Journal of Structural Engineering

Current methods and practices for modeling and numerical simulation of disproportionate collapse of reinforced concrete (RC) frame buildings are reviewed. Modeling advances at the component, connection, and system levels for large-deformation analyses and the consideration of relevant failure modes are summarized. However, the review excludes advances in meso and micro-scale approaches for explicitly modeling material failure. The advances discussed in the paper focus primarily on the alternate path method, in which collapse resistance is assessed by the ability of systems to find alternate load paths following the sudden loss of a structural member. Experimental and field testing of components, frames, and complete building systems are examined within the context of facilitating model validation. Finally, some recent developments in robustness assessment of buildings against disproportionate collapse are presented. The paper concludes with a list of unresolved issues and needed developments to enable accurate simulation of disproportionate collapse of RC frame structures.

Relative to ductile anchors, nonductile anchors have long been subject to increased design safety margins in U.S. building codes for nonstructural building components. Historically, a safety factor was applied at the end of the calculation process, effectively modifying all elements within a given load case. This factor’s most recent implementations in the building codes narrowed its application to the horizontal earthquake component of the seismic load cases, taking the form of the overstrength factor, ${\mathrm{\Omega }}_0$, as a demand multiplier for nonductile anchor performance. From a rational combination of empirical observation and precedent, ${\mathrm{\Omega }}_0$ was set to 2.5, but minimal experimental or analytical evidence exists to support this value. A research project was thus initiated with funding from Hilti Corporation at San Diego State University to study the overstrength approach through a combination of dynamic structural testing and nonlinear time-history analyses of an idealized nonstructural component with various anchor behaviors. The latter is presented in this paper, which made use of a customized analysis tool that allowed for rapid evaluation of unidirectional earthquake response for a wide range of component and anchor characteristics.

As demonstrated by terrorist attacks against the Murrah Building in Oklahoma City and a U.S. Embassy building in Nairobi, Kenya, some structures may be vulnerable to progressive collapse. Previous computational studies have shown that floor systems play a key role in redistributing loads during progressive collapse events, but only a few experimental studies support these results. The aim of the current research is to experimentally characterize the behavior of steel-concrete composite floor slabs under column loss scenarios. Two large-scale tests on isolated sections of a steel-framed building were conducted until complete collapse. The two specimens were designed and detailed according to commonly used practices found in buildings in the United States. No special provisions to mitigate progressive collapse were included in the design. The first specimen was an interior $2\text{-}\times 2$-bay section, and the second specimen was an exterior $2\text{-}\times 1$-bay section. Both specimens were tested under a center column loss scenario. The column was statically removed while the floor slab was uniformly loaded under service load conditions. Because both specimens survived the column removal stage, the slab was subsequently loaded with a uniformly distributed load until total collapse was achieved. Observations from the test program indicate the potential for significant capacity of composite floor systems following column loss.

The lack of simple methods to determine the simultaneous alongwind, crosswind, and torsional loading and response of slender structures and structural elements is a major shortcoming in design practice and wind standards. In this regard structural engineers are now familiar with determining the gust factor and dynamic coefficient of the alongwind loading and response. Meanwhile, they are becoming more and more familiar with evaluating the crosswind loading and response of slender structures subjected to critical vortex shedding conditions. On the other hand, structural engineers often forget to inspect or ignore the crosswind and torsional loading and response attributable to gust buffeting, at most limiting themselves to carrying out static analyses based on peak wind actions and unit dynamic coefficients. This is typical, for instance, in the design of bridges and footbridges, chimneys, lighting poles, telecommunication towers, and single elements of lattice structures and industrial frameworks. However, crosswind and torsional actions on slender structures and structural elements caused by the buffeting loading frequently exceed the alongwind buffeting loading and the crosswind loading caused by critical vortex shedding. In addition, provided that crosswind and torsional actions attributable to the buffeting loading do not prevail on the alongwind ones, their evaluation cannot be ignored and their load effects have to be combined with the alongwind ones. Starting from a general but quite hermetic solution developed by Piccardo and Solari at the end of the 1990s, this paper introduces a series of simplifications that, without limiting the correctness and generality of this approach, lead to simplified formulas for evaluating the alongwind, crosswind, and torsional equivalent static actions on slender structures and structural elements, which can be easily transferred to design practice and code provisions. These formulas also correct a slight mistake in the previous solution.

