Numerical modelling of light gauge cold-formed steel compression members subjected to distortional buckling at elevated temperatures

Fire safety design of building structures has received greater attention in recent times due to continuing loss of properties and lives during fires. However, fire performance of light gauge cold-formed steel structures is not well understood despite its increased usage in buildings. Cold-formed steel compression members are susceptible to various buckling modes such as local and distortional buckling and their ultimate strength behaviour is governed by these buckling modes. Therefore a research project based on experimental and numerical studies was undertaken to investigate the distortional buckling behaviour of light gauge cold-formed steel compression members under simulated fire conditions. Lipped channel sections with and without additional lips were selected with three thicknesses of 0.6, 0.8, and 0.95 mm and both low and high strength steels (G250 and G550 steels). More than 150 compression tests were undertaken first at ambient and elevated temperatures. Finite element models of the tested compression members were then developed by including the degradation of mechanical properties with increasing temperatures. Comparison of finite element analysis and experimental results showed that the developed finite element models were capable of simulating the distortional buckling and strength behaviour at ambient and elevated temperatures up to 800 °C. The validated model was used to determine the effects of mechanical properties, geometric imperfections and residual stresses on the distortional buckling behaviour and strength of cold-formed steel columns. This paper presents the details of the numerical study and the results. It demonstrated the importance of using accurate mechanical properties at elevated temperatures in order to obtain reliable strength characteristics of cold-formed steel columns under fire conditions.

Behaviour and design of cold-formed steel beams subject to lateral-torsional buckling at elevated temperatures

Cold-formed steel beams are increasingly used as floor joists and bearers in buildings and often their behaviour and moment capacities are influenced by lateral-torsional buckling. With increasing usage of cold-formed steel beams their fire safety design has become an important issue. Fire design rules are commonly based on past research on hot-rolled steel beams. Hence a detailed parametric study was undertaken using validated finite element models to investigate the lateral-torsional buckling behaviour of simply supported cold-formed steel lipped channel beams subjected to uniform bending at uniform elevated temperatures. The moment capacity results were compared with the predictions from the available ambient temperature and fire design rules and suitable recommendations were made. European fire design rules were found to be over-conservative while the ambient temperature design rules could not be used based on single buckling curve. Hence a new design method was proposed that includes the important non-linear stress-strain characteristics observed for cold-formed steels at elevated temperatures. Comparison with numerical moment capacities demonstrated the accuracy of the new design method. This paper presents the details of the parametric study, comparisons with current design rules and the new design rules proposed in this research for lateral-torsional buckling of cold-formed steel lipped channel beams at elevated temperatures.

Cold-formed steel columns subject to local buckling at elevated temperatures

Fire safety design of building structures has received greater attention in recent times due to continuing losses of properties and lives in fires. However, the structural behaviour of thin-walled cold-formed steel columns under fire conditions is not well understood despite the increasing use of light gauge steels in building construction. Cold-formed steel columns are often subject to local buckling effects. Therefore a series of laboratory tests of lipped and unlipped channel columns made of varying steel thicknesses and grades was undertaken at uniform elevated temperatures up to 700°C under steady state conditions. Finite element models of the tested columns were also developed, and their elastic buckling and nonlinear analysis results were compared with test results at elevated temperatures. Effects of the degradation of mechanical properties of steel with temperature were included in the finite element analyses. The use of accurately measured yield stress, elasticity modulus and stress-strain curves at elevated temperatures provided a good comparison of the ultimate loads and load-deflection curves from tests and finite element analyses. The commonly used effective width design rules and the direct strength method at ambient temperature were then used to predict the ultimate loads at elevated temperatures by using the reduced mechanical properties. By comparing these predicted ultimate loads with those from tests and finite element analyses, the accuracy of using this design approach was evaluated.

