Plastic Hinge Location Research Articles

Inelastic deformation and failure of partially strengthened profiled blast walls

Blast walls that separate the potentially hazardous regions of the topside on an offshore platform were designed to resist lower loads than those envisaged today thus it is desirable to upgrade their blast resistance in a cost-effective and non-intrusive manner. One proposal is to retrofit the existing blast walls partially with centrally located composite patches. This study presents an assessment tool, which provides understanding of the effect of a composite patch on the blast resistance of blast walls. Numerical simulations of a proposed retrofitted wall are performed to gain insight into the failure progression of the wall ab initio. Damage in the composite patch was considered, and the numerical simulations showed that fiber fracture did not occur thus there was no significant loss of in-plane stiffness and strength. Based on these observations, the rapid assessment tool, analytically formulated to incorporate the effect of the composite patch which strengthens the wall and moves the plastic hinge locations away from the wall centre to the composite-steel edge, is deemed a suitable tool. The assessment tool and the numerical simulations are partially validated by the experimental results. The tool runs quickly and provides reasonable accurate predictions for the deformation response of the walls.

Seismic Evaluation of the ACI Code Provisions for Lap Splicing of Longitudinal Bars in R/C Rectangular Bridge Columns

In this study, the adequacy of the ACI code provisions for detailing of lap-spliced reinforcement in R/C rectangular bridge columns was numerically investigated. Pushover analysis was conducted on a total of 324 R/C rectangular bridge columns with lap-spliced reinforcement, using a modified version of previously developed computer program. The computer modeling is based on moment–curvature analysis of the column section with the inclusion of a bond/slip mechanism and concrete confinement model. In this study, the program was revised to integrate the effectiveness of lateral hoop reinforcement on both concrete confinement and lap-splice clamping. Constant axial load was applied in the analysis. The parameters involved in the study were lap-splice length, volumetric ratio of column hoops, and axial load ratio. The results indicate that the top lateral load–displacement characteristics of the column are enhanced when the lap-splice length at the column base increased. To ensure a minimum displacement ductility of 4.0 for the column, lap splices as short as 30φb (φb = longitudinal bar-diameter) should be avoided at expected plastic hinge locations. The best performance for a wide range of axial load ratios was exhibited by columns having the ACI’s classes A and B tension splices and laterally reinforced with hoops required by the ACI code for seismic design.

Curvature assessment of reinforced concrete beams using photogrammetric techniques

Innovative procedures have been proposed recently for monitoring laboratory tests using photogrammetry and image processing. In spite of the growing interest, most existing research is still highly focused on the theoretical development of the procedures, being experimental tests only performed for validation. This manuscript aims at providing a practical demonstration of the advantages of using these new techniques in laboratory tests up to failure. In this scope, focus is given to the assessment of the curvature of reinforced concrete beams, since this parameter is crucial for characterising the structural response both in service conditions and in ultimate limit states. In conclusion, it can be stated that these new techniques can be used in combination with, or even as a replacement of, more traditional methods (such as LVDTs and DEMECs), monitoring a significantly higher number of points and without placement restrictions. The limitation is mostly related to the strain precision that is not adequate for monitoring serviceability conditions. Nevertheless, the curvature can be assessed in short time intervals and lengths, respectively of few seconds and centimetres, independently of the presence of cracks and the plastic hinge location, in this case circumventing several of the drawbacks presented by traditional methods.

