Shear capacity of lipped channel beams with web openings : design rules and improvements

Cold-formed steel Lipped Channel Beams (LCB) with web openings are commonly used as floor joists and bearers in building structures. Shear behaviour of these beams is more complicated and their shear capacities are considerably reduced by the presence of web openings. Hence detailed numerical and experimental studies of simply supported LCBs under a mid-span load with aspect ratios of 1.0 and 1.5 were undertaken to investigate the shear behaviour and strength of LCBs with web openings. Experimental and numerical results showed that the current design rules in cold-formed steel structures design codes are very conservative. Improved design equations were therefore proposed for the shear strength of LCBs with web openings based on both experimental and numerical results. This research showed a significant reduction in shear capacities of LCBs when large web openings are included for the purpose of locating building services. A cost effective method of eliminating such detrimental effects of large circular web openings was also therefore investigated using experimental and numerical studies. For this purpose LCBS were reinforced using plate, stud, transverse and sleeve stiffeners with varying sizes and thicknesses that were welded and screw-fastened to the web of LCBs. These studies showed that plate stiffeners were the most suitable. Suitable screw-fastened plate stiffener arrangements with optimum thicknesses were then proposed for LCBs with web openings to restore their original shear capacities. This paper presents the details of finite element analyses and experiments of LCBs with web openings in shear, and the development of improved shear design rules. It then describes the experimental and numerical studies to determine the optimum plate stiffener arrangements and the results. The proposed shear design rules in this paper can be considered for inclusion in the future versions of cold-formed steel design codes.

Experimental studies of hollow flange channel beams subject to combined bending and shear actions

This paper presents the details of an experimental study of a cold-formed steel hollow flange channel beam known as LiteSteel Beam (LSB) subject to combined bending and shear actions. The LSB sections are produced by a patented manufacturing process involving simultaneous cold-forming and electric resistance welding. Due to the geometry of the LSB, as well as its unique residual stress characteristics and initial geometric imperfections resultant of manufacturing processes, much of the existing research for common cold-formed steel sections is not directly applicable to LSB. Experimental and numerical studies have been carried out to evaluate the behaviour and design of LSBs subject to pure bending actions and predominant shear actions. To date, however, no investigation has been conducted into the strength of LSB sections under combined bending and shear actions. Combined bending and shear is especially prevalent at the supports of continuous span and cantilever beams, where the interaction of high shear force and bending moment can reduce the capacity of a section to well below that for the same section subject only to pure shear or moment. Hence experimental studies were conducted to assess the combined bending and shear behaviour and strengths of LSBs. Eighteen tests were conducted and the results were compared with current AS/NZS 4600 and AS 4100 design rules. AS/NZS 4600 design rules were shown to grossly underestimate the combined bending and shear capacities of LSBs and hence two lower bound design equations were proposed based on experimental results. Use of these equations will significantly improve the confidence and cost-effectiveness of designing LSBs for combined bending and shear actions.

Non-invasive clinical measurement of the viscoelastic properties of tendon using acoustic wave transmission

Background. In isotropic materials, the speed of acoustic wave propagation is governed by the bulk modulus and density. For tendon, which is a structural composite of fluid and collagen, however, there is some anisotropy requiring an adjustment for Poisson's ratio. This paper explores these relationships using data collected, in vivo, on human Achilles tendon and then compares estimates of elastic modulus and hysteresis against published values from in vitro mechanical tests. Methods. Measurements using conventional B-model ultrasound imaging, inverse dynamics and acoustic transmission techniques were used to determine dimensions, loading conditions and longitudinal speed of sound in the Achilles tendon during a series of isometric plantar flexion exercises against body weight. Upper and lower bounds for speed of sound versus tensile stress in the tendon were then modelled and estimates of the elastic modulus and hysteresis of the Achilles tendon derived. Results. Axial speed of sound varied between 1850 and 2090 ms-1 with a non-linear, asymptotic dependency on the level of tensile stress (5-35 MPa) in the tendon. Estimates derived for the elastic modulus of the Achilles tendon ranged between 1-2 GPa. Hysteresis derived from models of the stress-strain relationship, ranged from 3-11%. Discussion. Estimates of elastic modulus agree closely with those previously reported from direct measurements obtained via mechanical tensile tests on major weight bearing tendons in vitro [1,2]. Hysteresis derived from models of the stress-strain relationship is consistent with direct measures from various mamalian tendon (7-10%) but is lower than previous estimates in human tendon (17-26%) [3]. This non-invasive method would appear suitable for monitoring changes in tendon properties during dynamic sporting activities.

