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A new analysis approach is devised herein to predict the response of reinforced concrete deep beams strengthened in flexure, shear or shear-flexure with fiber-reinforced polymer (FRP). The ...

Strongback-braced frames employ an essentially elastic truss, or strongback, that defines an elastic load path to redistribute seismic demands and mitigate the formation of story mechanisms...

Space trusses are extensively used to construct large free spans in roofs. In many countries, connections in such space trusses are made with tubes linked by typical space-truss connections...

The beam-truss model (BTM), developed for the nonlinear cyclic analysis of reinforced concrete components including softening, is extended to compute the out-of-plane buckling observed in p...

Two full-scale Howe trusses were instrumented and posttensioned to study their time-dependent behavior in outdoor conditions. Force, relative humidity, and temperature data were acquired fo...

An integrated strategy for sizing and shape optimization of truss structures, taking buckling constraints implicitly into truss design, is demonstrated here. Because the associated objectiv...

Aluminum alloy members of channel sections are widely used in lightweight structures, especially as pillars of curtain wall systems and brace and chord members in roof trusses. This paper presents both experimental and numerical studies on the behavior of aluminum alloy channel section beams. In this study, four-point bending tests under minor-axis and major-axis bending were carried out. The test specimens included plain and lipped channel sections of both 6063-T5 and 6061-T6 aluminum alloys. A finite-element (FE) model of the channel section beam was developed by using the FE package ABAQUS. The ultimate bending resistances and failure modes of the FE model were compared with the results from the bending tests. The validated model was employed for the parametric study to generate numerical simulation results. A total of 55 new experimental and numerical beam results were compared with predictions from existing aluminum alloy design specifications from the United States, Australia/New Zealand, Europe, and China. Additionally, two commonly used design approaches—the continuous strength method (CSM) and the direct strength method (DSM)—were applied to predict bending capacities for comparisons. A modified DSM approach for aluminum alloy channel section beams is proposed herein. Finally, reliability analyses were conducted to evaluate the aforementioned design methods. The results show that, in comparison with other considered design methods, the CSM provides more accurate and consistent results for aluminum alloy plain and lipped channel section beams.

The US design code provisions for steel special truss moment frames (STMFs) were formulated based on research work carried out in the 1990s with double-angle sections as truss members. To p...

In this paper, a damage identification framework for steel-truss railroad bridges, based on acceleration responses to operational train loading, is presented. The method is based on vertica...

The need for a very-long-span structure in sporting and industrial venues puts steel moment frames and braced frames at a disadvantage. In this regard, special truss moment frames (STMFs) c...

In the present paper, the coupled behavior of structural systems obtained by connecting a moment resisting frame structure with a vertical elastic truss, known in the literature as strongback, which acts as a mast by imposing to the structure a given lateral deformed shape, is investigated. The rigid behavior of the strongback, which has to be designed to remain in the elastic field under strong seismic ground motion, linearizes the lateral displacement profile of the adjacent frame through an exchange of mutual horizontal actions. The presence of the strongback should thus help in limiting undesired effects, such as soft-story and weak-story mechanisms. For the proper design of both the truss system forming the strongback and the frame members, the preliminary evaluation of the actions exchanged between the systems is of fundamental importance. The aim of the work is to develop analytical formulas for estimating mutual actions and internal actions in the frame members for the limiting cases of shear-type frames and pendulum-type frames. Finally, some numerical simulations of frame systems with strongback systems as subjected to earthquake ground motions are developed, including the cases of frames with flexible beams. It is found that the amplitudes and distributions of both mutual actions and internal actions in the frame are significantly affected by the beamto- column stiffness ratio. In the case of relatively stiff beams, the mutual actions tend to reduce the shear and bending moment at the lower stories, which are rather uniformly redistributed along the height. On the contrary, in the case of relatively flexible beams, large mutual actions and internal actions (shear and bending moments) are concentrated at the lower stories, with the upper stories remaining practically unloaded.

