Rosario Montuori

Plastic Design of Seismic Resistant V-Braced Frames

In this article, a new method for designing chevron concentrically braced steel frames is presented. The aim of the proposed method is the design of concentrically braced steel frames able to guarantee, under seismic horizontal forces, a collapse mechanism of global type. This result is of great importance in the seismic design of structures, because local failure modes give rise to a worsening of the energy dissipation capacity of structures and, therefore, to an higher probability of failure during severe earthquakes. With reference to the examined structural typology, the global mechanism is characterized by the yielding of tensile bracing diagonals and by the buckling of the compressed diagonals of all the stories. The proposed method is rigorously based on “capacity design approach” which requires that dissipative zones have to be designed to withstand the internal actions due to the seismic design horizontal forces and the vertical loads acting in the seismic load combination; while non dissipative zones have to be designed considering the maximum internal actions that dissipative zones, yielded and strain-hardened, are able to transmit. The new design issue covered by the proposed design procedure is the need to account for the contribution of the compressed diagonals in deriving the design axial force of non dissipative members. The seismic inelastic response of a sample structure is investigated by means of nonlinear dynamic analyses. The results carried out with reference to braced frames designed according to the proposed procedure are compared with those obtained with reference to the same structural schemes designed according to Eurocode 8.

Failure Mode Control of X-Braced Frames Under Seismic Actions

In this article, a new method for designing concentrically braced steel frames is presented. The aim of the proposed method is the design of concentrically braced steel frames able to guarantee, under seismic horizontal forces, a collapse mechanism of global type. This result is of great importance in the seismic design of structures, because local failure modes give rise to a worsening of the energy dissipation capacity of structures and, therefore, to an higher probability of failure during severe earthquakes. With reference to the examined structural typology, the global mechanism is characterized by the yielding of bracing diagonals of all the stories. The proposed method is rigorously based on “capacity design” which requires that non dissipative zones have to be designed to withstand the internal actions coming from the seismic design horizontal forces and the vertical loads acting in the seismic load combination, while non dissipative zones have to be designed considering the maximum internal actions that dissipative zones, yielded and strain-hardened, are able to transmit [Mazzolani and Piluso, 1996]. The new design issue covered by the proposed design procedure is the need to account for the contributions of the compressed diagonals in deriving the design axial force of non dissipative members (beams and columns). The seismic inelastic response of a sample structure is investigated by means of nonlinear dynamic analyses, which have been carried out by means of the PC-ANSR [Maison, 1992] program, where the cyclic behavior of brace elements has been accurately modeled by means of the Georgescu model [Georgescu et al., 1991]. The results of dynamic inelastic analyses carried out with reference to the braced frame designed according to the proposed procedure are compared with those obtained with reference to the same structural scheme designed according to Eurocode 8 [CEN, 2000; CEN, 2003]. In particular, it is pointed out that the application of Eurocode 8 design criteria leads to premature buckling of columns, so that the proposal of a new design approach is fully justified.

Failure Mode Control and Seismic Response of Dissipative Truss Moment Frames

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

Influence of Design Criteria on the Seismic Reliability of X-braced Frames

According to the most modern trend, performance-based seismic design is aimed at the evaluation of the seismic risk defined as the mean annual frequency of exceeding a threshold level of damage, i.e., a limit state. A procedure for performance-based seismic assessment is herein briefly summarized and applied to concentrically “X” braced steel frames, designed according to different criteria. In particular, two design approaches are examined. The first one corresponds to the provisions suggested by Eurocode 8, while the second approach is based on a rigorous application of the capacity design criteria aiming to the control of the failure mode, as suggested in a companion article. The aim of the presented work is to focus on the seismic reliability obtained through these design methodologies. The probabilistic approach is based on an appropriate combination of probabilistic seismic hazard analysis (PSHA), probabilistic seismic demand analysis (PSDA), and probabilistic seismic capacity analysis (PSCA). Regarding PSDA, nonlinear dynamic analyses have been carried out in order to obtain the parameters describing the probability distributions of demand, conditioned to given values of the earthquake intensity measure. It is demonstrated how the proposed design method leads to a very important improvement of the seismic performances with a negligible increase of the overall building cost.

Failure Mode and Drift Control of MRF-CBF Dual Systems

In this paper, a new method for designing moment resisting frame (MRF) - concentrically braced frame (CBF) dual systems failing in global mode is presented. Starting from the analyses of the typical collapse mechanisms of such structural typology subjected to seismic horizontal forces, the method is based on the application of the kinematic theorem of plastic collapse. Beam and diagonal sections are assumed to be known quantities, because they are designed to resist vertical loads and horizontal forces, respectively. Therefore, the column sections are the only unknowns of the design problem. Column sections are obtained by imposing that the equilibrium curve corresponding to the global mechanism has to lie below all the equilibrium curves corresponding to the undesired collapse mechanisms within a displacement range compatible with the local ductility supply of dissipative elements. Such procedure has been applied to design sev- eral MRF-CBF dual systems and has been validated by means of non-linear static analyses aimed to check the actual pat- tern of yielding.

