design of the mechanical column connections. Finally, the real-world behavior including strain evolution of the mechanical joints was understood by the strains of microscopic level obtained via the proposed numerical model. This study is expected to contribute to promoting the use of plates with high-yield strength, which possess the merits of bolted column-to-column splices, to implement mechanical joints in precast concrete assembly similar to how steel frames are assembled.

This paper presents the results of observed near-surface winds and wind-induced pressures on the gable roof of an instrumented low-rise building. The observations were made during the strongest typhoon to make landfall in China since 1949—Super Typhoon Rammasun. For comparison purposes, the paper also presents field measurements taken during four other tropical cyclones of lower strengths. This work first investigates the characteristics of near-surface winds, including those of turbulence intensities, turbulence integral length scales, gust factors, and wind turbulence spectra. The work then offers an analysis of the mean, RMS, and minimum pressure coefficients on the gable roof under oblique winds. To investigate the influences of windstorm strengths on the pressure coefficients, a comparative study is made of the measurements recorded during Super Typhoon Rammasun and those recorded during the four tropical cyclones. To explore the mechanisms of how high suctions are generated, spectral analysis is conducted for the wind pressures near the roof edges. In addition, the effects of elevation angle on the wind pressures are investigated. This study aims to shed light on the wind effects of extreme wind conditions on low-rise buildings and to provide useful information on how to improve the wind-resistant design of low-rise buildings.

This paper develops a method for dealing with the stress minimization of continuum structures based on the bidirectional evolutionary structural optimization (BESO) method. The modified p-norm approach has been used to assemble all the local stresses in one global function for saving computational cost. The BESO method has been extended for the p-norm stress minimization while the volume constraint has been satisfied for the specified value. For updating the discrete design variables, the elemental sensitivity numbers have been derived where the sensitivity filtering approach has been used. To validate the proposed method, numerical examples including the L-bracket, cantilever, and Eyebar beams are presented. Compared with the traditional stiffness optimization, the stress-based topology optimization developed in this paper significantly alleviates the maximum stress of the optimized design.

Eccentrically braced frames (EBFs) are a widely used steel seismic resisting system due to their combination of high elastic stiffness and high ductility. The key component of this system is the portion of the beam in the frame that is formed by an incoming offset brace or braces. In a seismic event, this link undergoes inelastic rotational deformations. Typically, short elements are used for this link, forcing it to yield primarily in shear. Due to a number of recent developments in the material properties and accepted testing protocols for shear links, this paper reexamined the current intermediate web stiffener spacing requirements. Furthermore, the current web stiffener spacing requirements are based on typical web aspect ratios that were used in practice at the time the requirements were drafted, because collector beams and links were of the same section size. Currently, there is an increased use of bolted links, which decouples this requirement. A full-scale, bolted, D-braced EBF was constructed in order to test link sections of various sizes. Three hot rolled section links and four built-up section links were designed, fabricated, and tested using the latest American Institute of Steel Construction link provisions and loading protocol. The links were grouped by their web aspect ratio, either being slender or stocky; stocky links had a ratio of web height to web thickness below 24. Non-code-compliant, unstiffened stocky links performed to an exceptional level, achieving inelastic rotations of 0.17 and 0.19 rad, compared with the 0.08 rad value required by the seismic standards. Attaching stiffeners to stocky webs was found to be either superfluous or detrimental. In order to correlate shear link performance to stiffener spacing design equations, a database of previously tested shear link performance results and geometries was constructed and incorporated the links tested herein. Design equations were derived for each of the web aspect ratio groups, with the specification for slender links remaining largely unchanged, and with the specification for stocky links taking account of the improved performance when fewer intermediate stiffeners are used. The stocky built-up specimens from this study exhibited higher overstrengths (1.80–2.00) than those typically expected based on the previous link testing literature (1.50), and will require appropriate factors for use in design. Further research is required to ascertain the cause of the overstrength, because currently available data does not provide a definitive answer.

