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.

Flexural-torsional buckling tests of cold-formed steel compression members at elevated temperatures

Current design standards do not provide adequate guidelines for the fire design of cold-formed steel compression members subject to flexural-torsional buckling. Eurocode 3 Part 1.2 (2005) recommends the same fire design guidelines for both hot-rolled and cold-formed steel compression members subject to flexural-torsional buckling although considerable behavioural differences exist between cold-formed and hot-rolled steel members. Past research has recommended the use of ambient temperature cold-formed steel design rules for the fire design of cold-formed steel compression members provided appropriately reduced mechanical properties are used at elevated temperatures. To assess the accuracy of flexural-torsional buckling design rules in both ambient temperature cold-formed steel design and fire design standards, an experimental study of slender cold-formed steel compression members was undertaken at both ambient and elevated temperatures. This paper presents the details of this experimental study, its results, and their comparison with the predictions from the current design rules. It was found that the current ambient temperature design rules are conservative while the fire design rules are overly conservative. Suitable recommendations have been made in relation to the currently available design rules for flexural-torsional buckling including methods of improvement. Most importantly, this paper has addressed the lack of experimental results for slender cold-formed steel columns at elevated temperatures.

Improving the moment capacities of hollow flange cold-formed Litesteel Beams using web stiffeners

The LiteSteel Beam (LSB) is a new hollow flange section developed in Australia with a unique geometry consisting of torsionally rigid rectangular hollow flanges and a relatively slender web. The LSB is subjected to a relatively new Lateral Distortional Buckling (LDB) mode when used as flexural members. Unlike the commonly observed lateral torsional buckling, lateral distortional buckling of LSBs is characterised by cross sectional change due to web distortion. Lateral distortional buckling causes significant moment capacity reduction for LSBs with intermediate spans. Therefore a detailed investigation was undertaken to determine the methods of reducing the effects of lateral distortional buckling in LSB flexural members. For this purpose the use of web stiffeners was investigated using finite element analyses of LSBs with different web stiffener spacing and sizes. It was found that the use of 5 mm steel plate stiffeners welded or screwed to the inner faces of the top and bottom flanges at third span points considerably reduced the lateral distortional buckling effects in LSBs. Suitable design rules were then developed to calculate the enhanced elastic lateral distortional buckling moments and the higher ultimate moment capacities of LSBs with the chosen web stiffener arrangement. This paper presents the details of this investigation and the results.

Effect of cold water immersion after exercise in the heat on muscle function, body temperatures, and vessel diameter

Cold water immersion (CWI) is a popular recovery modality, but actual physiological responses to CWI after exercise in the heat have not been well documented. The purpose of this study was to examine effects of 20-min CWI (14 degrees C) on neuromuscular function, rectal (T(re)) and skin temperature (T(sk)), and femoral venous diameter after exercise in the heat. Ten well-trained male cyclists completed two bouts of exercise consisting of 90-min cycling at a constant power output (216+/-12W) followed by a 16.1km time trial (TT) in the heat (32 degrees C). Twenty-five minutes post-TT, participants were assigned to either CWI or control (CON) recovery conditions in a counterbalanced order. T(re) and T(sk) were recorded continuously, and maximal voluntary isometric contraction torque of the knee extensors (MVIC), MVIC with superimposed electrical stimulation (SMVIC), and femoral venous diameters were measured prior to exercise, 0, 45, and 90min post-TT. T(re) was significantly lower in CWI beginning 50min post-TT compared with CON, and T(sk) was significantly lower in CWI beginning 25min post-TT compared with CON. Decreases in MVIC, and SMVIC torque after the TT were significantly greater for CWI compared with CON; differences persisted 90min post-TT. Femoral vein diameter was approximately 9% smaller for CWI compared with CON at 45min post-TT. These results suggest that CWI decreases T(re), but has a negative effect on neuromuscular function.

