Plastic Collapse Mechanism Research Articles

A new plastic global analysis approach for the fire design of steel and stainless steel structures

The new generation of structural codes for stainless steel allow carrying out global plastic analyses on certain types of stainless steel structures with plastic cross-sections at room temperature if the joints conforming the structure are classified as full-strength joints, a capability that has been long recognised for carbon steel structures. However, the requirements for the fire design of carbon and stainless steel structures in current and upcoming European design standards are still primarily based on the resistance of individual members, disregarding the redistribution of internal forces and strain hardening effects. Recent studies have proven that carbon and stainless steel frames with plastic cross-sections and full-strength joints are capable of redistributing internal forces at elevated temperatures, and failed describing global plastic collapse mechanisms under fire situation, suggesting that system effects are also relevant at elevated temperatures and could be taken into account for more efficient designs. On this basis, this paper develops an extensive numerical study focused on carbon and stainless steel frames under fire situation, and proposes a new methodology based on plastic global analysis to estimate the resistance of such structures under fire situation accounting for their redistribution capacity, improving the accuracy of the predicted fire time resistances significantly for the two materials.

Plastic collapse behavior of plate to CHS connection under biaxially symmetric load

This study investigates the plastic collapse behavior of a non-diaphragm type connection with flange plates connected to a circular hollow section (CHS) column, where four flanges were joined from two orthogonal directions. The analysis was conducted using the finite element method (FEM). The focus was on determining the collapse load of the flange joint under a biaxially symmetric load from the four flanges. In an initial numerical analysis, the fundamental collapse behavior of the cylindrical wall was explored. Finite element models of CHS tubes with perfectly elasto-plastic material properties were employed. The analysis revealed that the plastic collapse mechanism of the cylindrical wall was influenced by the axial force in the transverse flanges. Prediction equations for the collapse load of the joint were formulated, assuming four representative collapse mechanisms and employing the principle of virtual work based on the numerical analysis results. Additionally, the ultimate strength of the joint, determined by the plastic collapse of the cylindrical wall, was computed using finite element models of CHS tubes with realistic hardening properties. A comparison between predictions from the equations based on perfectly elasto-plastic CHS tubes and numerical solutions through finite element analysis (FEA) of CHS tubes with realistic hardening properties validates the accuracy of the proposed prediction equations, even when applied to realistic steel tubes.

Experimental investigation of steel frames made of hybrid steel welded I‐sections

AbstractAn experimental investigation into the structural behaviour of steel frames made up of hybrid steel welded I‐section members is presented in this paper. The tested hybrid steel welded I‐section profile had quenched and tempered S690 steel flanges and an S355 steel web. The experimental programme comprised four two‐dimensional, single storey, single bay frames subjected to different combinations of horizontal and vertical loading, thus enabling different beam, sway as well as combined beam and sway plastic collapse mechanisms to be examined. The frames were fully laterally restrained using a bespoke lateral bracing system to ensure that no out‐of‐plane instability phenomena were experienced during testing. The experimental setup, loading schemes, instrumentation and key experimental results are reported. The experimental results are fundamental to developing an understanding of the behaviour of hybrid steel welded I‐sections at the structural system level. Further research is underway to underpin the development of suitable design rules for steel frames made of such hybrid steel welded I‐section members.

Blast response of laminated glass: A gas-gun experimental investigation of the fracture pattern and yield lines observed in full-scale blast tests

The applications of architectural and automotive laminated glass continue to grow. This is largely due to the enhanced safety in extreme events, such as blast. However, the complex interaction between the glass fragments and the polymer interlayer after glass fracture is still only partially understood, with existing analysis methods adopting a semi-empirical approach for the post-fracture response. These include a plastic yield-line analysis based on a failure pattern repeatedly observed during blast tests. In recent research it was demonstrated that yield lines can develop in fractured laminated glass through the composite bending action of the glass fragments, working in compression, together with the interlayer working in tension. This paper investigates the influence of the inertia loading associated with blast response, which has not been explicitly studied previously, with the aim of understanding the pattern of yield lines observed in blast tests. Impact tests are performed on laminated glass specimens using foam projectiles launched from a gas gun, which simulate the loading from a blast pulse. These tests demonstrate that the yield line pattern formed under short-duration dynamic loading depends on the loading intensity, thereby providing further evidence of a dynamic, plastic collapse mechanism in which inertia plays a significant role.