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.

A comparison of surface doses for very small field size x-ray beams : Monte Carlo calculations and radiochromic film measurements

Stereotactic radiosurgery treatments involve the delivery of very high doses for a small number of fractions. To date, there is limited data in terms of the skin dose for the very small field sizes used in these treatments. In this work, we determine relative surface doses for small size circular collimators as used in stereotactic radiosurgery treatments. Monte Carlo calculations were performed using the BEAMnrc code with a model of the Novalis 15 Trilogy linear accelerator and the BrainLab circular collimators. The surface doses were calculated at the ICRU skin dose depth of 70 m all using the 6 MV SRS x-ray beam. The calculated surface doses varied between 15 – 12% with decreasing values as the field size increased from 4 to 30 mm. In comparison, surface doses were measured using Gafchromic EBT3 film positioned at the surface of a Virtual Water phantom. The absolute agreement between calculated and measured surface doses was better than 2.5% which is well within the 20 uncertainties of the Monte Carlo calculations and the film measurements. Based on these results, we have shown that the Gafchromic EBT3 film is suitable for surface dose estimates in very small size fields as used in SRS.

Locating delamination in composite laminated beams using the A0 Lamb mode

In this study, experimental and numerical investigations have been conducted to explore the possibility of using A0 mode in Lamb waves to detect the position of delamination in carbon fiber reinforced plastic (CFRP) laminated beams. An experimental technique for exciting and sensing the pure A0 mode has been developed. By measuring the propagation speed of A0 mode and traveling time of a signal reflected from the delamination, its location can be identified experimentally and numerically. Moreover, the numerical analysis has been extended to gain a better understanding of the complex interaction between A0 mode and a long delamination case.

Web crippling tests of hollow flange channel beams – end one flange and interior one flange load cases

LiteSteel beam (LSB) is a new cold-formed steel hollow flange channel section produced using a patented manufacturing process involving simultaneous cold-forming and dual electric resistance welding. The LSBs were commonly used as floor joists and bearers with web openings in residential, industrial and commercial buildings. Due to the unique geometry of LSBs, as well as its unique residual stress characteristics and initial geometric imperfections resultant of manufacturing processes, much of the existing research for common cold-formed steel sections is not directly applicable to LSBs. Many research studies have been carried out to evaluate the behaviour and design of LSBs subject to pure bending actions, predominant shear and combined actions. However, to date, no investigation has been conducted into the web crippling behaviour and strength of LSB sections. Hence detailed experimental studies were conducted to investigate the web crippling behaviour and strengths of LSBs under EOF (End One Flange) and IOF (Interior One Flange) load cases. A total of 26 web crippling tests was conducted and the results were compared with current AS/NZS 4600 design rules. This comparison showed that AS/NZS 4600 (SA, 2005) design rules are very conservative for LSB sections under EOF and IOF load cases. Suitable design equations have been proposed to determine the web crippling capacity of LSBs based on experimental results. This paper presents the details of this experimental study on the web crippling behaviour and strengths of LiteSteel beams under EOF and IOF load cases.

Numerical modelling and design of lipped channel beams subject to shear

Cold-formed steel members are increasingly used as primary structural elements in buildings due to the availability of thin and high strength steels and advanced cold-forming technologies. Cold-formed lipped channel beams (LCB) are commonly used as flexural members such as floor joists and bearers. Many research studies have been carried out to evaluate the behaviour and design of LCBs subject to pure bending actions. However, limited research has been undertaken on the shear behaviour and strength of LCBs. Hence a numerical study was undertaken to investigate the shear behaviour and strength of LCBs. Finite element models of simply supported LCBs with aspect ratios of 1.0 and 1.5 were considered under a mid-span load. They were then validated by comparing their results with test results and used in a detailed parametric study based on the validated finite element models. Numerical studies were conducted to investigate the shear buckling and post-buckling behaviour of LCBs. Experimental and numerical results showed that the current design rules in cold-formed steel structures design codes are very conservative for the shear design of LCBs. Improved design equations were therefore proposed for the shear strength of LCBs. This paper presents the details of this numerical study of LCBs and the results.