Inelastic deformation and failure of partially strengthened profiled blast walls

An integral part of a typical offshore module is the surrounding profiled blast walls that separate the potentially hazardous regions of the topside. Many of the blast walls in operation were designed to resist lower loads than those envisaged today [1] rendering them currently non-functional, thus it is desirable to upgrade their blast resistance in a cost-effective and non-intrusive manner. One proposal is to retrofit the existing blast walls partially with centrally located composite patches. This study presents the development of a rapid assessment tool which provides understanding of the effect of a composite patch on the blast resistance of profiled blast walls. The tool is based and is an improvement upon a previous analytical formulation for unstrengthened walls with realistic connection systems [2]. Numerical simulations of a proposed retrofitted wall are performed to gain insight into the failure progression of the wall. Damage in the composite patch is modelled using the Hashin damage model, and the numerical simulations showed that fibre fracture did not occur and that the small amounts of matrix failure occurring at the composite patch edges did not result in significant loss of in-plane stiffness and strength. Based on these observations the rapid assessment tool, analytically formulated to incorporate the effect of the composite patch which strengthens the wall and moves the plastic hinge locations away from the wall centre to the composite-steel edge, is deemed a suitable tool. The assessment tool and the numerical simulations are partially validated by the experimental results presented in [1] for unstrengthened blast walls. The tool runs quickly and provides reasonable predictions for the deformation response of the walls, and enables the user to quickly assess the effect of adding a composite patch. It allows for multiple deformation modes in the panels and the development of plastic hinges at the composite-steel edges and the wall connections, providing a significant advantage over conventional single-degree-of-freedom models. The numerical simulations and the rapid assessment tool give reasonable agreement for different loading regimes, given the anticipated use of the analytical approach.

Life‐cycle cost assessment of RC and ECC frames using structural optimization

SUMMARYIn this study life‐cycle cost (LCC) assessment of structural frames is performed. Two different materials, reinforced concrete (RC) and reinforced engineered cementitious composites (ECC), with different response characteristics are used to model the frames. ECC is characterized by high tensile ductility and energy absorption and reduced crack widths when compared to conventional concrete. However, the material is more expensive than conventional concrete; therefore, in order to quantify the potential benefits that could be obtained by replacing concrete with ECC, the life‐cycle performance is evaluated in an optimization framework. Three different structural frames are considered: an RC only frame, an ECC only frame and a multi‐material (MX) frame in which ECC is selectively applied at the potential plastic hinge locations while the remainder of the frame is made of RC. The structural capacity and earthquake demand are evaluated using rigorous analysis methods to capitalize on different characteristics of concrete and ECC, and both aleatory and epistemic uncertainties are incorporated into the LCC formulation. It is found that both the initial and LCC of frames that use ECC are lower due to savings in material and labor cost of transverse reinforcement for the former and due to increased capacity and reduced demand for the latter. Copyright © 2012 John Wiley & Sons, Ltd.

A Finite Element Model for the Prediction of the Behavior of an Unstiffened Top and Seat Angle Connection with Various Top Angle Bolt Gage Distances

This study aimed at proposing a finite element model for predicting the initial rotational stiffness and plastic moment capacity of the Type A top and seat angle connection without double web angles. The main parameter of the 3D nonlinear finite element analysis was the bolt gage distance of the top angle. The finite element analysis resulted not only in the rotational stiffness and the plastic moment capacity, but also in the stress distribution and the plastic hinge location. The study verified the applicability of the finite element model by comparing the results of the finite element analysis with those of existing experimental studies.

Practical Section Design Method of Widened Beam Flange Connections

By the method of the experiment and the finite element, the production, development regulation and location of the plastic hinge of widened beam flange connections were studied. The test results showed good agreement with FEM results and proved the finite analysis reliable. The test specimens were designed as the base samples. By choosing some different main references relating to section shape change of widened beam flange connections, a series of finite element specimens which include eighteen direct arc widened beam flange connection and eighteen welded side-plate widened beam flange connections were derived from the base samples. The influence of widened beam flange depth, length and distance on plastic hinge distribution is discussed respectively, at the same time, the plastic hinge location range was given and practical section design method of widened beam flange connection is provided by revising the parameter of plastic hinge center location ls.

Using genetic algorithm for the optimization of seismic behavior of steel planar frames with semi-rigid connections

Beam-column connections have a significant role in the results of the analysis and the design of steel frames. In this paper, a genetic algorithm has been used for the non-linear analysis and design of steel frames. For minimizing the weight of frames, while satisfying the applied constraints and restraints such as the limits of normal and combined stresses, criteria such as target displacement(s) and the number and locations of plastic hinges were used. To analyze and design the frame elements, I and box-shaped standard sections were used for beams and columns, respectively. Finally, some clues for finding optimizing semi-rigid connection stiffness values for beam-to-column connections have been obtained. The degrees of these rigidities are obtained by a genetic algorithm during the procedure of optimization in order to reach a frame with the minimum weight. SAP2000 structural analysis program was used to perform modal analysis and linear and non-linear static solutions as well as the design of the elements. A MATLAB program was written for the process of optimization. The procedure of optimization was based on a weight minimization carried out for 9 steel frames. Thus, the optimum connection stiffness could be obtained for minimizing the weight of the structure. The results show that the non-linear analysis gives less weight for short period frames with semi-rigid connections compared to those of linear ones. However, by increasing the periods of frames, much less weights are obtained in the case of non-linear analysis with semi-rigid connections.