This paper addresses the performance of masonry walls under combined in-plane and out-of-plane lateral loading with and without vertical precompression (referred to as multidirectional loading) through a series of interaction curves. It is hypothesized that the in-plane and the out-of-plane responses of the walls are not mutually exclusive. To examine the hypothesis, an explicit finite-element model, validated both for the in-plane and out-of-plane actions independently, based on a layered shell element and macroscopic masonry properties has been used and the interaction curves developed. Effects of precompression and aspect ratio to the interaction response of the walls subject to multidirectional loading have been examined. It is shown that the in-plane capacity reduces marginally up to and rapidly beyond a critical out-of-plane load level; therefore, determining in-plane capacity without regard to out-of-plane loading could be unsafe. A simplified nondimensional expression is developed to define the interaction curves for ease of design. It is shown that when the wall is reinforced, there exists two (lower and upper) critical out-of-plane load levels; therefore, the simplified nondimensional expression developed for the unreinforced masonry walls requires modification for application to reinforced masonry walls under combined loading.

A large-scale steel plate shear wall with partially encased composite (PEC) columns and reduced beam section (RBS) frame connections was tested at the University of Alberta to investigate the behavior of the system and quantify some key characteristics related to seismic design of this system. The use of RBS connections was intended to reduce the demand on the beam-to-column connection and obtain improved seismic performance. Subjected to quasi-static cyclic load until severe damage was observed, the specimen showed desirable characteristics such as high elastic lateral stiffness, ductility, and energy dissipation capacity. The use of RBS frame connections was proven to be a viable option to improve the seismic performance of these walls. The test observations indicated that the detailing of the PEC columns played an important role in improving the seismic performance of the specimen. Several design and detailing recommendations have been made based on the observations during this test and previous experimental studies.

This paper presents the seismic behavior of hollow-core fiber-reinforced polymer (FRP)-concrete-steel (HC-FCS) columns comparable with the conventional RC column. The typical HC-FCS column consists of a concrete shell sandwiched between an outer FRP tube and an inner steel tube. The HC-FCS column represents a compact engineering system; the steel and FRP tubes act together as stay-in-place formworks. The steel tube acts as a flexural and shear reinforcement. This paper studies three large-scale columns—one RC column having a solid cross section and two HC-FCS columns. Each column has an outer diameter of 610 mm (24 in.) and a shear span-to-diameter ratio of 4.0. The steel tube is embedded into the reinforced concrete footing with an embedded length of 1.6 times the steel tube diameter, whereas the FRP tube only confines the concrete shell and truncates at the top of the footing. The HC-FCS columns exhibits high lateral drift reaching 15.2% and fail gradually due to concrete crushing and local steel tube buckling, followed by FRP rupture. The reference RC column fails at a drift of 10.9% due to rebar fracture. Simple beam theory overpredicts the flexural strength of the columns by an average of 9%.

This paper discusses the findings from 10 full-scale steel column tests subjected to multiaxis cyclic loading. The columns use deep wide-flange cross sections typically seen in steel moment-resisting frames designed in seismic regions. The effects of boundary conditions, loading sequence, local web, and member slenderness ratios on the column hysteretic behavior are investigated. The test data underscore the influence of boundary conditions on the damage progression of steel columns. Local buckling followed by out-of-plane deformations near the plastified column base are the dominant failure modes in fixed base columns with a realistic flexible top end. Twisting may occur only at drifts larger than 3% even when the member slenderness is fairly large. The test data suggest that bidirectional loading amplifies the out-of-plane deformations but does not significantly affect the overall column performance. The loading sequence strongly affects the column’s plastic deformation capacity but only at story drifts larger than 2%. Above this drift amplitude, column axial shortening grows exponentially and becomes a controlling failure mode. Measurements of the lateral stability bracing force demands at the column top exceed the lateral brace design force specified in North American standards.

This paper presents experimental studies on the performance of planar moment steel frames with one column heated. The novelty of these tests is that the influences of key stages in the response of the heated column under gravity loading, including postbuckling and cooling phase after fire, on the progressive collapse resistance of steel frames were studied. Gas temperatures of the furnace, structural member temperatures, displacements, and strains in certain locations of the test frames were monitored during the tests. The test results show that steel columns with strong constraints from steel beams in a frame may fail in a quasi-static manner under fire, whereas those with weak constraints or large load ratios may fail with dynamic effects. In addition, the final equilibrium vertical displacement at the top of the column after sudden buckling can be even larger than the final displacement associated with gradual column removal. Moreover, in the cooling phase after fire further damage may occur to other members of the frame because of the thermal contraction of the heated column.

