Rigid-plastic Analysis Research Articles

Flexural performance of innovative sustainable composite steel-concrete beams

Composite beams comprising of concrete slabs and steel beams joined by conventional headed stud shear connectors are commonly used in modern steel-framed building construction. However, because the headed stud shear connectors are welded onto the top flange of the steel beam and cast into the in situ concrete slab, deconstruction of the composite beam and the reuse of its components at the end of structural life in defence to demolition is virtually impossible, which is at odds with the increasing demands placed on improving the sustainability of building infrastructure. As an alternative, an innovative sustainable composite beam and slab system is proposed, in which precast geopolymer concrete panels are attached to the steel beams using high-strength friction-grip bolts instead of cast in situ floors with pre-welded headed stud connectors. The advantages of a low-carbon design, both by the use of geopolymer concrete elements and system deconstructability, can be achieved in this proposed system. In this paper, a three-dimensional finite element model is developed to investigate the structural behaviour of the proposed sustainable composite beam and slab system. Material non-linearities and the interaction of the structural components are included in the model. The accuracy and reliability of the finite element formulation developed are validated by comparisons with experimental results. Extensive parametric studies are conducted to elucidate the effects of the change in the concrete panel configuration, the number and diameter of the bolts, the type and strength of the concrete and the grade of the steel beam on the behaviour of the system. The use of modified rigid plastic analysis is assessed, and a modification is suggested to predict the flexural strengths of the composite beams and slab system.

Theoretical analysis on the effect of uniform and localized impulsive loading on the dynamic plastic behaviour of fully clamped thin quadrangular plates

This paper presents an approximate theoretical analysis of inelastic behaviour of fully clamped thin quadrangular plates subjected to two different distributions of impulsive loading. The presented analysis has been developed based on plastic work of plate and kinetic energy in which it assumes that the plate behaves rigid perfectly plastic. The rigid plastic analysis uses an interaction yield surface based on reasonable assumption that only membrane force considers for plastic flow and employs the Cowper-Symonds equation to cater for material strain rate effect. In this study, the applied load is estimated by assuming the initial velocity field of flat plate based on the boundary conditions of plate and geometry of explosive charge setup. Obtained models predict final deflection of the quadrangular plate loaded by uniformly and localized loading. The proposed solution permits consideration of characteristic influence of the load and material on the response of plate. It is observed that the present theoretical models are in good agreements with experimental results and also in comparison with other approximate solution, the present models are found to be simpler and in better agreements with experimental values.

Web crippling of beams under ITF loading: A novel DSM-based design approach

A new approach to estimate the web crippling failure load of cold-formed steel beams under Internal Two Flange (ITF) loading using the Direct Strength Method (DSM) is proposed in this paper. After the description of the existing test data to calibrate the DSM-based formula, the accuracy of the analytical expressions given in Eurocode 3 [1] and the North-American Specification [2] is briefly assessed. In order to obtain additional information on the web crippling behaviour of each test specimen, several types of analyses are performed: (i) quasi-static non-linear analyses (using finite elements), (ii) elastic buckling analyses (using finite elements and the GBTWEB software), and (ii) rigid-plastic analyses (using yield-line theory). The coefficients of a DSM-based formula are determined on the basis of the set of 85 experimental results available in the literature and the corresponding buckling and plastic load values. In spite of the different cross-sections, fastening conditions and test set-ups considered in the calibration procedure, it is possible to establish a clear relationship between the web crippling slenderness and the nominal-to-plastic load ratio. Finally, it is shown that the proposed DSM-based formula for ITF loading yields reasonable predictions of web crippling loads and provides safe estimates of flange crushing loads.

