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This work presents a modified modal strain energy change (M-MSEC) method and its corresponding iteration process to detect damage to frame structures. Analytical results of a three-dimensional frame structure demonstrate that the quantity of damage can be identified correctly by using different modes in the M-MSEC method. A full-scale experimental study is also performed to evaluate the robustness of the M-MSEC method on damage detection as well as damage quantification. Satisfactory results are shown in relation to the modeling error, noise effect, and limited measurements. DOI: 10.1061/(ASCE)0733-9399(2008)134:11(1000) CE Database subject headings: Damage; Structural dynamics; Strain energy; Three-dimensional analysis; Framed structures.

Two altemative formulations based on the concept of simultaneous analysis and design are presented and evaluated for optimal design of framed structures. Different behavior variables, such as nodal displacements and member forces, are also treated as optimization variables in addition to the actual design variables for the problem. With these formulations, the equilibrium equations become equality constraints in the optimization process. The objective and all constraints become explicit functions of the optimization variables. Therefore, their derivatives can be obtained quite easily compared to those for the conventional approach where special design sensitivity analysis procedures must be used to calculate derivatives. It is also easier to use existing analysis software for optimization with the alternative formulations because the sensitivity equations are not formed or solved. A sequential quadratic programming method that exploits sparsity of problem functions is used to solve sample problems and evaluate the formulations. Implementation of the alternative formulations with an existing analysis program is explained. Advantages and disadvantages of the formulations are discussed. It is concluded that the alternative formulations work quite well for optimization of framed structures and have potential for further development. CE Database subject headings: Simulation; Optimization; Framed structures; Computer programming; Frames.

In a companion paper, a structural optimization computer program based on tabu search (TS) was developed and used to optimize three two-dimensional moment resisting frames. All three frames were representative of current design practice for steel structures in the Los Angeles area and were part of an SAC program of study following the Northridge earthquake. The weight reduction obtained for the three-story/three-bay, the nine-story/five-bay, and the twenty-story/five-bay frames in the initial study were 26.4, 18.3, and 25.5%, respectively. In this paper, the seismic performance of the optimized structures is evaluated by calculating the rotation demands in the plastic hinges that form in the structural elements during nonlinear time history analyses. Twenty ground motion records having the return probability of 10% in 50 years are considered in the study. The frames were expected to achieve the Life Safety performance level as outlined in the FEMA-273 guidelines, and in general, they were able to achieve this level of performance. Next, the same frames are optimized using the optimization module of a commercially available program, with the same assumptions (starting point sections, loading, etc.). The TS optimization program was able to achieve a larger weight reduction than the commercially available program. The performance of the final commercial program designs is then briefly evaluated by one nonlinear time history analysis for each building using the ground motion record that produced the most severe responses for the TS designs. Performance of these frames was very similar to the TS design frames. Finally, the performance of the three TS designed frames is compared to that of the original design frames, which were designed under the same code lateral forces. The original frame designs are analyzed for the ground motion record (or records) that resulted in the largest plastic hinge rotations in the TS design frames. The values of the maximum story plastic hinge rotations, story displacements, and interstory drift ratios are compared. The response of the TS optimized frames was comparable to the original frames. CE Database subject headings: Weight; Optimization; Seismic effects; Frames; Structural analysis.

A class of search techniques, heuristic search methods, and their suitability for structural optimization are considered for discrete optimization problems. The tabu search method is selected for application to structural weight optimization of skeleton structures. The search method is first tested to find the minima of a function in a nonlinear nonconvex optimization mathematical problem, and an algorithm is developed. Further, a computer program is developed that uses tabu search for weight minimization of two-dimensional framed structures. The program, written in the FORTRAN computer language, performs search, structural analysis, and structural design in an iterative procedure. The program is used to optimize the weight of three previously designed frames including three-story/three-bay, nine-story/five-bay, and 20-story/five-bay steel moment resisting frames. The program demonstrated its capability of optimizing the weight of these medium size frames in a reasonable amount of time without requiring engineer interference during the search. The structural weights for the three frames are reduced by an average of 23.4% from their original design weight. CE Database subject headings: Weight; Optimization; Seismic effects; Frames; Structural analysis.

