Journal of Structural Engineering

Current practice for the design of steel beam-columns (i.e., members under combined axial load and bending) subject to fire is to calculate the capacity of these members assuming a uniform temperature distribution through the depth of the section. This assumption may be acceptable for some members, but there are cases where the member will be heated nonuniformly, thereby developing a thermal gradient through its depth. This paper analyzes the effects of thermal gradients on the combined axial load $\left(P\right)$ -moment $\left(M\right)$ yield capacity of beam-columns and compares the yield capacity of members with temperature gradients to those with uniform temperature profiles. The prototype beam-columns used in this study are wide-flange (WF) steel sections that are part of a high-rise moment-resisting steel building. This study evaluates the effects of plate thickness, section depth, and the direction of bending (i.e., strong versus weak axis) on the plastic $P\text{-}M$ interaction diagram of WF sections with thermal gradients. Results show that a thermal gradient may have a significant effect on the yield capacity of beam-columns, and evaluations that are made assuming a uniform temperature through the section may lead to overestimations or underestimations of the true strength of the section.

The properties of special concentrically braced frames (SCBFs) enable them to be designed to meet performance-based seismic design (PBSD) criteria. SCBFs have large stiffness and strength to meet serviceability performance states. Life-safety and collapse-prevention PBSD limit states are controlled by inelastic postbuckling and tensile yield deformation of the brace. In SCBF construction, the braces are connected to the frame using gusset plates. Inelastic deformation of the brace places severe inelastic demands on gusset-plate connections. To improve the understanding and design of the seismic performance of SCBF connections, a coordinated analytical and experimental research study was undertaken. This paper describes the analytical component and includes a brief description of the experimental results, which were used in the development and validation of the model. The validated model was used to evaluate the inelastic performance of structural elements and to determine the frame ductility and concentration of plastic strains at potential locations of member or weld tearing or fracture. Detailed comparisons between experimental observations and computed results show that the analyses provided good correlation to actual behavior. The results were used to develop a methodology to predict tearing or cracking of key elements in the frame.

Current design practices use a strength-based design approach to design gusset plate connections in special concentrically braced frames (SCBFs), in which the expected tensile and compressive capacities of the brace are used to design the gusset plate and the weld used to connect the brace to the frame. To achieve brace end rotation, the gusset plate is sized using a linear offset rule, and large, uneconomical gusset plate connections may result. A research program was undertaken to improve the economy and performance of gusset plate connections. A new approach is proposed in which the gusset plate design is based on a balanced design approach in which the yield mechanisms of the brace are balanced with the yield mechanisms of the connection and the failure modes of the system to achieve a target yielding hierarchy and suppress unwanted failure modes. Full-scale one-story, one-bay frames were designed and tested to investigate the seismic performance of current and proposed design methods. In the test program, variations in balance factors between the brace, gusset plate, and weld were considered to study the proposed method, to evaluate possible yield mechanisms and failure modes, and to obtain the desired yielding hierarchy. Comparison of the observed and measured performance of each specimen is made and specific design expressions to improve the seismic engineering of SCBF systems are proposed.

I-shaped steel girders with tubular flanges have been studied for application in highway bridges because of their large lateral torsional buckling (LTB) strength relative to conventional I-shaped steel plate girders. This paper discusses the LTB strength of tubular flange girders, focusing on concrete-filled tubular flange girders (CFTFGs) where the concrete-filled tube is the compression flange. Using finite-element (FE) models of CFTFGs, a parametric study was conducted to investigate the influence of girder geometry and material strength on the LTB strength. Design flexural strength formulas, considering LTB, for construction conditions and for ultimate strength in the final constructed condition, were developed based on the results of the parametric study. These formulas estimate the LTB strength of CFTFGs that are perfectly braced laterally and torsionally at brace points. A similar FE study of conventional I-girders was conducted and the results are compared with those of CFTFGs.

This study investigates the effect of base plate flexibility on the behavior and fatigue performance of welded socket connections commonly used in sign support structures. The results of a three specimen static load testing program, extensive finite-element analysis, and parametric study are discussed. Results clearly show that base plate flexibility, primarily base plate thickness, has a major influence on the stress distribution in the tube wall adjacent to the welded socket connection. Currently, AASHTO gives no specific guidance on the design of the base plates for sign support structures that explicitly address flexibility. Increasing base plate thickness is shown to be a very effective method to improve the fatigue resistance of this detail. Based on this trend, a simple procedure that incorporates the influence of base plate flexibility into the infinite life, nominal stress approach to fatigue design is proposed.