Flexural behaviour of composite steel–concrete beams utilising blind bolt shear connectors

This paper investigates the feasibility of utilising blind bolts as shear connectors to develop demountable steel–concrete beams. The flexural behaviour of composite beams with two blind bolt types and welded stud connectors were experimentally investigated using full-scale beam specimens. A set of push-test specimens was tested based on the Eurocode 4 to compare the slip response of these connectors. The ultimate design loads of the test beams were calculated based on rigid plastic analysis (RPA) using the actual material properties. The beam experiments were simulated by using three-dimensional non-linear finite element models (FEMs). The material behaviour for concrete and steel in FEMs was described using concrete damage plasticity and steel plasticity models respectively. The FEMs were validated by comparing the load–midspan deflection curves of the beam specimens obtained from the experiments and modelling. The effects of the concrete compressive strength, steel yield strength and the shear connection ratio on the flexural behaviour of the composite beams were studied by utilising the validated FEMs. The experimental and numerical results suggest that the ability of the blind bolts to achieve and maintain composite action in steel–concrete beams under flexural loading is comparable to that of the welded stud connectors.

Numerical modeling of particle embedment during solid particle erosion of ductile materials

Particle embedment may occur in erosion testing, abrasive jet machining, blast cleaning and other industrial processes in which high speed impact of particles on relatively ductile targets occurs. It may strongly affect erosion rates, and lead to undesirable changes in surface roughness. Three-dimensional smoothed particle hydrodynamics (SPH) simulations were used to simulate particle embedment when 219.2µm and 362.9µm angular silicon carbide particles impacted a strain and strain rate hardening 6061-T6 aluminum alloy target under various process conditions. The models were assessed by comparison with measured embedment. Analysis of the results showed the following: (i) once the value of the effective friction coefficient between the substrate and the abrasive was determined by comparing predicted and measured embedment at one set of process conditions (particle velocity, size, angle of attack), the same friction coefficient could be used in models of all other combinations of process conditions to correctly predict embedment. (ii) Consistent with a previous simplified rigid-plastic analysis of idealized rhomboid particles impacting a polymer target, the static frictional force occurring after the maximum depth has been reached, the particle orientation and the impact angle all strongly affected embedment. Unlike the previous simplified model, the present model considered local strain rate and strain hardening, making it applicable for ductile metal targets. (iii) Consistent with some, but not all, reports in the literature, embedment at a given velocity increased with particle size. (iv) For a given particle size, embedment increased with incident velocity. (v) A critical minimum velocity below which embedment would not occur was predicted. The trends were discussed in terms of embedment mechanisms and particle impact kinematics. Overall, the work demonstrates that SPH methods can be used to provide insight into complex solid particle erosion phenomena.

Strengthening of existing composite steel-concrete beams utilising bolted shear connectors and welded studs

This paper considers the flexural behaviour of steel-concrete composite beams retrofitted with two types of bolted connectors and welded stud connectors. Three composite beams, one from each connector type, and four non-composite beams were cast together. Three of the non-composite beams were retrofitted using the three connector types respectively. The connectors were installed through holes cored in the concrete slabs of the beams. The holes were backfilled using structural grout. The beams were then tested under static flexural loading. The load-slip behaviour of these connectors under normal and retrofitted conditions was investigated using push-tests. The flexural behaviour of the retrofitted beams was compared with that of the normal composite beams and non-composite beams. The ultimate loads of the test specimens were compared with the design ultimate loads of these beams calculated using Rigid Plastic Analysis (RPA). The vertical deflection of the beams under serviceable load regimes was also compared. The beam experiments were simulated using Finite Element (FE) models developed with ABAQUS. Material models with damage parameters were specified for the concrete and grout used in the test specimens using the Concrete Damage Plasticity (CDP) option. The effects of the concrete and grout strength, grout-hole size and shear connection ratio on the flexural behaviour of retrofitted beams were investigated by carrying out a parametric analysis. The results obtained from full-scale beam and push-test experiments and also the analytical results from RPA and FE analyses are presented and discussed in detail in this paper.

