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.

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.

Studies on the in-plane shear response of confined masonry shear walls

The prime aim of this research project is to evaluate the performance of confined masonry walls under in-plane shear with a view to contributing to the national masonry design standard through a set of design clauses. This aim stems from the criticisms of the current provisions of the in-plane shear capacity equations in the Australian Masonry Standard AS3700 (2011) being highly non-conservative. This PhD thesis is an attempt to address this gap in the knowledge through systematic investigation of the key parameters that affects the in-plane shear strength of the masonry walls through laboratory experiments and extensive finite element analyses.

Finite element analysis of the in-plane shear behaviour of masonry panels confined with reinforced grouted cores

A combined experimental and numerical program was conducted to study the in-plane shear behaviour of hollow concrete masonry panels containing reinforced grout cores. This paper is focused on the numerical program. A two dimensional macromodelling strategy was used to simulate the behaviour of the confined masonry (CM) shear panels. Both the unreinforced masonry and the confining element were modelled using macromasonry properties and the steel reinforcement was modelled as an embedded truss element located within the grout using perfectly bonded constraint. The FE model reproduced key behaviours observed in the experiments, including the shear strength, the deformation and the crack patterns of the unconfined and confined masonry panels. The predictions of the validated model were used to evaluate the existing in-plane shear expressions available in the national masonry standards and research publications.

Generalized azimuthal shear deformations in compressible isotropic elastic materials

In this article we study the azimuthal shear deformations in a compressible Isotropic elastic material. This class of deformations involves an azimuthal displacement as a function of the radial and axial coordinates. The equilibrium equations are formulated in terms of the Cauchy-Green strain tensors, which form an overdetermined system of partial differential equations for which solutions do not exist in general. By means of a Legendre transformation, necessary and sufficient conditions for the material to support this deformation are obtained explicitly, in the sense that every solution to the azimuthal equilibrium equation will satisfy the remaining two equations. Additionally, we show how these conditions are sufficient to support all currently known deformations that locally reduce to simple shear. These conditions are then expressed both in terms of the invariants of the Cauchy-Green strain and stretch tensors. Several classes of strain energy functions for which this deformation can be supported are studied. For certain boundary conditions, exact solutions to the equilibrium equations are obtained. © 2005 Society for Industrial and Applied Mathematics.

On helical shear of a compressible elastic circular cylindrical tube

In this paper we examine the combined azimuthal and axial shear of a compressible isotropic elastic circular cylindrical tube of finite extent, otherwise referred to as helical shear (which is an isochoric deformation). The equilibrium equations are formulated in terms of the principal stretches, and explicit necessary and sufficient conditions on the strain-energy function for the material to support this deformation are obtained and compared with those obtained previously for this problem. Several classes of strain-energy functions are derived and in some general cases complete solutions of the equilibrium equations are obtained. Existing results are recovered as special cases and some new results for the strain-energy functions derived are determined and discussed.

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.

Experimental investigation and design of lipped channel beams in shear

Cold-formed high strength steel members are increasingly used as primary load bearing components in low rise buildings. Lipped channel beam (LCB) is one of the most commonly used flexural members in these applications. In this research an experimental study was undertaken to investigate the shear behaviour and strengths of LCB sections. Simply supported test specimens of back to back LCBs with aspect ratios of 1.0 and 1.5 were loaded at mid-span until failure. Test specimens were chosen such that all three types of shear failure (shear yielding, inelastic and elastic shear buckling) occurred in the tests. The ultimate shear capacity results obtained from the tests were compared with the predictions from the current design rules in Australian/NewZealand and American cold-formed steel design standards. This comparison showed that these shear design rules are very conservative as they did not include the post-buckling strength observed in the shear tests and the higher shear buckling coefficient due to the additional fixity along the web-flange juncture. Improved shear design equations are proposed in this paper by including the above beneficial effects. Suitable lower bound design rules were also developed under the direct strength method format. This paper presents the details of this experimental study and the results including the improved design rules for the shear capacity of LCBs. It also includes the details of tests of LCBs subject to combined shear and flange distortion, and combined bending and shear actions, and proposes suitable design rules to predict the capacities in these cases.