This article presents a refinement of the rotating-angle softened truss model (RA-STM) for prestressed concrete (PC) membrane elements. To refine the RA-STM, an efficient solution procedure...

In this paper, the design of truss systems configured with a periodic pattern is proposed for obtaining the frequency response of truss units by the recursive finite-element method and moni...

This paper presents a reliability study of metal-plated (MP) wood truss webs laterally braced by single or double braces, and the results provide a reference for amending relevant prescript...

Progressive collapse incidents of truss structures are often reported; however, studies on the collapse resistance of truss structures are comparatively few. In order to investigate the collapse-resisting mechanisms of truss structures, this paper presents a comprehensive and detailed study on the collapse-resisting performance of planar trusses subjected to local damage at various locations, using both finite-element (FE) and analytical approaches. An improved FE analysis procedure is proposed to improve the computational efficiency. The main conclusions include the following: (1) in the case of a sudden loss of a top chord member or a diagonal member, catenary action will be the primary mechanism to provide the bridging-over capacity of the remaining structure, and severer damage can result when the removed member locates in the midspan; and (2) if a bottom chord member is suddenly lost, arch action will be the main mechanism to provide the bridging-over capacity of the remaining structure, and severer damage can result when the removed member locates next to the support or in the midspan

Shear deformations of reinforced concrete (RC) beams are not negligible after shear cracking. However, unlike the well-established procedure for calculating bending deformations of cracked beams, the calculation of shear deformations is still ignored in codes of practice due to a lack of practical models. This study aims to develop a practical approach for estimating instantaneous shear deformations of RC beams under service loads. Based on the truss analogy, an explicit equation for evaluating the yield shear stiffness of fully diagonally cracked beams is derived. It is discovered that the shear retention factor (ratio of the yield shear stiffness to the initial elastic shear stiffness) is approximately the cubic root of the shear-reinforcement ratio. An analytical approach for evaluating the degradation of effective shear stiffness and the development of shear deformation is proposed. Two restrained I-beams with thin webs are tested. This test and shear-deformation tests available in the literat...

To support the repair and maintenance of steel eyebars in bridges, tension stresses are sometimes estimated from the observed member natural frequencies. Although the ends of such eyebars are often essentially fixed, a pin-ended model has typically been used to predict tensions because closed-form solutions do not exist for any other end conditions. An approximation that reflects vibrating stretched wires with fixed ends has also been used, but this still incurs considerable error at lower member slenderness and stress levels. To provide for better estimates of eyebar tensions from observed vibrations, this paper presents exact tabular solutions for determining the direct tension stress in undamped steel bars, generalized for any length or thickness, where both ends of the member are fixed or where one end is fixed and the other pinned. Approximation equations derived from these exact solutions are also developed. Examples demonstrate the application of these new tools and the potential increase i...

Many models to determine the shear capacity of shear reinforced beams are based on the truss analogy. Various proposals have been formulated in recent years, all of which differ with regard to the limits of strut inclination. Remarkably, those limits do not depend on the type of concrete, which could be expected to be critical for the shear friction capacity of the cracks, which is supposed to be a major influencing factor with regard to the limit of strut rotation. Tests on beams with I-shaped cross sections have been carried out on beams made of normal, lightweight, and high-strength concrete. The experimental results are compared, in Part I of this paper, with those obtained by analytical models and, in Part II, with those obtained by nonlinear finite element programs tailored to this specific application. The result is that the type of concrete does not lead to significant changes in strut rotation capacity, so that the strut rotation limit values have general validity. The level of approximation approach, as presented in the Federation Internationale du Beton/International Federation for Structural Concrete (fib) Model Code of Concrete Structures 2010 is justified: more sophisticated calculation models lead indeed to more accuracy in the determination of the shear capacity.

