Effective shear modulus approach for two dimensional solids and plate bending problems by meshless point collocation method

For the analysis of material nonlinearity, an effective shear modulus approach based on the strain control method is proposed in this paper by using point collocation method. Hencky’s total deformation theory is used to evaluate the effective shear modulus, Young’s modulus and Poisson’s ratio, which are treated as spatial field variables. These effective properties are obtained by the strain controlled projection method in an iterative manner. To evaluate the second order derivatives of shape function at the field point, the radial basis function (RBF) in the local support domain is used. Several numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method and comparisons have been made with analytical solutions and the finite element method (ABAQUS).

Wider reinforced masonry shear walls subjected to cyclic lateral loading

Partially grouted wider reinforced masonry wall, built predominantly with the use of face shell bedded hollow concrete blocks, is adopted extensively in the cyclonic areas due to its economy. Its out-of-plane response to lateral pressure loading is well definied; however its in-plane shear behaviour is less well understood, in particular it is unclear how the grouted reinforced cores affect the load paths within the wall. For the rational design of the walls, clarification is sought as to whether the wall acts as a composite of unreinforced panels surrounded by the reinforced cores or simply as a continuum embedded with reinforcement at wider spacing. This paper reports four full scale walls tested under in-place cyclic shear loading to provide some insight into the effect of the grout cores in altering the load paths within the wall. The global lateral load - lateral deflection hysteretic curves as well as the local responses of some critical zones of the shear walls are presented. It is shown that the aspect ratio of the unreinforced masonry panels surrounded by the reinforced grouted cores within the shear walls have profound effect in ascertaining the behaviour of the shear walls.

Numerical Modelling of LiteSteel Beams Subject to Shear

Abstract: LiteSteel beam (LSB) is a new cold-formed steel hollow flange channel beam produced using a patented manufacturing process involving simultaneous cold-forming and dual electric resistance welding. It has the beneficial characteristics of torsionally rigid closed rectangular flanges combined with economical fabrication processes from a single strip of high strength steel. Although the LSB sections are commonly used as flexural members, no research has been undertaken on the shear behaviour of LSBs. Therefore experimental and numerical studies were undertaken to investigate the shear behaviour and strength of LSBs. In this research finite element models of LSBs were developed to investigate their nonlinear shear behaviour including their buckling characteristics and ultimate shear strength. They were validated by comparing their results with available experimental results. The models provided full details of the shear buckling and strength characteristics of LSBs, and showed the presence of considerable improvements to web shear buckling in LSBs and associated post-buckling strength. This paper presents the details of the finite element models of LSBs and the results. Both finite element analysis and experimental results showed that the current design rules in cold-formed steel codes are very conservative for the shear design of LSBs. The ultimate shear capacities from finite element analyses confirmed the accuracy of proposed shear strength equations for LSBs based on the North American specification and DSM design equations. Developed finite element models were used to investigate the reduction to shear capacity of LSBs when full height web side plates were not used or when only one web side plate was used, and these results are also presented in this paper.

New design rules for the shear strength of LiteSteel Beams

Abstract: The LiteSteel Beam (LSB) is a new cold-formed hollow flange channel section produced using dual electric resistance welding and automated continuous roll-forming technologies. The innovative LSB sections have many beneficial characteristics and are commonly used as flexural members in building construction. However, limited research has been undertaken on the shear behaviour of LSBs. Therefore a detailed investigation including both numerical and experimental studies was undertaken to investigate the shear behaviour of LSBs. Finite element models of LSBs in shear were developed to simulate the nonlinear ultimate strength behaviour of LSBs including their elastic buckling characteristics, and were validated by comparing their results with experimental test results. Validated finite element models were then used in a detailed parametric study into the shear behaviour of LSBs. The parametric study results showed that the current design rules in cold-formed steel structures design codes are very conservative for the shear design of LSBs. Significant improvements to web shear buckling occurred due to the presence of torsionally rigid rectangular hollow flanges while considerable post-buckling strength was also observed. This paper therefore proposes improved shear strength design rules for LSBs within the current cold-formed steel code guidelines. It presents the details of the parametric study and the new shear strength equations. The new equations were also developed based on the direct strength method. The proposed shear strength equations have the potential to be used with other conventional cold-formed steel sections such as lipped channel sections.