Cold-water immersion decreases cerebral oxygenation but improves recovery after intermittent-sprint exercise in the heat

This study examined the effects of post-exercise cooling on recovery of neuromuscular, physiological, and cerebral hemodynamic responses after intermittent-sprint exercise in the heat. Nine participants underwent three post-exercise recovery trials, including a control (CONT), mixed-method cooling (MIX), and cold-water immersion (10 °C; CWI). Voluntary force and activation were assessed simultaneously with cerebral oxygenation (near-infrared spectroscopy) pre- and post-exercise, post-intervention, and 1-h and 24-h post-exercise. Measures of heart rate, core temperature, skin temperature, muscle damage, and inflammation were also collected. Both cooling interventions reduced heart rate, core, and skin temperature post-intervention (P < 0.05). CWI hastened the recovery of voluntary force by 12.7 ± 11.7% (mean ± SD) and 16.3 ± 10.5% 1-h post-exercise compared to MIX and CONT, respectively (P < 0.01). Voluntary force remained elevated by 16.1 ± 20.5% 24-h post-exercise after CWI compared to CONT (P < 0.05). Central activation was increased post-intervention and 1-h post-exercise with CWI compared to CONT (P < 0.05), without differences between conditions 24-h post-exercise (P > 0.05). CWI reduced cerebral oxygenation compared to MIX and CONT post-intervention (P < 0.01). Furthermore, cooling interventions reduced cortisol 1-h post-exercise (P < 0.01), although only CWI blunted creatine kinase 24-h post-exercise compared to CONT (P < 0.05). Accordingly, improvements in neuromuscular recovery after post-exercise cooling appear to be disassociated with cerebral oxygenation, rather reflecting reductions in thermoregulatory demands to sustain force production.

Shear design of cold-formed steel beams using direct strength method

This paper presents the direct strength method (DSM) equations for cold-formed steel beams subject to shear. Light gauge cold-formed steel sections have been developed as more economical building solutions to the alternative heavier hot-rolled sections in the commercial and residential markets. Cold-formed lipped channel beams (LCB), LiteSteel beams (LSB) and hollow flange beams (HFB) are commonly used as flexural members such as floor joists and bearers. However, their shear capacities are determined based on conservative design rules. For the shear design of cold-formed web panels, their elastic shear buckling strength must be determined accurately including the potential post-buckling strength. Currently the elastic shear buckling coefficients of web panels are determined by assuming conservatively that the web panels are simply supported at the junction between the flange and web elements and ignore the post-buckling strength. Hence experimental and numerical studies were conducted to investigate the shear behaviour and strength of LSBs, LCBs and HFBs. New direct strength method (DSM) based design equations were proposed to determine the ultimate shear capacities of cold-formed steel beams. An improved equation for the higher elastic shear buckling coefficient of cold-formed steel beams was proposed based on finite element analysis results and included in the DSM design equations. A new post-buckling coefficient was also introduced in the DSM equation to include the available post-buckling strength of cold-formed steel beams.

Estimating the effects of ambient temperature on mortality : methodological challenges and proposed solutions