This paper presents the method and results of a study whose objective was to investigate the seismic performance of a new light- frame cold-formed steel-frame system. The system includes floor trusses, open panels, V-braced panels, columns, and connections. To do this, aseriesofreversed-cyclictestswereconductedonsubassemblies.Theresultsofthisexperimentalprogramprovidedinsightintothebehaviorof the subassemblies under cyclic loading, which in turn provided key information for numerical modeling of the subassemblies and the whole systemaswellasfailuremechanismsoftheframe.Nonlineartimehistoryanalyseswereperformedusinganewformulation fora4-storyframe usingasuiteofearthquakegroundmotionstodemonstratethebehaviorofatypicalV-bracedsysteminamoderateearthquake.Bothtestresults andnumericalanalysisindicatethatthesystemhasgoodductilityasaresultofthescrewedplateconnectionsbetweenthelight-gaugemembers and between the light-gauge members and square columns. The frame system performed very well at four stories making it a viable midrise construction option in seismic regions of the United States and around the world. DOI: 10.1061/(ASCE)ST.1943-541X.0000683. © 2013 American Society of Civil Engineers. CE Database subject headings: Cold-formed steel; Bracing; Earthquake loads; Steel frames; Seismic effects. Author keywords: Cold-formed steel; V-brace; Earthquake loading; Light frame; light-gauge steel; Seismic performance.

This paper seeks to examine the concrete contribution to shear strength and determine the inclination of the compressive strut within the variable truss model for slender RC shear-critical beams with stirrups. Using the modified compression field theory in place of the conventional statistical regression of experimental data, the expression for the concrete contribution to shear strength was derived, and the inclination of compressive struts was determined. A simplified explicit expression for shear strength was then provided, with which shear strength can be calculated without extensive iterative computations. This method was then verified using the available experimental data of 209 RC rectangular beams with stirrups and compared with the current methods from the American Concrete Institute and the Canadian Standards Association. The theoretical results are shown to be consistent with the experimentally observed behavior of shear-critical RC beams.

A new force visualization and design tool employing hybrid topology optimization is introduced for RC and prestressed concrete structural members. The optimization scheme couples a minimum compliance (maximum stiffness) objective function with a hybrid truss-continuum ground structure that can generate a strut-and-tie model for any general concrete member, loading, and set of boundary conditions. The truss ground structure represents discrete steel reinforcing bars (tensile load paths) that can be sized based on axial forces output directly by the optimization routine, whereas the continuum elements simulate concrete compression struts. This separation of compressive and tensile load-carrying elements is achieved through bilinear elastic models with an orthotropic constitutive relationship for the continuum. Examples are provided demonstrating the potential value of the optimization tool to RC design. Reinforcing layouts that can minimize cracking and reduce steel quantities when compared with tra...

Experimental observations on 11 Reinforced Concrete (RC) columns tested at Nanyang Technological University (NTU), and existing experimental data of 79 shear-critical RC columns are presented. Significant arch action is found in columns of small shear span-to-depth ratio and high axial-load ratio under shear force. Utilizing the sectional method for shear strength of these types of columns, which does not consider arch action, would give a more conservative prediction. Based on the truss-arch model, an expression to predict the shear strength of shear-critical RC columns is presented, which considers both the contributions of concrete and transverse reinforcement to shear strength in the truss model as well as the contribution of arch action through compatibility of deformation. The proposed model is compared with other shear strength models using the available column test data consisting of 90 shear-critical RC columns, and the results show that the proposed model can improve the accuracy of shear strength predictions for shear-critical RC columns Accepted version

Membrane fabric structures are spatial structures that allow for long span and lightweight roofs. In many cases, membrane roofs are supported with trusses or masts and prestressed together with cables to obtain a resistant shape for a given loading condition. For the design of membrane structures, geometrically nonlinear analysis is required. Additionally, modeling of each membrane element and form-finding of the shape are of great importance in the design process. First, an equilibrium-finding analysis is conducted for the purpose of obtaining the optimal shape of the membrane structure, during which the initial stresses of the membrane and cables must be balanced. Next, the stress-deformation analysis is performed for the required loading condition. This analysis allows understanding of the behavior of the structure and confirms that the design of the membrane satisfies the required safety factor for the construction. The analyses of the Southwestern Baseball Dome in Seoul and the Jeju Stadium D...

