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.

The analogue shear zone : from rheology to associated geometry

The geometry of ductile strain localization phenomena is related to the rheology of the deformed rocks. Both qualitative and quantitative rheological properties of natural rocks have been estimated from finite field structures such as folds and shear zones. We apply physical modelling to investigate the relationship between rheology and the temporal evolution of the width and transversal strain distribution in shear zones, both of which have been used previously as rheological proxies. Geologically relevant materials with well-characterized rheological properties (Newtonian, strain hardening, strain softening, Mohr-Coulomb) are deformed in a shear box and observed with Particle Imaging Velocimetry (PIV). It is shown that the width and strain distribution histories in model shear zones display characteristic finite responses related to material properties as predicted by previous studies. Application of the results to natural shear zones in the field is discussed. An investigation of the impact of 3D boundary conditions in the experiments demonstrates that quantitative methods for estimating rheology from finite natural structures must take these into account carefully.

Experimental studies of the shear behavior and strength of LiteSteel beams with stiffened web openings

Abstract: LiteSteel beam (LSB) is a new cold-formed steel hollow flange channel section produced using a patented manufacturing process. It is commonly used as flexural members in residential, industrial and commercial 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. Test results have shown that the shear capacity of LSBs can be reduced considerably by the inclusion of web openings. A cost effective method of eliminating the detrimental effects of a large web opening is to attach suitable stiffeners around the web openings of LSBs. A detailed experimental study consisting of 17 shear tests was therefore undertaken to investigate the shear behaviour and strength of LSBs with stiffened circular web openings. Both plate and stud stiffeners with varying sizes and thicknesses were attached to the web elements of LSBs using a number of screw-fastening arrangements in order to develop a suitable stiffening arrangement for LSBs. Simply supported test specimens of LSBs with an aspect ratio of 1.5 were loaded at mid-span until failure. This paper presents the details of this experimental study of LSBs with stiffened web openings, and the results of their shear capacities and associated behavioural characteristics. Suitable screw-fastened plate stiffener arrangements have been recommended in order to restore the original shear capacity of LSBs.

Shear buckling characteristics of cold-formed steel channel beams

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 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. For the shear design of LCB web panels, their elastic shear buckling strength must be determined accurately including the potential post-buckling strength. Currently the elastic shear buckling coefficients of LCB web panels are determined by assuming conservatively that the web panels are simply supported at the junction between their flange and web elements. Hence finite element analyses were conducted to investigate the elastic shear buckling behavior of LCBs. An improved equation for the higher elastic shear buckling coefficient of LCBs was proposed based on finite element analysis results and included in the ultimate shear capacity equations of the North American cold-formed steel codes. Finite element analyses show that relatively short span LCBs without flange restraints are subjected to a new combined shear and flange distortion action due to the unbalanced shear flow. They also show that significant post-buckling strength is available for LCBs subjected to shear. New equations were also proposed in which post-buckling strength of LCBs was included.

Fiber Bragg grating strain modulation based on nonlinear string transverse force amplifier

The only effective method of Fiber Bragg Grating (FBG) strain modulation has been by changing the distance between its two fixed ends. We demonstrate an alternative being more sensitive to force based on the nonlinear amplification relationship between a transverse force applied to a stretched string and its induced axial force. It may improve the sensitivity and size of an FBG force sensor, reduce the number of FBGs needed for multi-axial force monitoring, and control the resonant frequency of an FBG accelerometer.

Shear thinning and shear thickening non-Newtonian confined fluid flow over rotating cylinder

In present work, numerical solution is performed to study the confined flow of power-law non Newtonian fluids over a rotating cylinder. The main purpose is to evaluate drag and thermal coefficients as functions of the related governing dimensionless parameters, namely, power-law index (0.5 ≤ n ≤ 1.4), dimensionless rotational velocity (0 ≤ α ≤ 6) and the Reynolds number (100 ≤ Re ≤ 500). Over the range of Reynolds number, the flow is known to be steady. Results denoted that the increment of power law index and rotational velocity increases the drag coefficient due to momentum diffusivity improvement which is responsible for low rate of heat transfer, because the thicker the boundary layer, the lower the heat transfer is implemented.

Shear strengths of lipped channel beams with stiffened web openings using numerical studies

This paper presents the details of numerical studies on the shear behaviour and strength of lipped channel beams (LCBs) with stiffened web openings. Over the last couple of decades, cold-formed steel beams have been used extensively in residential, industrial and commercial buildings as primary load bearing structural components. Their shear strengths are considerably reduced when web openings are included for the purpose of locating building services. Our research has shown that shear strengths of LCBs were reduced by up to 70% due to the inclusion of web openings. Hence there is a need to improve the shear strengths of LCBs with web openings. A cost effective way to improve the detrimental effects of a large web opening is to attach appropriate stiffeners around the web openings in order to restore the original shear strength and stiffness of LCBs. Hence numerical studies were undertaken to investigate the shear strengths of LCBs with stiffened web openings. In this research, finite element models of LCBs with stiffened web openings in shear were developed to simulate the shear behaviour and strength of LCBs. Various stiffening methods using plate and LCB stud stiffeners attached to LCBs using screw-fastening were attempted. The developed models were then validated by comparing their results with experimental results and used in parametric studies. Both finite element analysis and experimental results showed that the stiffening arrangements recommended by past re-search for cold-formed steel channel beams are not adequate to restore the shear strengths of LCBs with web openings. Therefore new stiffener arrangements were proposed for LCBs with web openings based on experimental and finite element analysis results. This paper presents the details of finite element models and analyses used in this research and the results including the recommended stiffener arrangements.