Improving the shear capacities of lipped channel beams with web openings using plate stiffeners

Cold-formed steel lipped channel beams (LCB) are used extensively in residential, industrial and commercial buildings as load bearing structural elements. Their shear capacities are considerably reduced when web openings are included for the purpose of locating building services. Past research has shown that the shear capacities of LCBs were reduced by up to 70% due to the inclusion of these web openings. Hence there is a need to improve the shear capacities of LCBs with web openings. A cost effective way of eliminating the detrimental effects of large web openings is to attach suitable stiffeners around the web openings and restore the original shear strength and stiffness of LCBs. Hence detailed experimental studies were undertaken to investigate the behaviour and strength of LCBs with stiffened web openings subject to shear, and combined bending and shear actions. Both plate and stud stiffeners with varying sizes and thicknesses were attached to the web elements of LCBs using different screw-fastening arrangements. Simply supported test specimens of LCBs with aspect ratios of 1.0 and 1.5 were loaded at mid-span until failure. Numerical studies were also undertaken to investigate the strength of LCBs with stiffened web openings. Finite element models of LCBs with stiffened web openings under shear, combined bending and shear actions were developed to simulate the behaviour of tested LCBs. The developed models were then validated by comparing their results with experimental results and used in further studies. Both experimental and finite element analysis results showed that the stiffening arrangements recommended by past research and available design guidelines are not adequate to restore the original shear strengths of LCBs. Therefore new stiffener arrangements were proposed based on screw fastened plate stiffeners. This paper presents the details of this research study and the results.

Studies on the failure of unreinforced masonry shear walls

This thesis aims at studying the structural behaviour of high bond strength masonry shear walls by developing a combined interface and surface contact model. The results are further verified by a cost-effective structural level model which was then extensively used for predicting all possible failure modes of high bond strength masonry shear walls. It is concluded that the increase in bond strength of masonry modifies the failure mode from diagonal cracking to base sliding and doesn't proportionally increase the in-plane shear capacity. This can be overcome by increasing pre-compression pressure which causes failure through blocks. A design equation is proposed and high bond strength masonry is recommended for taller buildings and/ or pre-stressed masonry applications.

Compressive and shear force generated in the lumbar spine of female rowers

Rowers have and accrue greater lumbar spine bone mineral density (BMD) associated with mechanical loading produced during rowing. The aim of this study was to estimate the mechanical loading generated at the lumbar spine (LS) that is apparently providing an osteogenic benefit. The cohort comprised 14 female rowers (average age: 19.7yrs; height: 170.9 cm, weight: 59.5 kg) and 14 female matched controls (average age: 20.9 m yrs; height: 167.5 cm; weight: 58.1 kg). BMD was assessed using the Hologic QDR 2000+ bone densitometer, indicating higher lumbar spine BMD in the rowers compared to the control subjects (1,069 +/- 0.1 vs. 1,027 +/- 0.1 g/cm2). No significant difference existed for BMD at any other site. All rowers performed a six-minute simulated race on a Concept II rowing ergometer. Mechanical loading generated at the lumbar spine during this task was assessed using a two-dimensional model of the spine, enabling the calculation of the compressive and shear forces at L4/L5. The shear force was the joint reaction force perpendicular to the spine at the L4/L5 joint. Peak compressive and shear force at the lumbar spine of the rowers were 2,694 +/- 609 (N) and 660 +/- 117 (N), respectively. Peak compressive force at the LS relative to body weight was 4.6 times body weight. The literature would suggest that forces of this magnitude, generated at the LS during maximal rowing, may be contributing to the site specific higher LS BMD found in the rowers.

Shear tests of hollow flange channel beams with real support conditions

This paper presents the details of experimental studies on the effect of real support conditions on the shear strength of hollow flange channel beams, known as 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 many applications in the building industry LSBs are used with only one web side plate (WSP) at their supports. The WSPs are also often not full height plates. Past research studies showed that these real support connections did not provide the required 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 a detailed experimental study based on 25 shear tests was undertaken to investigate the shear behaviour and strength of LSBs with real support conditions. 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. Suitably improved support connections were developed to improve the shear capacity of LSBs based on test results. Details of the recommended support connections and shear capacity results are given in this paper.

Improved shear design rules of cold-formed steel beams

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 triangular hollow flange beams (THFB) are commonly used as flexural members such as floor joists and bearers while rectangular hollow flange beams (RHFB) are used in small scale housing developments through to large building structures. However, their shear capacities are determined based on conservative design rules. For the shear design of cold-formed steel beams, their elastic shear buckling strength and the potential post-buckling strength must be determined accurately. Hence experimental and numerical studies were conducted to investigate the shear behaviour and strength of LCBs, LSBs, THFBs and RHFBs. Improved shear design rules including the direct strength method (DSM) based design equations were developed to determine the ultimate shear capacities of these open and hollow flange 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 design equations. A new post-buckling coefficient was also introduced in the design equations to include the available post-buckling strength of cold-formed steel beams. This paper presents the details of this study on cold-formed steel beams subject to shear, and the results. It proposes generalised and improved shear design rules that can be used for any type of cold-formed steel beam.