Refined plastic hinge analysis of steel frame structures comprising non-compact sections : II : verification

Application of "advanced analysis" methods suitable for non-linear analysis and design of steel frame structures permits direct and accurate determination of ultimate system strengths, without resort to simplified elastic methods of analysis and semi-empirical specification equations. However, the application of advanced analysis methods has previously been restricted to steel frames comprising only compact sections that are not influenced by the effects of local buckling. A refined plastic hinge method suitable for practical advanced analysis of steel frame structures comprising non-compact sections is presented in a companion paper. The method implicitly accounts for the effects of gradual cross-sectional yielding, longitudinal spread of plasticity, initial geometric imperfections, residual stresses, and local buckling. The accuracy and precision of the method for the analysis of steel frames comprising non-compact sections is established in this paper by comparison with a comprehensive range of analytical benchmark frame solutions. The refined plastic hinge method is shown to be more accurate and precise than the conventional individual member design methods based on elastic analysis and specification equations.

Local plastic mechanisms in thin steel plates under in-plane compression

Thin-walled steel plates subjected to in-plane compression develop two types of local plastic mechanism, namely the roof-shaped mechanism and the so-called flip-disc mechanism, but the intriguing question of why two mechanisms should develop was not answered until recently. It was considered that the location of first yield point shifted from the centre of the plate to the midpoint of the longitudinal edge depending on the b/t ratio, imperfection level, and yield stress of steel, which then decided the type of mechanism. This paper has verified this hypothesis using analysis and laboratory experiments. An elastic analysis using Galerkin's method to solve Marguerre's equations was first used to determine the first yield point, based on which the local plastic mechanism/imperfection tolerance tables have been developed which give the type of mechanism as a function of b/t ratio, imperfection level and yield stress of steel. Laboratory experiments of thin-walled columns verified the imperfection tolerance tables and thus indirectly the hypothesis. Elastic and rigid-plastic curves were them used to predict the effect on the ultimate load due to the change of mechanism. A finite element analysis of selected cases also confirmed the results from simple analyses and experiments.

Local buckling behaviour of steel plate elements supported by a plastic foam material

Sandwich panels comprising steel facings and a polystyrene foam core are increasingly used as roof and wall claddings in buildings in Australia. When they are subjected to loads causing bending and/or axial compression, the steel plate elements of their profiled facing are susceptible to local buckling. However, when compared to panels with no foam core, they demonstrate significantly improved local buckling behaviour because they are supported by foam. In order to quantify such improvements and to validate the use of available design buckling stress formulae, an investigation using finite element analyses and laboratory experiments was carried out on steel plates that are commonly used in Australia of varying yield stress and thickness supported by a polystyrene foam core. This paper presents the details of this investigation, the buckling results and their comparison with available design buckling formulae.

Pseudo plastic zone analysis of steel frame structures comprising non-compact sections

Application of `advanced analysis' methods suitable for non-linear analysis and design of steel frame structures permits direct and accurate determination of ultimate system strengths, without resort to simplified elastic methods of analysis and semi-empirical specification equations. However, the application of advanced analysis methods has previously been restricted to steel frames comprising only compact sections that are not influenced by the effects of local buckling. A concentrated plasticity method suitable for practical advanced analysis of steel frame structures comprising non-compact sections is presented in this paper. The pseudo plastic zone method implicitly accounts for the effects of gradual cross-sectional yielding, longitudinal spread of plasticity, initial geometric imperfections, residual stresses, and local buckling. The accuracy and precision of the method for the analysis of steel frames comprising non-compact sections is established by comparison with a comprehensive range of analytical benchmark frame solutions. The pseudo plastic zone method is shown to be more accurate and precise than the conventional individual member design methods based on elastic analysis and specification equations.

Second-order inelastic analysis of composite framed structures based on the refined plastic hinge method

Composite steel-concrete structures experience non-linear effects which arise from both instability-related geometric non-linearity and from material non-linearity in all of their component members. Because of this, conventional design procedures cannot capture the true behaviour of a composite frame throughout its full loading range, and so a procedure to account for those non-linearities is much needed. This paper therefore presents a numerical procedure capable of addressing geometric and material non-linearities at the strength limit state based on the refined plastic hinge method. Different material non-linearity for different composite structural components such as T-beams, concrete-filled tubular (CFT) and steel-encased reinforced concrete (SRC) sections can be treated using a routine numerical procedure for their section properties in this plastic hinge approach. Simple and conservative initial and full yield surfaces for general composite sections are proposed in this paper. The refined plastic hinge approach models springs at the ends of the element which are activated when the surface defining the interaction of bending and axial force at first yield is reached; a transition from the first yield interaction surface to the fully plastic interaction surface is postulated based on a proposed refined spring stiffness, which formulates the load-displacement relation for material non-linearity under the interaction of bending and axial actions. This produces a benign method for a beam-column composite element under general loading cases. Another main feature of this paper is that, for members containing a point of contraflexure, its location is determined with a simple application of the method herein and a node is then located at this position to reproduce the real flexural behaviour and associated material non-linearity of the member. Recourse is made to an updated Lagrangian formulation to consider geometric non-linear behaviour and to develop a non-linear solution strategy. The formulation with the refined plastic hinge approach is efficacious and robust, and so a full frame analysis incorporating geometric and material non-linearity is tractable. By way of contrast, the plastic zone approach possesses the drawback of strain-based procedures which rely on determining plastic zones within a cross-section and which require lengthwise integration. Following development of the theory, its application is illustrated with a number of varied examples.

