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.

Bending and torsion of hollow flange channel beams

The LiteSteel beam (LSB) is a cold-formed high strength steel channel section made of two torsionally rigid closed flanges and a slender web. Due to its mono-symmetric characteristics, its centroid and shear centre do not coincide. The LSBs can be used in floor systems as joists or bearers and in these applications they are often subjected to transverse loads that are applied away from the shear centre. Hence they are often subjected to combined bending and torsion actions. Previous researches on LSBs have concentrated on their bending or shear behaviour and strengths, and only limited research has been undertaken on their combined bending and torsion behaviour. Therefore in this research a series of nine experiments was first conducted on LSBs subject to combined bending and torsion. Three LSB sections were tested to failure under eccentric loading at mid-span, and appropriate results were obtained from seven tests. A special test rig was used to simulate two different eccentricities and to provide accurate simple boundary conditions at the supports. Finite element models of tested LSBs were developed using ANSYS, and the ultimate strengths, failure modes, and load–displacement curves were obtained and compared with corresponding test results. Finite element analyses agreed well with test results and hence the developed models were used in a parametric study to investigate the effects of load locations, eccentricities, and spans on the combined bending and torsion behaviour of LSBs. The interaction between the ultimate bending and torsional moment capacities was studied and a simple design rule was proposed. This paper presents the details of the tests, finite element analyses, and parametric study of LSBs subject to combined bending and torsion, and the results.

Analytical test functions for free vibration analysis of rotating non-homogeneous Timoshenko beams

In this paper, the governing equations for free vibration of a non-homogeneous rotating Timoshenko beam, having uniform cross-section, is studied using an inverse problem approach, for both cantilever and pinned-free boundary conditions. The bending displacement and the rotation due to bending are assumed to be simple polynomials which satisfy all four boundary conditions. It is found that for certain polynomial variations of the material mass density, elastic modulus and shear modulus, along the length of the beam, the assumed polynomials serve as simple closed form solutions to the coupled second order governing differential equations with variable coefficients. It is found that there are an infinite number of analytical polynomial functions possible for material mass density, shear modulus and elastic modulus distributions, which share the same frequency and mode shape for a particular mode. The derived results are intended to serve as benchmark solutions for testing approximate or numerical methods used for the vibration analysis of rotating non-homogeneous Timoshenko beams.

Modeling Nonlinear Peeling of Ductile Thin Films-Critical Assessment of Analytical Bending Models Using FE Simulations

Three analytical double-parameter criteria based on a bending model and a two-dimensional finite element analysis model are presented for the modeling of ductile thin film undergoing a nonlinear peeling process. The bending model is based on different governing parameters: (1) the interfacial fracture toughness and the separation strength, (2) the interfacial fracture toughness and the crack tip slope angle, and (3) the interfacial fracture toughness and the critical Mises effective strain of the delaminated thin film at the crack tip. Thin film nonlinear peeling under steady-state condition is solved with the different governing parameters. In addition, the peeling test problem is simulated by using the elastic-plastic finite element analysis model. A critical assessment of the three analytical bending models is made by comparison of the bending model solutions with the finite element analysis model solutions. Furthermore, through analyses and comparisons for solutions based on both the bending model and the finite element analysis model, some connections between the bending model and the finite element analysis model are developed. Moreover, in the present research, the effect of different selections for cohesive zone shape on the ductile film peeling solutions is discussed.

Assessment of Microscale Test Methods of Peeling and Splitting along Surface of Thin-Film/Substrates

Peel test methods are assessed through being applied to a peeling analysis of the ductile film/ceramic substrate system. Through computing the fracture work of the system using the either beam bend model (BB model) or the general plane analysis model (GPA model), surprisingly, a big difference between both model results is found. Although the BB model can capture the plastic dissipation phenomenon for the ductile film case as the GPA model can, it is much sensitive to the choice of the peeling criterion parameters, and it overestimates the plastic bending effect unable to capture crack tip constraint plasticity. In view of the difficulty of measuring interfacial toughness using peel test method when film is the ductile material, a new test method, split test, is recommended and analyzed using the GPA model. The prediction is applied to a wedge-loaded experiment for Al-alloy double-cantilever beam in literature.