Behaviour and design of composite beams subjected to sagging bending and axial compression

This paper presents an experimental and numerical study on the ultimate strength of steel–concrete composite beams subjected to the combined effects of sagging (or positive) bending and axial compression. Six full-scale composite beams were tested experimentally under sagging bending and increasing levels of axial compression. A nonlinear finite element model was also developed and found to be capable of accurately predicting the nonlinear response and the combined strength of the tested composite beams. The numerical model was then used to carry out a series of parametric analyses on a range of composite sections commonly used in practice. It was found that the sagging moment resistance of a composite beam is not reduced under low-to-moderate axial compression, while it significantly deteriorates under high axial compression. Sectional rigid plastic analyses confirmed the experimental results. The moment–axial force interaction does not change significantly between full and partial shear connection. Based on the experimental and numerical results, a sagging moment–axial compression interaction law is proposed which will allow for a more efficient design of composite beams.

Rigid Plastic Analysis of Metal Parts using Meshless Approach

Plastic deformation of metal parts has been a matter of concern for investigators in academia, industry and research institutions all over the world. Literature reveals that earlier researchers have applied efforts for predicting plastic deformations using mesh based approach. A truly meshless formulation for rigid plastic analysis of metal parts has been developed in the present study for both plane stress and plane strain cases. In the present formulation, the governing equations are obtained for different set of scattered nodes over the problem domain and the integral equation for rigid plastic behavior is obtained through weak form over a local sub-domain. The meshless solution functions are obtained for different set of scattered nodes through moving least square technique. Essential boundary conditions are enforced through Penalty approach. The rigid plastic constitutive relationships incorporate only small deformation. Material constitutive relationship include Von-Mises yield criterion with rate independent associative flow theory. The solution algorithm for rigid plastic analysis of metal parts using meshless approach is discussed in the present work. Numerical results have been computed through two test functions using both linear and quadratic basis function which shows that presented formulation is accurate and robust for carrying out the rigid plastic analysis of metal parts.

Rigid-plastic analysis and moment–shear interaction for hierarchy criteria of inverted Y EB-Frames

One of the primary purposes in structural design of seismic-resistant structures is the prevention of undesired collapse mechanisms, involving only a few storeys, which are not satisfactory in terms of energy dissipation capacity.The optimization of the seismic structural response can be achieved with a collapse mechanism of global type, because, in this case, all the dissipative zones are involved in the corresponding pattern of yielding, while all the other non-dissipative structural parts remain in elastic range. In order to promote the development of a collapse mechanism of global type, modern seismic codes provide simple design rules based on so-called hierarchy criteria. However, even though these simple criteria are able to ensure that “soft storey” mechanisms are prevented, they are not able to lead to the development of a collapse mechanism of global type. Therefore, more sophisticated design procedures based on rigid-plastic analysis have been proposed to assure such design goal.In this paper, within the framework of the theory of plastic mechanism control, rigid-plastic analysis of EB-Frames with inverted Y-scheme is carried out including moment–shear interaction aiming to the development of simple hierarchy criteria to be applied with reference to the single storeys to prevent undesired collapse mechanisms. Therefore, reference is made to the simple one-storey scheme. Conversely, the whole theory of plastic mechanism control for EB-Frames with inverted Y-scheme will be presented in a forthcoming paper dealing with multi-storey EB-Frames.Finally, the effectiveness of the proposed hierarchy criteria has been verified by several push over analyses.

Strength prediction and failure modes of concrete specimens subjected to the split test

This paper deals with modelling and test of concrete specimens subjected to the Brazilian split test. Based on the fictitious crack concept, a simple model for the crack propagation process in the splitting plane is developed. From the model, it is possible to determine the distribution of residual tensile strength as crack propagation take place. The residual tensile strength is thereafter used in a rigid plastic analysis of the splitting failure. Based on this combined approach, the ultimate load may either be governed by crack propagation or by a plastic failure, which then terminates the crack growth process. It is shown that the model is able to replicate a number of experimental observations. This includes size effect and influence of loading width.

