# Journal of Structural Engineering

Published by American Society of Civil Engineers

Print ISSN: 0733-9445

Published by American Society of Civil Engineers

Print ISSN: 0733-9445

Publications

Passive isolator, active vibration absorber, and an integrated passive/active (hybrid) control are studied for their effectiveness in reducing structural vibration under seismic excitations. For the passive isolator, a laminated rubber bearing base isolator which has been studied and used extensively by researchers and seismic designers is considered. An active vibration absorber concept, which can provide guaranteed closed-loop stability with minimum knowledge of the controlled system, is used to reduce the passive isolator displacement and to suppress the top floor vibration. A three-story building model is used for the numerical simulation. The performance of an active vibration absorber and a hybrid vibration controller in reducing peak structural responses is compared with the passively isolated structural response and with absence of vibration control systems under the N00W component of El Centro 1940 and N90W component of the Mexico City earthquake excitation records. The results show that the integrated passive/active vibration control system is most effective in suppressing the peak structural acceleration for the El Centro 1940 earthquake when compared with the passive or active vibration absorber alone. The active vibration absorber, however, is the only system that suppresses the peak acceleration of the structure for the Mexico City 1985 earthquake.

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This paper investigates the in-plane nonlinear elastic and inelastic buckling behaviour and the strength of fixed circular steel arches by using a rational finite element model. It is found that the elastic and inelastic buckling behaviour of a fixed arch is quite different from that of a pin-ended arch. The design equation for pin-ended steel arches in uniform compression cannot be used directly for the design of fixed steel arches, nor can the design interaction equation for pin-ended steel arches be used for the design of fixed steel arches that are subjected to combined axial compressive and bending actions produced by general in-plane loading. A design equation for the strength of fixed steel arches that are subjected to uniform compression is proposed. The finite element investigations show that this proposed design equation provides good predictions for the strengths of fixed steel arches in uniform compression. An interaction equation for strength design of fixed steel arches that are subjected to combined bending and axial compressive actions against in-plane failure is also proposed. The finite element investigations show that the proposed design equation provides good lower bound predictions for the strengths of fixed steel arches in combined compressive and bending actions.

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This paper outlines the design economics, cost function and modelling of optimal design of reinforced concrete beams for different design conditions. It is shown that there can be large variations in the cost of a beam depending on the unit cost of the materials and shuttering, the beam dimensions and the reinforcement ratio. As there are an infinite number of alternative beam dimensions and reinforcement ratios that yield the same moment of resistance, it becomes difficult to achieve the least-cost design by the conventional methods. This paper presents a geometric programming model which gives the unique least-cost design of a beam, considering the cost of materials and shuttering and the structural requirements. Application of this new design technique is illustrated with example problems.

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An experimental study of block shear of coped beams with a welded clip angle connection is presented in this paper. Twelve full-scale coped steel I-beam tests were conducted. The test parameters included the web block aspect ratio (height to width ratio of the web block connected to the clip angle) and the connection rotational stiffness. Out of the 12 test specimens, eight test specimens failed in block shear of the connection, namely, tensile fracture of the block width (the web underneath the clip angle) and shear yielding of the block height (the web along the vertical side of the clip angle). Two test specimens failed by local web buckling at the cope, one test specimen failed in the welds and the remaining one did not fail due to the limited capacity of the loading jack.The test results showed that in general the block shear capacity of the test specimens increased with increasing web block aspect ratio and increasing connection rotational stiffness. The current design specifications (AISC-LRFD, CAN/CSA-S16-09, CAN/CSA-S16-01, BS EN 1993-1-8-2005, BS5950-1:2000, and AIJ-1990) provide conservative estimates of the block shear capacity of the test specimens except for the specimen that had the smallest connection rotational stiffness. It should be noted that none of the design equations evaluated in this programme consider the influence of the web block aspect ratio and the connection rotational stiffness.

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An efficient computational method for lowering the cost of the free vibration, stress, and buckling analyses of multilayered composite cylinders is presented. The analytical methodology is based on the linear three-dimensional theory of elasticity where the cylinders are assumed to have simply supported curved edges, and the fibers of the different layers are either in the circumferential or in the longitudinal direction. The full equations of the finite element model are solved for a single pair of Fourier harmonics, and the response that corresponds to the other Fourier harmonics is generated utilizing a reduced system with considerably fewer degrees of freedom.

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: The critical design decisions in bridge design are made at the preliminary design stage. This stage depends on the expertise of the designer, built up from extensive experience. Experience is difficult to acquire, and may be entirely lacking when new technology is introduced. As a result, there is little shareable and transferable collective design knowledge within the profession. This paper explores how preliminary design knowledge may be generated, updated and used, utilizing techniques of machine learning from the field of artificial intelligence. A model of the preliminary design process is first presented as a sequence of five tasks and then specialized to the design of cable-stayed bridges. A computer tool serving as a design support system is described whose design follows the model of the preliminary design process, and a design example using the tool is presented. The key property of the system is its adaptive nature: it acquires knowledge from information on existing bridge...