A new method via inverse problem formulation including frame stability (P-[delta] and P-[DELTA] effects) is presented for state-specified design of an arbitrary planar elastic frame. The well-known governing equations for second-order analysis with respect to unknown displacements for a set of prescribed member stiffnesses of a frame are here regarded as those with respect to unknown member stiffnesses for a set of prescribed member-end strains and displacements. A method of sequential mapping for such a 'direct design' problem is generalized for a hybrid inverse problem of an arbitrary plane frame such that a combined set of unknown member stiffnesses and unknown member-end strains (or displacements) is to be found for a set of prescribed member-end strains (or displacements) and prescribed member stiffnesses. The concept of 'state-design vector' is shown to be useful for such a general problem of hybrid-inverse mapping. A general design program has been developed on the basis of the proposed algorithm on the first-order equations. Four design examples not only demonstrate the program performance but also disclose P-[delta] and P-[DELTA] effects on the design. A guideline is described for practical application in compliance with an allowable stress design code. DOI: 10.1061/(ASCE)0733-9445(2006) 132:9(1441) CE Database subject headings: Structural design; Stiffness; Frames; Structural stability; Buckling; Mapping; Computer programming.

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. DOI: 10.1061/(ASCE)0733-9445 (2006) 132:9(1334) CE Database subject headings: Steel beams; Seismic design; Cyclic loads; Slenderness ratio; Numerical analysis; Structural stability.

A beam element is presented for analysis of the elastoplastic large deflection of three-dimensional (3D) frames that have steel members with semirigid joints. A plastic hinge type formulation was employed, combining the 'modified incremental stiffness method,' the updated Lagrangian formulation, and numerical integration about the end sections of the element. The end sections of the element are discretized into small areas to estimate the plastic deformations of the element. The elastic and plastic deformations of the element are treated separately. The behavior of a semirigid joint is modeled as the element-end compliance. The method can treat comprehensively the plastic deformations due to torsion and warping. Considering the assumptions of the method, a four-element approximation for a member gives excellent results for a 3D analysis of semirigid and pin-connected steel frames as well as for rigid frames. The adequacy of the method is verified by comparing the results with experimental ones obtained by the writer. Some examples are presented to demonstrate the accuracy and efficiency of the method. DOI: 10.1061/(ASCE)0733-9445(2003)129:9(1259) CE Database subject headings: Steel frames; Elastoplasticity; Deflection; Joints; Plastic hinges; Warpage.

A method of analysis is presented to predict the behavior of prestressed concrete structures with internal or external tendons up to ultimate. The structure is modeled as an assemblage of plane frame members connected at nodes. The prestressing tendon is treated as a member with a small moment of inertia connected to the structural nodes with short arms. Because the centroidal axis changes with cracking and time-dependent effects, the nodes are located on an arbitrarily chosen axis called the reference axis. The analysis includes the effects of tension stiffening, and geometric and material nonlinearities. Any nonlinear stress-strain relationship for concrete and reinforcements can be applied. The analysis accounts for friction and slip of external tendons at deviators, variation of tendon eccentricity with applied load (geometric nonlinearity), and opening of joints in precast segmental construction. The computer program developed to perform the analysis method is verified using experiments on simple and continuous beams with internal or external tendons. DOI: 10.1061/(ASCE)0733-9445(2002)128:12(1493) CE Database keywords: Prestressing; Tendons; Computer models; Concrete structures.

A high degree of local bending was observed in the beam flange of a beam-to-column connection modeled with 3D finite-element analyses. The regions of high stress concentration were shown to occur at the weld access hole and the intersection of the bottom beam flange and column flange. The use of a specially designed part termed a 'stress diffuser' with a beam-to-column connection, in which the beam web and bottom beam flange are separated near the weld access hole, was found to eliminate the high stress concentration at the weld access hole and reduce the high degree of local bending in the beam flange by 49%. The maximum principal stress at 2.54 mm from the column face was reduced by 31%. CE Database keywords: Connections; Beams; Columns; Welds; Fractures; Frames; Seismic effects.