Chapter 17, “Seismic Design Requirements for Seismically Isolated Structures,” in the 2016 edition of the ASCE 7 Standard, Minimum Design Loads and Associated Criteria for Buildings and Other Structures, includes major revisions to the design requirements for seismically isolated buildings. One important objective of the revisions was to simplify the design process by expanding the applicability of the Equivalent Lateral Force (ELF) procedure. The ELF procedure is now permitted for the design of typical regular isolated structures with effective periods less than 5 s. To support extended application of the ELF, a robust method to estimate lateral design forces in the superstructure was developed. The ASCE 7-16 Seismic Subcommittee Task Committee 12 (TC-12 committee) proceeded with a rigorous review of a previous study, and developed lateral force distribution equations based on a revised data set that more rigorously considered the effects of superstructure flexibility, long period and highly damped isolation systems, and hysteresis loop shape. In this paper, the dynamic analysis parameter study and statistical analysis procedures to develop the lateral force equations are explained and validated, and the new ELF code design equations are summarized. Design case studies demonstrating the application of the equations are presented and compared to response history analysis results.

RC elements are often subjected to combined actions including torsion under seismic events. Understanding the behavior of RC members under combined actions including torsion is essential for safe design. Behavioral predictions of RC columns under combined loading can be improved by including the bidirectional stress effects. The objective of this work is to propose the improved combined actions softened-membrane model (CA-SMM) for predicting the behavior of RC elements under combined torsion (T) and shear loading (V). In this approach, the rectangular cross section is modeled as an assembly of four cracked shear panels. The applied external loads are distributed among these four shear panels. This assumption helps in reducing the complex stress state from combined loading to four different simple stress states on these panels. Additional equilibrium and compatibility conditions are imposed, and the system of nonlinear equations are solved by using an optimization technique called the gradient descent method. The developed improved model (CA-SMM) is validated with the experimental data available in the literature. After that, an interaction between the shear and torsion is developed to understand the behavior under various combinations of torsion and shear. A parametric study is carried out for understanding the effect of various sectional parameters such as longitudinal reinforcement ratio, transverse reinforcement ratio, and concrete strength. The predictions of the improved model had a close correlation with the test results.

This study investigates the seismic response of a two-degrees-of-freedom structure with supplemental rotational inertia at its first story. The proposed response-modification strategy uses an inerter—a mechanical device the resisting force of which is proportional to the relative acceleration between the first story and the ground. This arrangement complements the traditional supplemental damping strategies, which are also examined in this work. The paper develops a time-domain and a frequency-domain formulation for the response analysis and shows that the seismic protection of structures with supplemental rotational inertia suppresses effectively interstory drifts at the expense of transferring appreciable forces at the support of the inerter. Both a single inerter and a pair of inerters that can only resist the motion of the structure are examined. The paper examines the extent to which a compliant support of the inerter affects the dynamics of the structure and concludes that as the compliance of the support frame increases, a single inerter may lead to a more favorable response. The proposed response-modification strategy is attractive for cases with large relative displacement demands.

Concentric braced frames (CBFs) are commonly used all over the world to resist seismic forces in buildings. Buckling, however, is a major concern for CBFs, in which they lose their strength and stiffness when subjected to load reversals during earthquakes. To tackle this problem, a novel easy-to-fabricate low-cost spring-based piston bracing (SBPB) system is developed with single and double friction spring configurations. In this system, a brace member is able to carry a large magnitude of tension and compression forces using a special spring in the piston cylinder. Stable and self-centering hysteresis behavior is achieved when the system is subjected to qualifying quasi-static loading. The strain rate effect is assessed and comparable results are achieved without any performance degradation. Numerical simulation shows excellent matching with the test results. Two 4-story braced steel buildings are designed utilizing buckling-restrained braces (BRBs) and SBPB, and their performances are compared in terms of interstory drift and residual drift. The proposed system experiences zero residual deformations but relatively larger drift values when compared with BRBs.

This article deals with the dynamic behavior of a reinforced and posttensioned concrete structure for applications in wind turbine towers. Measurements were performed using triaxial accelerometers in a 30 m high tower model, and the experimental setup is described in detail. The natural frequencies and mode shapes of the structure were extracted using operational modal analysis (OMA). The structure’s Young’s modulus was calculated analytically from the natural frequency of the radial-circumferential bending mode and their values were compared with the results obtained in static tests conducted on a concrete bar. The dynamic stiffness was calculated based on the frequency of the bending mode. Soil–foundation–structure interaction is reported in this article by calculating the displacement produced in the foundation and tower structure using data from the first tower bending mode. A simplified finite-element model was created to study the influence of elasticity and stiffness parameters on the modal shape of the structure and validate the results obtained from the experimental data.