Higher-order non-linear analysis of steel structures. Part II : refined plastic hinge formulation

In the companion paper, a fourth-order element formulation in an updated Lagrangian formulation was presented to handle geometric non-linearities. The formulation of the present paper extends this to include material non-linearity by proposing a refined plastic hinge approach to analyse large steel framed structures with many members, for which contemporary algorithms based on the plastic zone approach can be problematic computationally. This concept is an advancement of conventional plastic hinge approaches, as the refined plastic hinge technique allows for gradual yielding, being recognized as distributed plasticity across the element section, a condition of full plasticity, as well as including strain hardening. It is founded on interaction yield surfaces specified analytically in terms of force resultants, and achieves accurate and rapid convergence for large frames for which geometric and material non-linearity are significant. The solutions are shown to be efficacious in terms of a balance of accuracy and computational expediency. In addition to the numerical efficiency, the present versatile approach is able to capture different kinds of material and geometric non-linearities on general applications of steel structures, and thereby it offers an efficacious and accurate means of assessing non-linear behaviour of the structures for engineering practice.

Inelastic finite element analysis of composite beams on the basis of the plastic hinge approach

This paper emphasizes material nonlinear effects on composite beams with recourse to the plastic hinge method. Numerous combinations of steel and concrete sections form arbitrary composite sections. Secondly, the material properties of composite beams vary remarkably across its section from ductile steel to brittle concrete. Thirdly, concrete is weak in tension, so composite section changes are dependent on load distribution. To this end, the plastic zone approach is convenient for inelastic analysis of composite sections that can evaluate member resistance, including material nonlinearities, by routine numerical integration with respect to every fiber across the composite section. As a result, many researchers usually adopt the plastic zone approach for numerical inelastic analyses of composite structures. On the other hand, the plastic hinge method describes nonlinear material behaviour of an overall composite section integrally. Consequently, proper section properties for use in plastic hinge spring stiffness are required to represent the material behaviour across the arbitrary whole composite section. In view of numerical efficiency and convergence, the plastic hinge method is superior to the plastic zone method. Therefore, based on the plastic hinge approach, how to incorporate the material nonlinearities of the arbitrary composite section into the plastic hinge stiffness formulation becomes a prime objective of the present paper. The partial shear connection in this paper is by virtue of the effective flexural rigidity as AISC 1993 [American Institute of Steel Construction (AISC). Load and resistance factor design specifications. 2nd ed., Chicago; 1993]. Nonlinear behaviour of different kinds of composite beam is investigated in this paper, including two simply supported composite beams, a cantilever and a two span continuous composite beam.

Nonlinear analysis of plastic ball grid array solder joints

A nonlinear finite element analysis was carried out to investigate the viscoplastic deformation of solder joints in a ball grid array (BGA) package under temperature cycle. The effects of constraint on print circuit board (PCB) and stiffness of substrate on the deformation behaviour of the solder joints were also studied. A relative damage stress was adopted to analyze the potential failure sites in the solder joints. The results indicated that high inelastic strain and strain energy density were developed in the joints close to the package center. On the other hand, high constraint and high relative damage stress were associated with the joint closest to the edge of the silicon chip. The joint closest to the edge of the silicon chip was regarded as the most susceptible failure site if cavitation instability is the dominant failure mechanism. Increase the external constraint on the print circuit board (PCB) causes a slight increase in stress triaxiality (m/eq) and relative damage stress in the joint closest to the edge of silicon die. The relative damage stress is not sensitive to the Young’s modulus of the substrate.