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This paper summarizes the results of a comprehensive statistical study of inelastic displacement ratios that allow the estimation of maximum lateral inelastic displacement demands from maximum elastic displacement demands for structures built on soft soil sites. These ratios were computed for single-degree-of-freedom systems undergoing six levels of inelastic deformation when subjected to 116
earthquake ground motions recorded on bay-mud sites of the San Francisco Bay Area and on sites in the former lake-bed zone of Mexico City. These soft soil deposits are characterized by low shear wave velocities, high water contents, and high plasticity indices. The influence of period of vibration normalized by the predominant period of the ground motion, the level of inelastic deformation, earthquake magnitude, and epicentral distance are evaluated and discussed. Mean inelastic displacement ratios and their corresponding dispersion are presented. The effect of stiffness degradation on inelastic displacement ratios is also considered. For this purpose, mean ratios of
maximum inelastic displacement demands of stiffness degrading systems to maximum inelastic displacement demands of nondegrading systems are presented. Finally, a simplified equation to estimate mean inelastic displacement ratios obtained through nonlinear regression analyses is provided to aid designers estimate inelastic displacement demands of structures built on soft soil sites.

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A new connection system for a concrete filled steel tube composite column and reinforced concrete beams is proposed. In this connection, the steel tube is interrupted while the reinforced concrete beams are continuous in the joint zone. Multiple lateral hoops that constitute the stiffening ring are used to confine the core concrete in the connection zone. The transfer of moment at the beam ends can be ensured by continuous rebars; the weakening of the axial load bearing capacity due to the interruption of the steel tube can be compensated by the confinement of the stiffening ring. Using these configurations, concrete casting and tube lifting can be made more convenient since welding and hole drilling in situ can be avoided. Axial compression experiments on six specimens and reversed cyclic loading tests on three interior column specimens and three corner column specimens were conducted to evaluate this new beam-column system; load-deflection performance, typical failure modes, stress and strain distributions, and the energy dissipation capacity were obtained. The experimental results showed that the effective confinement can be achieved by the stiffening ring, and an excellent axial bearing capacity can be obtained, as well as a superior ductility and energy dissipation capacity. As a new connection system for the concrete filled steel tube composite column with reinforced concrete beams, it can also be applied to other types of confined concrete columns.

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A near full-scale 3D jointed precast prestressed concrete beam to column connection designed and constructed in accordance with an emerging Damage Avoidance Design (DAD) philosophy is tested under displacement controlled quasi-static reverse cyclic loading. The performance of the subassembly is assessed under unidirectional loading along both orthogonal directions as well as under concurrent bi-directional loading. The specimen is shown to perform well up to 4% column drift with only some minor flexural cracking in the precast beams, while the precast column remains uncracked and damage-free. This superior performance is attributed to steel armoring of the beam-ends to mitigate the potential for concrete crushing. Under bi-directional loading a tapered shear-key layout is used to effectively protect the beams against adverse torsional movements. A three-phase force-displacement relationship is proposed which gives due consideration to: the prerocking flexural deformation of the beam; the rigid body kinematics during the rocking phase; and the yielding of the external dissipaters and post-tensioning tendons. Good agreement between the proposed theoretical model and experimental observation is demonstrated. An equivalent viscous damping model is also proposed to represent both change in the prestress force in the subassembly and yielding of the supplemental energy dissipaters in the rocking connection.

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This paper discusses the optimum design of tuned mass damper (TMD) for seismically excited building structures. In the design process the multi degree of freedom structures are considered so that it makes improvement to the available design procedures so far, where usually only single mode model is considered. The H-2 norm of the transfer function from the external disturbance to a certain regulated output is taken as a performance measure of the optimization criterion. The genetic algorithm, which has been successfully applied in many applications, is used to find the optimum value of TMD parameters. The numerical examples for optimum parameters of TMD for multi degree of freedom structures are presented to show the effectiveness of this design procedure. II is shown that by using the proposed procedure, the optimum value of the mass damper can be determined without specifying the modes to be controlled. A comparison is also made to the Den Hartog and Warburton approaches.

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A tensegrity is a lightweight space structure consisting of compression members surrounded by a network of tension members. They can be easily dismantled and therefore provide innovative possibilities for reusable and modular structures. Tensegrities can adapt their shape by changing their self stress, and when equipped with sensors and actuators, they can adapt to changing environments. A full-scale prototype of an adjustable tensegrity has been built and tested at Swiss Federal Institute of Technology (EPFL). This paper begins with a description of important aspects of the design, assembly, and static testing. Tests show that the structure behaves linearly when subjected to vertical loads applied to a single joint. Nonlinearities are detected for small displacements, for loads applied to several joints and for adjusting combinations of telescoping compression members. To predict behavior, dynamic relaxation - a nonlinear method - has been found to be reliable. Appropriate strut adjustments found by a stochastic search algorithm are identified for the control goal of constant roof slope and for the load conditions studied. When adjusting struts, an excessive number of adjustable members does not necessarily lead to improved performance.