Topology optimization can be divided into continuum and discrete types, the latter being the emphasis of the present work. In the field of discrete structural topology optimization of trusses, the generation of an initial ground structure is crucial. Thus, this paper examines the generation of ground structures for generic structural domains in two and three dimensions. It compares two methods of discretization, Voronoi-based and structured quadrilateral discretizations, and proposes two simple and effective ground structure generation approaches: the macroelement and macropatch approaches. Both can be implemented with either type of discretization. This work presents several features of these approaches, including the efficient generation of initial ground structures, a reduction in matrix bandwidth for the global stiffness matrix, finer control of bar connectivity, and a reduction in the number of overlapped bars. Generic examples and practical structural engineering designs are presented. They ...

This paper proposes a general approach for topology-finding of tensegrity structures. The ground structure method that is widely used in topology optimization of truss structures is employed. An optimization model, using the member connections and the internal forces of members as variables, is developed to find self-stressed tensegrities under given constraints on member distribution, configuration symmetry, and node stability. Mixed integer linear/quadratic programming is used to solve the optimization problem. Numerical examples are carried out to verify the proposed approach. Compared to previous approaches, the proposed approach is able to find a wider scope of tensegrity structures that have a maximum of k (k≥1) struts connecting to a single node and is able to deal with objective functions in quadratic form.

Biconcave cable trusses are widely utilized in engineering applications, representing an economical solution for large span roofs. The most common modeling approach is via the finite-element method (FEM). Analytical approaches have been proposed for biconcave cable trusses to provide good approximations while reducing the number of variables of the problem, but most of them do not take into account the slackening of cables. The approach proposed in this paper is based on the classical Ritz approach, using polynomial functions to approximate the deformed shape of the cable truss. The equilibrium configuration is found via minimization of total potential energy. The approach is suitable for most load conditions (distributed and concentrated). The model takes into account the nonlinearities attributable to the slackening of both vertical harnesses and bracing cables. The number of variables is reduced compared to a FEM approach, while the results show a good agreement with the FEM solution. This gene...

This paper investigates the behavior of precast concrete sandwich panels (PCSPs) made with truss shear connectors, which accounts for partial shear interaction. A theoretical model is developed based on variational principles and equations of equilibrium that account for the axial and bending rigidities of reinforced concrete (RC) layers and their potential cracking, the shear and normal rigidities of the insulation layer, and the elastic flexibility of the diagonal truss connectors. This layered modeling approach is general and can be used to describe the structural behavior under various loading patterns and boundary conditions, with the influence of the partial shear interaction as an automatic outcome of the analysis. As such, it provides a better and a more reliable tool than other existing simplified models in the literature for describing the complex structural behavior of PCSPs. A parametric study is presented, which investigates key parameters in the design of concrete sandwich panels, su...

The roofing systems of low-rise buildings are commonly made of thin, high-strength steel roof sheeting and battens. These light-gauge steel roofing systems are subjected to high-wind uplift loads during tropical cyclones and thunderstorms. In recent times, roof batten–to–rafter or truss connection failures have been identified as a major cause of severe roof failures during high-wind events. Most of these connection failures are in the form of localized pull-through failures of the bottom flanges of steel roof battens at their screw connections. The design practice at present is based on expensive and time-consuming full-scale tests or inappropriate small-scale tests. Hence, there is an urgent need to develop suitable test methods to determine the pull-through capacity of roof battens. This paper presents the details of an experimental study undertaken to investigate pull-through failures of light-gauge steel roof battens using both full-scale and small-scale tests. The investigation showed that t...