Plastic redistribution capacity of stainless steel frames in fire

Stainless steel frames with compact cross-sections are capable of redistributing internal forces at room temperature and forming plastic failure mechanisms, which is reflected in the new generation of structural codes for stainless steel by allowing to carry out global plastic analyses on certain types of stainless steel if the joints conforming the structure are classified as full-strength joints. Nevertheless, the requirements for the fire design of stainless steel structures in current standards is still primarily based on the resistance of individual members, disregarding strain hardening effects and the redistribution of internal forces, mainly because the influence of the performance of stainless steel joints on the response of the frames under fire situation is yet unknown. On this basis, this paper presents a numerical study focused on stainless steel frames with compact rectangular hollow sections, both at room temperature and at elevated temperatures, to analyse the influence of full-strength joints on the frame's response by means of two joint modelling techniques, and to assess the plastic redistribution capacity of stainless steel frames, especially under fire situation. In addition, an exhaustive revision of the failure criteria for stainless steel frames under fire situation is carried out and a new failure criterion is proposed based on the results derived from the parametric study. The results demonstrate that stainless steel frames are also capable of redistributing internal forces and forming plastic collapse mechanisms under fire situations, suggesting a new procedure to predict the response of these structures under fire situation more accurately.

Comparative analysis of aluminium core honeycomb with 3D woven Kevlar honeycomb composite

Sandwich structures have a high capacity for stiffness, strength, and energy absorption, and are frequently used as lightweight composite components in shipbuilding and aeronautical engineering. In this work, mechanical characterisation of aluminium honeycomb and 3D-woven Kevlar honeycomb composite sandwich panels with respect to their flatwise, edgewise compression, and three-point bending tests was carried out. The experimental results show that the 3D-woven Kevlar honeycomb is better than the aluminium honeycomb for flatwise and three-point bending behaviour. In the case of edgewise compression, aluminium honeycomb shows significant results. Aluminium honeycomb cores show the plastic collapse mechanism, while Kevlar honeycomb indicates the occurrence of buckling before failure.

Nonlinear time history seismic analysis of inelastic 3D frame buildings in a reduced modal space

This research investigates the formulation of a reduced modal space for the nonlinear dynamic seismic analysis of elasto-plastic 3D frame buildings. Starting from a full finite element model, the modal shapes of the reduced model for the kinematics are selected as the relevant linear elastic modes of the generalized stiffness/mass linear eigenvalue problem in terms of participation factor plus collapse mechanisms associated to appropriate static lateral loads. The internal forces are evaluated on the full model to guaranty an accurate description of the constitutive laws. The equations of motion are then projected in the modal space for the step-by-step solution by a Newmark average acceleration scheme. The advantage is that the Newton iteration of the implicit method are carried out by inverting only the reduced tangent matrix. The proposed reduction method is tested for a reinforced concrete building varying frequency content, direction and amplitude of the ground motion. Accuracy and robustness are demonstrated employing a few tens of modes, including elastic modes and plastic collapse mechanisms. The need for plastic modes for describing the structural dynamics in case of seismic actions leading to significant plastic excursions is highlighted, together with the limits of simplified approaches, as the pushover analysis, based on the hypothesis of shape conservation in the inelastic range regardless of the building regularity.

Cyclic behaviour of demountable metallic corrugated shear panel dampers

This study aims to develop a new demountable corrugated shear panel damper (DCSPD). The developed device is to upgrade the flat shear panel of the classical shear panel damper (classical SPD) using a corrugated shear panel. And the energy dissipating parts of the damper are demountable, allowing for easy processing, transport, and assembly onsite. Moreover, the new damper can make full use of the geometrical properties of the corrugated shear panel to overcome the shortcomings of the classical SPD, such as low initial stiffness and poor energy dissipation. A series of tests were conducted to systematically study the seismic performance of the proposed damper under quasi-static cyclic loading conditions. The effects of three key design parameters are discussed, including the corrugated direction and thickness of the shear panel and the thickness of the flange plate. The experimental results demonstrate that the direction of the corrugated shear panel changes the plastic failure modes of the dampers, resulting in the overall out-of-plane buckling failure of demountable horizontally corrugated shear panel damper (DCSPD-H) and the local buckling failure of demountable vertically corrugated shear panel damper (DCSPD-V). Therefore, the shear bearing capacity, ductility coefficient, and energy dissipation capacity of DCSPD-H are 5.56%, 10.23%, and 35.37% higher than those of the DCSPD-V, respectively. Moreover, an increase in the thickness of the shear panel will significantly improve the seismic performance of the damper, whereas an increase in the thickness of the flange plate may hinder the deformability of the damper. Further, the finite element models of tested dampers were established, and the plastic collapse mechanisms and the sharing of energy-absorbing of each part were investigated. Finally, simple design equations are presented through parametric studies of dampers with different geometric dimensions.