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Wind pressure differences were measured across the rain screen and across the air barrier assembly of precast open rain screen wall panels. Twelve panels were instrumented mostly on the west, north and east walls of the 24th floor of a 27 storey office building in Montreal, U.S.A. The maximum load measured on the rain screen in one year of continuous monitoring was 285 Pa, duration of one second. The largest pressure difference across an entire panel of the building envelope never coincided with peak pressure differences on the rain screen. However, maxima due to wind only, across windward panels, ranged from 400 Pa to 475 Pa. Pressure differences across the air barrier assembly of wall panels included stack and heating, ventilating and air conditioning effects of up to 150 Pa when outside temperatures dropped to -20DEGREESC.

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DOI: 10.1061/(ASCE)0733-9445(2003)129:10(1312) This paper delineates the development of a prototype hybrid knowledge-based system for the optimum design of liquid retaining structures by coupling the blackboard architecture, an expert system shell VISUAL RULE STUDIO and genetic algorithm (GA). Through custom-built interactive graphical user interfaces under a user-friendly environment, the user is directed throughout the design process, which includes preliminary design, load specification, model generation, finite element analysis, code compliance checking, and member sizing optimization. For structural optimization, GA is applied to the minimum cost design of structural systems with discrete reinforced concrete sections. The design of a typical example of the liquid retaining structure is illustrated. The results demonstrate extraordinarily converging speed as near-optimal solutions are acquired after merely exploration of a small portion of the search space. This system can act as a consultant to assist novice designers in the design of liquid retaining structures.
Keywords: Algorithms; Knowledge-based systems; Liquids; Structural design.

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A truck passing over a bridge induces loads which vary with time. To test the ability of available analytical techniques to estimate fatigue life under such loading, crack growth rate tests are conducted with eleven compact‐type specimens using constant and variable amplitude load‐time histories. One variable amplitude load‐time history used in these tests is recorded from an in‐service bridge; other histories used are constructed to isolate minor cycle amplitude and minor cycle mean relative to major cycle mean as test variables. The data show that the mean level of minor cycles within a complex cycle significantly affects the damage caused by the complex cycle, causing the standard rainflow counting‐Miner's rule fatigue life estimating technique to be unconservative. Furthermore, cycles below the constant amplitude fatigue stress range threshold are shown to be damaging when applied as part of a variable amplitude load‐time history. It is proposed that complex load‐time histories be converted to single equivalent cycles through a damage index.

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This paper investigates the minimum and maximum crack spacings in concrete pavements from the energy viewpoint and explores mechanisms that control spacing. An analytical model, which is composed of two cohesive cracks and an elastic bar restrained by distributed elastic springs, is proposed as an idealization of the cracking pattern in the concrete. By varying the length of the elastic bar of the analytical model, the tensile forces acting on the cohesive cracks and the energy profiles are investigated. It is demonstrated that the cracking pattern varies with the length of the elastic bar (i.e., the spacing between the two possible cracks), from which the minimum and maximum crack spacings are obtained. Numerical analyses are made of a model pavement and the results indicate that it is the energy minimization principle that governs the cracking pattern. The practical spacings evaluated by numerical analyses fall within the minimum and maximum crack spacings given by the practical observation.

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Structural analyses of tensegrity structures must account for geometrical nonlinearity. The dynamic relaxation method correctly models static behavior in most situations. However, the requirements for precision increase when these structures are actively controlled. This paper describes the use of neural networks to improve the accuracy of the dynamic relaxation method in order to correspond more closely to data measured from a full-scale laboratory structure. An additional investigation evaluates training the network during the service life for further increases in accuracy. Tests showed that artificial neural networks increased model accuracy when used with the dynamic relaxation method. Replacing the dynamic relaxation method completely by a neural network did not provide satisfactory results. First tests involving training the neural net work online showed potential to adapt the model to changes during the service life of the structure.

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Recent earthquakes such as Loma Prieta, Northridge, and Kobe have demonstrated a need for a new design philosophy of bridge piers that avoids damage in order to ensure post-earthquake serviceability and reduce financial loss. Damage Avoidance Design (DAD) is one such emerging philosophy that meets these objectives. DAD details require armoring of the joints; this eliminates the formation of plastic hinges. Seismic input energy is dissipated by rocking coupled with supplemental energy dissipation devices. In this paper the theoretical performance of a DAD bridge pier is validated through bi-directional quasi-static and pseudodynamic tests performed on a 30% scale specimen. The DAD pier is designed to rock on steel-steel armored interfaces. Tension-only energy dissipaters are used to increase tie down forces and further reduce dynamic response. The seismic performance of the DAD pier is compared to that of a conventional ductile pier. Results show that one can have 90 percent confidence that the DAD pier will survive a design basis earthquake without sustaining any damage, whereas for the conventional design substantial damage is sustained.