Fracture properties of silicon carbide thin films by bulge test of long rectangular membrane

This paper reports the mechanical properties and fracture behavior of silicon carbide (3C-SiC) thin films grown on silicon substrates. Using bulge testing combined with a refined load-deflection model of long rectangular membranes, which takes into account the bending stiffness and prestress of the membrane material, the Young's modulus, prestress, and fracture strength for the 3C-SiC thin films with thicknesses of 0.40 and 1.42 mu m were extracted. The stress distribution in the membranes under a load was calculated analytically. The prestresses for the two films were 322 +/- 47 and 201 +/- 34 MPa, respectively. The thinner 3C-SiC film with a strong (111) orientation has a plane-gstrain moduli of 415 +/- 61 GPa, whereas the thicker film with a mixture of both (111) and (110) orientations exhibited a plane-strain moduli of 329 +/- 49 GPa. The corresponding fracture strengths for the two kinds of SiC films were 6.49 +/- 0.88 and 3.16 +/- 0.38 GPa, respectively. The reference stresses were computed by integrating the local stress of the membrane at the fracture over edge, surface, and volume of the specimens and were fitted with Weibull distribution function. For the 0.40-mu m-thick membranes, the surface integration has a better agreement between the data and the model, implying that the surface flaws are the dominant fracture origin. For the 1.42-mu m-thick membranes, the surface integration presented only a slightly better fitting quality than the other two, and therefore, it is difficult to rule out unambiguously the effects of the volume and edge flaws.

Fatigue behavior of laser-welded NiTi wires in small-strain cyclic bending

NiTi wires and their weldments are commonly used in micro-electro-mechanical systems (MEMS), and in such applications, cyclic loading are commonly encountered. In this paper, the bending-rotation fatigue (BRF) test was used to study the bending fatigue behavior of NiTi wire laser weldment in the small-strain regime. The fracture mechanism, which includes crack initiation, crack growth and propagation of the weldment in the BRF test, was investigated with the aid of SEM fractography and discussed in terms of the microstructure. It was found that crack initiation was primarily surface-condition dependent. The cracks were found to initiate at the surface defects at the weld zone (WZ) surface, and the crack propagation was assisted by the gas inclusions in the WZ. The weldment was finally fractured in a ductile manner. The fatigue life was found to decrease with increasing surface strain and also with increasing bending frequency (controlled by the rotational speed in the BRF test). In comparison, the fatigue life of the unwelded NiTi wires was higher than their welded counterparts at all strain levels and bending frequencies. The decrease in fatigue resistance of the weldment could be attributed to the surface and microstructural defects introduced during laser welding.

Influence of embedded length on strength of BFRP rods bonded parallel to the grain in low grade timber by pullout-bending tests

Bonded-in rod connections in timber possess many desirable attributes in terms of efficiency, manufacture, performance, aesthetics and cost. In recent years research has been conducted on such connections using fibre reinforced polymers (FRPs) as an alternative to steel. This research programme investigates the pull-out capacity of Basalt FRP rods bonded-in in low grade Irish Sitka Spruce. Embedded length is thought to be the most influential variable contributing to pull- out capacity of bonded-in rods after rod diameter. Previous work has established an optimum embedded length of 15 times the hole diameter. However, this work only considered the effects of axial stress on the bond using a pull-compression testing system which may have given an artificially high pull out capacity as bending effects were neglected. A hinge system was utilised that allows the effects of bending force to be taken in to consideration along with axial forces in a pull-out test. This paper describes an experimental programme where such pull-bending tests were carried out on samples constructed of 12mm diameter BFRP bars with a 2mm glueline thickness and embedded lengths between 80mm and 280mm bonded-in to low-grade timber with an epoxy resin. Nine repetitions of each were tested. A clear increase in pull-out strength was found with increasing embedded length.

