Theory Of Plastic Mechanism Control Research Articles

A review: plastic analysis in structures

Purpose Brief introduction on the importance and the need for plastic analysis methods were presented in the beginning section of this review. The plastic method for analysis was considered to be the more advanced method of analysis because of its ability to represent the true behaviour of the steel structures. Then in the following section, a literature analysis has been carried out on the previous investigations done on steel plates, steel beams and steel frames by other authors. The behaviour of them under different types of loading were presented and are under the investigation of innovative new analysis methods. Design/methodology/approach Structure member connections also have the potential for plastic failure. In this study, the authors have highlighted a few topics to be discussed. The three topics in this study are T-end plate connections to a square hollow section, semi-rigid connections and cold-formed steel storage racks with spine bracings using speed-lock connections. Connection is one of the important parts of a structure that ensures the integrity of the structure. Finally, in this technical paper, the authors introduce some topics related to seismic action. Application of the Theory of Plastic Mechanism Control in seismic design is studied in the beginning. At the end, its in-depth application for moment resisting frames-eccentrically braced frames dual systems is investigated. Findings When this study involves the design of a plastic structure, the design criteria must involve the ultimate load rather than the yield stress. As the steel behaves in the plastic range, it means the capacity of the steel has reached the ultimate load. Ultimate load design and load factor design are the methods in the range of plastic analysis. After the steel capacity has reached beyond the yield stress, it fulfills the requirement in this method. The plastic analysis method offers a consistent and logical approach to structural analysis. It provides an economical solution in terms of steel weight, as the sections designed using this method are smaller compared with elastic design methods. Originality/value The plastic method is the primary approach used in the analysis and design of statically indeterminate frame structures.

Probabilistic design procedure for steel moment resisting frames equipped with FREEDAM connections

In this work, the Theory of Plastic Mechanism Control (TPMC) is combined with a probabilistic method to account for the influence of random material variability. Reference is made to steel Moment Resisting Frames (MRFs) equipped with FREEDAM connections. FREEDAM connections are beam-to-column connections equipped with friction dampers to dissipate the seismic input energy. TPMC is used to guarantee that in case of destructive seismic events the structural members such as beams and columns remain undamaged. To this scope, the structure is designed to assure a collapse mechanism characterized by the activation of all the friction dampers of the beam ends and the formation of plastic hinges at the base of the first storey columns only. From the probabilistic point of view, the random uncertainties are given by the static friction coefficient of the contact surfaces and the preloading of the bolts of the friction dampers as well as the yielding resistance of the steel members. The failure domain is related to all the possible failure events, where the term “failure” concerns the development of an undesired mechanism different from the global one. Generally, the design conditions to prevent undesired collapse mechanisms are stochastic events within the framework of the kinematic theorem of plastic collapse. The limit state function corresponding to each event can be represented by a hyperplane in the space of random variables. Consequently, the failure domain is a surface resulting from the intersection of the hyperplanes corresponding to the limit states of each single failure event. Since dissipative zones (member ends or friction dampers) in the frame members are common to many different mechanisms, the single limit state functions are correlated. Therefore, the probability of failure can be evaluated by means of the Bimodal or Ditlevsen bounds by assuming that the failure events are located in series. The output of the work is a simple relationship which provides the overstrength factor of FREEDAM connections to be considered in the column design phase to account for random material variability thus assuring a given level of reliability in the application of TPMC.

Design procedure for failure mode control of linked column frames

This paper investigates the seismic behaviour linked column frames (LCFs). This structural system, traditionally, consists of moment frames for the gravity loads and dual columns interconnected with bolted links for the horizontal actions. An optimized design approach is herein developed for the LCFs according to the Theory of Plastic Mechanism Control (TPMC) through a closed form solution assuring the maximum energy dissipation, i.e., the development of a collapse mechanism of global type. Several structural schemes are designed according to the proposed design approach considering different geometry, link length and structural height. The accuracy of the TPMC is evaluated through nonlinear static and dynamic analyses. In particular, the dynamic analyses are developed for a selection of designed fames to highlight the difference in terms of performances among the structures with short, long and intermediate links.