Analysis of steel–concrete composite column subject to blast

The single-degree-of-freedom method is commonly used to approximate the dynamic response of structures subjected to blast loading. One of the limitations of this method is that it cannot capture the multi-failure modes of the structural members. The rigid–plastic method is thus, proposed in this paper as an alternative analytical approach to estimate the blast response of concrete-filled steel composite columns. The rigid–plastic results are compared with single-degree-of-freedom calculations as well as numerical simulations in order to assess the competency of the proposed method. Due to the assumption of rigid–plastic material behaviour in the rigid–plastic analysis, the accuracy of this method is influenced by the extent of plastic deformation of the structural member. For the case of impulsive blast loading, the rigid–plastic estimations are found to be closer to the numerical results than those obtained using the single-degree-of-freedom method. Numerical analysis was also conducted to compare the performance of concrete-filled steel composite column to a reinforced concrete column. A significant improvement in the blast resistance of the composite column was observed from the comparison.

Elasticity Effect in Dynamic Response of Beams with Pre-Cracks Impinged by Striker

To examine the effect of elasticity in dynamic response of imperfect structures, by densely setting meshes in the vicinity of the imperfections, pre-cracked beams impinged by a striker are modeled and numerically investigated. The dynamic response patterns and failure history for two specific configurations are obtained. It is found that complex alternations of the elastic-plastic stress distribution exhibit, and the striker is rebounded and then separated from the beam, which well reflects the effect of material elasticity. The high stress and large deformation zones, corresponding to the plastic hinges in the rigid-plastic model, appear at the impinging position and the supporting ends, and the locations coincide with those in the modal pattern in rigid-plastic response. From comparison, it is concluded that when the impinging is intense, despite the effect of elasticity displaying in the early stage, the widely employed rigid-plastic analysis is still capable of providing favorable prediction on the final response parameters.

Behaviour and design of composite beams subjected to negative bending and compression

This paper investigates the behaviour of steel–concrete composite beams subjected to the combined effects of negative bending and axial compression. For this study, six full-scale tests were conducted on composite beams subjected to negative moment while compression was applied simultaneously. The level of the applied axial compression varied from low to high. Following the tests, a nonlinear finite element model was developed and calibrated against the experimental results. The model was found to be capable of predicting the nonlinear response and the ultimate failure modes of the tested beams. The developed finite element model was further used to carry out a series of parametric analyses on a range of composite sections commonly used in practice. It was found that, when a compressive load acts in the composite section, the negative moment capacity of a composite beam is significantly reduced and local buckling in the steel beam is more pronounced, compromising the ductility of the section. Rigid plastic analysis based on sectional equilibrium can reasonably predict the combined strength of a composite section and, thus, can be used conservatively in the design practice. Detailing with longitudinal stiffeners in the web of the steel beam in the regions of negative bending eliminate web buckling and increase the rotational capacity of the composite section. Based on the experimental outcomes and the finite element analyses a simplified design model is proposed for use in engineering practice.

Numerical and simplified analytical methods for analysis of the residual strength of ship double bottom

This paper presents a numerical simulation and simplified methods for estimating the residual strength of a damaged double bottom. A typical double-bottom structure from a shuttle tanker was modelled. The structure was idealised to a small degree. Imperfections were introduced to the whole structure according to design rules. The most severe situation of the fully loaded condition was investigated. Hull girder bending was considered. Damage was caused by a variety of indenters that were specially designed to obtain a desired damage profile. A total of 16 numerical-calculation cases were investigated using the explicit commercial code LS-DYNA 971. A simplified method was derived. This method includes elastic plus rigid-plastic analyses of a 3-span, single-stiffener model. Unlike Smith's method, the present approach takes damaged stiffened panels into account in the residual strength assessment. The elastic and rigid-plastic analyses were combined to provide the load-end shortening curve for the damaged stiffeners. A simplified damage mechanism for the tripping of stiffeners is presented, as is a 3-span single stiffener model with proper boundary conditions. Both the analytical and single stiffener models were used to estimate the residual strength of a damaged double bottom. Both methods were validated with a non-linear, finite-element analysis (NLFEA) simulation carried out using LS-DYNA 971.