A reduced order model for nonlinear time history seismic analyzes of elasto‐plastic 3D frame structures

AbstractA reduced order model for the nonlinear dynamic seismic analysis of elasto‐plastic 3D frame structures is presented. It is based on an approximated solution space for the displacement field that is assumed as the sum of two subspaces. The first subspace is generated by the relevant linear elastic modes of the generalized stiffness/mass linear eigenvalue problem in terms of participation factor. The second one is defined by collapse mechanisms associated to appropriate static load distributions. The time history analyzes are carried out within the reduced solution space, while the internal forces are evaluated on the full model to guarantee an accurate description of the constitutive laws. The proposed reduction method was tested for different structural geometries varying frequency content, direction and amplitude of the ground motion. Numerical results show accuracy and robustness also employing a few tens of modes, including elastic modes and plastic collapse mechanisms. In particular, the need for plastic modes in capturing the structural dynamics in case of seismic actions leading to significant plastic excursions is emphasized. This highlights the limits of simplified approaches based on the hypothesis of shape conservation in nonlinear problems, regardless of the building regularity.

3D concrete printing modelling of thin-walled structures

Failures induced by either instability (elastic buckling) or green strength (plastic collapse) mechanisms have been commonly encountered in 3D concrete printed (3DCP) structures. In this work, a numerical model of the 3D concrete printing process is implemented to simulate these two failure mechanisms. Early-age mechanical properties of two printable mixes are used as input data for the simulation. The finite element (FE) modelling is then validated by comparison with 3DCP experiments of a hollow cylinder. The numerical analysis program can accurately predict the deformation and its failure modes during the 3D concrete printing process. Besides, the FE model is also used for validating a printed free thin wall. Further, sensitivity and parametric analyses are investigated to unveil the influence of printing process parameters, i.e., printing speed, extrusion width, and different mesh sizes on buildability.

Progressive collapse analysis of a bulk carrier hull girder under longitudinal vertical bending moment considering cracking damage

Existence of crack causes reduction of the load carrying capacity of ship hull structural elements and eventually reduces the hull girder strength. Previous numerical and semi-analytical studies by the same authors revealed that in addition to the value of ultimate strength, the deflection shape and plastic collapse mechanism of ship hull structural elements will change due to existence of cracking damage. In this paper results from previous studies are used to investigate the way cracks affect ultimate longitudinal strength of ship hull girder. Progressive collapse analysis of an ISSC2000 bulk carrier is carried out to estimate its ultimate strength considering existence of cracking damages at different locations of the hull girder; namely bottom, double bottom, side and deck structures. For this reason, HULLST software which is based on Smith's method was modified to be able to model specific cracks anywhere in the ship hull girder. Results show that the way cracking damage effects the ultimate strength of the ship depends highly on the ship's collapse modes in hogging and sagging conditions as well as behavior of the ship structural elements.

Cyclic behavior of shear-type hysteretic dampers with different cross-sectional shapes

Metallic shear-type dampers are widely used as seismic-energy-absorbing devices because they are easy to produce, install, and maintain. This study investigated a metallic shear-type damper constructed with a circular hollow section; an H-shaped section damper, which is commonly used as a metallic shear damper, was included in the study for comparison. A structural equation for calculating the strength and initial stiffness is provided based on the plastic collapse mechanism of the two types of dampers. For both types, a cyclic loading test was conducted to investigate their mechanical characteristics as hysteretic dampers. Damper specimens with each of the two cross-sectional shapes were fabricated using low-yield-point steel and were designed to have nearly the same full plastic shear strength, initial stiffness, and weight. The experimental results confirm that both types of damper exhibit stable spindle-shaped hysteresis characteristics and have sufficient plastic deformation capacity and energy absorption capacity. Consequently, under identical loading conditions, the two types of damper have nearly the same strength increase ratio and deformation capacity. The local plastic strain was evaluated using a finite element analysis of monotonic loading; the results verify the validity of the proposed plastic collapse mechanism of the circular hollow section damper and H-shaped shear panel damper. The sharing of energy dissipation among the damper components was also analyzed.