This work addressed two issues pertaining to the ultrasonic inspection of steel-moment-frame buildings that may have suffered damage as a result of the 1994 Northridge earthquake ground motion. These were: (1) Are the AWS D1.1 Code procedures reliable enough to detect flaws in the structural weldments of interest? and (2) Are there alternative Code-supplemental procedures that can be applied manually for not only improved flaw detection, but also flaw location, classification, and sizing? Twelve mockup specimens containing a total of 17 intentional worst-case-scenario flaws in representative beam-to-column weld geometries were fabricated. The Code-based detection results were marred by four misses and more than ten false alarms. In contrast, use of Code-supplemental procedures assured that no intentional test flaws were missed and false alarms were kept to a minimum. Only the Code-supplemental advanced procedures were used to characterize (as to type, location, orientation, depth, and length) a detected test flaw. In 95% of the measurements, the XYZ flaw location, length, and depth estimated were within 5 mm (0.2 in.) of the intended values. CE Database keywords: Welds; Inspection; Steel frames; California; Earthquake damage; Buildings.

This paper presents a statistical analysis of structural fragility curves. Both empirical and analytical fragility curves are considered. The empirical fragility curves are developed utilizing bridge damage data obtained from the 1995 Hyogo-ken Nanbu (Kobe) earthquake. The analytical fragility curves are constructed on the basis of the nonlinear dynamic analysis. Two-parameter lognormal distribution functions are used to represent the fragility curves with the parameters estimated by the maximum likelihood method. This paper also presents methods of testing the goodness of fit of the fragility curves and estimating the confidence intervals of the two parameters (median and log-standard deviation) of the distribution. An analytical interpretation of randomness and uncertainty associated with the median is provided.

Control of the seismic response of multistory building frames using optimally placed viscoelastic dampers (VEDs) is investigated. Responses are obtained in frequency domain using spectral analysis for narrow and broad band stationary random ground motions. Optimal locations of passive VEDs are found with the help of a controllability index, which is obtained with the help of the root-mean-square value of the interstory drift. To highlight the effect of modeling and optimal location of VEDs on the response reduction, three different mathematical models of the VEDs and three alternative schemes of placement of VEDs are considered. The response of the 20-story shear-frame model is controlled by the proposed strategy. It is shown that the scheme of the optimal placement of VEDs provides more reduction in response compared with other schemes of placement of VEDs considered in the study. Furthermore, the optimal placement of dampers is sensitive to the nature of excitation force, total quantity of viscoelastic material used, and the modeling of VEDs.

This paper presents an evaluation in terms of constructability, cost, and seismic performance of an alternative structural system for high seismic risk zones made of composite reinforced concrete-steel (RCS) special moment-resisting frames. Interior beam-column joints and the effects of a reinforced concrete slab on composite metal decking are investigated. The major issues discussed are related to seismic design philosophy and constructability of a three-dimensional RCS special moment frame system for low-rise and mid-rise construction. The key conclusion from this work is that the proposed RCS frame system has advantages over steel frame systems in high seismic risk zones in terms of having a cost-effective construction process and possessing certain stable hysteretic performance during inelastic excursions.

Local, modal, and overall damage indicators for reinforced concrete shear frames subject to seismic excitation are defined and studied. Each story of the shear frame is represented by a Clough and Johnston hysteretic oscillator with a degrading elastic fraction of the restoring force. The local maximum softening damage indicators are defined in a closed form based on the variation of the eigenfrequency of the local oscillators due to the local stiffness and strength deterioration. The modal maximum softening damage indicators are calculated from the variation of the eigenfrequencies of the structure during excitation. The linear and nonlinear parameters of the local oscillators are assumed to be known. Next, a statistical analysis is performed where a sample five-story shear frame is subject to sinusoidal and simulated earthquake excitations. The shear frame is subject to 30 independent simulations of the earthquake excitation, which is modeled as a stationary Gaussian stochastic process with the Kanai-Tajimi spectrum, multiplied by an envelope function. Equations of motion of the storys are solved by a Runge-Kutta fourth-order scheme, where the local softening value is recorded. The modal maximum softening indicators are calculated from the known instantaneous stiffness matrix, which is a function of the structural properties and local damage. Alternatively, a Fourier analysis is performed for consecutive time windows to measure the same evolution using the top story displacement. Finally, the relationship between local and modal damage indices are investigated statistically.

The dynamic properties of linear damping joints in traveling-wave formation are discussed. First, a traveling-wave model for frame structures is developed. The concept of the virtual member is then introduced to analyze the frame structure with complicated joints. The virtual member serves to convert the complicated joint into simple and rigid joints so that the existing model of traveling-wave can be used. Numerical examples for the frame structure are then presented as evidence.