Effect of real support conditions on the shear strength of hollow flange channel beams

This paper presents the details of experimental studies on the effect of real support conditions on the shear strength of LiteSteel beams (LSB). The LSB has a unique shape of a channel beam with two rectangular hollow flanges, made using a unique manufacturing process. In some applications in the building industry LSBs are used with only one web side plate (WSP) at their supports and are not used with full height web side plates (WSP) at their supports. Past research studies showed that theses real support connections did not provide simply supported conditions. Many studies have been carried out to evaluate the behaviour and design of LSBs with simply supported conditions subject to pure bending and predominant shear actions. To date, however, no investigation has been conducted into the effect of real support conditions on the shear strength of LSBs. Hence detailed experimental studies were undertaken to investigate the shear behaviour and strength of LSBs with real support conditions. A total of 28 experimental tests were conducted as part of the studies. Simply supported test specimens of LSBs with aspect ratios of 1.0 and 1.5 were loaded at mid-span until failure. It was found that the effect of using one WSP on the shear behaviour of LSB is significant and there is about 25% shear capacity reduction due to the lateral movement of the bottom flange at the supports. Shear capacity of LSB was also found to decrease when full height WSPs were not used. Suitable support connections were developed to improve the shear capacity of LSBs based on test results.

Web crippling tests of hollow flange channel beams : ETF AND ITF load cases

This paper presents the details of an experimental study of a cold-formed steel hollow flange channel beam known as LiteSteel Beam (LSB) subject to web crippling actions (ETF and ITF). Due to the geometry of the LSB, as well as its unique residual stress characteristics and initial geometric imperfections resultant of manufacturing processes, much of the existing research for common cold-formed steel sections is not directly applicable to LSB. Experimental and numerical studies have been carried out to evaluate the behaviour and design of LSBs subject to pure bending actions, predominant shear actions and combined actions. To date, however, no investigation has been conducted into the web crippling behaviour and strength of LSB sections under ETF and ITF load conditions. Hence experimental studies were conducted to assess the web crippling behaviour and strengths of LSBs. Twenty eight web crippling tests were conducted and the results were compared with the current AS/NZS 4600[1] and AISI S100 [2]design equations. Comparison of the ultimate web crippling capacities from tests showed that AS/NZS 4600[1] and AISI S100 [2] design equations are unconservative for LSB sections under ETF and ITF load cases. Hence new equations were proposed to determine the web crippling capacities of LSBs. Suitable design rules were also developed under the DSM format.

Numerical studies and design of hollow flange channel beams subject to combined bending and shear actions

LiteSteel beam (LSB) is a cold-formed steel hollow flange channel section produced using a patented manufacturing process involving simultaneous cold-forming and dual electric resistance welding. It is commonly used as floor joists and bearers in residential, industrial and commercial buildings. Design of the LSB is governed by the Australian cold-formed steel structures code, AS/NZS 4600. Due to the geometry of the LSB, as well as its unique residual stress characteristics and initial geometric imperfections resultant of manufacturing processes, currently available design equations for common cold-formed sections are not directly applicable to the LSB. Many research studies have been carried out to evaluate the behaviour and design of LSBs subject to pure bending actions and predominant shear actions. To date, however, no investigation has been conducted into the strength of LSB sections under combined bending and shear actions. Hence experimental and numerical studies were conducted to assess the combined bending and shear behaviour of LSBs. Finite element models of LSBs were developed to simulate their combined bending and shear behaviour and strength of LSBs. They were then validated by comparing the results with available experimental test results and used in a detailed parametric study. The results from experimental and finite element analyses were compared with current AS/NZS 4600 and AS 4100 design rules. Both experimental and numerical studies show that the AS/NZS 4600 design rule based on circular interaction equation is conservative in predicting the combined bending and shear capacities of LSBs. This paper presents the details of the numerical studies of LSBs and the results. In response to the inadequacies of current approaches to designing LSBs for combined bending and shear, two lower bound design equations are proposed in this paper.