The health impacts of exposure to ambient temperature have been drawing increasing attention from the environmental health research community, government, society, industries, and the public. Case-crossover and time series models are most commonly used to examine the effects of ambient temperature on mortality. However, some key methodological issues remain to be addressed. For example, few studies have used spatiotemporal models to assess the effects of spatial temperatures on mortality. Few studies have used a case-crossover design to examine the delayed (distributed lag) and non-linear relationship between temperature and mortality. Also, little evidence is available on the effects of temperature changes on mortality, and on differences in heat-related mortality over time. This thesis aimed to address the following research questions: 1. How to combine case-crossover design and distributed lag non-linear models? 2. Is there any significant difference in effect estimates between time series and spatiotemporal models? 3. How to assess the effects of temperature changes between neighbouring days on mortality? 4. Is there any change in temperature effects on mortality over time? To combine the case-crossover design and distributed lag non-linear model, datasets including deaths, and weather conditions (minimum temperature, mean temperature, maximum temperature, and relative humidity), and air pollution were acquired from Tianjin China, for the years 2005 to 2007. I demonstrated how to combine the case-crossover design with a distributed lag non-linear model. This allows the case-crossover design to estimate the non-linear and delayed effects of temperature whilst controlling for seasonality. There was consistent U-shaped relationship between temperature and mortality. Cold effects were delayed by 3 days, and persisted for 10 days. Hot effects were acute and lasted for three days, and were followed by mortality displacement for non-accidental, cardiopulmonary, and cardiovascular deaths. Mean temperature was a better predictor of mortality (based on model fit) than maximum or minimum temperature. It is still unclear whether spatiotemporal models using spatial temperature exposure produce better estimates of mortality risk compared with time series models that use a single site’s temperature or averaged temperature from a network of sites. Daily mortality data were obtained from 163 locations across Brisbane city, Australia from 2000 to 2004. Ordinary kriging was used to interpolate spatial temperatures across the city based on 19 monitoring sites. A spatiotemporal model was used to examine the impact of spatial temperature on mortality. A time series model was used to assess the effects of single site’s temperature, and averaged temperature from 3 monitoring sites on mortality. Squared Pearson scaled residuals were used to check the model fit. The results of this study show that even though spatiotemporal models gave a better model fit than time series models, spatiotemporal and time series models gave similar effect estimates. Time series analyses using temperature recorded from a single monitoring site or average temperature of multiple sites were equally good at estimating the association between temperature and mortality as compared with a spatiotemporal model. A time series Poisson regression model was used to estimate the association between temperature change and mortality in summer in Brisbane, Australia during 1996–2004 and Los Angeles, United States during 1987–2000. Temperature change was calculated by the current day's mean temperature minus the previous day's mean. In Brisbane, a drop of more than 3 �C in temperature between days was associated with relative risks (RRs) of 1.16 (95% confidence interval (CI): 1.02, 1.31) for non-external mortality (NEM), 1.19 (95% CI: 1.00, 1.41) for NEM in females, and 1.44 (95% CI: 1.10, 1.89) for NEM aged 65.74 years. An increase of more than 3 �C was associated with RRs of 1.35 (95% CI: 1.03, 1.77) for cardiovascular mortality and 1.67 (95% CI: 1.15, 2.43) for people aged < 65 years. In Los Angeles, only a drop of more than 3 �C was significantly associated with RRs of 1.13 (95% CI: 1.05, 1.22) for total NEM, 1.25 (95% CI: 1.13, 1.39) for cardiovascular mortality, and 1.25 (95% CI: 1.14, 1.39) for people aged . 75 years. In both cities, there were joint effects of temperature change and mean temperature on NEM. A change in temperature of more than 3 �C, whether positive or negative, has an adverse impact on mortality even after controlling for mean temperature. I examined the variation in the effects of high temperatures on elderly mortality (age . 75 years) by year, city and region for 83 large US cities between 1987 and 2000. High temperature days were defined as two or more consecutive days with temperatures above the 90th percentile for each city during each warm season (May 1 to September 30). The mortality risk for high temperatures was decomposed into: a "main effect" due to high temperatures using a distributed lag non-linear function, and an "added effect" due to consecutive high temperature days. I pooled yearly effects across regions and overall effects at both regional and national levels. The effects of high temperature (both main and added effects) on elderly mortality varied greatly by year, city and region. The years with higher heat-related mortality were often followed by those with relatively lower mortality. Understanding this variability in the effects of high temperatures is important for the development of heat-warning systems. In conclusion, this thesis makes contribution in several aspects. Case-crossover design was combined with distribute lag non-linear model to assess the effects of temperature on mortality in Tianjin. This makes the case-crossover design flexibly estimate the non-linear and delayed effects of temperature. Both extreme cold and high temperatures increased the risk of mortality in Tianjin. Time series model using single site’s temperature or averaged temperature from some sites can be used to examine the effects of temperature on mortality. Temperature change (no matter significant temperature drop or great temperature increase) increases the risk of mortality. The high temperature effect on mortality is highly variable from year to year.

The effects of cold air (-110°C) and water (8°C) cryotherapy on knee skin temperature

Exposure to cold air, whole body cryotherapy (WBC), is a novel treatment employed by athletes. In WBC individuals dressed in minimal clothing are exposed to a temperature below -100°C for 2-4 min. The use of WBC has been advocated as a treatment for various knee injuries. PURPOSE: To compare the effects of two modalities of cryotherapy, -110°C WBC and 8°C cold water immersion (CWI) on knee skin temperature (Tsk). METHODS: With ethical approval and written informed consent 10 healthy active male participants (26.5±4.9 yr, 183.5±6.0 cm, 90.7±19.9 kg, 26.8±5.0 kg/m2, 23.0±9.3% body fat (measured by DXA), 7.6 ± 2.0 mm patellar skin fold; mean±SD) were exposed to 4 min of CWI and WBC. The treatment order was randomised in a controlled crossover design, with a minimum of 7 days between treatments. During WBC participants stood in a chamber (-60±3°C) for 20 s before entering the main chamber (-110°C±3°C) where they remained for 3 min and 40 s. For CWI participants were seated in a tank filled with cold water (8±0.3°C) and immersed to the level of the sternum for 4 min. Right knee Tsk was assessed via non-contact, infrared thermal imaging. A quadrilateral region of interest was created using inert markers placed 5 cm above and below the most superior and inferior aspect of the patella. Tsk within this quadrilateral was recorded pre, immediately post and every 10 min thereafter for 60 min. Tsk changes were examined using a two-way (treatment x time) repeated measures analyses of variance. In addition, a paired sample t-test was used to compare baseline Tsk before both treatments. RESULTS: Knee Tsk was similar before treatment (WBC: 29.9±0.7°C, CWI: 29.6±0.9°C, p>0.05). There was a significant main effect for treatment (p<0.05) and time (p<0.001). Compared to baseline, Tsk was significantly reduced (p<0.05) immediately post and at 10, 20, 30, 40, 50 and 60 min after both cooling modalities. Knee Tsk was lower (p<0.05) immediately after WBC (19.0±0.9°C) compared to CWI (20.5±0.6°C). However, from 10 to 60 min post, knee Tsk was lower (p<0.05) following the CWI treatment. CONCLUSION: WBC elicited a greater decrease in knee Tsk compared to CWI immediately after treatment. However, both modalities display different recovery patterns and Tsk after CWI was significantly lower than WBC at 10, 20, 30, 40, 50 and 60 min after treatment.