Most codes of practice, such as EC2 and ACI 318-05, recommend the use of strut-and-tie models for the design of reinforced concrete deep beams. However, studies on the validity of the strut-and-tie models for continuous deep beams are rare. This paper evaluates the strut-and-tie model specified by ACI 318-05 and mechanism analysis of the plasticity theory in predicting the load capacity of 75 reinforced concrete continuous deep beams tested in the literature. The influence of such main parameters as compressive strength of concrete, shear span-to-overall depth ratio, main longitudinal bottom reinforcement, and shear reinforcement on the load capacity is also investigated using both methods and experimental results. Experimental results were closer to the predictions obtained from the mechanism analysis than the strut-and-tie model. The strut-and-tie model highly overestimated the load capacity of continuous deep beams without shear reinforcement.

The combined effects of creep and shrinkage of concrete and relaxation of prestressing tendons cause gradual changes in the internal forces and deflections of composite beams. However, most of the research work conducted on prestressed steel–concrete composite beams has focused on short-term behavior; research findings on the long-term behavior are scarce in the literature. For the wide-scale use of prestressed composite beams in civil engineering applications, the long-term behavior must be investigated. This paper presents an experimental program designed to examine the long-term behavior of prestressed composite beams under sustained load conditions for one year. The test program consisted of two prestressed composite beams and one nonprestressed composite beam. On the basis of the age-adjusted effective modulus method and energy principle, the creep stiffness matrix and the creep force matrix of prestressed composite beams were developed. A time-dependent analytical model is presented to predict the long-term behavior of prestressed composite beams. Close agreement is observed between the analytical and experimental results. It is proposed that the Multiplier 3.1 of the instantaneous deflection be used to calculate the deflection of prestressed composite beams for one year.

Accurate estimation of stress in unbonded tendons at the nominal strength limit state is essential for calculating the in-plane flexural strength of posttensioned masonry walls. These walls gain their lateral strength and desirable seismic properties through the utilization of vertical unbonded posttensioning. Unlike walls with bonded tendons where the tendon stress can be found through strain compatibility with the surrounding masonry, the stress in unbonded tendons results from wall deformation between the two tendon anchorages. International masonry codes, including ASCE 5-05 (Masonry Standards Joint Committee), provide varying equations for calculating tendon stress at the nominal strength limit state but in no case have these equations been verified for in-plane loading. A finite-element model validated against large-scale in-plane structural testing of posttensioned concrete masonry walls is used to demonstrate the accuracy of existing code equations. A revised equation is then shown to provide a more accurate prediction of tendon stress for walls loaded in-plane and is recommended for inclusion in future masonry code revisions.

Adequate shear strength between the web(s) and the flange(s) in flanged masonry shear walls is essential for the wall to provide the required stiffness and strength. In this regard, an experimental investigation was conducted to study the behavior of flanged concrete block walls. The study focused on investigating different specimen configurations to study the shear transfer mechanism between wall flanges and webs. Seven preliminary specimens with different configurations and different flange-web connections were tested in order to choose the most appropriate specimen configuration for the main set of 15 specimens. The ultimate capacity, deformation characteristics, and crack propagation were investigated. In addition, proposed analytical models based on shear-friction failure mechanism were compared with the experimental results and showed good agreement.

This paper presents the results of testing stone masonry wallettes in compression or in diagonal compression. The specimens that simulate a portion of perimeter walls of historic structures are made of three-leaf rubble stone masonry; they are horizontally reinforced with timber ties. Tests have proven that timber ties contribute to substantial enhancement of the ultimate strain of masonry subjected to compression, accompanied by reduction of the opening of vertical cracks. When timber reinforced masonry is subjected to diagonal compression, the cracking load is several times higher than that of the unreinforced masonry, whereas large diagonal cracks may open without disintegration of masonry. The experimental results are in accordance with in situ observations in historic structures.