Theory of Plastic Mechanism Control for Linked Column Frames

AbstractThe main purpose of this work is to define a design procedure for dissipative replaceable link frames (LCFs). These structural schemes are characterized by the columns connected with link elements representing the plastic zones of the structure and, consequently, they assure the maximum dissipation of seismic energy in input. The design rules, proposed in this paper, are based on the Theory of Plastic Mechanism Control (TPMC). This procedure is based on the extension of the kinematic theorem of limit analysis to the concept of the equilibrium curves of the failure mechanisms and it guarantees the achievement of the global collapse mechanism under severe seismic actions. In order to evaluate the accuracy of this procedure, a case study is presented. In particular, a LCF with four storeys and three bays is designed by means of the proposed design rules. Finally, the same steel frame is implemented in SAP2000 program, and a pushover analysis is performed to evaluate the ultimate behaviour of the modelled structure.

Design and seismic evaluation of MRFs in DC2 ductility class introduced in the new prEN1998 draft and comparison with TPMC

This work aims to analyse and evaluate the design rules proposed for DC2 ductility class in the new prEN1998 by means the design and assessment of MRFs with different height and length of the spans. DC2 is a medium ductility class, introduced in the new prEN1998 draft for a more economical design, so simplified design rules are proposed for avoiding only the so-called soft storey mechanism. The purpose of the work is the evaluation of the effectiveness of the proposed rules and the comparison with a more theoretically compliant design rules developed in the framework of the Theory of Plastic Mechanism Control (TPMC) adapted to be used according to the DC2 philosophy. A wide parametric analysis is developed on different structural schemes and the performance evaluation is made through pushover and IDA analyses. It can be pointed out that the soft storey mitigation criteria for the DC2 ductility class is not able to satisfy the design condition. Conversely, the approach based on the TPMC is able to assure the design goal.

Theory of plastic mechanism control: A new approach for the optimization of seismic resistant steel frames

AbstractThis paper presents an important improvement in seismic design of structures based on the application of the Theory of Plastic Mechanism Control (TPMC). TPMC was originally proposed in the ‘90s requiring an iterative algorithm and upgraded in 2015 leading to the so‐called closed form solution. In the recent years, TPMC has shown its value as an effective design procedure which can be applied to any structural typology. Moreover, it has been used as a code competitor design tool in important RFCS founded research projects confirming its effectiveness, simplicity, and suitability to any structural typology. The aim of the TPMC is the design of structures able to exhibit at collapse a global type mechanism. The TPMC was originally based on the extension of the kinematic theorem of plastic collapse to the concept of mechanism equilibrium curve, working in the plane (being α the multiplier of the seismic forces and δ the top sway displacement). The novelty of this work is improvement of the design procedure by working in the plane, being θ the plastic rotation. This new TPMC approach, namely TPMC(θ), has demonstrated to be as reliable as the former approach, thus leading to structures able to develop a collapse mechanism of global type but with the optimization of the structure using lighter columns. The effectiveness of the new procedure has been confirmed by both pushover and dynamic non‐linear analyses.

Simplified Approach for the Seismic Assessment of Existing X Shaped CBFs: Examples and Numerical Applications

The capacity of a structure can be assessed using inelastic analyses, requiring sophisticated numerical procedures such as pushover and incremental dynamic analyses. A simplified method for the evaluation of the seismic performance of steel Concentrically Braced Frames (CBFs) to be used in everyday practice and the immediate aftermath of an earthquake has been recently proposed. This method evaluates the capacity of an existing building employing an analytical trilinear model without resorting to any non-linear analysis. The proposed methodology has been set up through a large parametric analysis, carried out on 420 frames designed according to three different approaches: the first one is the Theory of Plastic Mechanism Control (TPMC), ensuring the design of structures showing global collapse mechanisms (GCBFs), the second one is based on the Eurocode 8 design requirements (SCBFs), and the third is a non-seismic design, based on a non-seismic design (OCBFs). In this paper, some examples of the application of this simplified methodology are proposed with references to structures that are supposed to exhibit global, partial, and soft storey mechanisms.

Performance-based rules for the simplified assessment of steel CBFs

In this work, a simplified method for the evaluation of the seismic performance of steel Concentrically Braced Frames (CBFs) in everyday practice is presented. This method, applicable in the immediacy of a seismic event and for quick mapping of the seismic vulnerability of a built area is fully analytical, allowing the representation of the capacity curve of a structure through a trilinear approximation and considering the second order-effects. To set the methodology, extensive parametric analysis is performed on 420 simple CBFs designed according to 3 different approaches namely the Theory of Plastic Mechanism Control ensuring the design of structures characterized by global collapse mechanism (Global Concentrically Braced Frames (GCBFs), the Eurocode 8 provisions (Special Concentrically Braced Frames (SCBFs)) and the design for seismic forces only (Ordinary Concentrically Braced Frames (OCBFs)) without any hierarchy criterion. The capacity-demand checking procedure according to the code-compliant approach and Nassar & Krawinkler is also reported.