Effects of grout sleeve defects and their repair on the seismic performance of precast concrete frame structures

Precast concrete frame structures with grouted sleeve connections are widely used. An experimental study was conducted investigating the seismic performance of precast concrete frame structures having backflow defects in their grout sleeves. Repair of such defects is also demonstrated using a simple grout injection technique. Four two-storey precast concrete frame structures having grout sleeve connections in their columns were designed and tested under reversed cyclic loading. The performance of frames having no grout defects and those with defects and repaired defects is described in terms of failure modes, hysteresis characteristics, load-carrying capacity, ductility and energy dissipation capacity. The results indicate that the plastic collapse mechanism of the frames remains unchanged, the performance is affected by the presence of the grout sleeve defects. Despite the defects only reducing the capacity of one of three columns in the frame either 6% or 19%, the effect on the global behavior of the frame was evident in terms of reduced capacity, stiffness, ductility and energy absorption. Injecting grout into defective grout sleeves restored their capacity, and that of the frames, to a defect-free condition.

Effect of Plastic Anisotropy on the Collapse of a Hollow Disk under Thermal and Mechanical Loading

Plastic anisotropy significantly affects the behavior of structures and machine parts. Given the many parameters that classify a structure made of anisotropic material, analytic and semi-analytic solutions are very useful for parametric analysis and preliminary design of such structures. The present paper is devoted to describing the plastic collapse of a thin orthotropic hollow disk inserted into a rigid container. The disk is subject to a uniform temperature field and a uniform pressure is applied over its inner radius. The condition of axial symmetry in conjunction with the assumption of plane stress, permits an exact analytic solution. Two plastic collapse mechanisms exist. One of these mechanisms requires that the entire disk is plastic. According to the other mechanism, plastic deformation localizes at the inner radius of the disk. Additionally, two special solutions are possible. One of these solutions predicts that the entire disk becomes plastic at the initiation of plastic yielding (i.e., plastic yielding simultaneously initiates in the entire disk). The other special solution predicts that the plastic localization occurs at the inner radius of the disk with no plastic region of finite size. An essential difference between the orthotropic and isotropic disks is that plastic yielding might initiate at the outer radius of the orthotropic disk.

Practical approach to plastic collapse of conical shells under axial compression

Steel cylindrical shell structures such as silos and tanks are very sensitive to geometric imperfections and prone to a plastic instability failure known as elephant's foot (EF) buckling. This type of buckling arises under axial compression. The aim of this paper is to explore the plastic collapse response in conical shells with low semi-vertex angle values under compression. In a first step, the initial geometric imperfection shapes that dictate which plastic mechanisms arise were identified using finite element (FE) models. In a second step, a parametric study reported two plastic collapse mechanisms and showed that the elephant's foot plastic collapse mechanism is the most likely to appear in compressed conical shells with low d/t values, followed by the Yoshimura collapse mechanism, more common with larger d/t values. Finally, a practical model in which the parameters have been adjusted from numerical models has been derived for the elephant's foot plastic mechanism. This model provides the load-deformation behaviour of compressed conical shells at the post-collapse region. The load vs. end-shortening curves provided by the model have been validated through comparison with curves given by the FE models. The good agreement between the results proves the efficiency of the practical model to predict the collapse response of conical shells.

Analytical models for predicting the load-bearing strength of beam-to-column joints in a composite steel frame

Two analytical models are developed to predict the load-bearing capacity of a beam-to-column joint inside a slim-floor composite frame. The load inside the joint is transferred mainly by a steel console welded to a concrete-filled steel column. Because of the asymmetric nature of plastic collapse mechanism of the steel console, a two-parameter model is developed in two mechanisms: a mechanism excluding the axial force at hinge lines, and an intuitive mechanism including the influence of arising axial force. The models are verified by numerical results and used further for parametric studies. The results indicate that both models predict the limit load of the joint well. The studies also show that the model excluding the normal force is simple to use but can be a bit conservative, whereas the model including the normal force better predicts the load-bearing capacity of the joint, particularly if larger indentation is allowed. Based on the parametric studies, a general equation is then proposed. Compared to the method provided in design code as EN 1993-1-8, the proposed equation predicts the higher load-bearing capacity; thus leading to a more economical design in practice.