Vibration has become a serious serviceability problem due to the large openings of girder, lightweight floor systems, and high-strength materials used in practice. The results from both heel-drop and jumping floor vibration tests of a large-span prestressed cable RC truss (PCT) floor system are presented. System parameters such as peak acceleration, fundamental frequency, and damping ratios were considered and studied. The results and comparisons were taken based on the on-site test data. The comparison results indicate inconsistencies with the heel-drop or jumping impact models proposed by other researchers. The results from heel-drop and jumping tests were comprehensively compared against published codes. Based on the classic plate theory, a derived accurate formula for a PCT floor system is proposed. Lastly, a simplified method is suggested, which uses the constant moment of inertia for the cross section of a PCT girder.

For simplified shear design of slender reinforced concrete (RC) beams with stirrups, a modified variable-angle truss model is developed in this paper. In this model, an analytical solution of the inclination of struts (θ) is derived by combining the theory of plasticity and the concrete softening of the modified compression field theory (MCFT). It is found that there is a decreasing linear relationship between cotθ and lnω, where lnω is the natural logarithm of the mechanical shear-reinforcement ratio. On this basis, a new shear design equation is proposed for slender RC beams with stirrups, which is shown to be not only simpler, but to also provide improved prediction compared with the shear design provisions of some of the existing codes.

© 2015 American Society of Civil Engineers. Realistic truss design optimization problems are often governed by practical constraints. Because of the complexity of these constraints, usually only member constraints are taken into account during the optimization, and joint constraints are accounted for in a manual postprocessing step. This paper proposes a method to account for joint constraints in the global discrete size optimization of a steel truss structure. The design of an N-type truss girder is considered first without and then with the joint constraints specified in the Eurocode. To guarantee global optimality in both cases, the optimization problem is reformulated as a mixed-integer linear program. A statically determinate analysis model is adopted so as to ensure that all joint constraints can be reformulated as linear functions. If the joint constraints are not considered in the optimization, a design is obtained where the joints need additional strengthening. This can be done by manually selecting heavier sections, which often leads to a suboptimal result, or by strengthening the joints (e.g., by means of stiffening plates), which has a serious effect on the fabrication cost. If the joint constraints are considered in the optimization, they are automatically satisfied by the final design. The weight of this design is about 15% higher than in the first case. This shows that the joint constraints have a significant effect on the optimal design. If the joint constraints are accounted for in a suboptimal way (e.g., by manually selecting heavier sections), the additional weight may be even higher. Taking into account joint constraints in the optimization leads to a cost reduction at two levels: in terms of engineering cost (no manual postprocessing step is needed) and fabrication cost (using unnecessarily heavy sections and joint strengthening are avoided). ispartof: JOURNAL OF STRUCTURAL ENGINEERING vol:142 issue:2 status: published

Steel moment frame (MF) is one of the most prevalent and well researched steel seismic force resisting systems worldwide. However, efficiency and feasibility of using MF diminishes for large spans. In this paper, a recently developed steel seismic force resisting system, named buckling-restrained knee-braced truss moment frame (BRKBTMF), is suggested as a better alternative system. The BRKBTMF uses buckling-restrained knee-braces with open web trusses. In this paper, a four-story prototype office building was designed using both MF and BRKBTMF systems. Performance of the prototype building with different span lengths was systematically studied. The results show that BRKBTMF uses less structural steel, yet it performs better with lower structural damage, repair costs, and probability of collapse as compared with the MF for all span lengths and under all earthquake intensities considered. Hence, it is concluded that BRKBTMF is a viable and effective alternative seismic force resisting system for lon...

In this paper, a new design approach for dissipative truss moment frames (DTMFs) able to guarantee, under seismic forces, the development of a yield mechanism of global type is presented and applied. In particular, DTMFs consist of a truss moment frame where the energy dissipation is provided by means of special devices located at the ends of the truss girders at the bottom chord level. The proposed design methodology is based on the kinematic theorem of plastic collapse. The method is based on the assumption that sections of truss elements and the yield threshold of dissipative parts (i.e., special devices) are known, and therefore the column sections are the unknowns of the design problem, which are obtained by imposing that the equilibrium curve corresponding to the global mechanism has to lie below those corresponding to all the possible mechanisms within a displacement range compatible with local ductility supply of dissipative elements. The design methodology has been implemented in a comput...