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Reactions, moments, displacements, and rotations due to axle loading in a two‐span continuous, composite‐steel girder test bridge were analyzed and compared with those calculated by finite element, American Association of State Highway and Transportation Officials (AASHTO), and the National Cooperative Highway Research Program (NCHRP) analysis methods. The simulated truck axle loads were applied on the test bridge on one, two, and three lanes to maximize positive moment at 0.4 L and negative moment at 1.0 L. The results of the study show that finite element analysis most accurately predicted the bridge behavior under the truck axle loading. The AASHTO and NCHRP analysis methods gave inaccurate results, since the loads were applied away from the supports.

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Experimental and theoretical studies have been performed to predict the fire resistance of circular hollow steel columns filled with bar-reinforced concrete. A mathematical model to calculate the temperatures, deformations, and fire resistance of the columns is presented, Calculated results are compared with those measured. The results indicate that the model is capable of predicting the fire resistance of circular hollow steel columns, filled with bar-reinforced concrete, with an accuracy that is adequate for practical purposes. The model enables the expansion of data on the fire resistance of circular concrete-filled steel columns, which at present consists predominantly of data for columns filled with plain concrete, with that for columns filled with bar-reinforced concrete. Using the model, the fire resistance of circular concrete-filled steel columns can be evaluated for any value of the significant parameters, such as load, column-section dimensions, column length, and percentage of reinforcing steel without the necessity of testing.

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Experimental and theoretical studies have been carried out to predict the fire resistance of rectangular hollow steel columns filled with bar-reinforced concrete. A mathematical model to calculate the temperatures, deformations, and fire resistance of the columns is presented in this paper. Calculated results are compared with those measured. The results indicate that the model is capable of predicting the fire resistance of square hollow steel columns, filled with bar-reinforced concrete, with an accuracy that is adequate for practical purposes. The model enables the expansion of data on the fire resistance of square concrete-filled steel columns, which at present consists predominantly of data for columns filled with plain concrete with data for columns filled with bar-reinforced concrete. Using the model, the fire resistance of square concrete-filled steel columns can be evaluated for any value of the significant parameters such as load, column-section dimensions, column length, and the percentage of reinforcing steel, without the necessity of testing.

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This paper is primarily concerned with the formation of barrel-vault space trusses derived from a flat configuration by posttensioning. To obtain a fairly general picture of the shape-formation process by means of posttensioning, both gently and sharply curved barrel-vault models are studied. The structures are devised to be near mechanisms during the posttensioning operation. They are considered to be near mechanisms because only the flexural stiffness of the top chords provides any appreciable resistance to deformation apart from friction and self weight. Therefore, no appreciable axial force is induced in the members of the structures during the shape-formation process. The result of experimental and theoretical work on the shape formation of barrel-vault space trusses by means of posttensioning is presented here. The shape-formation process, referred to as self-erection, can lead to significant economies in the construction of large-span lightweight structures by eliminating or minimizing the need for scaffolding and heavy cranes.

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A series of shallowly embedded steel column base consisting of an exposed column base and a covering reinforced concrete floor slab were tested under horizontal cyclic loading to very large deformation. By adjustments to the floor slab thickness, shape, and reinforcing bars in the slab, the initial stiffness, maximum strength, and dissipated energy of the shallowly embedded column base increase significantly with respect to those of the exposed column base. It is found to be practical to strengthen the shallowly embedded column base so that it would behave like a fully embedded column base. Punching shear failure in the floor slab around the column due to the uplift of the base plate occurs when the shallowly embedded column base fails. Based on the plastic theory, a mechanical model that considers the contributions of the anchor bolts and the bearing and punching shear of the floor slab is proposed to evaluate the maximum strength. The evaluated results have good agreement with the test results, with errors not greater than 20%.

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When crest-fixed thin steel roof and wall cladding systems are subjected to wind uplift or suction loading, local pull-through or pull-out failures occur prematurely at their screwed connections. During high wind events such as storms and hurricanes these localised failures then lead to severe damage to buildings and their contents. In recent times, the use of thin steel battens/purlins has increased considerably. This has made the pull-out failures more critical in the design of steel cladding systems. Recent research has developed a design formula for the static pull-out strength of screwed connections in steel cladding systems. However, the effects of fluctuating wind uplift or suction loading that occurs during high wind events are not known. Therefore a series of cyclic wind uplift/suction tests has been undertaken on connections between thin steel battens made of different thicknesses and steel grades, and screw fasteners with varying diameter and pitch. Tests revealed a significant reduction to pull-out strength caused by fluctuating wind loading. Simple design equations and suitable recommendations were developed to take into account this strength reduction. This paper presents the details of the cyclic tests and the results.

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Optimal shapes are found for the flange of an H-beam. A forced displacement is given at the free end of the cantilever beam so that the average deformation angle reaches the specified value. The objective function to be maximized is the dissipated energy, and a constraint is given for the maximum equivalent plastic strain at the fixed end. Globally optimal solutions are searched by a simulated annealing, which is successfully combined with a commercial finite element analysis code. It is shown that the energy dissipation capacity is significantly improved by optimizing the flange shape.