Existing state determination procedures for force-based finite elements use either an iterative scheme at the element level or a noniterative scheme at the element level that relies on an iterative solution algorithm for the global equilibrium equations. The former cannot ensure convergence in real-time computations, whereas the latter requires an implicit direct integration algorithm; therefore, these procedures are not applicable to real-time hybrid simulation (RTHS) utilizing an explicit direct integration algorithm. A new procedure is developed based on a fixed number of iterations and an unconditionally stable explicit model-based integration algorithm. If the maximum number of iterations is reached, element resisting forces are corrected to re-establish compatibility, and unbalanced section forces are carried over to and corrected in the next time step. This procedure is used in the numerical simulation and RTHS of an earthquake-excited two-story reinforced concrete building. Results show that an accurate solution can be obtained even without performing any iteration. The influence of the model-based parameters of the integration algorithm on the stability and accuracy of the RTHS is also studied.

The strength of thin-walled cold formed steel (CFS) lipped channel compression members may be governed by yielding, local, distortional, or global buckling or any possible interaction among these buckling modes. The interaction between buckling modes reduces the strength of thin-walled members to values below its strengths as affected by any one of the independent buckling modes. The direct strength method (DSM), which significantly simplified the evaluation of design strength of CFS members, recognizes this reduction in strength caused by interaction of buckling modes, but explicitly handles local-global interaction only. A simple and accurate interaction equation that accounts for interaction between all possible buckling failure modes for CFS lipped channel compression members is proposed in this paper. The method requires the use of modified DSM equations for evaluating the strength under the different independent buckling modes (local and distortional). The proposed interaction equation is validated with both experimental as well as numerical results.

Structures assembled with cross-laminated timber (CLT) panels, and designed to resist gravity and lateral loads, are being considered as viable options for low-rise to mid-rise buildings. In this paper, an analytical approach based on the minimum total potential energy principle has been developed in order to determine the mechanical behavior of 1-story multipanel CLT walls. Expressions for determination of the elastic stiffness and capacity are proposed that take into account the geometry of the panels and stiffness of hold-down and vertical joint connections. Kinematic models demonstrated in the case of relatively stiff hold-down connections that each panel has an absolute center of rotation, whereas for relatively flexible hold-down connections panels can exhibit progressively increasing uplift. An analytical expression to evaluate the elastic strength of an entire wall is presented for different kinematic cases. Results are verified by comparing them with predictions made using detailed numerical models.

Tests were carried out on two continuous one-way slab specimens, representing, at a scale of 1:1.5, the floor slabs of a multistory building most affected by a postulated instant loss of a perimeter column owing to accidental loading. The bottom bars in the first specimen were discontinuous over the central support, and top reinforcement extended only over the supports. In the second specimen, reinforcing bars were continuous from one outer support to the other on both faces of the slab. Thanks to the membrane action due to the horizontal restraint by the rest of the floor system, both specimens—especially the one with continuous top bars—sustained the distributed load of the slab plus a line load along the sinking outer support of $10\mathrm{kN}/\mathrm{m}$ without collapse in full scale, with settlement of that support as high as 0.5 m. The main features of the force-deformation behavior can be captured by a simple, hand-calculation model, taking into account geometric nonlinearities, including large deformations. Model predictions compare best with test results when tension stiffening is neglected; moreover, they are not very sensitive to the exact location where the slab first cracks or develops the critical plastic hinge. Test results were combined with those of the perimeter beams on which the slabs are supported to estimate the margin of bearing capacity of these beams over and above self weight, finishings, and quasipermanent loads on the slab. Membrane action in the slab seems to become a prime player in the global response to the loss of a perimeter column when the beam’s flexural mechanism and arch action are past their peak resistance. The slab’s membrane mechanism, together with the arch and catenary actions that develop at the edge beam in the transverse direction when the full structure is considered, are important for maintaining the capacity margin close to its peak value at larger beam deflections. This is better achieved if the slab is reinforced throughout its top surface.