Flexural–torsional buckling behaviour and design of cold-formed steel compression members at elevated temperatures

Current design rules for the member capacities of cold-formed steel columns are based on the same non-dimensional strength curve for both fixed and pinned-ended columns at ambient temperature. This research has investigated the accuracy of using current ambient temperature design rules in Australia/New Zealand (AS/NZS 4600), American (AISI S100) and European (Eurocode 3 Part 1.3) standards in determining the flexural–torsional buckling capacities of cold-formed steel columns at uniform elevated temperatures using appropriately reduced mechanical properties. It was found that these design rules accurately predicted the member capacities of pin ended lipped channel columns undergoing flexural torsional buckling at elevated temperatures. However, for fixed ended columns with warping fixity undergoing flexural–torsional buckling, the current design rules significantly underestimated the column capacities as they disregard the beneficial effect of warping fixity. This paper has therefore recommended the use of improved design rules developed for ambient temperature conditions to predict the axial compression capacities of fixed ended columns subject to flexural–torsional buckling at elevated temperatures within AS/NZS 4600 and AISI S100 design provisions. The accuracy of the proposed fire design rules was verified using finite element analysis and test results of cold-formed lipped channel columns at elevated temperatures except for low strength steel columns with intermediate slenderness whose behaviour was influenced by the increased nonlinearity in the stress–strain curves at elevated temperatures. Further research is required to include these effects within AS/NZS 4600 and AISI S100 design rules. However, Eurocode 3 Part 1.3 design rules can be used for this purpose by using suitable buckling curves as recommended in this paper.

Design of cold-formed steel columns at elevated temperatures subject to flexural-torsional buckling

Cold-formed steel members are often subject to axial compression loads in a range of applications. These thin-walled members can be subject to various types of buckling modes, including flexural-torsional buckling. Design standards provide guidelines for columns subject to flexural-torsional buckling modes at ambient temperature. However, there are no specific design guidelines for elevated temperature conditions. Hence extensive research efforts have gone into the many investigations addressing the flexural-torsional buckling behaviour of cold-formed steel columns at elevated temperatures.This research has reviewed the accuracy of the current design rules in AS/NZS 4600 and the North American Specification in determining the member capacities of cold-formed steel columns using the results from detailed finite element analyses and an experimental study of lipped channel columns. It was found that the current ambient temperature Australian and American design rules accurately predicted the member capacities of pin ended lipped channel columns undergoing flexural torsional buckling at elevated temperatures by simply using the appropriate elevated temperature mechanical properties. However, for fixed ended columns with warping fixity undergoing flexural-torsional buckling, it was found that the current design rules significantly underestimated the column capacities as they disregard the beneficial effect of warping fixity. This research has therefore proposed improved design rules and verified their accuracy using finite element analysis and test results of cold-formed lipped channel columns made of three cross-sections and five different steel grades and thicknesses. This paper presents the details of this research study and the results.

Experimental studies of cold-formed steel hollow section columns at elevated temperatures

This paper reports the details of an experimental study of cold-formed steel hollow section columns at ambient and elevated temperatures. In this study the global buckling behaviour of cold-formed Square Hollow Section (SHS) slender columns under axial compression was investigated at various uniform elevated temperatures up to 700℃. The results of these column tests are reported in this paper, which include the buckling/failure modes at elevated temperatures, and ultimate load versus temperature curves. Finite element models of tested columns were also developed and their behaviour and ultimate capacities at ambient and elevated temperatures were studied. Fire design rules given in European and American standards including the Direct Strength Method (DSM) based design rules were used to predict the ultimate capacities of tested columns at elevated temperatures. Elevated temperature mechanical properties and stress-strain models given in European steel design standards and past researches were used with design rules and finite element models to investigate their effects on SHS column capacities. Comparisons of column capacities from tests and finite element analyses with those predicted by current design rules were used to determine the accuracy of currently available column design rules in predicting the capacities of SHS columns at elevated temperatures and the need to use appropriate elevated temperature material stress-strain models. This paper presents the important findings derived from the comparisons of these column capacities.