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This paper presents an analytical study on static moment redistribution and resultant reduction of lateral resistance caused by sudden beam fractures in steel moment frames. A numerical example is presented for a simple multispan frame, and the step-by-step processes of beam fractures, moment redistribution, and loss in resistance under statically increasing lateral deflection are examined. The mechanism of moment redistribution is interpreted using the three-moment equations, and the possibility of sequential fractures in the course of static moment redistribution is investigated. A sudden fracture of a beam changes moment distribution rather locally, particularly when plastic hinges are already formed in beams by the time of the fracture. Sequential fractures are less likely to occur during static moment redistribution when rotations corresponding to fracture are large (to simulate fractures after significant plastification) and vary from plastic hinge to plastic hinge (to allow for the random nature of fractures). It should be carefully noted that the above observations are applicable for static moment redistribution, and do not necessarily represent the effects of beam fractures on dynamic responses.

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Reversed cyclic loading tests of eight prestressed and two nonprestressed concrete exterior beam-column joint assemblies that failed inside the joint cores were conducted. The test results revealed no significant difference in the maximum story shear force between the prestressed and nonprestressed concrete test units although the horizontal input shear forces of the joint cores at the maximum story shear forces of the prestressed concrete units (calculated based on the column shear force and the forces in the reinforcing and the prestressing steels) were greater than those of the nonprestressed concrete units. On the basis of this result, the writers have concluded that prestressing force does not play a major role on the ultimate shear strength of beam-column joint cores. In addition, the design shear force acting on a beam-column joint core should be determined using the average shear force calculated from the bending moment at the beam-column interfaces, not by the horizontal input shear force. These conclusions led the writers to develop design equations for estimating design shear forces and ultimate shear capacities of prestressed concrete interior and comer joints. The equations were compared with test data on 51 beam-column joint assemblies that failed in shear in the joint cores. The test results agreed well with the estimations.

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The propagation of long cracks under constant amplitude cyclic loading is studied in complex welded box beams made of high strength low alloy (HSLA) steel. The 8 x 1 x 0.7 m box beams were designed to simulate the cellular structure of a double hull ship but the results of the experiments are equally applicable to other box systems such as bridges. These experiments were designed to evaluate the residual fatigue life after a significant fatigue crack has formed. After testing, residual stresses were measured on two box beams using the standardized strain gage hole-drilling method. The experiment results demonstrated the good crack tolerance of cellular structures. The residual life of a box beam (after a welded detail has failed) was significant. The crack driving force was evaluated using finite element modeling. Reasonable correlation between these large scale tests and the fatigue crack growth rate from small compact specimen was obtained only with models that included the effects of crack closure due to residual stresses. Linear elastic fracture mechanics proved to be sufficient to predict the behavior of long cracks in this case.

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The purpose of this study was to evaluate the fatigue strength of a particular welded diaphragm-to-beam connection. The connection consisted of wide flange diaphragm members welded directly to the web of a deeper main beam member. Cyclic tests were performed to determine the fatigue resistance of the detail and to evaluate three different repair methods. The repair methods investigated involved combinations of diaphragm removal, drilling holes at the beam crack tips, and peening the bottom flange weld toes. This study has shown that the web and bottom flange welds of nonstaggered diaphragms are more susceptible to fatigue cracking than comparable staggered diaphragm configurations. It was also found that the fatigue life of the detail is not greatly reduced because of the formation of web and bottom flange weld fatigue cracks, because cracks formed in the beam web at the end of the bottom flange diaphragm weld controlled the fatigue behavior. Moreover, the repair methods were found to be effective in significantly extending the cyclic life of the diaphragm detail.

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A data base is developed for examining the behavior of steel beam columns. This data base, mada in the format of a relational data base, contains the results of 237 tests carried out previously in Japan. By using the data base, the strength characteristics of steel beam columns are investigated statistically, and the following observations are made. The experimental strength is 16% larger on the average than the strength predicted by the load and resistance factor design (LRFD)specification with the coeffisient of variation as 0.10. Variation in the yield stress, with respect to the nominal yield stress, makes the experimental strength larger than the predicted strength by 7% but does not change the coefficient of variation. The experimental strength is 40% larger on the average than the design strength stipulated in the LRFD specification. The experimental strength is larger by 10 - 15% for beam columns with steep moment gradient than for those with uniform moment, and also for beam columns whose yield ratio is below 0.7 than for those with a larger yield ratio. The aforementioned observation demonstrates that the effect of strain hardening on the strength of beam columns is conspicuous.

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The concept of confined concrete has been widely accepted throughout the structural engineering field, such as the spiral, steel tube, or carbon fiber composite shell confined concrete, etc. In the present study, this concept has not only been used in the structural columns, but also in joints. In this connection system, the steel tube is interrupted at the floor, the concrete in the connection zone is confined by a stiffening ring with multiple lateral hoops, and the reinforced concrete beams are continuously arranged through the joint. The structural behavior of this new connection system in axial compression tests and reversed cyclic loading tests is presented in a companion paper. In the present study, the bearing strength of composite columns and the joint in axial compression is obtained based on the stress and strain analyses. The critical volume fraction of transverse stirrups of the composite column and the effective confining radius in the stiffening ring are proposed based on the thick cylinder model with the assumption of plane stress state. By using these solutions, it is favorable to obtain the stress distribution in confining concrete and the bearing strength of the confined concrete. For the reversed cyclic loading tests, the Clough hysteresis model is used to simulate the hysteresis loops of the specimens without considering the stiffness degradation in the unloading process. The results of the theoretical modeling are generally in good agreement with the experimental observations.