Surface dosimetry for very small X-ray beams

Introduction The dose to skin surface is an important factor for many radiotherapy treatment techniques. It is known that TPS predicted surface doses can be significantly different from actual ICRP skin doses as defined at 70 lm. A number of methods have been implemented for the accurate determination of surface dose including use of specific dosimeters such as TLDs and radiochromic film as well as Monte Carlo calculations. Stereotactic radiosurgery involves delivering very high doses per treatment fraction using small X-ray fields. To date, there has been limited data on surface doses for these very small field sizes. The purpose of this work is to evaluate surface doses by both measurements and Monte Carlo calculations for very small field sizes. Methods All measurements were performed on a Novalis Tx linear accelerator which has a 6 MV SRS X-ray beam mode which uses a specially thin flattening filter. Beam collimation was achieved by circular cones with apertures that gave field sizes ranging from 4 to 30 mm at the isocentre. The relative surface doses were measured using Gafchromic EBT3 film which has the active layer at a depth similar to the ICRP skin dose depth. Monte Carlo calculations were performed using the BEAMnrc/EGSnrc Monte Carlo codes (V4 r225). The specifications of the linear accelerator, including the collimator, were provided by the manufacturer. Optimisation of the incident X-ray beam was achieved by an iterative adjustment of the energy, spatial distribution and radial spread of the incident electron beam striking the target. The energy cutoff parameters were PCUT = 0.01 MeV and ECUT = 0.700 - MeV. Directional bremsstrahlung splitting was switched on for all BEAMnrc calculations. Relative surface doses were determined in a layer defined in a water phantom of the same thickness and depth as compared to the active later in the film. Results Measured surface doses using the EBT3 film varied between 13 and 16 % for the different cones with an uncertainty of 3 %. Monte Carlo calculated surface doses were in agreement to better than 2 % to the measured doses for all the treatment cones. Discussion and conclusions This work has shown the consistency of surface dose measurements using EBT3 film with Monte Carlo predicted values within the uncertainty of the measurements. As such, EBT3 film is recommended for in vivo surface dose measurements.

Dense plasmas in magnetic traps : generation of focused ion beams with controlled ion-to-neutral flux ratios

Customized magnetic traps were developed to produce a domain of dense plasmas with a narrow ion beam directed to a particular area of the processed substrate. A planar magnetron coupled with an arc discharge source created the magnetic traps to confine the plasma electrons and generate the ion beam with the controlled ratio of ion-to-neutral fluxes. Images of the plasma jet patterns and numerical vizualizations help explaining the observed phenomena.

Effective control of ion fluxes over large areas by magnetic fields : from narrow beams to highly uniform fluxes

An effective control of the ion current distribution over large-area (up to 103 cm2) substrates with the magnetic fields of a complex structure by using two additional magnetic coils installed under the substrate exposed to vacuum arc plasmas is demonstrated. When the magnetic field generated by the additional coils is aligned with the direction of the magnetic field generated by the guiding and focusing coils of the vacuum arc source, a narrow ion density distribution with the maximum current density 117 A m-2 is achieved. When one of the additional coils is set to generate the magnetic field of the opposite direction, an area almost uniform over the substrate of 103 cm2 ion current distribution with the mean value of 45 A m-2 is achieved. Our findings suggest that the system with the vacuum arc source and two additional magnetic coils can be effectively used for the effective, high throughput, and highly controllable plasma processing.

Shear capacities of rivet fastened Rectangular Hollow Flange Channel Beams

The intermittently rivet fastened Rectangular Hollow Flange Channel Beam (RHFCB) is a new cold-formed hollow section proposed as an alternative to welded hollow flange beams. It is a monosymmetric channel section made by intermittently rivet fastening two torsionally rigid rectangular hollow flanges to a web plate. This method will allow the development of optimum sections by choosing appropriate combinations of web and flange plate widths and thicknesses. RHFCBs can be commonly used as flexural members in buildings. Many experimental and numerical studies have been carried out in the past to investigate the shear behaviour of lipped channel beams. However, no research has been undertaken on the shear behaviour of rivet fastened RHFCBs. Therefore a detailed experimental study involving 19 shear tests was undertaken to investigate the shear behaviour and capacities of rivet fastened RHFCBs. Simply supported test specimens of RHFCB with aspect ratios of 1.0 and 1.5 were loaded at mid-span until failure. Comparison of experimental results with corresponding predictions from the current Australian cold-formed steel design rules showed that the current design rules are very conservative for the shear design of rivet fastened RHFCBs. Significant improvements to web shear buckling occurred due to the presence of rectangular hollow flanges while considerable post-buckling strength was also observed. Appropriate improvements have been proposed for the design rules of shear strength of rivet fastened RHFCBs within the Direct Strength Method format. This paper presents the details of this study and the results.