Semi-analytic approach for sandwich plate U-bending considering shear deformation of the core

The deformation mechanism of a sandwich plate during U-bending was theoretically investigated by rigid-plastic analysis considering shear deformation of the core and the frictional effect. The deformed shapes of a sandwich plate, which were described as a combination of straight lines and arcs, were calculated by Newton method to minimize the total internal work dissipation. Homogenized properties of core shear stress–shear strain curves calculated by using pure shear FE-analyses were used in the analysis. For the numerical verification of the proposed analysis, U-bending simulations were carried out for sandwich plates with various inner structures including a pyramidal truss core, a honeycomb core, corrugated cores, and a sheared dimple core. The analytic scheme has enabled the acceptable prediction of the load curves and deformed shapes during U-bending.

Steel square hollow sections subjected to transverse blast loads

Thin-walled steel hollow sections are used extensively in the construction, offshore, mining and security industries. Such members subjected to blast loads are of interest due to increased security demands and the occurrence of accidental or intentional explosive events. This paper reports an experimental and analytical investigation of steel square hollow sections subjected to transverse blast load, applied with explosive uniformly distributed along the length of the member. Three different section sizes were tested over three different lengths, and the members were fully clamped at their ends. The explosive loads were sufficient in magnitude to cause plastic deformation of the cross-section (local deformation), plastic flexural deformation of the overall member (global deformation), and tensile tearing at the supports. The energy dissipated in the local deformation is determined using rigid-plastic analysis and yield line mechanisms of the deformed cross-sections. The total input energy minus the energy dissipated in local deformation is assumed to be expended in flexural deformation. Analytical solutions using the energy consumed in flexural deformation are shown to produce bounded solutions of the transverse plastic deformation of the members. Finally, a semi-empirical solution is suggested that can be used to aid in design.

Failure mechanism of expanded metal tubes under axial crushing

The failure mechanism of expanded metal tubes under axial crushing is addressed herein. Experimental results have shown that when collapsing the tubes, the expanded metal cells closes until the plastic moment in all nodes along the mid-section of the tubes is attained exhibiting a plastic collapse mechanism. From this deformed configuration, a simple analytical expression is developed for the ultimate strength of the tube based on a rigid-plastic analysis of a frame-like structure. In addition, the energy absorption capacity of the tubes is also calculated. Theoretical predictions for both strength and energy are in good agreement with experimental results taken from the literature. Thereafter, a numerical study was conducted in order to investigate the validity of the theoretical model depending on the expanded metal cell geometry. It is found that the load-displacement response and failure mechanism of the tubes depend upon the aspect ratio of the expanded metal cell.

Rigid-Plastic FEM Simulation of Orthogonal Cutting Process

This paper presents a rigid-plastic finite element method for orthogonal cutting process by adopting Lagrange method. The rigid-plastic FEM analysis model is established and the rigid-plastic FEM analysis toolkit was developed. Meanwhile, two relevant key problems are discussed systematically, including the rule of chip-workpiece separation and the criterion of tool-chip separation. At last, a simulation example of planing an aluminium alloy (ZL-301) workpiece was conducted. The effects of the cutting stroke, the tool rake angle and the friction coefficient on chip were observed. The numerical simulation results have a good agreement with their experimental ones. It is indicated that the presented FEM model and algorithm are efficient and correct.