The effect of skin passing on the material behavior of metal strip in pure bending and tension

The metal strip used in roll forming has often been preprocessed by (tension or roller) leveling or by skin-pass rolling, and as a consequence, may contain residual stresses. These stresses are not well observed by the tensile test, but could have a significant effect on the bending and springback behavior. With the advent of improved process design techniques for roll forming, including advanced finite element techniques, the need for precise material property data has become important. The major deformation mode of roll forming is that of bending combined with unloading and reverse bending, and hence property data derived from bend tests could be more relevant than that from tensile testing.

This work presents a numerical study on the effect of skin passing on the material behavior of stainless steel strip in pure bending and tension. A two dimensional (2-D) numerical model was developed using Abaqus Explicit to analyze the affect of skin passing on the residual stress profile across a section for various working conditions. The deformed meshes and their final stress fields were then imported as pre-defined fields into Abaqus Standard, and the post-skin passing material behavior in pure bending was determined. The results show that a residual stress profile is introduced into the steel strip during skin passing, and that its shape and stress level depend on the overall thickness reduction as well as the number of rolling passes used in the skin passing process. The material behavior in bending and the amount of springback changed significantly depending on the skin pass condition.

Analytic study on pure bending of metal sheets

In this work, analytical models of pure bending are developed to simulate a particular type of bend test and to determine possible errors arising from approximations used in analyzing experimental data. Analytical models proposed for steels include a theoretical solution of pure bending and a series of finite element models, based on the von Mises yield function, are subjected to different stress and strain conditions. The results show that for steel sheets the difference between measured and calculated results of the moment-curvature behaviour is small and the numerical results from the finite element models indicate that experimental results obtained from the test are acceptable in the range of the pure bending operation. Further for magnesium alloys, which exhibit unsymmetrical yielding, the algorithm of the yield function with a linear isotropic hardening model is implemented by programming a user subroutine in Abaqus for bending simulations of magnesium. The simulations using the proposed user subroutine extract better results than those using the von Mises yield function.

Spectral analysis of the electromyograph of the erector spinae muscle before and after a dynamic manual load-lifting test

The aim of the present study was to assess the spectral behavior of the erector spinae muscle during isometric contractions performed before and after a dynamic manual load-lifting test carried out by the trunk in order to determine the capacity of muscle to perform this task. Nine healthy female students participated in the experiment. Their average age, height, and body mass (± SD) were 20 ± 1 years, 1.6 ± 0.03 m, and 53 ± 4 kg, respectively. The development of muscle fatigue was assessed by spectral analysis (median frequency) and root mean square with time. The test consisted of repeated bending movements from the trunk, starting from a 45º angle of flexion, with the application of approximately 15, 25 and 50% of maximum individual load, to the stand up position. The protocol used proved to be more reliable with loads exceeding 50% of the maximum for the identification of muscle fatigue by electromyography as a function of time. Most of the volunteers showed an increase in root mean square versus time on both the right (N = 7) and the left (N = 6) side, indicating a tendency to become fatigued. With respect to the changes in median frequency of the electromyographic signal, the loads used in this study had no significant effect on either the right or the left side of the erector spinae muscle at this frequency, suggesting that a higher amount and percentage of loads would produce more substantial results in the study of isotonic contractions.