A high-performance wood-frame shear wall system, named the MIDPLY truss wall (MTW), was developed for application to midrise wood-frame buildings. The basic MTW system consists of metal-plate–connected wood trusses, sheathing panels, and steel tie-downs. The sheathing panels of the MTW system are placed between the wood trusses and connected with mechanical fasteners. The main concept of the MTW system is to increase the lateral load resistance of a shear wall by reconfiguring the wall frame members into lateral load–resisting wood trusses. In this study, the feasibility of the MTW system was investigated. Eight 2,440×2,440 mm MTW walls were constructed and tested under monotonic and cyclic loading in accordance with ASTM test standards. Shear stiffness, strength properties, and ductility of the MTW walls were evaluated and compared with those of comparable MIDPLY walls. Overall, the MTW system shows significant improvements in shear stiffness, yield load, peak load, and ductility. This paper cont...

The Shenzhen VANKE Center included both the required ground clearance to the first floor of 10–15 m as well as unsupported spans in excess of 50 m. The concept of building on cable-stayed bridges was finally selected. In this design, a system consisting of inclined prestressed cables and rigid composite floor systems is used to transfer the gravity loads from the superstructure to the tubes, walls, and columns. The simulation of the construction sequence of the cable prestressing and the structural behaviors are revealed. The innovative structural concept and design methods could be used as a reference. Long-span buildings are usually associated with specialpurpose structures (stadiums, airports, etc.), and the type of structural systems that consequently have evolved can be viewed as an extension of the concepts used in the construction of domes and arches. Until now, the conventional design of typical long-span office and mixed-use buildings has involved the use of transfer structures to support the main superstructure, such as in the incorporation of megatrusses, in which the height can exceed that of a single story. These transfer truss systems also provide additional lateral stiffness to the overall structure. The challenges posed by the architectural design of the Shenzhen VANKE Center included both the required ground clearance to the first floor of 10–15 m as well as that required for unsupported spans in excess of 50 m. Following a comparison of several structural schemes, the concept of building on cable-stayed bridges was finally selected. Moreover, after considering the architectural specifications and the requirements of the surrounding space, it was evident that anchoring cables could not be utilized in the proposed cable-stayed building scheme. Therefore, in this design, a system consisting of inclined prestressed cables and rigid composite floor systems was used to transfer the gravity loads from the superstructure to the tubes, walls, and columns. Four innovative concepts were introduced in the realization of the project: (1) techniques for preventing slack in the cables; (2) precise adjustment of prestressing forces in the cables; (3) self-balanced structural design and construction; and (4) control of lateral displacements during construction of the structure. The details of these concepts as well as the construction sequence of the cable prestressing and critical aspects of the structural system are presented in this paper.

Advancements in the nonlinear finite-element method have resulted in reliable simulations of response for reinforced concrete (RC) structures, provided that an analysis program with comprehensive models for material and structural behavior is employed. However, a need to provide simple, yet adaptive modeling guidelines for engineers and researchers using these tools exists, specifically for structures retrofitted with external materials for which bond behavior with the existing concrete surface is critical. Nonlinear analyses were conducted in this study to provide modeling procedures that can satisfactorily replicate the response of retrofitted RC shear walls. The retrofitting strategies included bolting of steel plates, bonding of external steel plates and fiber-reinforced polymer (FRP) sheets, and addition of steel plates with delay mechanisms. The modeling used simple rectangular and triangular membrane elements for concrete with smeared internal reinforcement, truss bar elements for external ...

Despite much experience that low-rise wood buildings are vulnerable to damage by extreme wind events, few such structures have been tested in fullsize to understand how they respond to wind loads as a whole system. This paper presents a study that measured internal force flows throughout the framing of a typical North American single-story structure with platform construction. Applied forces were concentrated horizontal loads normal to walls and patches of gravity loads on the sloped roof. Two series of load cells were embedded into the system, between the roof trusses and supporting walls and between the floor platform and the foundation. It was observed that even localized external forces have effects that propagate through the entire system. For instance, horizontal loads applied near eave level or to the roof were reacted at the top of the foundation around the entire wall perimeter of the building footprint, both parallel and transverse to the applied loading. For vertical loads, measurements showed ...