The buckling of frames and composite columns were examined using the classical lamination theory. The models established considered the bending and axial rigidities as the only parameters influencing the post-buckling response and the critical buckling load. They were formulated from the characteristics of composite materials and may be used by manufacturers for customizing material properties for specific applications. It can also be used in approximate determination of postbuckling responses.

An analytical macromodel based on an equivalent strut approach integrated with a smooth hysteretic model is proposed for representing masonry infill panels in nonlinear analysis of frame structures. The hysteresis model uses degrading control parameters for stiffness and strength degradation and slip 'pinching' that can be implemented to replicate a wide range of hysteretic force-displacement behavior resulting from different design and geometry. The paper presents the development of the hysteretic model and the definitions of the control parameters, which can be determined using any suitable theoretical model for masonry infills. An available theoretical model for simplified engineering evaluation of masonry infilled frames was explored for estimating the control parameters of the proposed macromodel. The macromodel was incorporated in a nonlinear structural analysis program, IDARC2D Version 4.0, for quasi-static cyclic and dynamic analysis of masonry infilled frames. Simulations of experimental force-deformation behavior of prototype infill frame subassemblies are performed to validate the proposed model. A lightly reinforced concrete frame structure is analyzed for strong ground motions to evaluate the influence of masonry infill panels on the dynamic response.

The dissipative capacity of friction-damped bracing systems is evaluated by a statistical characterization of the amplitude and frequency of the slip excursions during a seismic excitation. One-story, friction-damped braced frames are subjected to artificially generated stationary accelerograms, which are compatible with the normalized elastic response spectrum proposed by Eurocode 8. The dynamic response of these frames is analyzed by a step-by-step procedure, which accounts for the variation in the structural parameters, identified by suitably modeling the force-displacement cycle of the dissipative bracing system. Approximate analytical expressions of the aforementioned quantities, characterizing the hysteretic behavior of the frame, are also deduced. These expressions are then utilized to define the range of optimal values of the global slip load leading to a high performance of the devices. The criterion adopted to model the force-displacement cycle of the friction-damped bracing system can be opportunely applied to bracing systems involving different dissipative mechanisms, such that the results obtained can be generalized. Moreover, a criterion of equivalence is proposed, which makes it possible to extend the conclusions of the study to multistory braced frames for which the structural parameters of the equivalent one-story system represent global parameters. Some practical applications pertaining to the case of an actual seismic accelerogram show the validity of the design suggestions proposed.

This research examines the behavior of a large full-scale scaffold frame shoring subjected to pattern loads with various load paths. In this test program, sand bags were placed on the top of the scaffold frame shoring to simulate the weight of fresh concrete during construction. The routes of placing sand bags are based on the paths of placing fresh concrete in actual construction sites. The test results show that the axial tube forces of scaffolds just below the location of a newly placed sand bag increase sharply. In addition, the axial tube forces do not change significantly when sand bags are placed at other positions on formwork during the load path. It is shown that the effect of influence surfaces on the scaffold frame shoring is not apparent during the placing of sand bags. In addition, the maximum axial tube force of a scaffold subjected to different load paths is very close to the maximum axial tube force of this specific scaffold after the completion of the loading path. Thus, a typical uniform load as used for an applied concrete load in design can replace the actual fresh concrete pattern load during construction. Both lateral forces acted at the top of a scaffold frame shoring and the sidesway of scaffolds are small during tests. The regions of some larger axial forces in the scaffold frame shoring vary in different load paths.

In this paper we consider the problem of regulation of a flexible lumped parameter beam. The controller is an active/passive mass-spring-dashpot mechanism which is free to slide along the beam. In this problem the plant/controller equations are coupled and nonlinear, and the linearized equations of the system have two uncontrollable modes associated with a pair of pure imaginary eigenvalues. As a result, linear control techniques as well as most conventional nonlinear control techniques can not be applied. In earlier studies Golnaraghi (1991) and Golnaraghi et al. (1994) a control strategy based on internal resonance was developed to transfer the oscillatory energy from the beam to the slider, where it was dissipated through controller damping. Although these studies provided very good understanding of the control strategy, the analytical method was based on perturbation techniques and had many limitations. Most of the work was based on numerical techniques and trial and error. In this paper we use center manifold theory to address the shortcomings of the previous studies, and extend the work to a more general control law. The technique is based on reducing the dimension of system and simplifying the nonlinearities using center manifold and normal forms techniques, respectively. The simplified equations are used to investigate the stability and to develop a relation for the optimal controller/plant natural frequencies at which the maximum transfer of energy occurs. One of the main contributions of this work is the elimination of the trial and error and inclusion of damping in the optimal frequency relationship.