The effects of axial tension on the hogging-moment regions of composite beams

Structural parts commonly comprised of composite members such as bridge approaches, inclined parking ramps and stadium beams, can be subjected to a combination of high axial loads and bending moments. Steel–concrete composite construction is a popular solution for these types of structures due to the numerous advantages that they offer. Although, current design codes (e.g. Eurocode 4, American code AISC, Australian codes AS2327 and AS5100) provide rules for the design of composite columns subjected to flexure and axial load, however the design of composite beams, which are asymmetric in nature under the combined effects of tension and bending, is not yet fully addressed. This paper investigates the ultimate strength of composite beams under the combined effects of axial tension and negative (hogging) bending moment. An experimental programme carried out in the laboratory of the University of Western Sydney comprised of a total of six specimens representing composite beams and subjected to various levels of axial tension and bending moment. Ultimate failure modes were identified and the resulting interaction diagrams were compared to the results of sectional rigid plastic analysis. Following the tests, three-dimensional finite element models were employed using the ABAQUS finite element software to further investigate the nonlinear behaviour of the composite beams and extend the experimental observations by studying the effects of parameters such as the span length and the effect of partial shear connection. Finally, simple design rules and formulae are proposed for use in engineering practice.

Upper-bound yield-line rigid-plastic plane-stress analysis of core coupling-beams in tall buildings

Cores in tall buildings sub-divide and fire-separate vertical riser services such as lifts, stairs, air-conditioning systems, utilities and rooms requiring access to plumbing. This paper addresses the structural design of load-bearing concrete cores as distinct from framed structural steel cores fire-protected by gypsum plasterboard. Concrete cores are much more resistant to abnormal events such as earthquake, terrorist attack and disproportionate collapse, and also provide huge increases in structural stiffness and damping. Concrete cores seem to be universal for tall buildings in Australia perhaps because of local experience in the construction of wheat silos. A decision for a concrete core leaves open the decision to use concrete or structural steel for floor and façade framing. Concrete core-walls are penetrated by vertical families of openings for doors to stairs, lifts and other spaces. These openings separate the core as a whole into a number of sub-cores linked by coupling-beams (the residual strips of concrete core-wall above and below openings). Coupling-beams can be thought of as large-scale shear connectors providing composite action between distinct sub-cores. First yield will often occur in coupling-beams and spread vertically. The span/depth ratio of these beams is determined by architects and lift engineers and is often well into the ‘deep-beam' range prone to brittle behaviour. American seismic design practice, based on experimental research at the University of Canterbury, New Zealand, requires complete ‘X-reinforcement' consisting of tied rebar cages (as for columns) on both diagonals of coupling-beams. X-reinforcement can definitely improve the ductility of otherwise brittle elements. It does, however, create practical construction problems: ties are closely spaced (for Bauschinger buckling) and the crossing X-cages together with the ‘basketing' reinforcement (to avert injuries from falling concrete chunks) can amount to six to eight (or ten) layers of reinforcement across the thickness of a wall, which may also require 40 mm cover for fire-rating. Walls of 250 mm thickness are barely possible and 300 mm thick walls present difficulties. For regions of lower earthquake risk, such as the UK and Australia, one wonders whether there are reasonable alternatives to X-reinforcement, particularly when the beam size provided by lift engineers is large and only minimal rebar is required. Minimal rebar is not much more than the basketing reinforcement required with X-bars, and in some cases may be ample without large reliance on ductility. In New Zealand, more recent codes do permit buildings of limited ductility with stronger elements. In any case, the rigid-plastic collapse mechanisms provided and discussed here are quite capable of including X-bars and the present approach just provides the simplest first-pass treatment. The analyses presented here seem to agree with the conclusion reached by the late Professor Tom Paulay from experimental work at Canterbury beginning in 1967: that the bending ‘compression' rebars may be highly stressed in tension and this does reduce strength and ductility. The paper studies a range of in-plane yield-line mechanisms, starting with an almost conventional bending mechanism and then considering three shear mechanisms before arriving at a combined (bending/shear) mechanism which seems to be ‘exact'. One aim is to exemplify the variability of upper-bound analysis where, in this case, the highest bound is 2·6 times the ‘exact' result.