A Second-Order Inelastic Analysis of Plane Steel Frames Using a Work-Increment-Control Solution Technique

A refined plastic hinge analysis method, known as one of the most effective and practical second-order inelastic analysis methods for steel frames, is able to evaluate the ultimate structural behavior of steel frames by considering the geometric and material nonlinearities. However, an appropriate advanced nonlinear solution technique has to be incorporated to help structural engineers perform the rational design of steel frames by predicting the ultimate strength and post-failure structural behavior accurately. In this study, a refined plastic hinge analysis method, combined with a work-increment-control solution technique with an iterative procedure in incremental loading steps, was presented in order to overcome the shortcomings of the load-increment-control solution techniques employed in previous studies. In the work-increment-control solution technique of present study, one convergence criterion refining the problem of using two convergence criteria in the conventional increment/iteration procedure of work-increment-control solution techniques and an automatic incremental algorithm calculating the load factor and the magnitude of incremental work for next incremental loading step were employed. To verify the accuracy and appropriateness of the present approach, three representative plane steel frames employed in previous studies were analyzed, and the analysis results were compared with those by other approaches. The present approach, that evaluated fairly accurately the load-displacement relationships, ultimate loads, plastic hinge numbers and locations, and the post-critical responses up to the formation of collapse mechanism of the plane steel frames, proved to be acceptable.

Plastic hinge locations in steel columns

Some standards for the design of steel structures attempt to encourage column yielding at the member ends, rather than along the column length during inelastic action such as may occur during strong earthquake shaking. In this paper, effects of residual stress and stability are considered separately and then combined to obtain equations that are more simple and more accurate than those in current standards.

Application of direct displacement based design to long span bridges

The paper investigates the applicability of current direct displacement based seismic design (DDBD) procedure, developed by Priestley and his coworkers, for straight long span bridges under transverse seismic excitation synchronous to all supports. This category of bridges often possess some additional features such as massive tall piers, highly irregular distribution of mass and stiffness due to unequal superstructure spans and pier heights, large deformation capacity etc. that are absent in short-to-moderate span bridges for which DDBD has extensively been verified. It is shown that DDBD in its current form is unable to capture both displacement and base shear demand when compared with nonlinear dynamic analysis results. Accordingly, a simple mechanics based extension of the current procedure that takes into account the effect of pier mass while computing base shear demand as well as a modal combination rule for estimating displacement demand is proposed and validated using a series of parametric studies. The new procedure also allows engineer to allocate strength at the potential plastic hinge location in more general terms.

Seismic assessment of steel frames with the endurance time method

In the endurance time (ET) method, structures are subjected to a specially designed intensifying ground acceleration function and their performance is judged based on their response at various excitation levels. A range of equivalent intensities can be covered in a single numerical or experimental simulation, thus significantly reducing the computational demand as compared to full nonlinear response-history analyses. The applied excitation intensity at various times has been correlated with those of the scaled ground motions. Response spectra of seven ground motions on stiff soil were used to produce intensifying acceleration functions that at each time window produce a response spectrum that is compatible with the template spectrum and proportionally scale up with time. The drift ratios and plastic hinge rotations compare well with those from ground motions in steel frames with various numbers of stories and bays. The locations of plastic hinges are also predicted quite satisfactorily by ET analysis. The sensitivity of the results to the selection of a particular set of ground motions is also studied.