Periodic interior buckling of regular multistory and multibay rectangular elastic frames with elastic bracing is analyzed. It is shown that there exists a certain critical bracing stiffness for which the critical loads for the nonsway (symmetric) and sway (antisymmetric) buckling modes coincide. Simple formulae for the critical stiffness are given. For the critical and softer bracing, the type of postcritical buckling behavior is the unstable symmetric bifurcation, exhibiting imperfection sensitivity according to Koiter's 2/3-power law. For stiffer bracing, there is no imperfection sensitivity. The critical bracing, however, represents a naive optimal design which should be avoided because the imperfection sensitivity is the strongest. It is recommended that the truly optimal bracing should be significantly stiffer (perhaps 1.1 to 2 times as stiff). The buckling behavior, including the postcritical imperfection sensitivity, is similar to that of a portal frame analyzed before. The solution also provides a demonstration of a simple method for the initial postcritical analysis of frames recently proposed by Bazant and Cedolin, which is based on energy minimization. In this method, the distribution of cross section rotations is assumed to be the same as in the classical linearized theory. The curvatures and deflections are obtained from the rotations by integration with at least a second-order accuracy (in terms of the rotations), and the axial shortening with at least a fourth-order accuracy.

In current engineering practice, to evaluate the stability of columns in frames with rigid and semirigid connections, one must estimate the effective length factor (K-factor) of columns considering the effects of the nonlinear moment-rotation characteristics of beam-to-column connections. Herein, using the alignment chart approach and based on a recent study on the stability of semirigid frames and the concept of Shanley's inelastic column buckling theory, the governing equations on the K-factor of columns for various boundary conditions with rigid and semirigid beam-to-column connections are derived for unbraced frames. With a proper evaluation of the tangent connection stiffness for semirigid beam-to-column connections at buckling state and with the introduction of the modified relative stiffness factors, the alignment chart in the present American Institute of Steel Construction-load and resistance factor design specification can be applied to find the corresponding column K-factor in semirigid frames. This is described in the present paper. Furthermore, using a semirigid and unbraced portal frame example, the effects of the nonlinear moment-rotation characteristics of connections on the K-factor are numerically studied and the K-factors obtained by two simplified methods are also compared with the present method.

Smart structure with build-in sensor(s) and actuator(s) that can actively and adaptively change its physical geometry and properties has been considered one of the best candidates in vibration control applications. Implementation of neural networks to system identification and vibration suppression of a smart structure is conducted in this paper. Three neural networks are developed, one for system identification, the second for on-line state estimation, and the third for vibration suppression. It is shown both in analysis and in experiment that these neural networks can identify, estimate, and suppress the vibration of a composite structure by the embedded piezoelectric sensor and actuator. The controller is also shown to be robust to system parameter variations.

A balanced approach to shaping the closed-loop properties of the dissipative controllers for flexible structures is presented. In the balanced representation the properties of flexible structures are introduced, and a simple method of designing of the dissipative controllers is obtained. It relates the controller gains with the closed-loop pole locations. The examples illustrate the accuracy of the design method.

The paper describes beam elements with inelastic hinges capable of modeling softening due to damage in building frames under severe loadings. A condition for uniqueness on the element level is derived, and the behavior of the model is compared to analytical solutions of simple structures (a single column and a portal frame). An application to postpeak analysis of a multibay frame is presented. Depending on the beam-to-column stiffness ratio and on a certain ductility parameter, various failure modes can occur, ranging from distributed to highly localized ones. This leads to a special type of size effect on the peak load, which is assessed numerically and related to analytically derived solutions valid in extreme situations - the elastic limit and the plastic limit.

A consistent finite-element formulation is presented in order to analyze the spatial stability of shear deformable thin-walled space frames and circular arches. The displacement field of unsymmetric thin-walled cross sections is introduced based on the inclusion of second-order terms of Rodriguez's finite rotations, and the potential energy corresponding to the semitangential moments is consistently derived. For finite-element analysis, cubic Hermitian polynomials including shear deformation effects due to flexural and restrained warping shear stress are utilized as shape functions. Load correction stiffness matrices for the different types of moments and off-axis loadings are taken into account. For spatial buckling behaviors of space frames and circular arches, finite-element solutions using the two-noded straight frame element are presented and compared with the analytical solutions and the results in the literature.