Evolutive and Kinematic Limit Analysis Algorithms for Large-Scale 3D Truss-Frame Structures: Comparison Application to Historic Iron Bridge Arch

Two new computational algorithms for the Limit Analysis (LA) of large-scale 3D truss-frame structures recently proposed by the authors are reconsidered and adapted for a comparison prediction of the elastoplastic response of a strategic beautiful historic infrastructure, namely the Paderno d’Adda bridge (or San Michele bridge), a riveted wrought iron railway viaduct that was built in northern Italy in 1889. The first LA algorithm traces a fully exact evolutive piece-wise linear elastoplastic response of the structure, up to plastic collapse, by reconstructing the true sequence of activation of made-available plastic joints (as a generalization of plastic hinges), in the true spirit of LA. The second LA algorithm develops an independent kinematic iterative approach apt to directly determine the plastic collapse state, in terms of collapse load multiplier and plastic mechanism, based on the upper-bound theorem of LA. Specifically, the marvelous doubly built-in parabolic arch of the bridge is analyzed, under a static loading configuration at try-out stage, and its elastoplastic response is investigated, in terms of evolutive load-displacement curve, collapse load multiplier and plastic collapse mechanism. The two LA algorithms are found to much effectively run and perform, despite the rather large size of the computational model, with a number of dofs in the order of four thousands, by achieving good corresponding matches in terms of the estimate of the load-bearing capacity and of the collapse characteristics of the arch substructure, showing this to constitute a well-set structural element. Moreover, the direct kinematic method displays a rather dramatic performance, in truly precipitating from above onto the collapse load multiplier and rapidly adjusting to the collapse mode, in very few iterations, by a considerable saving of computational time, with respect to the complete evolutive elastoplastic analysis. This shall open up the way for further adoption of such advanced LA tools, with LA regaining a new momentum within the modern optimization analysis of structural design and form-finding problems.

Modeling criteria of older non-ductile concrete frame–wall buildings

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.

Resistance of slender austenitic stainless steel I- girders subjected to patch loading

This paper presents a numerical investigation on the patch loading resistance of slender austenitic stainless steel plate girders. Current design provisions for the resistance to patch loading of stainless steel girders are based on the plastic collapse mechanism observed in experimental and numerical studies conducted for carbon steel girders, disregarding the strain hardening capacities of stainless steel. At present, strength-curves approaches are used within European standards to deal with stability problems in steel plated structural elements. In this regard, three parameters require special attention: the yield load for plastic resistance, the resistance function depending on element slenderness, and the elastic buckling load. In this paper, an experimental dataset is firstly collected from the literature for comparative analysis. Subsequently, an extensive parametric study is conducted through nonlinear finite element analyses covering a wide range of slender stainless steel I-girder sections. Then, a resistance function is calibrated throughout a statistical evaluation of experimental and numerical results. Finally, the results show significant improvements in the predicted patch loading resistances of slender stainless steel I-girders.

Semi-analytical simulation of plastic collapse mechanism of cracked continuous unstiffened plates used in ship structure under in-plane longitudinal compression

The present study is undertaken based on a nonlinear finite element study carried out by the same authors for estimation of ultimate strength of cracked continuous unstiffened plates used in ship structures under in-plane longitudinal compression. Investigations show that in addition to the magnitude of ultimate strength, the deflection shape and plastic collapse mechanism will also change completely. Results show that deflection in the cracked half wave increases more rapidly than other half waves. Consequently generated half waves in a cracked plate will not have identical length and amplitude. This implies that the conventional plastic collapse mechanism cannot be used to predict the behavior of cracked plates in the post ultimate strength region. A new plastic collapse mechanism based on the FEM results is suggested and the principle of virtual work is used to derive the axial stress-deflection relation of the plate. However, due to inequality of the length and amplitude of generated half waves, the axial stress-deflection relation cannot be directly derived from the principle of virtual work. Therefore, in order to solve the virtual work equation, some auxiliary relations between the involved parameters are required. Auxiliary equations are derived using regression analysis based on FEM results. Finally, a semi-analytical formulation is derived to estimate post ultimate strength behavior of cracked plates. It is shown that the proposed semi-analytical formulation can predict both magnitude and slope of the stress-deflection curves with better accuracy compared to the conventional plastic collapse mechanism. The formulation can be used within the defined ranges of simulated crack lengths, slenderness and aspect ratios.