New design rules for the shear strength of LiteSteel Beams with web openings

Abstract: 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 are commonly used as floor joists and bearers with web openings in residential, industrial and commercial buildings. Their shear strengths are considerably reduced when web openings are included for the purpose of locating building services. However, no research has been undertaken on the shear behaviour and strength of LSBs with web openings. Therefore experimental and numerical studies were undertaken to investigate the shear behaviour and strength of LSBs with web openings. In this research, finite element models of LSBs with web openings in shear were developed to simulate the shear behaviour and strength of LSBs including their buckling characteristics. They were then validated by comparing their results with available experimental test results and used in a detailed parametric study. The results showed that the current design rules in cold-formed steel structures design codes are very conservative for the shear design of LSBs with web openings. Improved design equations have been proposed for the shear capacity of LSBs with web openings based on both experimental and parametric study results. An alternative shear design method based on an equivalent reduced web thickness was also proposed. It was found that the same shear strength design rules developed for LSBs without web openings can be used for LSBs with web openings provided the equivalent reduced web thickness equation developed in this paper is used. This is a significant advancement as it simplifies the shear design methods of LSBs with web openings considerably.

Shear behaviour and strength of LiteSteel Beams with web openings

Abstract: The LiteSteel Beam (LSB) is a new cold-formed steel hollow flange channel beam recently developed in Australia. It is commonly used as a floor joist or bearer in buildings. Current practice in flooring systems is to include openings in the web element of floor joists or bearers so that building services can be located within them. Shear behaviour of LSBs with web openings is more complicated while their shear strengths are considerably reduced by the presence of web openings. However, no research has been undertaken on the shear behaviour and strength of LSBs with web openings. Therefore a detailed experimental study involving 26 shear tests was undertaken on simply supported LSB test specimens with web openings and an aspect ratio of 1.5. This paper presents the details of this experimental study and the results of their shear capacities and behavioural characteristics. Experimental results showed that the current design rules in cold-formed steel structures design codes are very conservative for the shear design of LSBs with web openings. Improved design equations have been proposed for the shear strength of LSBs with web openings based on the experimental results from this study.

Shear tests of hollow flange channel beams with stiffened web openings

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 are commonly used as floor joists and bearers with web openings in residential, industrial and commercial buildings. Their shear strengths are considerably reduced when web openings are included for the purpose of locating building services. Shear tests of LSBs with web openings have shown that there is up to a 60% reduction in the shear capacity due to the inclusion of web openings. Hence there is a need to improve the shear capacity of LSBs with web openings. A cost effective way to eliminate the shear capacity reduction is to attach suitable stiffeners around the web openings. Hence experimental studies were undertaken to investigate the shear behaviour and strength of LSBs with stiffened web openings. In this research, various stiffening methods using plate and LSB stiffeners attached to LSBs using both welding and screw-fastening were attempted. Our test results showed that the stiffening arrangements recommended by past research for cold-formed steel channel beams are not adequate to restore the shear strengths of LSBs with web openings. Therefore new stiffener arrangements were proposed for LSBs with web openings. This paper presents the details of this experimental study and the results including the details of the optimum stiffener details for LiteSteel beams.

Shear tests of lipped chanel beams with web openings

Cold-formed steel members are increasingly used as primary structural elements in the building industries around the world due to the availability of thin and high strength steels and advanced cold-forming technologies. Cold-formed steel lipped channel beams (LCB) are commonly used as flexural members such as floor joists and bearers. However, their shear capacities are determined based on conservative design rules. Current practice in flooring systems is to include openings in the web element of floor joists or bearers so that building services can be located within them. However, limited research has been undertaken on the shear behaviour and strength of LCBs with web openings. Hence a detailed experimental study involving 32 shear tests was undertaken to investigate the shear behaviour and strength of LCBs with web openings. Simply supported test specimens of LCBs with an aspect ratio of 1.0 and 1.5 were loaded at mid-span until failure. This paper presents the details of this experimental study and the results of their shear capacities and behavioural characteristics. Experimental results showed that the current design rules in cold-formed steel structures design codes are very conservative for the shear design of LCBs with web openings. Improved design equations have been proposed for the shear strength of LCBs with web openings based on the experimental results from this study.

Tests of LiteSteel Beams subject to combined shear and bending actions

This paper presents the details of an experimental study of a cold-formed steel beam known as LiteSteel Beam (LSB) subject to combined shear and bending actions. The LSBs have the beneficial characteristics of torsionally rigid rectangular hollow flanges combined with economical fabrication processes from a single strip of high strength steel. They combine the stability of hot-rolled steel sections with the high strength to weight ratio of conventional cold-formed steel sections. The LSB sections are commonly used as flexural members in residential, industrial and commercial buildings. In order to ensure safe and efficient designs of LSBs, many research studies have been undertaken on the flexural and shear strengths of LSBs. To date, however, no investigation has been conducted into the strength of LSB sections under combined shear and bending actions. Hence a detailed experimental study involving 18 tests was undertaken to investigate the behaviour and strength of LSBs under combined shear and bending actions. Test results showed that AS/NZS 4600 design rules for unstiffened webs grossly underestimated the capacity of LSBs. Therefore improved design equations were proposed for the combined shear and bending capacities of LSBs based on experimental results.