The impact of the loss of an intermediate column on the most adversely affected subassembly of a multistory, multibay reinforced concrete (RC) frame was studied experimentally and analytically. Two subassemblies were considered: a monolithic one and another consisting of dry-jointed precast beams and columns, held together with the help of concentric unbonded prestressing of the beams. A uniformly distributed load was applied along the beams to realistically simulate the loading in a building with about the same geometry and loads in all floors above the failed column. The load-deflection response can be followed with a simple hand-calculation model, which takes into account the primary geometric and material nonlinearities, including arch action in the web of the beam and catenary action in the rebars and unbonded tendons. The model quantifies the difference between single-point loading of the beam, as is normally the case in other experimental campaigns, and distributed loading, as well as the contributions of the various resistance mechanisms and sensitivity to parameters. An interesting experimental finding is that a beam—even a monolithic one—does not behave as a well-integrated system of steel and concrete when it loses a column: the longitudinal reinforcement transfers the catenary tension to the beams of the adjacent bays, pulling the columns together, whereas compression from the arch action is transferred to the columns, pushing them apart. The test results are combined with those of one-way continuous slabs for simulated loss of support to an exterior beam to quantify the margins when support to a column is lost.

This paper investigates the inelastic response of a yielding single-degree-of-freedom oscillator coupled with a rocking wall. Configurations of both a stepping rocking wall and a pinned rocking wall that have been reported in the literature are examined. The full nonlinear equations of motions are derived, and the paper shows that a stepping wall suppresses peak and permanent displacements, with the heavier wall being most effective. In contrast, when the yielding oscillator is coupled with a pinned rocking wall, both peak and permanent displacements increase, with the heavier wall being most unfavorable. This unfavorable response is mainly because the moment from the weight of the pinned wall works against stability, and in most cases, it contributes to larger permanent displacements.

Presented in this paper are the results of an experimental program investigating the out-of-plane behavior of CLT panels under static and blast loading. A total of 18 CLT panels, with panel thicknesses of 105 and 175 mm corresponding to a 3-ply and 5-ply panel, respectively, were investigated with the aim to determine the dynamic increase factor (DIF). An average dynamic increase factor of 1.28 on the resistance and no apparent increase in stiffness from static to dynamic loading were observed. Two resistance material predictive models that account for high strain-rate effects and the experimentally observed post-peak residual behavior were developed. A single-degree-of-freedom model was validated using full-scale simulated blast load tests, and the predictions were found to match well with the experimental displacement-time histories.

A new macroelement model is presented in this paper for the simulation of the in-plane (IP) and out-of-plane (OOP) response of infilled frames subjected to seismic actions. The model consists of two diagonal, one horizontal, and one vertical struts. Each strut is represented by two fiber-section beam-column elements. The model is able to capture the arching action of the wall under an OOP load as well as the interaction between the IP and OOP actions. The proposed modeling approach is sufficiently simple and efficient that it can be used for the static or dynamic analysis of an entire structural system. An experimental validation has been carried out. A further numerical study performed with the macroelement model has shown that wall damage due to IP loads can significantly reduce the OOP resistance of the wall, and this influence depends on the slenderness (height/thickness) of the wall. A more slender wall will suffer a more significant loss of OOP resistance.

A new design philosophy that leads to efficient earthquake-resisting systems is presented. Commercially available technologies are used to propose an archetype that is capable of damage control, elimination or reduction of residual stresses, collapse prevention (CP), and postearthquake realignment and repairs (PERR). The new approach was inspired by the current state of knowledge and the need to develop sustainable earthquake-resisting systems. As a result, design-led analysis (DLA) was synthesized to develop repairable, earthquake-resistant rocking wall-moment frames (RWMFs). DLA is a displacement-based method of approach with built-in results. Explicit conditions for structural sustainability, CP, and PERR have been developed. The proposed formulae embrace the entire spectrum of seismic response, starting from zero loading to incipient collapse and from incipient collapse to full recovery. A number of generic details have been developed to support the expected performances. The proposed solutions are exact within the bounds of the theoretical assumptions and are ideally suited for preliminary design purposes.

A bracing system consisting of tension-only superelastic nickel-titanium shape-memory alloy (SMA) was developed and implemented as a retrofitting methodology for seismically deficient squat reinforced concrete shear walls. The bracing system incorporates SMA links that serve as resettable fuses with unique recentering and energy-dissipation properties that result in improved hysteretic response. This paper focuses on one-third-scale walls that represent pre-1970s reinforced concrete shear walls susceptible to shear sliding and diagonal tension cracking. Four walls, two control and two retrofitted with the SMA bracing system, were tested under reversed cyclic loading. The SMA braces demonstrated excellent performance as a retrofitting device, improving the seismic response of squat reinforced concrete shear walls, including lateral strength capacity, ductility, energy dissipation, and displacement recovery. The retrofitting system was central in minimizing damage at the base of the walls.