A theoretical and experimental analysis of cold-formed steel shapes subjected to bending - Channel and simple lipped channel

Cold-formed steel shapes have been widely employed in steel construction, where they frequently offer a lower cost solution than do traditional laminated shapes. A classic application of cold-formed steel shapes is purlins in the roof panel of industrial buildings, connected to the roof panel by means of screws. The combined effect of these two elements has been the subject of investigations in some countries. Design criteria were included in the AISI Code in 1991 and 1996. This paper presents and discusses the results obtained from bending tests carried out on shapes commonly used in Brazil, i.e., the channel and the simple lipped channel, Tests were carried out on double shapes with 4.5 and 6.0 meter spans, which were subjected to concentrated loads and braced against each other on the supports and at intermediary points in three different load situations. The panel shape was also analyzed experimentally, simulating the action of wind by means of a vacuum box designed specifically for this purpose. The test results were then compared to those obtained through the theoretical analysis, enabling us to extract important information upon which to base proposed design criteria for the new Brazilian code.

Rod length influence in torque measurement of SPT-T test

Since Ranzini suggested supplementing the SPT test with measurement of the torque required to turn the split spoon sampler after driving, many Brazilian engineers have been using this in the design of pile foundations. This paper presents a study of the rod length influence in the torque measurement. A theoretical study of material resistance considering torsion and bending in a thin wall tubular steel shaft was performed. It makes possible to conclude that the shearing tension caused by the proper weight represents less than 1% of the shearing tension caused by the turning moment. In addition, an experimental study was done with electric torquemeters fixed in a horizontal rod system. The tests were being carried out to analyze rods of one meter to twenty meters in length and the measurements were collected at the ends of each rod length verifying the efficiency data. As a result, it is possible to verify that the torque difference through rod length is lower than minimum scales of mechanical torquemeters that are used on practical engineering. Also a fact to be considered is a big torque loss for values under 20 N.m of applied torque. This way, the SPT-T is not adequate to low consistency soil. Copyright ASCE 2007.

Theoretical and experimental evaluation of the influence of the length of drill rods in the SPT-T test

The influence of soil drill rod length on the N value in the SPT-T test has been studied extensively by Mello (1971), Schmertmann & Palacios (1979), Odebrecht et al. (2002) and Cavalcante (2002). This paper presents an analysis of the Standard Penetration Test supplemented with torque measurement (SPT-T). A theoretical study of the resistance of the rod material to torsion and bending indicated that the shear stress caused by the rod self-weight represents less than 1% of that caused by the torsional moment. An experimental study with electric torquemeters attached to a horizontal rod system, as well as two field tests in the vertical direction, were also carried out to compare and substantiate the results. The purpose of these tests was to analyze changes along the length of the rod in response to successive increments at 1-meter intervals. Torque measurements were taken at each increment of the length to ascertain the accuracy of the theoretical data. The difference between the applied torque and the measured torque at the end of rod system was lower than the minimum scale of mechanical torquemeters used in practice.

ANALYSIS OF THE NATURAL VIBRATION FREQUENCY TEST METHOD TO OBTAIN THE MODULUS OF ELASTICITY OF WOOD STRUCTURAL COMPONENTS

There are several techniques to characterize the elastic modulus of wood and those currently using the natural frequencies of vibration stand out as they are non-destructive techniques, producing results that can be repeated and compared over time. This study reports on the effectiveness of the testing methods based on the natural frequencies of vibration versus static bending to obtain the elastic properties of reforested structural wood components usually employed in civil construction. The following components were evaluated: 24 beams of Eucalyptus sp. with nominal dimensions (40 x 60 x 2.000 mm) and 14 beams of Pinus oocarpa with nominal dimensions (45 x 90 x 2.300 mm) both without treatment; 30 boards with nominal dimensions (40 x 240 x 2.010 mm) and 30 boards with nominal dimensions (40 x 240 x 3.050 mm), both of Pinus oocarpa and with chromate copper arsenate (CCA) preservative treatment. The results obtained in thiswork show good correlation when compared to the results obtained by the static bending mechanical method, especially when applying the natural frequency of longitudinal vibration. The use of longitudinal frequency was reliable and practical, therefore recommended for determining the modulus of elasticity of wood structural elements. It was also found that no specific support is needed for the specimens using the longitudinal frequency, as well as no previous calibrations, reducing the execution time and enabling to test many samples.