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In this paper, nonhomogeneous Markov chains are proposed for modeling the cracking behavior of reinforced concrete beams subjected to monotonically increasing loads. The model facilitates prediction of the maximum crackwidth at a given load given the crackwidth at a lower load level, and thus leads to a better understanding of the cracking phenomenon. To illustrate the methodology developed, the results of three reinforced concrete beams tested in the laboratory are analyzed and presented.

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The writers wish to thank the discusser for his interest in the paper. The discusser raises four points. First, he asks how the shear connection stiffness in the finite-element model was derived, which should not be the stiffness in real beams. Second, he points out that the degree of shear connection should substantially decrease with a decrease in the span for the same section beam while keeping the ultimate longitudinal force resisted by shear connectors unchanged. Third, he argues that the threedimensional beam element used to model discrete stud shear connectors could simulate local stress distribution in concrete around the stud shear connectors, and then he demonstrates that the finite-element results presented in the discussed paper compare very well with experimental results given by others. Fourth, the discusser wants the writers to clarify the stress-strain curve used for steel in the finite-element model.

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The finite element method was used to develop accurate stress intensity factor (SIF) solutions for two-tip web cracks and symmetric three-tip cracks in I-beams under tension or bending. Governing parameters for cracked I-beams were determined. For web cracks, the SIF is a function of applied stress, crack length, eccentricity, and flange-to-web area ratio of W shape. For three-tip cracks in web and flange, the SIF is a function of applied stress, web and flange crack lengths, and flange-to-web area ratio. The flange-to-web area ratio accounts for the constraining effect of the flange on two-tip web cracks and the interaction effect on three-tip cracks. A total of 2,106 combinations of type of crack, type of loading, crack length, eccentricity, and flanges-to-web area ratio were analyzed. Numerical results were fitted with polynomial equations for ready use by practicing engineers.

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An analytical study was conducted on the cyclic loading behavior of beams in steel moment frames. Lateral-torsional buckling and local buckling were explicitly considered in the analysis. Beam cross-sectional dimensions were varied to represent a wide range of rolled wide flange shapes. The unbraced length of the beams corresponded to slenderness ratios about the weak axis ranging between 60 and 100. Based on the analyses, flange and web width-thickness limits were established that would permit the beam to achieve various target rotation capacities. These limits are presented in terms of limit curves which plot the flange width-thickness ratio against the web width-thickness ratio. The limit curves clearly show strong flange-web interaction. Different limit curves were developed for a range of target rotation angles, weak axis slenderness ratios, and residual strength levels. Postbuckling behavior and strength degradation mechanism were studied. The results of the analyses are compared against current building code requirements for beam stability in seismic steel moment frames, and the adequacy of the current code requirements are evaluated.

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A research study has been conducted on a newly proposed design of embedded steel plate composite coupling beams with shear studs in order to improve the performance of reinforced concrete (RC) coupling beams under severe wind or earthquake loading. The experimental results on three coupling beams tested under reversed cyclic loading are discussed in this paper. One of the coupling beams was conventionally reinforced, while each of the other two contained a vertically embedded steel plate along the whole span either with or without shear studs. It was found that embedded steel plates could improve the strength and the stiffness of coupling beams, while shear studs are required to enhance the plate/RC interaction in order to achieve good inelastic performance under large imposed shear deformations. Equations for calculating the required shear connection strength in the beam span to ensure the plate/RC composite action and for estimating the available plate/RC interface slips to mobilize shear studs have been proposed.

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This paper presents an analytical study of the lateral-torsional instability and lateral bracing effects of wide-flange steel beams subjected to cyclic loading. Numerical analysis using the large deformation theory was conducted to collect the necessary data. Examined were wide-flange steel beams bent in double curvature and subjected to cyclic loading with increasing amplitudes up to the maximum beam end rotation of 0.045 rad. Cross-sectional properties, slenderness ratios, material strength, loading history, and unbraced length were chosen as analysis variables. The lateral instability effect was found to differ significantly between cyclic and monotonic loading. For slenderness ratios about the weak axis not smaller than 100, the strength that can be sustained under cyclic loading was much smaller than that obtained under monotonic loading due to the accumulation of out-of-plane deformations. Equations are proposed for the beam unbraced length with which no detrimental reduction in strength is present in cyclic loading up to the maximum beam end rotation of 0.045 rad. It was also found that the unbraced length requirements stipulated in the American Institute of Steel Construction Seismic Provisions are a reasonably conservative measure to ensure sufficient beam rotation capacity. Lateral instability of reduced beam section (RBS) beams was also analyzed. It is notable that the RBS beam is not necessarily more susceptible to lateral instability than the corresponding standard beam, primarily because of a smaller yielding region and smaller forces induced in the cross section of the RBS beam. This phenomenon was interpreted using a simple flange buckling analogy. The lateral bracing requirements stipulated for standard beams are applicable to ensure sufficient rotation capacity for RBS beams if local buckling effects would not occur.