Local buckling studies of cold-formed steel compression members at elevated temperatures

Cold-formed steel members have been widely used in residential and commercial buildings as primary load bearing structural elements. They are often made of thin steel sheets and hence they are more susceptible to local buckling. The buckling behaviour of cold-formed steel compression members under fire conditions is not fully investigated yet and hence there is a lack of knowledge on the fire performance of cold-formed steel compression members. Current cold-formed steel design standards do not provide adequate design guidelines for the fire design of cold-formed steel compression members. Therefore a research project based on extensive experimental and numerical studies was undertaken to investigate the local buckling behaviour of light gauge cold-formed steel compression members under simulated fire conditions. First a series of 91 local buckling tests was conducted at ambient and uniform elevated temperatures up to 700oC on cold-formed lipped and unlipped channels. Suitable finite element models were then developed to simulate the behaviour of tested columns and were validated using test results. All the ultimate load capacity results for local buckling were compared with the predictions from the available design rules based on AS/NZS 4600, BS 5950 Part 5, Eurocode 3 Parts 1.2 and 1.3 and the direct strength method (DSM), based on which suitable recommendations have been made for the fire design of cold-formed steel compression members subject to local buckling at uniform elevated temperatures.

Numerical estimation of hotspot temperatures in electrodes subjected to pulsed electron beam heating in vacuum

A numerical solution for the transient temperature distribution in a cylindrical disc heated on its top surface by a circular source is presented. A finite difference form of the governing equations is solved by the Alternating Direction Implicit (ADI) time marching scheme. This solution has direct applications in analyzing transient electron beam heating of target materials as encountered in the prebreakdown current enhancement and consequent breakdown in high voltage vacuum gaps stressed by alternating and pulsed voltages. The solution provides an estimate of the temperature for pulsed electron beam heating and the size of thermally activated microparticles originating from anode hot spots. The calculated results for a typical 45kV (a.c.) electron beam of radius 2.5 micron indicate that the temperature of such spots can reach melting point and could give rise to microparticles which could initiate breakdown.

An operator-splitting finite element method for the efficient parallel solution of multidimensional population balance systems

A finite element method for solving multidimensional population balance systems is proposed where the balance of fluid velocity, temperature and solute partial density is considered as a two-dimensional system and the balance of particle size distribution as a three-dimensional one. The method is based on a dimensional splitting into physical space and internal property variables. In addition, the operator splitting allows to decouple the equations for temperature, solute partial density and particle size distribution. Further, a nodal point based parallel finite element algorithm for multi-dimensional population balance systems is presented. The method is applied to study a crystallization process assuming, for simplicity, a size independent growth rate and neglecting agglomeration and breakage of particles. Simulations for different wall temperatures are performed to show the effect of cooling on the crystal growth. Although the method is described in detail only for the case of d=2 space and s=1 internal property variables it has the potential to be extendable to d+s variables, d=2, 3 and s >= 1. (C) 2011 Elsevier Ltd. All rights reserved.

Finite Element Analysis of Stress Evolution in Al-Si Alloy

A 2D multi-particle model is carried out to understand the effect of microstructural variations and loading conditions on the stress evolution in Al-Si alloy under compression. A total of six parameters are varied to create 26 idealized microstructures: particle size, shape, orientation, matrix temper, strain rate, and temperature. The effect of these parameters is investigated to understand the fracture of Si particles and the yielding of Al matrix. The Si particles are modeled as a linear elastic solid and the Al matrix is modeled as an elasto-plastic solid. The results of the study demonstrate that the increase in particle size decreases the yield strength of the alloy. The particles with high aspect ratio and oriented at 0A degrees and 90A degrees to the loading axis show higher stress values. This implies that the particle shape and orientation are dominant factors in controlling particle fracture. The heat treatment of the alloy is found to increase the stress levels of both particles and matrix. Stress calculations also show that higher particle fracture and matrix yielding is expected at higher strain rate deformation. Particle fracture decreases with increase in temperature and the Al matrix plays an important role in controlling the properties of the alloy at higher temperatures. Further, this strain rate and temperature dependence is more pronounced in the heat-treated microstructure. These predictions are consistent with the experimentally observed Si particle fracture in real microstructure.

