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.

A novel iterative method for simulating patient-specific optimal deformation and fit of fracture fixation plates

This paper proposes a new iterative method to achieve an optimally fitting plate for preoperative planning purposes. The proposed method involves integration of four commercially available software tools, Matlab, Rapidform2006, SolidWorks and ANSYS, each performing specific tasks to obtain a plate shape that fits optimally for an individual tibia and is mechanically safe. A typical challenge when crossing multiple platforms is to ensure correct data transfer. We present an example of the implementation of the proposed method to demonstrate successful data transfer between the four platforms and the feasibility of the method.

Deformation properties of single red blood cell in a stenosed microchannel

Red Blood Cells (RBCs) exhibit different types of motions and different deformed shapes, when they move through capillaries. RBCs can travel through capillaries having smaller diameters than RBCs’ diameter, due to the capacity of high deformability of the viscoelastic RBC membrane. The motion and the steady state shape of the RBCs depend on many factors, such as the geometrical parameters of the microvessel through which blood flows, the RBC membrane bending stiffness and the flow velocity. In this study, the effect of the RBC’s membrane stiffness on the deformation of a single RBC in a stenosed capillary is comprehensively examined. Smoothed Particle Hydrodynamics (SPH) in combination with the two-dimensional spring network membrane model is used to investigate the motion and the deformation property of the RBC. The simulation results demonstrate that the membrane bending stiffness of the RBC has a significant impact on the RBCs’ deformability.

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.

A simulation-based large deflection and inelastic analysis of steel frames under fire

This paper presents an accurate and robust geometric and material nonlinear formulation to predict structural behaviour of unprotected steel members at elevated temperatures. A fire analysis including large displacement effects for frame structures is presented. This finite element formulation of beam-column elements is based on the plastic hinge approach to model the elasto-plastic strain-hardening material behaviour. The Newton-Raphson method allowing for the thermal-time dependent effect was employed for the solution of the non-linear governing equations for large deflection in thermal history. A combined incremental and total formulation for determining member resistance is employed in this nonlinear solution procedure for the efficient modeling of nonlinear effects. Degradation of material strength with increasing temperature is simulated by a set of temperature-stress-strain curves according to both ECCS and BS5950 Part 8, which implicitly allows for creep deformation. The effects of uniform or non-uniform temperature distribution over the section of the structural steel member are also considered. Several numerical and experimental verifications are presented.

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.

Performance-based structural fire design of steel frames using conventional computer software

Fire incident in buildings is common, so the fire safety design of the framed structure is imperative, especially for the unprotected or partly protected bare steel frames. However, software for structural fire analysis is not widely available. As a result, the performance-based structural fire design is urged on the basis of using user-friendly and conventional nonlinear computer analysis programs so that engineers do not need to acquire new structural analysis software for structural fire analysis and design. The tool is desired to have the capacity of simulating the different fire scenarios and associated detrimental effects efficiently, which includes second-order P-D and P-d effects and material yielding. Also the nonlinear behaviour of large-scale structure becomes complicated when under fire, and thus its simulation relies on an efficient and effective numerical analysis to cope with intricate nonlinear effects due to fire. To this end, the present fire study utilizes a second order elastic/plastic analysis software NIDA to predict structural behaviour of bare steel framed structures at elevated temperatures. This fire study considers thermal expansion and material degradation due to heating. Degradation of material strength with increasing temperature is included by a set of temperature-stress-strain curves according to BS5950 Part 8 mainly, which implicitly allows for creep deformation. This finite element stiffness formulation of beam-column elements is derived from the fifth-order PEP element which facilitates the computer modeling by one member per element. The Newton-Raphson method is used in the nonlinear solution procedure in order to trace the nonlinear equilibrium path at specified elevated temperatures. Several numerical and experimental verifications of framed structures are presented and compared against solutions in literature. The proposed method permits engineers to adopt the performance-based structural fire analysis and design using typical second-order nonlinear structural analysis software.

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.

Use of vibration characteristics to predict the axial deformation of columns

Vibration characteristics of columns are influenced by their axial loads. Numerous methods have been developed to quantify axial load and deformation in individual columns based on their natural frequencies. However, these methods cannot be applied to columns in a structural framing system as the natural frequency is a global parameter of the entire framing system. This paper presents an innovative method to quantify axial deformations of columns in a structural framing system using its vibration characteristics, incorporating the influence of load tributary areas, boundary conditions and load migration among the columns.

Performance-based structural fire design and testing of structures

Fire incident in buildings is common in Hong Kong and this could lead to heavy casualties due to its high population density, so the fire safety design of the framed structure is an important research topic. This paper describes a computer tool for determination of capacity of structural safety against various fire scenarios and the well-accepted second-order direct plastic analysis is adopted for simulation of material yielding and buckling. A computer method is developed to predict structural behaviour of bare steel framed structures at elevated temperatures but the work can be applied to structures made of other materials. These effects of thermal expansion and material degradation due to heating are required to be considered in order to capture the actual behavior of the structure under fire. Degradation of material strength with increasing temperature is included by a set of temperature-stress-strain curves according to BS5950 Part 8 mainly, which implicitly allows for creep deformation. Several numerical and experimental verifications of framed structures are presented and compared against solutions by other researchers. The proposed method allows us to adopt the truly performance-based structural fire analysis and design with significant saving in cost and time.

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.