The objective of this study is to develop and validate a practical finite-element modeling protocol for predicting the flexural strength and collapse behavior of thin-walled spirally welded tapered tubes that can be used as steel wind turbine towers. The overall modeling protocol consists of two parts: (1) a meshing protocol is developed considering the effects shell element type, aspect ratio, inclination angle, and density on the buckling moment relative to theoretical predictions; and (2) two patterns of geometric imperfections (eigenmode-affine and so-called weld depression) scaled to the thresholds of fabrication tolerance quality classes in Eurocode 3 are considered in nonlinear collapse shell finite-element models and the results are compared to a series of eight large-scale flexural tests of spirally welded tubes. The computational results are compared with test results in terms of moment-rotation response, stiffness, and buckling modes and show sufficient agreement to justify the further development of nonlinear analysis methods for the design of steel wind turbine towers made from thin-walled spirally welded tapered tubes.

This paper presents a new structural identification (St-Id) framework along with a damage indicator, displacement unit influence surface using computer vision–based measurements for bridge health monitoring. Unit influence surface (UIS) of a certain response (e.g., displacement, strain) at a measurement location on a beam-type or plate-type structure (e.g., single-span or multispan bridge with its deck) is defined as a response function of the unit load with respect to the any given location of the unit load on that structure. The novel aspect of this paper is a framework integrating vehicle load (input) modeling using computer vision and the development of a new damage indicator, UIS, using image-based structural identification. This framework is demonstrated on the large-scale bridge model in the University of Central Florida Structures Laboratory for verification and validation. The UIS damage indicators successfully identified the simulated damage on the bridge model, including damage detection and damage localization.

This paper deals with the shear behavior of steel stud connectors between a concrete slab and steel beam under static and impact loading. An experimental program involving four static and nine impact pushout tests was designed and carried out according to the descriptions in related specification. The failure modes and the time history of impact load and slippage displacement as well as the shear strength of stud connectors are presented and investigated. It is found from static tests that the shear capacity of stud connectors reasonably met the corresponding requirements in a related specification, while the dynamic shear capacities of the connectors were improved by 33–63% compared with the static results. Based on the dynamic responses, the shear mechanism of the steel stud shear connectors under impact loading is also examined, and the failure process can be divided into three typical stages. Furthermore, based on the equations given in some existing guidelines, a design proposal is developed to accurately predict the shear capacity of stud connectors under impact loading, where the strain-rate effect is considered according to the recommendations given in a published report for the concrete strength and in a published journal paper for the steel strength under impact loading. The testing results can provide essential data for future analytical and design-oriented study of composite beam with shear stud connectors under extreme loading conditions.

The objective of the present study is to contribute to the understanding of the seismic behavior and performance of reinforced concrete flexure-dominated walls when their boundaries are subjected to high compression. Typical structural wall specimens that conform to the current Japanese design code were investigated experimentally and analytically. The specimens failed in a brittle manner, with concrete crushing over a length of approximately 2.5 times the wall thickness, which was much shorter than that in the tensile plastic region. A model for the bending analysis considering such nonuniform hinge length was proposed to evaluate the structural performance of flexure-dominated walls. The analytical results simulated the experimental behavior well and clarified the bending-compression failure mechanism: the lateral strength deterioration was triggered by a loss of compressive resistance within the neutral axis depth and was then accelerated by a rapid increase of the neutral axis depth. On the basis of these findings, simplified formulas are presented for the evaluation of the ultimate deformations at the bending-compression failure for flexure-dominated walls.

Seismic damage affecting industrial-process components can cause severe disruption, leading to not-negligible profit reduction associated with business interruption. Hence, the implementation of a proper seismic risk mitigation strategy is often required, accounting for financial issues as well. This study presents a novel probabilistic seismic risk assessment framework able to quantify business-interruption losses on the basis of a company’s balance-sheet data. The framework contains a financial module that uses a profitability index (PI) for identifying the most profitable seismic retrofit strategy to be implemented, given a reference time window and available budget. Application of the framework to a typical Italian cheese factory is also illustrated. Results show how business-interruption losses are comparable with direct costs for the rehabilitation of seismically damaged components. Additionally, it is demonstrated that PI can be considered a suitable financial indicator, and evaluating the contemporary benefit has a primary importance when a retrofit strategy is applied to more components.