This paper presents a new formulation for the large-displacement analysis of thin-walled frames taking into account the effects of elastoplastic material behavior. The proposed formulation is derived in an Eulerian (convected) local system which allows relatively simple strain-displacement relationships to be used. Furthermore, the formulation uses the fiber approach for representing the spread of plasticity over a general open cross section, and is capable of modeling initial imperfections, residual stresses, and the Wagner effect. In accounting for material plasticity effects, consideration is given to the interaction between normal stresses and shear stresses due to twisting. Since the shear strain is directly related to the rate of twist, the shear stress in the yield function is replaced by an equivalent contribution to the cross-sectional torque, which leads to considerable computational advantages. This paper describes the formulation details and the implementation of material plasticity effects for kinematic and isotropic strain hardening, whereas the companion paper provides a number of verification and application examples.

The companion paper presents a new Eulerian formulation for the large-displacement analysis of thin-walled frames, accounting for the elastoplastic material response. This paper aims at verifying the proposed formulation and providing several examples of its application to thin-walled members and frames. In this regard, it is demonstrated that such a relatively simple formulation enables the accurate modeling of initial imperfections, residual stresses, the Wagner effect, the beam-column effect, lateral-torsional instability, and large displacements using a small number of elements and a coarse cross-sectional discretization. Moreover, it is shown that the formulation can be used in the assessment of the ultimate and postultimate response of thin-walled structures for which the design codes are either inaccurate or inapplicable. Such structures include continuous beams, simply supported beams with intermediate lateral restraints, as well as frames for which the ultimate limit state involves considerable interaction between the structural members.

This specification and supporting commentary cover the design of simply supported composite joists and trusses used in one-way floor systems. Basic design procedures are based on achieving nominal flexural strength before shear failure or local instability occur. The specification considers strength, serviceability, and construction criteria. A design example is included.

This is the first of two papers addressing the efficient and simultaneously accurate analysis of reinforced concrete frames through the use of adaptive nonlinear analysis techniques. The present paper discusses the requirements of adaptive analysis and highlights the essential need for a beam-column formulation that accurately models the behavior of reinforced concrete members in the range where the response can be considered elastic and fully recoverable A new elastic formulation is therefore proposed for reinforced concrete beam-columns; it assumes a quartic shape function for the transverse displacements and differs from conventional finite-element formulations in the use of the constant-axial-force criterion. The quartic formulation is capable o modeling a typical reinforced concrete member of arbitrary cross-sectional shap and reinforcement layout with only one element, including the effects of concrete tensile cracking, the nonlinear compressive response of concrete, and the beam-column action. Verification examples using the nonlinear analysis program ADAPTIC demonstrate the accuracy of the proposed formulation and its ability to model an entire reinforced concrete member using one element.

This is the second of two papers concerned with the application of adaptive techniques to the nonlinear analysis of reinforced concrete frames. The first paper presented a new nonlinear elastic formulation capable of representing an entire reinforced concrete member with one element, and the present paper discusses the use of such a formulation within the framework of adaptive inelastic analysis. This is followed by a description of an inelastic cubic formulation based on the layered approach, which complements the elastic formulation within the proposed methodology. The concept of automatic mesh refinement is then outlined, and comments are made regarding the applicability of the elastic formulation under low amplitude dynamic or cyclic loading. Finally, the accuracy find efficiency of adaptive analysis is verified through static and dynamic analyses using the nonlinear analysis program ADAPTIC. Comparisons are made where appropriate with the results of existing analysis methods for reinforced concrete frames to illustrate the advantages of the proposed methodology.