A Simplified Approach for Seismic Performances Estimation for Steel Moment Resisting Frames

AbstractSeismic events in recent years have underlined the need to quickly classify the built heritage in terms of seismic performances. The capacity of a structure can be assessed by means of inelastic analyses, requiring sophisticated numerical procedures. The simplified method herein proposed only requires use of common analyses such as the elastic structural analysis and the rigid‐plastic analysis. For this reason, it lends itself well to be used in the immediate aftermath of an earthquake, not requiring any static or dynamic non‐linear analyses. The proposed methodology has been set up by means of a large parametric analysis, carried out on 420 frames designed according to 3 different approaches: the first one is the Theory of Plastic Mechanism Control (TPMC), ensuring the design of structures showing global collapse mechanism (GMRFs), the second one is based on the Eurocode 8 design requirements (SMRFs) while the third is a non‐seismic design, based on design for vertical loads (OMRFs).

Rigid-Plastic Analysis of Seismic Resistant T-Frame considering Moment-Shear Interaction

To select a seismic resistant system, in addition to strength and stiffness, ductility and energy dissipation are important to be considered. Structures have nonlinear behavior under the influence of moderate and strong earthquakes. One of the primary aims in designing seismic resistant structures is to prevent the formation of undesirable collapse mechanisms such as the collapse in only a few storeys of the structure that leads to low energy dissipation. In order to achieve a global collapse mechanism, modern seismic codes provide simple rules for design, which is called the hierarchy criteria. Although these simple criteria could prevent the formation of a soft storey mechanism, they could not lead to an optimal global collapse mechanism. In these mechanisms, the energy dissipation zones include all the yielding zones such as beams, while all other parts of the structure have remained in the elastic range. TRF (T-resisting frame) is an innovative lateral resistant system introduced for architectural reasons and to provide more energy dissipating capability. This system has several collapse mechanisms due to the moment, shear, or moment-shear behavior of its members. In this paper, within the framework of the theory of plastic mechanism control, the rigid-plastic analysis of the TRF system to achieve the desired collapse mechanism is used by considering the moment-shear interaction. According to these analyses, which are performed on a single storey frame, simple hierarchy criteria are developed to create the desired collapse mechanism. Also, these criteria prevent undesired collapse mechanisms in order to have more energy dissipation and more ductility. Finally, the validity of the proposed criteria has been verified by the pushover analysis.

Evaluation of the Seismic Capacity of Existing Moment Resisting Frames by a Simplified Approach: Examples and Numerical Application

The capacity of a structure can be assessed using inelastic analysis, requiring sophisticated numerical procedures such as pushover and incremental dynamic analyses. A simplified method for the evaluation of the seismic performance of steel moment resisting frames (MRFs) to be used in everyday practice has been recently proposed. This method evaluates the capacity of buildings employing an analytical trilinear model without resorting to any non−linear analysis. Despite the methodologies suggested by codes, the assessing procedure herein described is of easy application, also by hand calculation. Furthermore, it constitutes a suitable tool to check the capacity of the buildings designed with the new seismic code prescriptions. The proposed methodology has been set up through a large parametric analysis, carried out on 420frames designed according to three different approaches: the theory of plastic mechanism control (TPMC), ensuring the design of structures showing global collapse mechanism (GMRFs), the one based on the Eurocode 8 design requirements (SMRFs), and a simple design against horizontal loads (OMRFs) without specific seismic requirements. In this paper, some examples of the application of this simplified methodology are proposed with references to structures supposed to exhibit global, partial and soft storey mechanism.

Theory of plastic mechanism control for seismic design of steel plate shear walls

The present study deals with the seismic design of steel plate shear walls (SPSWs) using the theory of plastic mechanism control (TPMC). The TPMC is based on the theory of kinematic rigid-plastic, which by applying the second-order effects, can prevent the development of undesirable generic mechanisms such as soft stories, and it can ensure that the structure reaches the global mechanism. The global mechanism is a mechanism in which the damage distribution is uniform, and therefore, the maximum energy dissipation in the structure can be fulfilled. The present study first presents the seismic design provisions of the SPSW and then the SPSW design algorithm using TPMC. For practical examples, three frames including three-, six-, and nine-story frames with SPSW were designed using the proposed algorithm. For validation of the design procedure, the designed frames were evaluated by means of non-linear static analysis, showing that the frames can reach the global mechanism and their excellent seismic performance.