New implicit higher-order accuracy (IHOA) time integration, which uses constant time step, is presented for dynamic analysis. By defining weighted factors, current displacement and velocity are assumed to be functions of the accelerations in the several previous time steps. Then, the optimum weighted factors are determined so that displacement and velocity errors in the Taylor series are minimized. The IHOA is conditionally stable and by using the Routh–Hurwitz criterion, permissible time step is obtained. For numerical verification of the proposed technique, some linear and nonlinear dynamic systems from finite element and finite difference will be analyzed and the results are compared with common implicit methods such as Newmark- $\beta$ and Wilson- $\theta$ approach. Further, the dynamic relaxation method is applied to solve equivalent static systems, obtained in implicit algorithms. Results show that the proposed time integration is stable for common time steps and exhibits improved accuracy. The highly accurate, unique procedures for all dynamic problems and automatic operations are the main merits of the new method.

Frame finite-element models permit obtaining, at moderate computational cost, significant information on the dynamic response behavior of steel–concrete composite (SCC) frame structures. As an extension of conventional monolithic beam models, composite beams with deformable shear connection were specifically introduced and adopted for the analysis of SCC beams, in which the flexible shear connection allows development of partial composite action influencing structural deformation and distribution of stresses. The use of beams with deformable shear connection in the analysis of frame structures raises very specific modeling issues, such as the characterization of the cyclic behavior of the deformable shear connection and the assembly of composite beam elements with conventional beam–column elements. In addition, the effects on the dynamic response of SCC frame structures of various factors, such as the shear connection boundary conditions and the mass distribution between the two components of the composite beam, are still not clear and deserve more investigation. The object of this paper is to provide deeper insight into the natural vibration properties and nonlinear seismic response behavior of SCC frame structures and how they are influenced by various modeling assumptions. For this purpose, a materially nonlinear-only finite-element formulation is used for static and dynamic response analyses of steel–concrete frame structures using composite beam elements with deformable shear connection. Realistic uniaxial cyclic constitutive laws are adopted for the steel and concrete materials of the beams and columns and for the shear connection. The resulting finite-element model for a benchmark problem is validated using experimental test results from the literature for quasi-static cyclic tests. The paper then focuses on the numerical simulation, based on various modeling assumptions, of the eigenproperties and seismic response of a realistic two-dimensional five-story two-bay moment resisting frame made of steel columns and SCC beams and designed according to the Eurocode. It is found that the inclusion of the deformability of the shear connection in the finite-element model has a significant effect on the global dynamic response of SCC frame structures. In modeling this type of structures by using frame elements with deformable shear connection, a proper representation of the shear connection boundary conditions for all composite beams is crucial for accurate response simulation.

In order to evaluate the structures’ behavior accurately, a suitable mathematical algorithm and a set of appropriate assumptions concerning the structures’ behavior must be adopted. The more accurate the algorithm and the assumptions adopted the more real behavior of the structures is determined. In the case of nonlinear analysis, the evaluation process is complex and cost effective. Therefore, for this aim, the researchers have presented simple relationships ignoring the effect of several factors. In the proposed method, in the case of nonlinear analysis, linear analysis is directly used first, and then by implementing simple or advanced iterative methods convergence is achieved in the equilibrium path. Using these methods, after passing limit points, the structure behavior is defined and so accurate design of the structure is possible. In the present study, for passing the equilibrium path of the space trusses, the Newton–Raphson iterative algorithm is used along the flow path perpendicular to the Davidenko curves with modified convergence rate. Contrary to the previous methods, this algorithm uses the homotopy approach, is based upon the new mathematical concepts, and has great ability for developing complex load-displacement paths of the structures with multidegrees of freedom. At the end, through three numerical examples, three structures have been analyzed using the algorithm presented in this paper and the results are compared with the previous advanced iterative methods that have been used for nonlinear analysis of those structures. The ability of the proposed method, particularly for passing the limit points, has been indicated by those numerical examples.

This paper describes a set of dynamic field tests performed on the Alfred Zampa Memorial Bridge (AZMB), also known as the New Carquinez Bridge, which is located $32\mathrm{km}$ northeast of San Francisco on interstate Highway I-80. The AZMB, opened to traffic in November 2003, is the first suspension bridge in the United States with an orthotropic steel deck, reinforced concrete towers, and large-diameter drilled shaft foundations. The dynamic field tests described herein were conducted just before the bridge opening to traffic. They included ambient vibration tests, mainly wind induced, and forced vibration tests based on controlled traffic loads and vehicle-induced impact loads. Four different controlled traffic load patterns and seven different vehicle-induced impact load configurations were used in the forced vibration tests. The dynamic response of the bridge was measured through an array of 34 uniaxial and 10 triaxial force-balanced accelerometers deployed along the whole length of the bridge. These dynamic field tests provided a unique opportunity to determine the dynamic (modal) properties of the bridge in its as-built (baseline) condition with no previous traffic loads or seismic excitation. Such properties could be used to validate and/or update the finite element models used in the design phase of this bridge. They could also be used as baseline for future health monitoring studies of this bridge. At the end of the paper, the ambient vibration test data were used to identify the bridge modal parameters (natural frequencies, damping ratios, and mode shapes) using the data-driven stochastic subspace identification method.