Theory of plastic mechanism control for MRF–CBF dual systems and its validation

In this paper the theory of plastic mechanism control is presented for moment resisting frame–concentrically braced frames dual systems, i.e. for structural systems combined by moment resisting frames and concentrically braced frames. It is aimed at the design of structures failing in global mode, i.e. whose collapse mechanism is characterised by the yielding of all the tensile diagonals and the occurrence of buckling in the compressed ones, and by plastic hinge formation at all the beam ends and at the base of first storey columns. The proposed methodology is based on the application of the kinematic theorem of plastic collapse, by imposing that the global mechanism equilibrium curve has to lie below all the other equilibrium curves corresponding to undesired mechanisms. The practical application of the design methodology is illustrated by means of a worked example. In addition, the results of a non-linear static pushover and dynamic analyses of the designed structure are also discussed in order to demonstrate the effectiveness of the proposed design procedure.

Seismic Design of MRF-EBF Dual Systems with Vertical Links: EC8 vs Plastic Design

Despite the fact that Eccentrically Braced Frames with Vertical Links (VL-EBFs), also referred to as inverted Y-scheme, are codified in Eurocode 8, the issues related to their seismic response and design have not been widely investigated, so that design criteria commonly applied for Eccentrically Braced Frames with Horizontal Links (HL-EBFs) are commonly applied. However, the Theory of Plastic Mechanism Control (TPMC) has been recently extended to the case of VL-EBFs. The aims of this article, on one hand, are to provide a further validation of the recently proposed design procedure, based on TPMC, and, on the other hand, are to compare the seismic performance of dual systems composed by a moment-resisting part and VL-EBF part designed by means of TPMC with those occurring when Eurocode 8 design criteria are applied. The validation of the proposed design procedure is carried out by means of Incremental Dynamic Analyses (IDA). The main purpose of such analyses is the check of the fulfilment of the design goal of TPMC, i.e., the development of a pattern of yielding consistent with the collapse mechanism of global type. Such mechanism is universally recognized as the one leading to the highest energy dissipation capacity. In case of MRF-EBF dual systems, it is characterized by the yielding of all the links and all the beams at their ends. Conversely, all the columns and the diagonal braces remain in elastic range. Obviously, exception is made for the base sections of first story columns. In particular, two case studies are analyzed which are characterized by a different number of stories. Each building structure is designed according to both TPMC and Eurocode 8 provisions. The seismic response obtained is investigated by both push-over and IDA analyses. The attention is focused on the pattern of yielding obtained, the maximum interstory drift demand, the link plastic rotation demand and sharing of the seismic base shear between the moment-resisting part and the bracing part of the structural system. The results obtained point out improvement of the seismic response, compared to Eurocode 8 provisions, achieved by means of TPMC.

Theory of Plastic Mechanism Control of Seismic-Resistant MR-Frames with Set-Backs

Seismic codes do not provide specific hierarchy criteria for irregular Moment Resisting Frames (MRFs). In fact, the provisions for irregular frames are exactly the same adopted for regular MRFs with the only exception of a 20% reduction of the design value of the q-factor, accounting for a presumed worsening of the frame energy dissipation capacity. It is well known that seismic code provisions, based on hierarchy criteria, are often unsuitable to prevent partial mechanisms and to assure the development of a global collapse mechanism. In particular, irregular structures are prone to develop partial or soft storey mechanisms in case of significant set-backs. As already showed in previous work [1-10] a rational design procedure based on plastic mechanism theory can be adopted for different design typologies leading to excellent results in the field of mechanism control. This procedure is herein briefly presented and applied to different study cases. It is based on the application of the kinematic theorem of plastic collapse extended to the concept of mechanism equilibrium curve in order to consider second order effects. Sending the reader back to the original work on the theory of plastic mechanism control [1] for an exhaustive presentation of the theory, referred to regular MR-Frames, the work herein presented focuses on the issues to be faced to apply such theory to the particular case of steel frames with setbacks. In order to verify the results obtained by the application of the proposed design procedure, non linear static analyses [11] have been carried out for all the structures considered and a comparison with the results coming from the application of Eurocode 8 design procedures [12] is also performed.

Moment frames – concentrically braced frames dual systems: analysis of different design criteria

In this paper, a design methodology based on the theory of plastic mechanism control (TPMC) is presented for dual systems combined by moment resisting frames and concentrically braced frames (MRF–CBF dual systems). The study is focused on the design of structures failing in global mode, i.e. whose collapse mechanism is characterised by the yielding of all the tensile diagonals, the buckling of the compressed ones, and the development of plastic hinges at all the beam ends and at the base of first-storey columns. The results of push-over analyses and nonlinear dynamic analyses carried out with reference to MRF–CBF dual systems designed according to the proposed procedure are compared with those obtained with reference to the same structural scheme designed according to Eurocode 8. The advantages obtained in terms of seismic performances are outlined and also economic issues are investigated pointing out the convenience of seismic design based on TPMC.

The influence of gravity loads on the seismic design of RBS connections

Connections with Reduced Beam Section (RBS) have been investigated in the last 20 years both from an ana- lytical point of view and from an experimental point of view. Several experimental tests demonstrated that RBS connec- tions designed according to themost modern seismic codes are able to obtain the desired goal: the protection of the con- nection due to the yielding of the adjacent RBS. But in all the past researches and experimental tests the role that vertical loads can play was neglected or not properly accounted for. This study proposes a new procedure for accurately comput- ing the relation between RBS location, vertical load and amount of section reduction for ensuring that plastic hinges de- velop in the reduced sections or in a reduced section and in an intermediate section of the beam.