Kinetic control of catalytic CVD for high-quality graphene at low temperatures.

Low-temperature (∼600 °C), scalable chemical vapor deposition of high-quality, uniform monolayer graphene is demonstrated with a mapped Raman 2D/G ratio of >3.2, D/G ratio ≤0.08, and carrier mobilities of ≥3000 cm(2) V(-1) s(-1) on SiO(2) support. A kinetic growth model for graphene CVD based on flux balances is established, which is well supported by a systematic study of Ni-based polycrystalline catalysts. A finite carbon solubility of the catalyst is thereby a key advantage, as it allows the catalyst bulk to act as a mediating carbon sink while optimized graphene growth occurs by only locally saturating the catalyst surface with carbon. This also enables a route to the controlled formation of Bernal stacked bi- and few-layered graphene. The model is relevant to all catalyst materials and can readily serve as a general process rationale for optimized graphene CVD.

Aromaticity on the fly: cyclic transition state stabilization at finite temperature.

We study the transition state of pericyclic reactions at elevated temperature with unbiased ab initio molecular dynamics. We find that the transition state of the intramolecular rearrangements for barbaralane and bullvalene remains aromatic at high temperature despite the significant thermal atomic motions. Structural, magnetic, and electronic properties of the dynamical transition state show the concertedness and aromatic character. Free-energy calculations also support the validity of the transition state theory for the present rearrangement reactions. The calculations demonstrate that cyclic delocalization represents a strong force to synchronize the thermal atomic motions even at high temperatures.

Finite element analysis of compressor disc heat transfer using the transient conduction method with sparse boundary collocation points

Surface temperature measurements from two discs of a gas turbine compressor rig are used as boundary conditions for the transient conduction solution (inverse heat transfer analysis). The disc geometry is complex, and so the finite element method is used. There are often large radial temperature gradients on the discs, and the equations are therefore solved taking into account the dependence of thermal conductivity on temperature. The solution technique also makes use of a multigrid algorithm to reduce the solution time. This is particularly important since a large amount of data must be analyzed to obtain correlations of the heat transfer. The finite element grid is also used for a network analysis to calculate the radiant heat transfer in the cavity formed between the two compressor discs. The work discussed here proved particularly challenging as the disc temperatures were only measured at four different radial locations. Four methods of surface temperature interpolation are examined, together with their effect on the local heat fluxes. It is found that the choice of interpolation method depends on the available number of data points. Bessel interpolation gives the best results for four data points, whereas cubic splines are preferred when there are considerably more data points. The results from the analysis of the compressor rig data show that the heat transfer near the disc inner radius appears to be influenced by the central throughflow. However, for larger radii, the heat transfer from the discs and peripheral shroud is found to be consistent with that of a buoyancy-induced flow.

Effects of elevated temperatures on bolted moment-connections between cold-formed steel members

Experimental investigations at ambient temperature into the behaviour of bolted moment-connections between cold-formed steel members have previously been described. Full-scale joint tests have demonstrated that the channel-sections being connected are susceptible to premature failure, the result of web buckling caused by the concentration of load transfer from the bolts. The results of tests on bolted lap joints have been used to propose design recommendations for the shear strength in bearing of the bolt-hole. For both types of test, the results of non-linear elasto-plastic finite element analyses have been shown to have good agreement. No consideration, however, has been given to the behaviour of such connections at elevated temperatures. This paper describes non-linear elasto-plastic finite element parametric studies into the effects of elevated temperatures on bolted moment-connections between cold-formed steel members. Two issues at elevated temperatures are investigated:

Cold-formed steel portal frames in fire: Full-scale testing and finite element analysis

A full-scale, non-uniform natural fire test on a cold-formed steel portal frame building is described. The results of the test are used to validate a non-linear, elasto-plastic, finite element shell idealisation, for the purposes of later forming the basis of a performance-based design approach for cold-formed steel portal frames at elevated temperatures.