This study presents an investigation of the performance of subspace techniques for modal identification using ambient vibration measurements. Several models and structures characterized by increasing degrees of complexity are investigated to assess the potential benefits of stochastic subspace identification algorithms, and the difficulties that might be experienced during a modal identification analysis. The case studies include a simple three-degree-of-freedom (3 DOF) mass-spring-dashpot model, the 120 DOF finite element model, as well as the physical laboratory model of a small scale steel frame, and a long span suspension bridge. Stabilization diagram and clustering analysis approaches are adopted for spurious mode rejection, and the latter is found to be promising for automating the mode selection process. The experiences with experimental data reveal that some preconditioning tools are quite helpful in order to properly focus on the structural modes of interest, and that preconditioning improves the performance of the subspace methods. On the whole, the approaches investigated in this study are found to perform quite satisfactorily for operational modal analysis of engineering structures.

Seismic code provisions in several countries have recently adopted the new concept of performance-based design. New analysis procedures have been developed to estimate seismic demands for performance evaluation. Most of these procedures are based on simple material models though, and do not take into account degradation effects, a major factor influencing structural behavior under earthquake excitations. More importantly, most of these models cannot predict collapse of structures under seismic loads. This study presents a newly developed model that incorporates degradation effects into seismic analysis of structures. A new energy-based approach is used to define several types of degradation effects. The model also permits collapse prediction of structures under seismic excitations. The model was used to conduct extensive statistical dynamic analysis of different structural systems subjected to a large ensemble of recent earthquake records. The results were used to propose approximate methods for estimating maximum inelastic displacements of degrading systems for use in performance-based seismic code provisions. The findings provide necessary information for the design evaluation phase of a performance-based earthquake design process, and could be used for evaluation and modification of existing seismic codes of practice.

An experimental study was conducted to investigate whether existing industry design procedures for tight-fitting metal plate connector truss joints can be applied to the design of joints made with round-end webs. Four joint configurations were tested with a range of connector-plate sizes: 45° with web in tension, 45–45° with one web in compression and the other in tension, 45–90° with the 45° web in compression and the 90° web in tension, and 45° with the web under compression. In total, 87 tight-fitting and 171 round-end joints were tested. As expected the tight-fitting joints were stronger and stiffer than round-end joints. Both the shear strength of the metal plate connector and the teeth pullout strength were smaller in the round-end joints than in the tight-fitting joints. The line contacts between the round-end webs in compression produced greater crushing of the wood, causing buckling of the connector plates, and reducing the ultimate loads on these joints. Design guidelines are suggested for round-end joints.

Concrete-filled steel tubes (CFTs) have recently been used for columns and bridge piers, especially in seismic regions, for their enhanced strength and ductility over the conventional steel and concrete construction. This enhancement is due to the composite actions of the concrete infill and the steel tube: The concrete compressive strength is significantly increased by the lateral confinement provided by the steel; and local buckling of the steel tube is delayed by the concrete infill. Similar enhancement has also been observed in flexural strength of CFT. A novel concept of posttensioning the concrete core inside circular steel tubes to further enhance the synergistic interactions has been developed, and numerical analyses have shown significant increase in their flexural strength over nonprestressed CFT. A numerical algorithm has been developed for predicting the moment capacities of circular CFT. The increased concrete strength and ductility due to confinement were taken into account. The analytical predictions compared well with flexural test data. The validated algorithm was further developed to include the posttensioning effects. Numerical results suggest that moment capacity of a CFT can be significantly increased by prestressing the concrete core with only moderate posttensioning forces.

A structural damage detection method based on the change of strain energy in each element before and after the occurrence of damage is presented. The proposed method can localize and quantify both single and multiple damages. The algorithm requires only the stiffness and mass matrices of the baseline structure and a few measured mode shapes of the current structure to find the location and severity of damage. The proposed method is applied to a benchmark problem sponsored by the IASC-ASCE Task Group on Structural Health Monitoring, which was developed in order to facilitate the comparison of various damage identification methods.