Strength of Super-Structure UN-ECE R66 Rollover Approval of Coaches based on Thin-Walled Framework Structures

Around 30,000 bus or coach occupants are injured every year in the European Union (EU).The prime objective of this paper is to describe Cranfield Impact Centre’s (CIC’s) structural crashworthiness approach for coach rollover certification process as defined by the United Nations-Economic Commission for Europe (UN-ECE) Regulation R66 [1].CIC was instrumental in the formulation of UN-ECE Regulation R66, the first ever “virtual testing approach” approved by the UK Government, for coach rollover approval.The virtual testing approach is based on the concept of thin-walled framework structures through Finite Element (FE) modelling.It is supported by a series of static and dynamic tests of the floor, waist and roof cant-rail joints. The main reasons for component testing importance in determining the bus and coach super-structure collapse responses are twofold – Firstly, to provide a calculation model with elasto-plastic stiffness data for all the possible plastic hinge locations (recorded as moment/rotation data for each joint) and secondly, to assess the structural integrity of the super-structure joints under quasi-static and dynamic loadings.The R66 regulation has been adopted by EU member states, together with Australia, South Africa and India, in a modified form, to improve the occupant safety by providing a safe zone within the vehicle during rollover [1 and 3].The methodology adopted to develop the rollover coach models is based on extending the problem from a quasi-static approach to a more complex dynamic situation that includes the influence of super-structure to ground interactions.

Strength of Super-Structure UN-ECE R66 Rollover Approval of Coaches based on Thin-Walled Framework Structures

Around 30,000 bus or coach occupants are injured every year in the European Union (EU).The prime objective of this paper is to describe Cranfield Impact Centre’s (CIC’s) structural crashworthiness approach for coach rollover certification process as defined by the United Nations-Economic Commission for Europe (UN-ECE) Regulation R66 [1].CIC was instrumental in the formulation of UN-ECE Regulation R66, the first ever “virtual testing approach” approved by the UK Government, for coach rollover approval.The virtual testing approach is based on the concept of thin-walled framework structures through Finite Element (FE) modelling.It is supported by a series of static and dynamic tests of the floor, waist and roof cant-rail joints. The main reasons for component testing importance in determining the bus and coach super-structure collapse responses are twofold – Firstly, to provide a calculation model with elasto-plastic stiffness data for all the possible plastic hinge locations (recorded as moment/rotation data for each joint) and secondly, to assess the structural integrity of the super-structure joints under quasi-static and dynamic loadings.The R66 regulation has been adopted by EU member states, together with Australia, South Africa and India, in a modified form, to improve the occupant safety by providing a safe zone within the vehicle during rollover [1 and 3].The methodology adopted to develop the rollover coach models is based on extending the problem from a quasi-static approach to a more complex dynamic situation that includes the influence of super-structure to ground interactions.

Plastic-hinge approach for inelastic analysis of steel–concrete framed structures

This paper presents an application of a computational tool, denoted as SAAFE Program, developed to provide a nonlinear inelastic analysis of steel and composite (steel–concrete) 2D framed structures. This procedure allows an accurate description of the structural nonlinear response, with less computational effort when compared to the general FEM formulation. The method, although similar in concept to earlier plastic-hinge approaches, differs with regard to numerical implementation methodology and precision. The proposed plastic-hinge model is formulated in a succinct format based on the following characteristics: (i) stiffness parameter η , evaluated as a function of the yielding progress at each plastic-hinge location; (ii) effective tangent modulus E t concept which reduces the modulus of elasticity in the element stiffness calculation, considering both the residual stress and out-of-straightness effects; (iii) second-order formulation, based on an incremental stiffness approach in which conventional stability functions are used to reflect the effect (on member stiffness) of axial loads on displacements, allowing accurate identification of member instability. Verification examples are analysed by the proposed approach, in which results are compared with those of FEM numerical and available experimental data, showing good agreement. Based on the obtained results, it is possible to infer about the efficiency and robustness of the proposed model to perform inelastic analysis for isolated and full frame members, incorporating geometric and material nonlinearity.

Nonlinear dynamic analysis of frames with plastic hinges at arbitrary locations

AbstractThis paper presents a method for nonlinear dynamic analysis of frames subjected to distributed loads, which is based on the semi‐rigid technique and moving node strategy. The plastic hinge is modelled as a pseudo‐semi‐rigid connection with nonlinear hysteretic moment–curvature characteristics at element ends. The stiffness matrix with material and geometric nonlinearities is expressed as a sum of products of the standard and geometric stiffness matrices with their corresponding correction matrices based on the plasticity‐factors developed from the section flexural stiffness at the plastic hinge locations. Each beam member is modelled by two elements. The moving node strategy is applied to the intermediate node to track the exact location of any intermediate plastic hinge that may be formed. Equilibrium iterations and geometry updating are carried out in every time step. Stiffness degradation is adopted to describe the deterioration of plastic hinges, and the effects of various parameters in the degradation model are evaluated. Examples are used to illustrate the applicability and excellent performance of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.