Wind pressures acting on a cubic building with openings exposed to stationary tornadolike vortices were studied experimentally. The effects of opening ratio, single central opening azimuth, and radial distance between the building model and tornadolike vortex on external and internal wind pressure distributions were the focus of this study. Particular attention was paid to the difference between tornado-induced wind pressure coefficients and those obtained in conventional boundary-layer wind flow, American design code, and Chinese design code. The results indicate that the measured wind pressures on the model are due to the combined effects of pressure drop accompanying a tornado and flow-structure aerodynamic interaction. Both the opening ratio and large single opening azimuth influence the internal wind pressure and vertical wind force on roof structure. The low-rise building model experiences maximum wind forces when it is located at the tornado core radius. Additionally, owing to the high negative pressure drop accompanying a tornado, tornado-induced wind pressure coefficients exceed the provisions of American design code and Chinese design code by large factors.

Defining the collapse probability of existing nonseismically designed RC buildings is a challenge mainly due to the fact that its determination relies on the simulation of the brittle failure modes controlling the collapse mechanism. Routine nonlinear dynamic analysis of ductile RC frames is not applicable for such buildings, which often fail prior to the attainment of their flexural capacity. An alternative approach to define collapse probability is proposed in this paper through the explicit definition of the failure mode hierarchy. A number of brittle failure modes are considered as credible and the corresponding capacity is calculated. The prevalent collapse mode is identified through capacity prioritization of the failure modes, and the corresponding peak ground acceleration at collapse is defined. This value, along with the associated variability, is substituted in a lognormal distribution to derive fragility curves for typical design and construction details. The main conclusion drawn from the processing of the results is that disregarding the brittle failure modes and accounting solely for flexural ductile behavior greatly underestimates the probability of collapse of such buildings.

A high-fidelity simulation-based system reliability calculation methodology was implemented for steel floor diaphragms framed from cold-formed steel joists topped with wood sheathing, leading to design recommendations that consider the sensitivity of the system performance to fastener component reliability and load paths provided by the sheathing and steel. Diaphragm structural response under in-plane equivalent lateral seismic forces was obtained from high-fidelity computational simulations verified with a full-scale diaphragm test. The model included sheathing-to-joist and joist-to-ledger connection load-slip nonlinearities and randomness from the bearing, tilting, and screw shear, obtained from independent and isolated fastener tests. An uncertainty-modeling scheme provided a statistical distribution for the diaphragm system capacity, which was used to calculate the diaphragm system reliability. The variation in diaphragm system reliability with the fastener component reliability, i.e., the reliability sensitivity, was quantified to guide the diaphragm design to a predefined system-reliability target.

This paper investigates second-order effects on wind-induced structural dynamic behavior of a 60-story high-rise steel structure known as the Commonwealth Advisory Aeronautical Research Council (CAARC) building model. These effects are considered in the structural analysis by using a geometric stiffness method allowing the dynamic analysis to be performed without iterations. Data sets of the aerodynamic pressure on the CAARC building model for suburban exposure are used in the database-assisted design (DAD) procedure to calculate, in addition to overturning moments and shear forces at the base, members’ demand-to-capacity indexes (DCIs), interstory drift ratios, and resultant accelerations. Dynamic analyses are performed using four reference mean hourly wind speeds at the rooftop for suburban terrain exposure ($U_{ref}=20$ and $40\mathrm{m}/\mathrm{s}$ for serviceability analysis, and 60 and $80\mathrm{m}/\mathrm{s}$ for strength analysis). The second-order effects decrease natural frequencies of vibration of the building by up to 12%. In the strength analysis with $U_{ref}=80\mathrm{m}/\mathrm{s}$, second-order effects increase nondirectional peak global responses by up to 15% for overturning moments, 9% for base shears, and 10% for torsional moments. The responses of 21 members selected in this study are increased by up to 19% for columns, 41% for beams, and 31% for diagonal bracings in the case of the DCIs for the interaction of axial forces and bending moments ($B_{ij}^{PM}$) and by up to 67% for columns, 26% for beams, and 13% for diagonal bracings in the case of the DCIs for the shear forces ($B_{ij}^V$). In the serviceability analysis with $U_{ref}=40\mathrm{m}/\mathrm{s}$, second-order effects increase the interstory drift ratios by up to 17% and the resultant accelerations at the top floor by up to 2%. This case study shows that the second-order effects can considerably affect not only drift control but also the design of members for strength.