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.

Evaluation of shear stress and slip relationship of composite lap joints

Advanced composite materials offer remarkable potential in the strengthening of Civil Engineering structures. This research is targeted to provide in depth knowledge and understanding of bond characteristics of advanced and corrosion resistant material carbon fibre reinforced polymer (CFRP) that has a unique design tailor-ability and cost effective nature. The objective of this research is to investigate and compare the bonding mechanism between CFRP strengthened single and double strap steel joints. Investigations have been made in regards to failure mode, ultimate load and effective bond length for CFRP strengthened double and single strap joints. A series of tensile tests were conducted with different bond lengths for both type of joints. The bond behaviour of these specimens was further investigated by using nonlinear finite element analysis. Finally a bilinear relationship of shear stress-slip has been proposed by using the Finite element model for single and double strap joints.

The time course of in vivo recovery of transverse strain in high-stress tendons following exercise

Objective To evaluate the time course of the recovery of transverse strain in the Achilles and patellar tendon following a bout of resistance exercise. Methods Seventeen healthy adults underwent sonographic examination of the right patellar (n=9) and Achilles (n=8) tendons immediately prior to and following 90 repetitions of weight-bearing quadriceps and gastrocnemius-resistance exercise performed against an effective resistance of 175% and 250% body weight, respectively. Sagittal tendon thickness was determined 20 mm from the enthesis and transverse strain, as defined by the stretch ratio, was repeatedly monitored over a 24 h recovery period. Results Resistance exercise resulted in an immediate decrease in Achilles (t7=10.6, p<0.01) and patellar (t8=8.9, p<0.01) tendon thickness, resulting in an average transverse stretch ratio of 0.86±0.04 and 0.82±0.05, which was not significantly different between tendons. The magnitude of the immediate transverse strain response, however, was reduced with advancing age (r=0.63, p<0.01). Recovery in transverse strain was prolonged compared with the duration of loading and exponential in nature. The average primary recovery time was not significantly different between the Achilles (6.5±3.2 h) and patellar (7.1±3.2 h) tendons. Body weight accounted for 62% and 64% of the variation in recovery time, respectively. Conclusions Despite structural and biochemical differences between the Achilles and patellar tendon, the mechanisms underlying transverse creep recovery in vivo appear similar and are highly time dependent. These novel findings have important implications concerning the time required for the mechanical recovery of high-stress tendons following an acute bout of exercise.

The acute transverse strain response of the patellar tendon to quadriceps exercise

Introduction: The human patellar tendon is highly adaptive to changes in habitual loading but little is known about its acute mechanical response to exercise. This research evaluated the immediate transverse strain response of the patellar tendon to a bout of resistive quadriceps exercise. Methods: Twelve healthy adult males (mean age 34.0+/-12.1 years, height 1.75+/-0.09 m and weight 76.7+/-12.3 kg) free of knee pain participated in the research. A 10-5 MHz linear-array transducer was used to acquire standardised sagittal sonograms of the right patellar tendon immediately prior to and following 90 repetitions of a double-leg parallel-squat exercise performed against a resistance of 175% bodyweight. Tendon thickness was determined 20-mm distal to the pole of the patellar and transverse Hencky strain was calculated as the natural log of the ratio of post- to pre-exercise tendon thickness and expressed as a percentage. Measures of tendon echotexture (echogenicity and entropy) were also calculated from subsequent gray-scale profiles. Results: Quadriceps exercise resulted in an immediate decrease in patellar tendon thickness (P<.05), equating to a transverse strain of -22.5+/-3.4%, and was accompanied by increased tendon echogenicity (P<.05) and decreased entropy (P<.05). The transverse strain response of the patellar tendon was significantly correlated with both tendon echogenicity (r = -0.58, P<.05) and entropy following exercise (r=0.73, P<.05), while older age was associated with greater entropy of the patellar tendon prior to exercise (r=0.79, P<.05) and a reduced transverse strain response (r=0.61, P<.05) following exercise. Conclusions: This study is the first to show that quadriceps exercise invokes structural alignment and fluid movement within the matrix that are manifest by changes in echotexture and transverse strain in the patellar tendon., (C)2012The American College of Sports Medicine