Global RC Structural Damage Index Based on the Assessment of Local Material Damage

This study presents a computational method to estimate a damage index of a RC construction. The method is based on the evaluation of local damage combined with an analysis of the probable collapse mechanism of the structure. A constitutive model for reinforced concrete, including damage variables for concrete and steel elasto-plastic models, is integrated in a multilayered finite element code. The locations of pseudo plastic hinges in a structure are obtained in the areas of maximal damage through simulation by the FE method. The index is derived from a specific formula taking into account the damage recorded in the critical zones of the structure (pseudo plastic hinges) and the damage computed in the less damaged areas. The proposed method is validated on a RC frame structure application. The diagram global index vs. loading shows a specific shape and gives interesting results for the discussion of the possibility of reparation.

Structural resistance of longitudinal double plates-to-RHS connections

The purpose of the study reported herein is to investigate the behavior of longitudinal double plates-to-RHS connections in a T-configuration. A total of seven specimens (5 for double-plate type, 2 for single-plate type) were tested under compression. The main experimental parameters were the width ratio of the branch plate to the chord ( β ) and the type (or number) of branch plates. Test results showed that the value of β and thereby the strength of the double-plate type specimens increased due to the space between the plates. Furthermore, a combined failure of chord flange yielding and chord web buckling, which was not generally observed in longitudinal single plate-to-RHS connections, was observed in one of the double-plate specimens. A yield line analysis was also performed for different locations of plastic hinges, considering the corner radius of the HSS chord, as well as the welds for the plates. The strengths based on the proposed yield line model showed good agreement with the experimental results when the plastic hinges were assumed to be located at the web of the HSS chord adjacent to the corner radius, and at the toe of the welds.

Response of laterally loaded group shafts for bridge foundations in cohesionless soils using a 3D FE soil-structure model

The lateral stiffness of bridge foundations has a major effect on its response to lateral loads. Response values such as maximum moments, maximum displacements, and plastic hinge location below ground need to be accurately predicted for a safe and sound design. Many approaches have been used to model foundation lateral stiffness such as the Winkler beam (spring models) and the concept of length of fixity to simplify the design. This paper discusses the response of laterally loaded group shafts using three-dimensional finite element (FE) soil–structure models for single shaft–soil system and group shaft–soil system in cohesionless soils. Parameters investigated include soil modulus, shaft slenderness, shaft–soil interface, soil effective zone, shear interaction, and support conditions at the bottom of the shaft. Results from this investigation provide criteria for the effective volume of soil that needs to be included in the FE analysis for single and group shaft analysis. It also showed that shaft spacing...

DYNAMIC ANALYSIS OF FRAMES WITH MATERIAL AND GEOMETRIC NONLINEARITIES BASED ON THE SEMIRIGID TECHNIQUE

This paper presents a method for nonlinear dynamic analysis of frames with material and geometric nonlinearities which is based on the semirigid technique. The plastic hinge that accounts for the material nonlinearity is modeled as a pseudo-semirigid connection with nonlinear hysteretic moment-curvature characteristics at the element ends. The stiffness matrix of a frame element with material and geometric nonlinearities is expressed as the sum of products of the standard stiffness matrix and the geometric stiffness matrix of the element, with their corresponding correction matrices based on the plasticity factors developed from the section flexural stiffness at the plastic hinge locations. The combined stress yield condition is used for the force state determination of plastic hinges, and force equilibrium iterations and geometry updating for frames are carried out in every time step. When the key parameters of a structure are updated in a time step, the time step is split up into substeps to ensure accuracy while keeping the computations to a reasonable amount. The plastic rotation history can be calculated directly or in an approximate indirect way. The method is computationally efficient and it needs no additional connection elements, which makes it convenient for incorporation into existing linear dynamic analysis programs. Besides, the method can handle accurately and efficiently the dynamic analysis of nonlinear frames using relatively large time steps in conjunction with time step subdivision to cope with key parameter changes. A portal frame is used to verify the correctness of the proposed method. A more complicated five-story frame is used to illustrate the applicability and performance of the proposed method.