A simplified performance based approach for the evaluation of seismic performances of steel frames

Recent earthquakes have underlined the need for a prompt classification of buildings in terms of seismic performances. The capacity of a structure can be assessed by means of inelastic analysis, requiring sophisticated numerical procedures. Therefore, a simplified method for the evaluation of seismic performance of steel frames to be used in the everyday practice is proposed in this paper. This method can evaluate the capacity of an existing building without resorting to any static non-linear or dynamic non-linear analyses. To set up the method, an extensive parametric analysis was carried out on 420 frames designed according to 3 different approaches: the first is the Theory of Plastic Mechanism Control and ensures the design of structures characterized by global collapse mechanism (Global Moment Resisting Frames (GMRFs)), the second is based on the application of the Eurocode 8 requirements (Special Moment Resisting Frames (SMRFs)) while the third is a non-seismic design, based on sizing for vertical loads only (Ordinary Moment Resisting Frames (OMRFs)).

Plastic design of knee-element connection frames (KCFs) using mechanism control

In the past two decades, extensive research has been conducted to evaluate the seismic performance of Knee-element Connection Frames (KCFs) and to determine the most efficient configurations. KCFs are of particular advantage over other load-resisting systems in terms of their ample access for maintenance and enhanced structural performance. This paper presents an enhanced energy-based plastic design for KCFs using mechanism control. The design methodology developed in this study constitutes the design criteria employed in Performance-based Plastic Design (PBPD) and Theory of Plastic Mechanism Control (TPMC) at the same time. In this design approach, the external forces are derived from the energy balance equation directly considering second-order effects, and design is carried out according to the PBPD method. Then, undesired collapse mechanisms are identified and prevented by the use of a Design-Capacity Ratio-based (DCR-based) approach as the controlling criteria. To evaluate the design performance, nonlinear static and dynamic analyses were performed. The results indicate an acceptable correlation between the expected general yield mechanism and structural response and an acceptable economy in terms of material usage compared to comparable moment resisting frames.

Toward seismic design of tall steel moment resisting frames using the theory of plastic mechanism control

The kinematic approach and mechanism equilibrium curve in the rigid-plastic analysis framework are the basis of the theory of plastic mechanism control (TPMC). Applying this method for structural design will lead to a global collapse mechanism and prevent undesired collapse mechanisms. In this paper, to satisfy the TPMC conditions in tall moment-resisting frames (MRFs), linear programming (LP) is applied such that the TPMC conditions are defined as the optimization formulation. To investigate the effects of different structural constraints such as preventing the partial beam plastic hinge mechanisms (PBM), partial column plastic hinge mechanisms (PCM), and also to consider the strong-column weak-beam (SCWB) criterion in design MRFs by TPMC, a series of three (10, 15 and 20-story) MRFs is studied. Each frame is designed in the four different categories of the constraints: 1) PBM, 2) PBM + SCWB, 3) PBM + PCM, and 4) PBM + SCWB + PCM. The accuracy of the proposed design procedure is evaluated using pushover and nonlinear time history analyses. The results show that the designed structures reveal excellent seismic performance, and the global mechanisms are successfully achieved. The obtained nonlinear responses show that the seismic performances of the examined frames with different constraints are similar, and the PBM constraint is adequate for preventing undesired collapse mechanisms.

Consideration of second-order effects on plastic design of steel moment resisting frames

This work mainly aims to propose a new design procedure combining the benefits of the Performance-Based Plastic Design approach (PBPD) with a rigorous accounting of second-order effects. In fact, by exploiting the kinematic theorem of plastic collapse, second-order effects can be accounted for employing the concept of collapse mechanism equilibrium curve. The same tool constitutes the base of the Theory of Plastic Mechanism Control (TPMC) design approach. Besides, the paper reports a critical comparison between TPMC and PBPD, both having the scope to design structures exhibiting a collapse mechanism of global type. These two approaches are also compared with the refined PBPD where second-order effects are accounted for by the kinematic approach. Many steel moment resisting frames are designed according to PBPD, TPMC and refined PBPD and their performances have been compared on the bases of push-over analyses.