This article presents a numerical approach in which the implicit finite element method and fracture mechanics concepts are applied to simulate crack propagation at the interface of fire insulation and truss members in steel framed buildings. An intrinsic cohesive zone model (CZM) in conjunction with contact interaction analysis is applied to model the progression of fracture at the interface of fire insulation and slender steel truss members. Experimentally determined cohesive zone properties are utilized to simulate the progressive delamination in three types of commercially available spray-applied fire-resistive material (SFRM) applied on a truss chord. The numerical model, which is initially validated against the previously conducted fracture experiments, is employed to perform a sensitivity analysis with respect to CZM parameters, SFRM elastic modulus, and thickness of SFRM. Results obtained from a sensitivity study are subsequently utilized to define a delamination characteristic parameter (d...

Concrete-filled steel tubular (CFST) members have been used in various kinds of construction projects. They can be subjected to tension when they are used as chord members in trusses or subjected to combined tension and bending in building columns. However, to date research on the behavior of CFST members under eccentric tension is still limited. This paper thus presents both experimental and numerical investigations on the eccentrically loaded CFST tensile members. The experimental parameters include the eccentricity of the load and the steel ratio of the cross section. The failure modes show that the in-filled concrete works effectively with the steel tube, and the outer tube improves the crack pattern of the concrete. The finite-element (FE) model is also developed and validated by experimental results. The validated FE model is then used to assess the load and moment distributions as well as the load-moment interaction relationship. Finally, the load-carrying capacities of CFST members under e...

A structural analysis framework called the finite particle method (FPM) for structure failure simulation is presented in this paper. The traditional finite-element method is generated from continuum mechanics and the variational principle; vector mechanics form the basis of FPM. It discretizes the domain with finite particles whose motions are described by Newton’s second law. Instead of imposing a global equilibrium of the entire continuous system, FPM enforces equilibrium on each particle. Thus, particles are free to separate from one another, which is advantageous in the simulation of structural failure. One of the features of this approach is that no iterations to follow nonlinear laws are necessary, and no global matrices are formed or solved in this method. A convected material frame is used to evaluate the structure deformation and internal force. The explicit time integration is adopted to solve the equation of motion. To simulate the truss structure failure, a failure criterion on the basis of th...

This paper proposes a solution methodology for the application of the fixed-angle theory to predict the shear response of reinforced concrete (RC) beams subjected to the combined actions of shear and flexure. The proposed solution, based on the fixed-angle theory, takes into account the effect of flexural moment on the shear strength of RC beams and calculates the concrete constitutive relationships by transforming the concrete stresses and strains from the principal direction of concrete stresses to that of the applied stresses. To verify the effectiveness of the proposed solution method, seven shear-critical RC beams were tested and their corresponding experimental shear stress-strain relationships were compared with the predicted ones by using the proposed methodology. Furthermore, the shear strengths of 150 RC test beams, reported in the literature with various shear span-to-depth ratios, steel reinforcing ratios, and support conditions, were compared with the predicted shear strengths obtained by the proposed method and other existing truss models. The results presented in this paper show that the proposed formulation can predict the shear response of RC beams with reasonable accuracy.

The property of dynamic stress amplification resulting from the sudden failure of a tension member in a truss bridge is investigated by a precise dynamic response analysis. The primary sources of the dynamic stress amplification are from two types of impacts. The primary impact is attributable to longitudinal strain wave propagation from a failure point. The secondary impact is a result of the dynamic transition of equilibrium from a prefailure to a postfailure state. However, the effect of the primary impact is so small that it can be ignored in evaluating the impact coefficients used for the structural redundancy analysis. The impact coefficients for critical members in a structure take almost a constant value that ranges from 1.4 to 1.8, for which 5% structural damping is assumed, following the single degree of freedom model employed to evaluate the existing impact coefficient of 1.854. To avoid a cumbersome dynamic response analysis, the root mean square mode combination method is applied to calculate approximately the impact coefficients. The impact coefficients so calculated are moderately accurate for practical purposes.