Extremely cold and hot temperatures increase the risk of ischaemic heart disease mortality : epidemiological evidence from China

Objective: To examine the effects of extremely cold and hot temperatures on ischaemic heart disease (IHD) mortality in five cities (Beijing, Tianjin, Shanghai, Wuhan and Guangzhou) in China; and to examine the time relationships between cold and hot temperatures and IHD mortality for each city. Design: A negative binomial regression model combined with a distributed lag non-linear model was used to examine city-specific temperature effects on IHD mortality up to 20 lag days. A meta-analysis was used to pool the cold effects and hot effects across the five cities. Patients: 16 559 IHD deaths were monitored by a sentinel surveillance system in five cities during 2004–2008. Results: The relationships between temperature and IHD mortality were non-linear in all five cities. The minimum-mortality temperatures in northern cities were lower than in southern cities. In Beijing, Tianjin and Guangzhou, the effects of extremely cold temperatures were delayed, while Shanghai and Wuhan had immediate cold effects. The effects of extremely hot temperatures appeared immediately in all the cities except Wuhan. Meta-analysis showed that IHD mortality increased 48% at the 1st percentile of temperature (extremely cold temperature) compared with the 10th percentile, while IHD mortality increased 18% at the 99th percentile of temperature (extremely hot temperature) compared with the 90th percentile. Conclusions: Results indicate that both extremely cold and hot temperatures increase IHD mortality in China. Each city has its characteristics of heat effects on IHD mortality. The policy for response to climate change should consider local climate–IHD mortality relationships.

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.

Experimental study of load bearing cold-formed steel wall systems under fire conditions

Light Gauge Steel Framing (LSF) walls made of cold-formed and thin-walled steel lipped channel studs with plasterboard linings on both sides are commonly used in commercial, industrial and residential buildings. However, there is limited data about their structural and thermal performance under fire conditions while past research showed contradicting results about the benefits of using cavity insulation. A new composite wall panel was recently proposed to improve the fire resistance rating of LSF walls, where an insulation layer was used externally between the plasterboards on both sides of the wall frame instead of using it in the cavity. In this research 11 full scale tests were conducted on conventional load bearing steel stud walls with and without cavity insulation, and the new composite panel system to study their thermal and structural performance under standard fire conditions. These tests showed that the use of cavity insulation led to inferior fire performance of walls, and provided supporting research data. They demonstrated that the use of insulation externally in a composite panel enhanced the thermal and structural performance of LSF walls and increased their fire resistance rating. This paper presents the details of the LSF wall tests and the thermal and structural performance data and fire resistance rating of load-bearing wall assemblies lined with varying plasterboard-insulation configurations under two different load ratios. Fire test results including the time–temperature and deflection profiles are presented along with the failure times and modes.

