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The hexagonal plastic collapse surface model has been explored as an effective approach for seismic response analysis in multi-degree-of-freedom (MDOF) structures. This study establishes the theoretical background of hexagonal analysis for multistory structures, emphasizing the consistency between experimental and analytical results. A simplified nonlinear dynamic analysis (SNDA) is introduced, integrating limit analysis with static proportional loading and a hexagonal plastic collapse surface model to define the internal safety zone within the mode restoring force space. The approach considers multiple vibration modes, which significantly impact elastic–plastic behavior in seismic conditions. To validate its effectiveness, a comparative evaluation is conducted between experimental data and SAP2000 dynamic time history analysis, showing strong alignment in deformation response trends. The results confirm that the hexagonal model accurately predicts failure mechanisms while improving computational efficiency, providing a practical framework for collapse prediction in structural engineering applications.

Pipe bends are a crucial component of the pipeline industry because they experience more stresses and deformations than straight pipes of the same dimensions and material properties under the same loading conditions. For a reliable and safe piping system, the plastic collapse moment of pipe bends must be estimated accurately. The current study aims to find which bending mode is critical to failure for pipe bends; for that, the collapse moment under in-plane closing (IPC), in-plane opening (IPO) and out-of-plane (OP) bending moments are compared using finite element (FE) analysis. The comparison accounts for various values of internal pressure, bend angle and initial geometric imperfection. The FE analysis considers elastic-perfectly plastic (EPP) and strain-hardening (SH) material models. Twice-elastic-slope (TES) method is implemented to evaluate plastic collapse moment for all considered cases. The comparison of collapse moment shows that under unpressurized conditions, pipe bends are critical to IPC bending moment. However, it is difficult to identify which bending mode is critical under pressurized conditions. Therefore, plastic collapse moment under all three bending modes should be known and for that plastic collapse moment equations under all bending modes should be proposed.

PurposeThe aim of this study is to ensure the structural integrity of 90° back-to-back (B2B) pipe bends by developing a closed-form numerical solution for estimating the collapse load of shape distorted 90° B2B pipe bends using non-linear finite element (FE) analysis.Design/methodology/approachThe collapse behaviour of 90° B2B pipe bends with ovality (Co) and thinning (Ct) has been evaluated by non-linear FE approach. Moment load is applied in the form of in-plane closing moment (IPCM). The current FE approach was evaluated by the numerical solution for the plastic collapse moment of pipe bends, which has been published in the literature. The collapse moments were obtained from the twice elastic slope (TES) method using the moment-rotation curve of every individual model.FindingsThe implication of Ct/Cth on collapse load is found to be highly insignificant in terms of increasing bend radius and Co. Co weakens the geometry, and its effect on the collapse load is substantial. A closed-form numerical solution has been proposed to calculate the collapse load of 90° B2B pipe bend with shape imperfections.Originality/valueThe implications of shape distortion (Co and Ct) in the failure analysis (collapse load) of 90° B2B pipe bends has not been investigated and reported.

The purpose of seismic provisions included in modern building codes is to obtain a satisfactory structural performance of buildings during earthquakes. However, in the United States and elsewhere, there are large inventories of buildings designed and constructed several decades ago, under outdated building codes. Some of these buildings are classified as non-ductile buildings. Currently, under the ATC-78 project, a methodology is being developed to identify seismically hazardous frame–wall buildings through a simple procedure that does not require full nonlinear analyses by the responsible engineer. This methodology requires the determination of the controlling plastic collapse mechanism, the base shear strength, and the ratio between the story drift ratio and the roof drift ratio, called parameter \\[\\alpha\\], at collapse level. The procedure is calibrated with fully inelastic nonlinear analyses of archetype buildings. In this paper we first introduce an efficient scheme for modeling frame–wall buildings using the software OpenSees. Later, the plastic collapse mechanism, the base shear strength, and values of \\[\\alpha\\] are estimated from nonlinear static and dynamic analyses considering a large suite of ground-motion records that represent increasing hazard levels. The analytical experiment included several frame–wall combinations in 4 and 8-story buildings, intended to represent a broad range of conditions that can be found in actual buildings, where the simplified methodology to evaluate the risk of collapse can be applicable. Analysis results indicate that even walls of modest length may positively modify the collapse mechanism of nonductile bare frames preventing soft story failures.