Steel coupling beams have emerged as a viable alternative to conventionally and diagonally reinforced concrete coupling beams because of their superior energy-dissipation characteristics, smaller member depth, and ease of construction, to name but a few advantages. Conventional steel coupling beams are designed to yield under design-level ground motions; hence, postevent repair requires replacement of the entire beam that is embedded into wall piers and interfaced with a significant amount of wall pier reinforcement. Such a repair will be costly, intrusive, and very likely impractical. A new system involving a replaceable midspan fuse located in the coupling beam was developed. In this system, the fuse acts as the primary energy-dissipating component, while the remainder of the beam span and its embedments into the wall piers remain elastic when the building is subjected to design-level ground motions. Hence, it is only necessary to replace the accessible damaged fuses since the rest of the beam and wall piers remain undamaged. This paper presents a design methodology for using steel coupling beams that have a replaceable fuse. Laboratory test data were found to validate the methodology. A 20-story prototype building was designed according to the proposed methodology and results from nonlinear static and dynamic analyses indicate that the building performed according to the objectives of the presented design methodology. That is, (1) the midspan fuses are the primary energy-dissipating components; (2) the fuses develop their capacity before the embedded beams reach their expected shear or elastic flexural capacities; (3) the wall piers experience little or no damage under design ground motions; (4) the wall piers maintain their integrity for maximum credible ground motions; and (5) residual deformations are small, permitting new fuses to be installed following design-level ground motions.

Multistory steel braced frames tend to concentrate damage in a few weak stories in response to severe earthquake shaking. This paper presents the numerical and experimental results for a strongback system, a modification of the conventional braced frame that uses an essentially elastic truss that vertically spans the structure’s height to delay or prevent weak-story behavior. A cyclic test is performed on a nearly full-scale two-story specimen in which the strongback is introduced as a seismic retrofit of an existing vintage-era concentrically braced frame. The retrofit design is composed of two halves: an inelastic truss using a buckling-restrained brace (BRB) to dissipate seismic input energy and an elastic vertical truss designed to control weak-story behavior. The strongback specimen prevented formation of a weak-story mechanism and mobilized the reserve strength of other structural components, even after the core of the BRB ruptured. Test results establish that the strongback system can be a successful method of mitigating weak-story behavior. A simple numerical model incorporating a low-cycle fatigue material is able to predict the global response of the frame, including the rupture of the BRB.

A three-dimensional (3D) sonic anemometer at a height of 2.5 m serendipitously recorded a tornado event in Arizona on October 6, 2010. The anemometer, which was in place for carbon flux experiments and sampling at 20 Hz, recorded a peak instantaneous wind speed of $83\mathrm{m}/\mathrm{s}$. Over a 45-s period, which included the peak wind speed, the wind speed and direction time history showed evidence of seven distinct periods of behavior. These periods corresponded to rapid changes in wind speed (i.e., acceleration) and wind direction. This period also included significant positive and negative vertical wind speeds. Although 9 s of recorded data in this period was missing due to issues with data recording, these data could be an invaluable starting point for the future of tornado-based structural design. Analyzing the record in the context of wind engineering, variables and statistics typically used in wind engineering showed marked differences from those assumed in wind load codes and standards, including large gust factors for very short averaging times and significant changes in pressure coefficients for a roof corner. These differences should be further researched and quantified.

A constitutive model for simulating the compressive response of unreinforced brick masonry subjected to cyclic loading is presented and discussed. The developed formulations are consistent with the smeared rotating crack approach and may be easily implemented in finite element codes for nonlinear analysis. The analysis approach includes different features such as nonlinear curves for capturing the shape of the unloading/reloading branches, both in case of full unloading from the envelope curve and partial unloading/reloading. A unified model for predicting the residual plastic strain as a function of the strain recovered during unloading is also proposed. Particular attention is paid to the stiffness degradation occurring during reloading and to the prediction of the stress and strain values at which the reloading branch intersects the envelope. The calibration of most of the proposed formulations is based on experimental results reported in the literature, as well as from two uniaxial cyclic compression tests carried out within the present work. Finally, the model effectiveness is tested with some verification examples.