Commissioning of a new commercial plastic scintillator system for radiotherapy

Introduction Since 1992 there have been several articles published on research on plastic scintillators for use in radiotherapy. Plastic scintillators are said to be tissue equivalent, temperature independent and dose rate independent [1]. Although their properties were found to be promising for measurements in megavoltage X-ray beams there were some technical difficulties with regards to its commercialisation. Standard Imaging has produced the first commercial system which is now available for use in a clinical setting. The Exradin W1 scintillator device uses a dual fibre system where one fibre is connected to the Plastic Scintillator and the other fibre only measures Cerenkov radiation [2]. This paper presents results obtained during commissioning of this dosimeter system. Methods All tests were performed on a Novalis Tx linear accelerator equipped with a 6 MV SRS photon beam and conventional 6 and 18 MV X-ray beams. The following measurements were performed in a Virtual Water phantom at a depth of dose maximum. Linearity: The dose delivered was varied between 0.2 and 3.0 Gy for the same field conditions. Dose rate dependence: For this test the repetition rate of the linac was varied between 100 and 1,000 MU/min. A nominal dose of 1.0 Gy was delivered for each rate. Reproducibility: A total of five irradiations for the same setup. Results The W1 detector gave a highly linear relationship between dose and the number of Monitor Units delivered for a 10 9 10 cm2 field size at a SSD of 100 cm. The linearity was within 1 % for the high dose end and about 2 % for the very low dose end. For the dose rate dependence, the dose measured as a function of repetition the rate (100–1,000 MU/min) gave a maximum deviation of 0.9 %. The reproducibility was found to be better than 0.5 %. Discussion and conclusions The results for this system look promising so far being a new dosimetry system available for clinical use. However, further investigation is needed to produce a full characterisation prior to use in megavoltage X-ray beams.

Failure of discontinuous railhead edges due to plastic strain accumulation

Railhead is perhaps the highest stressed civil infrastructure due to the passage of heavily loaded wheels through a very small contact patch. The stresses at the contact patch cause yielding of the railhead material and wear. Many theories exist for the prediction of these mechanisms of continuous rails; this process in the discontinuous rails is relatively sparingly researched. Discontinuous railhead edges fail due to accumulating excessive plastic strains. Significant safety concern is widely reported as these edges form part of Insulated Rail Joints (IRJs) in the signalling track circuitry. Since Hertzian contact is not valid at a discontinuous edge, 3D finite element (3DFE) models of wheel contact at a railhead edge have been used in this research. Elastic–plastic material properties of the head hardened rail steel have been experimentally determined through uniaxial monotonic tension tests and incorporated into a FE model of a cylindrical specimen subject to cyclic tension load- ing. The parameters required for the Chaboche kinematic hardening model have been determined from the stabilised hysteresis loops of the cyclic load simulation and imple- mented into the 3DFE model. The 3DFE predictions of the plastic strain accumulation in the vicinity of the wheel contact at discontinuous railhead edges are shown to be affected by the contact due to passage of wheels rather than the magnitude of the loads the wheels carry. Therefore to eliminate this failure mechanism, modification to the contact patch is essential; reduction in wheel load cannot solve this problem.

Nonlinear geometric and material computational technique : higher-order element with refined plastic hinge approach

This paper addresses of the advanced computational technique of steel structures for both simulation capacities simultaneously; specifically, they are the higher-order element formulation with element load effect (geometric nonlinearities) as well as the refined plastic hinge method (material nonlinearities). This advanced computational technique can capture the real behaviour of a whole second-order inelastic structure, which in turn ensures the structural safety and adequacy of the structure. Therefore, the emphasis of this paper is to advocate that the advanced computational technique can replace the traditional empirical design approach. In the meantime, the practitioner should be educated how to make use of the advanced computational technique on the second-order inelastic design of a structure, as this approach is the future structural engineering design. It means the future engineer should understand the computational technique clearly; realize the behaviour of a structure with respect to the numerical analysis thoroughly; justify the numerical result correctly; especially the fool-proof ultimate finite element is yet to come, of which is competent in modelling behaviour, user-friendly in numerical modelling and versatile for all structural forms and various materials. Hence the high-quality engineer is required, who can confidently manipulate the advanced computational technique for the design of a complex structure but not vice versa.

Improvement of the mode II interface fracture toughness of glass fiber reinforced plastics/aluminum laminates through vapor grown carbon fiber interleaves

The effects of acid treatment, vapor grown carbon fiber (VGCF) interlayer and the angle, i.e., 0° and 90°, between the rolling stripes of an aluminum (Al) plate and the fiber direction of glass fiber reinforced plastics (GFRP) on the mode II interlaminar mechanical properties of GFRP/Al laminates were investigated. The experimental results of an end notched flexure test demonstrate that the acid treatment and the proper addition of VGCF can effectively improve the critical load and mode II fracture toughness of GFRP/Al laminates. The specimens with acid treatment and 10 g m−2 VGCF addition possess the highest mode II fracture toughness, i.e., 269% and 385% increases in the 0° and 90° specimens, respectively compared to those corresponding pristine ones. Due to the induced anisotropy by the rolling stripes on the aluminum plate, the 90° specimens possess 15.3%–73.6% higher mode II fracture toughness compared to the 0° specimens. The improvement mechanisms were explored by the observation of crack propagation path and fracture surface with optical, laser scanning and scanning electron microscopies. Moreover, finite element analyses were carried out based on the cohesive zone model to verify the experimental fracture toughness and to predict the interface shear strength between the aluminum plates and GFRP laminates.