This contribution studies failure by elastic buckling and plastic collapse of wall structures during extrusion-based 3D printing processes. Results obtained from the parametric 3D printing model recently developed by Suiker (Int J Mech Sci, 137: 145–170, 2018), among which closed-form expressions useful for engineering practice, are validated against results of dedicated FEM simulations and 3D concrete printing experiments. In the comparison with the FEM simulations, various types of wall structures are considered, which are subjected to linear and exponentially decaying curing processes at different curing rates. For almost all cases considered, the critical wall buckling length computed by the parametric model turns out to be in excellent agreement with the result from the FEM simulations. Some differences may occur for the particular case of a straight wall clamped along its vertical edges and subjected to a relatively high curing rate, which can be ascribed to the approximate form of the horizontal buckling shape used in the parametric model. The buckling responses computed by the two models for a wall structure with imperfections of different wavelengths under increasing deflection correctly approaches the corresponding bifurcation buckling length. Further, under a specific change of the material properties, the parametric model and the FEM model predict a similar transition in failure mechanism, from elastic buckling to plastic collapse. The experimental validation of the parametric model is directed towards walls manufactured by 3D concrete printing, whereby the effect of the material curing rate on the failure behaviour of the wall is explored by studying walls of various widths. At a relatively low curing rate, the experimental buckling load is well described when the parametric model uses a linear curing function. However, the experimental results suggest the extension of the linear curing function with a quadratic term if the curing process under a relatively long printing time is accelerated by thermal heating of the 3D printing facility. In conclusion, the present validation study confirms that the parametric model provides a useful research and design tool for the prediction of structural failure during extrusion-based 3D printing. The model can be applied to quickly and systematically explore the influence of the individual printing process parameters on the failure response of 3D-printed walls, which can be translated to directives regarding the optimisation of material usage and printing time.

The paper investigates the available ductility of the steel beams under cyclic action. The study is based on the concept of the plastic collapse mechanism, previously developed for monotonic loading, and further implements the concept of the initial cumulative deformation; it aims to calculate the main parameters that affect the rotation capacity of steel I and H beams made by European sections. The findings show that the loading type defined by the increasing or the constant amplitude, the number of cycles producing strength and the ductility degradation and the cross section conformation are the factors of primary importance whereas, in general, the steel quality and the material variability have a secondary detrimental effect.

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.

A displacement-based dislocation map has been used to build the eigenstress stress, which is the base of the structure’s limit analysis. The limit load has been calculated as the upper bound of any equilibrated stress that respects the compatibility inequalities by means of a linear optimization program. The eigenstress stress nodal parameters were assumed as the design variables, and the compatibility inequalities have been obtained from the Mises–Schleicher criterion, assuming that the stress belongs to the corresponding plastic domain. The numerical application has considered a linear secant representation of the domain, with a penalty factor on stresses, to correct the linearization error. Examples concerning a simply supported cantilever beam, a pipe section, and a plate with a circular hole highlighted the accuracy of the procedure with respect to the established literature. Moreover, the procedure has been applied to investigate plane structure examples. A square plate with variable elliptic holes has been analyzed, and the influence of ellipticity on the collapse load has been shown. The effects of porosity and heterogeneity of the structure with respect to the collapse load are shown considering the porous cantilever and representative volume element. The evaluation of the limit load along different element directions envisaged a point-wise calculation of the compatibility domain of the porous material to be used in the macro-scale analysis of the structures made of porous micro-cells.

Aluminum (Al) and Al–4.5Cu wt% open-cell foams were produced by the replication casting technique in two different pore sizes, avoiding subsequent heat treatments. All produced samples were physically characterized by means of He pycnometry. Microstructural and chemical analyses were carried out using scanning electron microscopy, energy dispersive X-ray spectroscopy, X-ray diffraction and image processing techniques. Uniaxial compression tests were conducted, with the aim of generate the stress–strain curves of the Al and Al–4.5Cu wt% foams. It was found that plastic collapse and plateau stresses increased from ~ 3 and ~ 12 MPa to ~ 10 and ~ 30 MPa, while the energy absorption capacity of the Al–4.5Cu wt% foams was almost trebled regard the pure Al foams. These outcomes were attributed to the formed microstructure, constituted by dendritic arrangement of α -Al (~ 57 HV) and θ -Al 2 Cu (~ 326 HV). Thus, this work gives way to produce mechanically enhanced open-cell Al foams derived from the Cu addition. Graphic abstract

In this paper a new approach to the consistent identification of the deformation pattern vital for the precise determination of the plastic limit load of a cylindrical shell from MNA when using modified Southwell (MS) and Tangent Stiffness (TS) plots is presented. It is proposed that the formalised assessment of the plastic collapse load can be done by the application of the relation between the load factor increment Δ and the arc length – for an identification of achievement of the complete plastic collapse mechanism from MNA, and then the MS or TS plot for the displacement pattern that corresponds to the identified plastic mechanism.