A beam-column element with springs connected in series is presented for efficient and effective geometric and material nonlinear analysis of steel frames with semirigid connections. When incorporated into a computer program fo non-linear analysis of steel framed structures, the effects of semirigid connections and material yielding can be accounted for in a simple and direct manner. Proposed mathematical models for various joint types and assumed patterns for material yielding can also be simulated independently, while the combined effect can be included in the analysis automatically. The obvious and direct method of adding the connection and plastic springs to the clement matri and to condense out the internal or dummy degrees of freedom for the final element matrix is also discussed in this paper and noted to be computationally infeasible due to the finite accuracy in computer analysis and the odd values o very large and small stiffness encountered during an ultimate analysis. This paper proposes an efficient and simple method to trace the equilibrium path of steel frames, allowing for geometrical, material, and joint stiffness nonlinearities up to the ultimate load. The benchmarked problem (Vogel's six-story frame) is analyzed and extended to include the effects of semirigid connections, which is new and is recommended to be used for validation of computer programs for this type of analysis.

The paper describes a method of inelastic analysis for steel frames that provides the accuracy of distributed plasticity methods with the computational efficiency of elastic-plastic-hinge methods. It accounts for spread-of-plasticity effects without the need for through-section and lengthwise discretization of a beam-column element. This is accomplished through nonlinear equations for the force-strain relationships of the cross section that are calibrated to data from inelastic analyses and numerical integration of the cross-section model along the element length to obtain inelastic flexibility coefficients for the member. The flexibility coefficients are employed in generating an inelastic stiffness matrix in which geometric nonlinearity is also accounted for. The proposed model has been implemented and tested using several example problems known to be sensitive to spreading-plasticity effects.

The computational models used for compression members in the nonlinear analysis of space trusses are classified by decreasing order of computational effort into finite-segment, finite-difference, and single-member solutions. The common assumptions and derivations used with single-member solutions are reviewed. A chronological review of the models is given indicating the contributions each has made. Single-member solutions can often give results similar to those that use more computationally demanding methods. However, the success of a model at correlating with experimental behavior depends on the assumptions made. Single-member solutions that include partial plasticity appear more accurate than those that assume full plasticity at midlength. It is observed that consideration also needs to be given to the relationship between the member and the structure to which the member is attached. Thus, internal snap-through or dynamic jump can occur in the postbuckling regime of compression members in a relatively compliant adjacent structure.

This paper investigates theoretically the effect of bolt slippage on the deflection and ultimate-strength responses of lattice structures. For the purpose of this study, two idealized bolt-slippage models are presented. The effect of bolt slippage was incorporated into the previously developed nonlinear finite element computer program, AK TOWER, by Al-Bermani and Kitipornchai, in 1992. Two lattice structures are used to study the influence of bolt slippage. Results of this study illustrate that while the slippage of bolts may have some effect on deflection, it does not significantly influence the ultimate strength of lattice structures.

An equivalent frame approach is presented for nonlinear seismic analysis of reinforced-concrete flat plate buildings. The approach employs a parametric hysteretic model and is based on the effective slab-width concept. Unlike in the previous equivalent frame approaches, the proposed method targets both the moment-transfer capacity as well as stiffness of the interior and exterior slab-column connections. The hysteretic parameters and the effective slab width factors are determined from results of laboratory tests on slab-column connections for the class of flat plate buildings constructed prior to the 1960s with reinforcing detail typical of gravity load design. The validity of the approach is justified by comparing the calculated and the measured responses of two-bay flat plate subassemblies tested under earthquake-type loading. With the proposed equivalent frame approach, the response of flat plate buildings for seismic loading could be predicted more realistically over a wide range of lateral drift levels.

The stability behavior of rigid and semirigid frames bent in the weak axis is investigated using a hardening plastic hinge method. The stability limit load of frames is usually overpredicted by the simple plastic hinge analysis neglecting the effect of partial plastification. The plastic zone analysis can predict the limit load more accurately but a large number of elements must be used. Hence, it is costly and time-consuming. An alternative method called the 'hardening plastic hinge method' is developed here for practical use. In the proposed method, one element is used per beam-column. The initial yield surface including residual stress is first determined from the normalized moment-curvature-thrust relationship of W8 X 31 section. The member stiffness is then modified to simulate the effect of partial plastification through the concept of work-hardening in which the average degradation of tangent stiffness of a cross section is calibrated against the slopes of the exact moment-curvature-thrust relationship. The stability limit loads of planar steel frames predicted by this and several other methods are compared. The results predicted by the hardening-hinge method are found close to that of the plasticzone method and experimental results.