In this paper, new schemes are presented for the dynamic relaxation DR method so that the snap-through and the snap-back regions can be traced automatically. These procedures are based on the minimization of the residual force MRF and minimization of the residual energy MRE, and they are capable of updating the load factor in each DR iteration. The suggested techniques are perfectly automatic. Therefore, they do not require any additional parameters such as arc length, incremental displacement, etc. For numerical verification, some frame and truss structures, all possessing geometrical nonlinear behaviors, are analyzed. Tracing the statical path shows that both the MRF and MRE methods can be used successfully in structures with snap-through and snap-back regions. The numerical results indicate that the MRE scheme traces the statical path with a greater number of increments than the MRF. While the jumping probability of the MRE is less than that of the MRF, the analysis time may increase in the MRE. Also, a comparison between the proposed DR methods and arc-length approach shows that the MRF and MRE procedures can present the limit points with higher accuracy.

The behavior and design of four-legged controlled rocking bridge steel truss piers to three components of seismic excitation are presented in this paper. The controlled rocking approach for seismic protection allows a pier to uplift from its base, limiting the force demands placed on the bridge pier and deck, and can allow the structure to remain elastic during an earthquake, preventing damage toward the goal of keeping the bridge operational immediately following the earthquake. Passive energy dissipation devices [steel yielding devices (SYDs) or fluid viscous dampers (VDs)] are used at the uplifting location to control pier response. The bidirectional kinematic and hysteretic cyclic behavior of controlled rocking piers with SYDs is presented and verified with nonlinear static pushover analysis. This fundamental behavior is used to develop design equations to predict peak pier displacements, uplifting displacements, and forces (frame shear and leg axial force). Dynamic response history analyses are performed, compared with the design equations, and shown to provide reasonably accurate results for design. The use of fluid VDs in the controlled rocking system is then discussed.

Shake table testing of a 1/5 scale model of a slender bridge steel truss pier that uses a controlled rocking approach as a means of seismic protection was conducted. The controlled rocking approach allows the pier to uplift from its base while passive energy dissipation devices (steel yielding devices or fluid viscous dampers) are implemented across the uplifting location to control the response. The fundamental static and dynamic bidirectional behavior of controlled rocking four-legged bridge piers has been developed and evaluated in past research. This paper discusses the experimental specimen's design, setup, and results of the testing. The testing program included the use of three sets of steel yielding devices and a set of fluid viscous dampers as the passive control devices. The specimens were subjected to ground motion records with increasing amplitude. The results of the testing were used to verify and further investigate the behavior of piers designed by the controlled rocking approach. Much of the fundamental behavior (self-centering, hysteretic behavior, and higher mode participation) are evident in the experimental results. Comparisons between the experimental results with design predictions and nonlinear time history analysis are made that show reasonable prediction of response.

Longitudinal elongation develops in reinforced concrete members that exhibit flexural yielding during cyclic loading. The longitudinal elongation can decrease the shear strength and deformation capacity of the members. In the present study, nonlinear truss model analysis was performed to study the elongation mechanism of reinforced concrete beams and the effects of various design variables on the elongation. The results showed that residual tensile plastic strain of the longitudinal reinforcement in the plastic hinge is the primary factor causing the member elongation and that the shear-force transfer mechanism of diagonal concrete struts has a substantial effect on the magnitude of the elongation. Based on the elongation mechanism found by truss model analysis, a simplified method for evaluating member elongation was developed. The proposed method was applied to test specimens with various design parameters and loading conditions.

This paper presents the results of an experimental study on the critical buckling load and lateral bracing force of metal plate connected wood truss assemblies. Material property tests—including th...