Finite element modelling of load bearing cold-formed steel wall systems under fire conditions

Light Gauge Steel Framing (LSF) walls are made of cold-formed, thin-walled steel lipped channel studs with plasterboard linings on both sides. However, these thin-walled steel sections heat up quickly and lose their strength under fire conditions despite the protection provided by plasterboards. A new composite wall panel was recently proposed to improve the fire resistance rating of LSF walls, where an insulation layer was used externally between the plasterboards on both sides of the wall frame instead of using it in the cavity. A research study using both fire tests and numerical studies was undertaken to investigate the structural and thermal behaviour of load bearing LSF walls made of both conventional and the new composite panels under standard fire conditions and to determine their fire resistance rating. This paper presents the details of finite element models of LSF wall studs developed to simulate the structural performance of LSF wall panels under standard fire conditions. Finite element analyses were conducted under both steady and transient state conditions using the time-temperature profiles measured during the fire tests. The developed models were validated using the fire test results of 11 LSF wall panels with various plasterboard/insulation configurations and load ratios. They were able to predict the fire resistance rating within five minutes. The use of accurate numerical models allowed the inclusion of various complex structural and thermal effects such as local buckling, thermal bowing and neutral axis shift that occurred in thin-walled steel studs under non-uniform elevated temperature conditions. Finite element analyses also demonstrated the improvements offered by the new composite panel system over the conventional cavity insulated system.

Review of current fire design rules for cold-formed steel wall systems

Light gauge steel frame wall systems are commonly used in industrial and commercial buildings, and there is a need for simple fire design rules to predict their load capacities and fire resistance ratings. During fire events, the light gauge steel frame wall studs are subjected to non-uniform temperature distributions that cause thermal bowing, neutral axis shift and magnification effects and thus resulting in a combined axial compression and bending action on the studs. In this research, a series of full-scale fire tests was conducted first to evaluate the performance of light gauge steel frame wall systems with eight different wall configurations under standard fire conditions. Finite element models of light gauge steel frame walls were then developed, analysed under transient and steady-state conditions and validated using full-scale fire tests. Using the results from fire tests and finite element analyses, a detailed investigation was undertaken into the prediction of axial compression strength and failure times of light gauge steel frame wall studs in standard fires using the available fire design rules based on Australian, American and European standards. The results from both fire tests and finite element analyses were used to investigate the ability of these fire design rules to include the complex effects of non-uniform temperature distributions and their accuracy in predicting the axial compression strength of wall studs and the failure times. Suitable modifications were then proposed to the fire design rules. This article presents the details of this investigation on the fire design rules of light gauge steel frame walls and the results.

Development of improved fire design rules for cold-formed steel wall systems

Traditionally the fire resistance rating of LSF wall systems is based on approximate prescriptive methods developed using limited fire tests. Therefore a detailed research study into the performance of load bearing LSF wall systems under standard fire conditions was undertaken to develop improved fire design rules. It used the extensive fire performance results of eight different LSF wall systems from a series of full scale fire tests and numerical studies for this purpose. The use of previous fire design rules developed for LSF walls subjected to non-uniform elevated temperature distributions based on AISI design manual and Eurocode3 Parts 1.2 and 1.3 was investigated first. New simplified fire design rules based on AS/NZS 4600, North American Specification and Eurocode 3 Part 1.3 were then proposed in this study with suitable allowances for the interaction effects of compression and bending actions. The importance of considering thermal bowing, magnified thermal bowing and neutral axis shift in the fire design was also investigated. A spread sheet based design tool was developed based on the new design rules to predict the failure load ratio versus time and temperature curves for varying LSF wall configurations. The accuracy of the proposed design rules was verified using the test and FEA results for different wall configurations, steel grades, thicknesses and load ratios. This paper presents the details and results of this study including the improved fire design rules for predicting the load capacity of LSF wall studs and the failure times of LSF walls under standard fire conditions.

Improved design rules for cold-formed steel columns

Current design rules for determining the member strength of cold-formed steel columns are based on the effective length of the member and a single column capacity curve for both pin-ended and fixed-ended columns. This research has reviewed the use of AS/NZS 4600 design rules for their accuracy in determining the member compression capacities of slender cold-formed steel columns using detailed numerical studies. It has shown that AS/NZS 4600 design rules accurately predicted the capacities of pinned and fixed ended columns undergoing flexural buckling. However, for fixed ended columns undergoing flexural-torsional buckling, it was found that current AS/NZS 4600 design rules did not include the beneficial effect of warping fixity. Therefore AS/NZS 4600 design rules were found to be excessively conservative and hence uneconomical in predicting the failure loads obtained from tests and finite element analyses of fixed-ended lipped channel columns. Based on this finding, suitable recommendations have been made to modify the current AS/NZS 4600 design rules to more accurately reflect the results obtained from the numerical and experimental studies conducted in this research. This paper presents the details of this research on cold-formed steel columns and the results.