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An experimental test program was conducted at McGill University which incorporated 14 castellated steel beams provided by Chaparral Steel. The notable feature of these beams is their thin webs. The modes of failure and their corresponding loads were predicted based on a number of previous studies. A nonlinear finite element analysis was carried out in order to provide a new assessment tool. The program used was NASTRAN. The geometrics of the castellated steel beams were predicted to be susceptible to web post buckling. The applied load which causes the formation of the mechanism failure (Redwood 1978), and the load which causes a horizontal yield failure, (Blodgett 1963), were calculated and compared to the predicted buckling load to anticipate the mode of failure. The web post buckling loads were predicted based on an analysis by Blodgett (1963), Aglan and Redwood (1974) and on the finite element analysis. The above analyses were repeated for five of the seven beams tested by Bazile and Texier (1968) and which failed by web post buckling. The beams tested were susceptible to web post buckling, as predicted. The web post buckling analysis suggested by Blodgett (1963) resulted in large variations from the experimental failure load. The analysis suggested by Aglan and Redwood (1974) yielded conservative results. The finite element buckling analysis showed a good correspondence with the experimental buckling load and may be a good tool to conduct a more complete parametric study.

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http://dx.doi.org/10.1061/(ASCE)0733-9445(2006)132:1(13) This first part of two companion papers deals with the numerical modeling of timber–concrete composite beams (TCCs) under long-term loading. All phenomena affecting the long-term behavior of timber, concrete, and the connection system, such as creep, mechanosorptive creep, shrinkage/swelling, and temperature variations, are fully considered. The structural problem is solved through a uniaxial finite element model with flexible connection and a step-by-step numerical procedure over time. The important role played by the environmental thermohygrometric variations on TCCs is highlighted through some analyses. The proposed numerical procedure is validated on two long-term experimental tests in outdoor conditions. Despite some uncertainties in environmental conditions and material properties, a good fit between experimental and numerical results is obtained. A parametric analysis is performed in the second part, showing the contribution of different rheological phenomena and thermohygrometric variations on beam deflection and connection slip. Based on results carried out, a simplified approach for long-term evaluation of TCCs is then proposed.

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Despite experimental evidences, the contributions of the concrete slab and composite action to the vertical shear strength of simply supported steel-concrete composite beams are not considered in current design codes, which lead to conservative designs. In this paper, the finite element method is used to investigate the flexural and shear strengths of simply supported composite beams under combined bending and shear. A three-dimensional finite element model has been developed to account for geometric and material nonlinear behavior of composite beams, and verified by experimental results. The verified finite element model is than employed to quantify the contributions of the concrete slab and composite action to the moment and shear capacities of composite beams. The effect of the degree of shear connection on the vertical shear strength of deep composite beams loaded in shear is studied. Design models for vertical shear strength including contributions from the concrete slab and composite action and for the ultimate moment-shear interaction ate proposed for the design of simply supported composite beams in combined bending and shear. The proposed design models provide a consistent and economical design procedure for simply supported composite beams.

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http://dx.doi.org/10.1061/(ASCE)0733-9445(2006)132:1(23) This second part of two companion papers investigates the contribution of different rheological phenomena and thermohygrometric variations on long-term behavior of timber–concrete composite beams (TCCs) in outdoor conditions. The numerical algorithm presented and validated against two experimental tests in the first part is employed with this aim. Such a model fully considers all rheological phenomena and, therefore, leads to rigorous solutions. Effects on the beam response include the creep and mechanosorptive creep of both timber and connection, along with concrete creep and shrinkage, and may markedly increase the elastic deflection due to live load. The inelastic strains due to yearly and daily variations of environmental conditions (temperature and relative humidity) produce an important fluctuation of the deflection. A simplified method, which is suitable for practical design of TCCs under long-term loading, is at last proposed. The effects of load, concrete shrinkage, and inelastic strains due to environmental variations are evaluated one by one using approximate formulas and are then superimposed. Creep and mechanosorptive creep are taken into account by adopting modified elastic moduli. The reliability of the proposed method is checked by way of some comparisons with numerical results. The applicability for the case of TCCs in heated indoor conditions is also discussed.

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Steel plates in double skin composite (DSC) panels are restrained by a concrete core and welded stud shear connectors at discrete positions. Local buckling of steel plates in DSC panels may occur in a unilateral mode between stud shear connectors when subjected to combined states of stresses. This paper studies the local and postlocal buckling strength of steel plates in DSC panels under biaxial compression and in-plane shear by using the finite element method. Critical local buckling interaction relationships are presented for steel plates with various boundary conditions that include the shear stiffness effects of stud shear connectors. A geometric and material nonlinear analysis is employed to investigate the postlocal buckling interaction strength of steel plates in biaxial compression and shear. The initial imperfections of steel plates, material yielding, and the nonlinear shear-slip behavior of stud shear connectors are considered in the nonlinear analysis. Design models for critical buckling and ultimate strength interactions are proposed for determining the maximum stud spacing and ultimate strength of steel plates in DSC panels.