Annoying vibrations in grandstand structures have been receiving more attention due to the increasing slenderness of the architectural components and the complexity of the crowd loading for engineers. The vibration serviceability checks under these conditions become a challenge in the design and operation stages. Regarding human comfort, excessive vibrations due to occupant activities may affect comfort and/or cause panic, especially for passive occupants who do not participate in generating excitations. Although durations of excessive vibrations have been considered as one of the most important factors affecting occupant comfort, incorporating the vibration duration in the occupant comfort analysis has not been addressed yet. In addition, the currently available approaches using raw acceleration, weighted RMS acceleration, vibration dose values (VDV), and so on may not always be sufficient for serviceability assessment due to the lack of guided procedure for calculating the integration time and implementing the duration of vibration into the process. Therefore this study proposes a new parameter and framework for assessing human comfort which incorporates the duration of vibration with conventional data processing. The aim is to better examine vibration levels and the corresponding occupant response focusing on grandstand structures. A new parameter, the area of RMS (ARMS), is introduced using the running RMS values of acceleration weighted by the frequency weighting functions. Furthermore, perception ranges for human comfort levels based on the proposed parameter are presented. The experimental study reveals that the proposed framework can successfully address the impact of duration time on determining the levels of vibrations and comfort using the proposed parameter.

This paper describes a research program involving wood-sheathed and cold-formed steel (CFS) framed diaphragm assemblies. The diaphragm’s response to in-plane monotonic and reversed cyclic lateral loading is investigated in an effort to characterize the seismic performance of this assembly. The work presented herein focuses on the response to loading of the isolated diaphragm subsystem and serves as a complementary study to a research project involving the dynamic testing of full-scale two-story CFS framed buildings, known as the CFS–Network for Earthquake Engineering Simulation (NEES) project. Laboratory testing included eight $3.66\times 6.1\text{-}\mathrm{m}$ diaphragm specimens, that is, four configurations, comprising oriented strand board (OSB) sheathing screw connected to CFS C-Channel joists. The response to loading is directly related to screw pattern and size, the use of panel edge blocking, and the type of sheathing. By means of a comparison of design and experimental shear strength and stiffness values, the provisions of the AISI S400 standard were shown to be in need of improvement regarding the number of listed diaphragm configurations. Deflection predications at the design load level were considered to be reasonable.

Strut-and-tie models (STMs) are often used for the design of shear critical deep members because they can rationalize the shear transfer within discontinuous or disturbed regions in reinforced concrete structural elements. Most current codes of practice adopt the strut-and-tie method but provide very little guidance on how to select appropriate strut-and-tie layout and dimensions. Furthermore, the effectiveness factors used to account for the biaxial state of stresses in struts of deep beams are not reliable. This paper reviews the application of STMs for the design of RC deep beams and evaluates current formulations of the effectiveness factor. Experimental and numerical studies are used to assess how the effectiveness factor is influenced by different parameters, including concrete compressive strength, shear span:depth ratio, and shear reinforcement ratio, and to arrive at a more reliable strain-based effectiveness factor. Various effectiveness factors are examined against an extensive database of experimental results on RC deep beams with and without shear reinforcement. The results show that the proposed effectiveness factor yields the most-reliable and most-accurate predictions and can lead to more-economical and safer design guidelines.

Quantitative reports on postearthquake infrastructure condition are valuable to engineers, building owners, local government entities, and the public. Despite their utility, sensor-based protocols have not been widely embraced, primarily due to a lack of proper demonstrations. This paper introduces a methodology for determining the postearthquake strength of a steel moment-resisting frame with multiple beam-column fractures based on local monitoring data. The damage index ($DI$), an existing metric based on dynamic strain measurements, is applied to quantify damage-induced reductions in bending stiffness at each beam end in the frame with decoupling damage interaction effects. An analytical model with updated local stiffness information enables the estimation of the building’s reduced strength. The proposed methodology may be automated to provide crucial structural information that can optimize and supplement visual inspections immediately after an earthquake so that emergency plans may be initiated promptly. The methodology is first validated using experimental observations and sensor data collected during a substructure test. Then its application to strength reduction estimation of multistory, multibay frames is examined with shake table tests on a large-scale three-story steel frame. Fractures at beam-column connections are perfectly tracked in all damage stages using $DI$. Estimated reductions in base shear and stiffness are among the results produced, which permit explicit comparisons to performance design limits. Appropriate FEMA connection damage index values are included in the discussions.