Behaviour of LiteSteel beams subject to combined shear and bending actions

This paper presents the details of a numerical study of a cold-formed steel beam known as LiteSteel Beam (LSB) subject to combined shear and bending actions. The LSB sections are produced by a patented manufacturing process involving simultaneous cold-forming and electric resistance welding. They have a unique shape of a channel beam with two rectangular hollow flanges. To date, however, no investigation has been conducted into the strength of LSB sections under combined shear and bending actions. Hence a numerical study was undertaken to investigate the behaviour and strength of LSBs subject to combined shear and bending actions. In this research, finite element models of LSBs were developed to simulate the combined shear and bending behaviour and strength of LSBs. They were then validated by comparing their results with test results and used in a parametric study. Both experimental and finite element analysis results showed that the current design equations are not suitable for combined shear and bending capacities of LSBs. Hence improved design equations are proposed for the capacities of LSBs subject to combined shear and bending actions.

Shear strength of hollow flange channel beams with stiffened web openings

This 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 are commonly used as floor joists and bearers with web openings in buildings. Their shear strengths are considerably reduced when web openings are included for the purpose of locating building services. Shear tests of LSBs with web openings have shown that there is up to 60% reduction in the shear capacity. Hence there is a need to improve the shear capacity of LSBs with web openings. A cost effective way to eliminate the shear capacity reduction is to stiffen the web openings using suitable stiffeners. Hence numerical studies were undertaken to investigate the shear capacity of LSBs with stiffened web openings. In this research, finite element models of LSBs with stiffened web openings in shear were developed to simulate the shear behaviour and strength of LSBs. Various stiffening methods using plate and LSB stiffeners attached to LSBs using both welding and screw-fastening were attempted. The developed models were then validated by comparing their results with experimental results and used in further studies. Both finite element and experimental results showed that the stiffening arrangements recommended by past research for cold-formed steel channel beams are not adequate to restore the shear strengths of LSBs with web openings. Therefore new stiffener arrangements were proposed for LSBs with web openings. This paper presents the details of this research project using numerical studies and the results.

Finite element analyses of lipped channel beams with Web openings in 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. Shear behaviour of LCBs with web openings is more complicated and their shear capacities are considerably reduced by the presence of web openings. However, limited research has been undertaken on the shear behaviour and strength of LCBs with web openings. Hence a numerical study was undertaken to investigate the shear behaviour and strength of LCBs with web openings. 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. 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 with web openings. Improved design equations were therefore proposed for the shear strength of LCBs with web openings. This paper presents the details of this numerical study of LCBs with web openings, and the results.

Shear tests of lipped channel beams with stiffened web openings

Cold-formed steel lipped channel beams (LCB) are used extensively in residential, industrial and commercial buildings as load bearing structural elements. Their shear strengths 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 the LCBs. Hence detailed experimental studies were undertaken to investigate the shear behaviour and strength of LCBs with stiffened web openings. 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. Test results showed that the plate stiffeners established using AISI recommendations are inadequate to restore the shear strengths of LCBs with web openings. Hence new stiffener arrangements have been proposed for LCBs based on experimental results. This paper presents the details of this experimental study on the shear strength of lipped channel beams with stiffened web openings, and the results.

Networking of shear zones at the brittle-to-viscous transition (Cap de Creus, NE Spain)

A crustal-scale shear zone network at the fossil brittle-to-viscous transition exposed at Cap de Creus, NE Spain evolved by coeval fracturing and viscous, mylonitic overprinting of an existing foliation. Initial fracturing led to mylonitic shearing as rock softened in ductilely deformed zones surrounding the fractures. Mylonitic shear zones widened by lateral branching of fractures from these shear zones and by synthetic rotation of the existing foliation between the fractures and shear zones. Shear zones lengthened by a combination of fracturing and mylonitic shearing in front of the shear zone tips. Shear zones interconnected along and across their shearing planes, separating rhomb-shaped lozenges of less deformed rock. Lozenges were subsequently incorporated into the mylonitic shear zones by widening in the manner described above. In this way, deformation became homogeneous on the scale of initial fracturing (metre- to decametre-scale). In contrast, the shear zone network represents localisation of strain on a decametre-length scale. The strength of the continental crust at the time of coeval fracturing and viscous shearing is inferred to have decreased with time and strain, as fracturing evolved to mylonitic shearing, and as the shear zones coalesced to form a through-going network subparallel to the shearing plane. Crustal strength must therefore be considered as strain- and scale-dependent.