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In steel construction, sometimes bolts and welds must be combined in a single joint. Provisions for the design of these combination joints can be found in existing specifications, but the design rules generally have not been verified by physical tests. In addition, the rules appear to be illogical in some cases. An experimental study using full-scale tension lap splices that combined high-strength bolts and fillet welds was carried out in order to develop a better understanding of combination joints. The results showed that the orientation of the welds and the bearing condition of the bolts are two key factors that must be considered when determining the extent of load sharing in combination joints. Design recommendations based on the results of this study are presented.

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This paper investigates the influence of bond slip on crack spacing in reinforced concrete. A bond-link element is used to account for the influence of the bond slip between the concrete and the reinforcing steel. Following a previous work, the writers treat crack spacing as a strain localization problem. A new numerical model for prediction of crack spacing in reinforced concrete is applied. It is assumed that the deformation pattern of crack spacing consumes the least energy among all kinematically admissible deformations, and the energy minimization approach is applied to predict crack spacing. To simplify the problem, a lattice model is used, in which the cracking process is represented by the damage of the concrete bar elements. The influence of the bond slip on the cracking patterns have been studied through three numerical examples. The results show that without considering bond slip, the damage near the reinforcement is distributed rather than localized, whereas considering bond slip, the damage near the reinforcement is localized. The influence of bond slip on crack spacing is significant.

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A new general critical excitation method is developed for a damped linear elastic single-degree-of-freedom structure. In contrast to previous studies considering amplitude nonstationarity only, no special constraint of input motions is needed on nonstationarity. The input energy to the structure during an earthquake is introduced as a new measure of criticality. It is shown that the formulation of earthquake input energy in the frequency domain is essential for solving the critical excitation problem and deriving a bound on the earthquake input energy for a class of ground motions. It is remarkable that no mathematical programming technique is required in the solution procedure. This enables structural engineers to use the method in their structural design practice without difficulty. The constancy of earthquake input energy for various natural periods and damping ratios is discussed based on an original sophisticated mathematical treatment. Through numerical examinations for four classes of recorded ground motions, the bounds under acceleration and velocity constraints (time integral of the squared base acceleration and time integral of the squared base velocity) are clarified to be meaningful in the short and intermediate/long natural period ranges, respectively.

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Concrete filled steel columns have seen an increased usage in building structures throughout the world. In Australia, the use of thin-walled steel sections coupled with concrete infill has been used on various building projects with great advantage. The major advantages of the use of thin-walled steel sections are the reduced structural steel costs and the economy in construction that the method provides. This paper presents both an experimental and theoretical treatment of coupled local and global buckling of concrete filled steel columns sometimes termed interaction buckling. The paper then concludes with comparisons of design recommendations for the strength evaluation of slender composite columns with thin-walled steel sections.

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An efficient beam element, the modified elastofiber (MEF) element, has been developed to capture the overall features of the elastic and inelastic responses of slender columns and braces under axial cyclic loading without unduly heavy discretization. It consists of three fiber segments, two at the member ends and one at midspan, with two elastic segments sandwiched in between. The segments are demarcated by two exterior nodes and four interior nodes. The fiber segments are divided into 20 fibers in the cross section that run the length of the segment. The fibers exhibit nonlinear axial stress-strain behavior akin to that observed in a standard tension test of a rod in the laboratory, with a linear elastic portion, a yield plateau, and a strain-hardening portion consisting of a segment of an ellipse. All the control points on the stress-strain law are user defined. The elastic buckling of a member is tracked by updating both exterior and interior nodal coordinates at each iteration of a time step and checking force equilibrium in the updated configuration. Inelastic postbuckling response is captured by fiber yielding, fracturing, and/or rupturing in the nonlinear segments. The key features of the element include the ability to model each member using a single element, easy incorporation of geometric imperfection, partial fixity support conditions, member susceptibility to fracture defined in a probabilistic manner, and fiber rupture leading to complete severing of the member. The element is calibrated to accurately predict the Euler critical buckling load of box and I sections with a wide range of slenderness ratios (L/r=40, 80, 120, 160, and 200) and support conditions (pinned-pinned, pinned-fixed, and fixed-fixed). Elastic postbuckling of the Koiter-Roorda L frame (tubes and I sections) with various member slenderness ratios (L/r=40, 80, 120, 160, and 200) is simulated and shown to compare well against second-order analytical approximations to the solution even when using a single-MEF element to model each leg of the frame. The inelastic behavior of struts under cyclic loading observed in the experiments of Black et al., Fell et al., and Tremblay et al. is accurately captured by single-MEF-element models. A FRAME3D model (using MEF elements for braces) of a full-scale six-story braced frame structure that was pseudodynamically tested at the Building Research Institute of Japan subjected to the 1978 Miyagi-Ken-Oki earthquake record is analyzed and shown to closely mimic the experimentally observed behavior.

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