The analysis of parasitic shear in the wide-column-frame analogy encounters difficulties in simulating vertical joints between adjacent wall panels by means of discrete connections at the nodes. The vertical forces at the nodes are a combination of forces associated with the bending moment of the wall panel. They are also the result of shear stresses distributed continuously along the wall joints. The addition of two new degrees of freedom associated with the longitudinal displacement will resolve the the two sources of the vertical forces.

A pointwise equilibrating polynomial (PEP) element is proposed for nonlinear analysis of frames in which each member can be modeled by one element in most cases. The formulation of the element is based on the imposition of compatibility conditions at end nodes as well as the satisfaction of equilibrium at mid-span. The resulting expression for this new element is accurate in describing the force-versus-displacement relations at the element level, is simple, and it does not lead to a significant numerical truncating error in the computer analysis. Its implementation in a nonlinear analysis program is straightforward. The accuracy of the analysis results by the element was found to be considerably higher than its cubic counterpart in a number of well-known examples. The limitation or inconvenience of the method of stability function such as the separation of the solution for tensile, compressive, and zero load cases is eliminated.

This paper investigates the behavior and performance of open-web truss-moment framing system under cyclic loading. An open-web truss-moment frame of a four-story building was designed as an ordinary moment resisting frame (OMRF) for this investigation. Three full-scale, half-span subassemblages from this building were tested under severe cyclic deformation to determine their hysteretic behavior. Based on the experimental results, a simple analytical model for inelastic cyclic behavior of open web truss frames was developed. This model was used to analytically evaluate the behavior and performance of the four-story building subjected to several severe earthquake excitations. The system performs poorly because of buckling and fracture of the web members, which led to unstable hysteretic loops.

The descending part of the hysteretic load-deformation history of a structure with softening behavior discloses important structural properties such as strength, ductility, residual deformation, hysteresis loop shape, and energy-dissipation capacity, especially under earthquake conditions. In the present paper, a finite-element algorithm for hysteresis analysis of bonded and unbonded prestressed-concrete frames subjected to arbitrary loading history including postultimate descending portion is put forward. One-dimensional constitutive models for concrete, tendon, and reinforcing steel are proposed. The crack-contact effect is included in the constitutive model for concrete. A bond-slip relation between tendon and grout is suggested. A method for implementing the bond-slip relation into the element in which tendons are embedded is also put forward. Being of self-correcting incremental type, the algorithm incorporates both increment-force and increment-displacement procedures whose transition from one into the other is automatically performed according to the variations of the hysteresis curve. The results of laboratory tests of three prestressed-concrete frames are reported. Comparison of computed results with experimental ones shows good agreement.

A formulation for modeling links in eccentrically braced steel frames (EBFs) subjected to random inelastic cyclic loading is presented. The formulation is plasticity-based, and includes shear and flexural yielding. In addition, combined isotropic and kinematic shear strain-hardening effects are accounted for, as well as flexural strain hardening. The formulation is shown to accurately predict the behavior of test specimens involving short links. Inelastic seismic analysis of EBFs with short links was conducted to illustrate the effect of link-modeling assumptions on EBF response. The analysis results show that link strain hardening can have a pronounced effect on EBF response, leading to larger member forces in braces and columns attached to the links. Furthermore, combined flexural and shear yielding occurred in the links adjacent to columns, indicating the need to include these types of inelastic deformations in the link-modeling formulation. Finally, the use in the analysis of viscous damping in the link was found to cause excessive axial forces to develop in braces and columns adjacent to yielded links. To reduce this effect, a form of nonproportional viscous damping is illustrated.

An optimal-control algorithm with acceleration, velocity, and displacement feedback is proposed. The algorithm, which is derived by minimizing a quadratic time-dependent performance index, includes constant control gains that need to be calculated once in the beginning of the control process. Numerical results indicate that for base-isolated structures, the utilization of acceleration feedback in the control scheme performs as well as the previously proposed algorithm that includes only velocity-displacement feedback. In the case of non-base-isolated structures, the new scheme demonstrates a better performance. Due to difficulties present in measuring the displacement of a system, inclusion of the acceleration feedback in the control algorithm increases its practical value for possible implementations.

The mechanics behind the geometrical imperfections of sway frames are analyzed. Results show that leaning columns are not capable of holding lateral loads, therefore the out-of-straightness effect must be derived for all leaning columns. Since moments of all columns in a story are never equal in the real world, the moment magnification factors must be derived by taking into account the stiffness factor and load-carrying capacity.