Probabilistic Theory of Plastic Mechanism Control for Steel Moment Resisting Frames

This work aims at the development of an advanced method for the seismic design of Moment Resisting Frames (MRFs) based on a target value of the failure probability in the attainment of a collapse mechanism of global type for stochastic frames (considering the aleatoric uncertainty of the material properties). Therefore, the method herein presented constitutes the probabilistic version of the Theory of Plastic Mechanism Control (TPMC) already developed for frames with deterministic material properties. With reference to MRFs whose members have random values of the yield strength, when structural collapse is of concern, the failure domain is related to all the possible collapse mechanisms. Within the probabilistic TPMC, the term “failure” does not mean the attainment of a structural collapse, but the development of a collapse mechanism different from the global one.The design requirements normally needed to prevent undesired collapse mechanisms are probabilistic events within the framework of the kinematic theorem of plastic collapse. The limit state function corresponding to each event is represented by a hyperplane in the space of random variables, so that the failure domain is a surface resulting from the intersection of the hyperplanes corresponding to the limit states representing the single failure events. Since plastic hinges in frame’s members are common to many different mechanisms, the single limit state events are correlated. Therefore, by applying the theory of binary systems and considering that the limit states are events located in series, the probability of failure can be computed by means of Ditlevsen bounds. This approach has been validated by means of Monte Carlo simulations.In order to achieve a predefined level of reliability in the attainment of the design goal, the reliability analysis is repeated for increasing values of the overstrength factor of the dissipative zones to be used in TPMC, aiming to its calibration. Finally, on the basis of the results of a parametric analysis, a simple relationship to compute the value of the overstrength factor needed to include the influence of random material variability in the application of TPMC is proposed.

Comparison Between Different Design Strategies For Freedam Frames: Push-Overs and Ida Analyses

Background:Modern seismic code design rules are known to be based on capacity design principles. They try to assure the damage to occur in the ductile parts of the structure, such as beam ends while the other have to remain in elastic range. Therefore, in the aftermath of design earthquakes, plastic deformations at member or connection level will imply high repair costs. In the last decades, innovative structural solutions based on the so-called supplementary energy dissipation strategy allow increasing the dissipative capacity of structures through equipping it with special damping devices. In the case of substitution of dissipative zones with dissipative devices the strategy takes the name of substitutive strategy. This is the case of Moment Resisting Frames investigated in this paper, where traditional dissipa-tive zones, are equipped with innovative low damage frictional devices. However, the current version of codes does not provide any rules to design of MRFs equipped with this type of friction joints.Methods:Therefore, this paper reports two design approaches amply investigated and compared. The first one is based on the application of the Beam-to-Column Hierarchy Criterion (BCHC) while the second one exploits the Theory of Plastic Mechanism Control (TPMC). The comparison between them is herein discussed on the basis of the results of nonlinear static and dynamic analyses.Conclusions:Structures equipped with low damage frictional connections show larger drift demand than conventional Moment Resisting Frames. However, differently from traditional structures, the larger displacement demand of MRFs equipped with friction joints does not corre-spond to structural damage, thus allowing the reparability of the structure.

The Use of TPMC for Designing MRFs Equipped with FREEDAM Connections: A Case Study

Within European Research Project “FREEDAM” supported by RFCS a design procedure for MRFs equipped with friction dampers has been developed. In particular, beam-to-column joints are equipped with friction dampers located at the bottom flange level namely “FREEDAM” dampers. Therefore, all the connections are conceived in order to prevent structural damage. A prototype structure has been designed according to a design procedure assuring a collapse mechanism of global type whose name is Theory of Plastic Mechanism Control, and its seismic performances have been investigated by means of IDA analyses in a companion paper.

11.09: Validation of probabilistic theory of plastic mechanism control by means of Monte Carlo simulations

ABSTRACTThis work aims at the validation of the Probabilistic Theory of Plastic Mechanism Control (P‐TPMC), reported in a companion paper, by means of Monte Carlo simulations. P‐TPMC is devoted to stochastic frames with the aim to assure a collapse mechanism of global type despite of the influence of random material variability. A mechanism of global type develops when all the beams are yielded at their ends while the columns remain in elastic range with the only exception of the base sections of the first storey columns.A parametric analysis is performed considering steel moment resisting frames having different number of bays and different number of storeys. Moreover, in order to achieve a predefined level of reliability in the attainment of the design goal, the parametric analysis is also repeated for increasing values of an overstrength factor of the dissipative zones aiming to its calibration. Finally, a quadratic regression has been derived to provide a simple relationship to compute the value of the overstrength factor needed to include the influence of random material variability in the application of deterministic Theory of Plastic Mechanism Control.