Paraxial Maxwell beams: transformation by general linear optical systems

Extending the work of earlier papers on the relativistic-front description of paraxial optics and the formulation of Fourier optics for vector waves consistent with the Maxwell equations, we generalize the Jones calculus of axial plane waves to describe the action of the most general linear optical system on paraxial Maxwell fields. Several examples are worked out, and in each case it is shown that the formalism leads to physically correct results. The importance of retaining the small components of the field vectors along the axis of the system for a consistent description is emphasized.

Vibrations of laminated beams

Governing equations in the form of simultaneous ordinary differential equations have been derived for natural vibration analysis of isotropic laminated beams. This formulation includes significant secondary effects such as transverse shear and rotatory inetia. Through a numerical example, the influence of these secondary effects has been studied.

Experimental and numerical investigation of the behaviour of CFRP strengthened CHS beams subjected to bending

This paper presents the results of an experimental and numerical program to investigate the circular hollow section (CHS) beams, strengthened using Carbon Fibre Reinforced Polymer (CFRP) sheets. The circular hollow shaped steel beams bonded with different CFRP layer orientations were tested under four-point bending. The mid-span deflection, service load and failure load were recorded. The LHL (where L, first inner longitudinal layer, H, second hoop layer and L, third outer longitudinal layer) and LLH (where L, first inner longitudinal layer, L, second longitudinal layer and H, third outer hoop layer) layer oriented strengthened beams perform slightly better than HHL (where H, first inner hoop layer, H, second hoop layer and L, third outer longitudinal layer) layer oriented strengthened beams. The LHL and LLH layer oriented treated beams showed very similar structural behaviour. Numerical analyses were then conducted on the CFRP strengthened steel CHS beams. The validity of the models has been assessed by comparing the failure loads and mid-span deflections. The effects of various parameters such as bond length, section types, tensile modulus of CFRP, adhesive layer thickness and adhesive types have been studied.

Active vibration suppression of non-linear beams using optimal dynamic inversion

Euler–Bernoulli beams are distributed parameter systems that are governed by a non-linear partial differential equation (PDE) of motion. This paper presents a vibration control approach for such beams that directly utilizes the non-linear PDE of motion, and hence, it is free from approximation errors (such as model reduction, linearization etc.). Two state feedback controllers are presented based on a newly developed optimal dynamic inversion technique which leads to closed-form solutions for the control variable. In one formulation a continuous controller structure is assumed in the spatial domain, whereas in the other approach it is assumed that the control force is applied through a finite number of discrete actuators located at predefined discrete locations in the spatial domain. An implicit finite difference technique with unconditional stability has been used to solve the PDE with control actions. Numerical simulation studies show that the beam vibration can effectively be decreased using either of the two formulations.

AE energy release during the fracture of HSC beams

An attempt has been made experimentally to investigate the acoustic emission (AE) energy release in high-strength concrete (HSC) beams subjected to monotonically increasing load. Acoustic emission energy release during the fracture process of the HSC beams is measured. Stress waves released during the fracture process in materials cause acoustic emissions. AE energy released during the fracture of a notched three-point bend plain concrete beam specimens having 28-day compressive strengths of 50.0 MPa, 69.0 MPa and 78.0 MPa and mortar (cement: sand (1: 4) by weight) specimens are studied. Mortar consists of one part cement and four parts sand by weight. The specimens were tested by a material testing system of 1200 kN capacity employing crack mouth opening displacement control at the rate of 0.0004 mm/s. The fracture energy and the AE energy released during the fracture process of all the tested TPB and mortar specimens are compared and discussed. The observations made in the present experimental study have some applications for monitoring the integrity of structures.

Non-linear bending of beams of variable cross-section

For the non-linear bending of cantilever beams of variable cross-section, the effect of large deformations, but with linear elasticity, is considered. The governing integral equation is solved by a numerical iterative procedure. Results for some typical cases are obtained and compared with some of those available in the literature.

Finite element analysis of laminated anisotropic beams of bimodulus materials

This paper presents finite element analysis of laminated anisotropic beams of bimodulus materials. The finite element has 16 d.o.f. and uses the displacement field in terms of first order Hermite interpolation polynomials. As the neutral axis position may change from point to point along the length of the beam, an iterative procedure is employed to determine the location of zero strain points along the length. Using this element some problems of laminated beams of bimodulus materials are solved for concentrated loads/moments perpendicular and parallel to the layering planes as well as combined loads.

Vibration of Non-Uniform Thin-Walled Beams of Arbitrary Shape

A generalised theory for the natural vibration of non-uniform thin-walled beams of arbitrary cross-sectional geometry is proposed. The governing equations are obtained as four partial, linear integro-differential equations. The corresponding boundary conditions are also obtained in an integro-differential form. The formulation takes into account the effect of longitudinal inertia and shear flexibility. A method of solution is presented. Some numerical illustrations and an exact solution are included.

Experimental studies of lipped channel beams subject to web crippling under two-flange load cases

Lipped channel beams (LCBs) are commonly used as flexural members such as floor joists and bearers in the construction 6 industry. These thin-walled LCBs are subjected to specific buckling and failure modes, one of them being web crippling. Despite considerable 7 research in this area, some recent studies have shown that the current web crippling design rules are unable to predict the test capacities under 8 end-two-flange (ETF) and interior-two-flange (ITF) load conditions. In many instances, web crippling predictions by the available design 9 standards such as AISI S100, AS/NZS 4600 and Eurocode 3 Part 1-3 are inconsistent, i.e., unconservative in some cases, although they 10 are conservative in other cases. Hence, experimental studies consisting of 36 tests were conducted in this research to assess the web crippling 11 behavior and capacities of high-strength LCBs under two-flange load cases (ETF and ITF). Experimental results were then compared with the 12 predictions from current design rules. Comparison of the ultimate web crippling capacities from tests showed that the design equations are 13 very unconservative for LCB sections under the ETF load case and are conservative for the ITF load case. Hence, improved equations were 14 proposed to determine the web crippling capacities of LCBs based on the experimental results from this study. Current design equations do 15 not provide the direct strength method (DSM) provisions for web crippling. Hence, suitable design rules were also developed under the DSM 16 format using the test results and buckling analyses using finite-element analyses.

Web crippling tests of hollow flange channel beams with flanges fastened to supports under two flange load cases

Thin-walled steel hollow flange channel beams known as LiteSteel beam (LSB) sections were developed for use as joists and bearers in various flooring systems. However, they are subjected to specific buckling and failure modes, one of them being web crippling. Despite considerable research in this area, much of the current design predictions for cold-formed steel sections are not directly applicable to LSBs. This is due to the geometry of the LSB, which consists of two closed rectangular hollow flanges, and its unique residual stress characteristics and initial geometric imperfections. Hence an experimental study was conducted to investigate the web crippling behaviour and capacities of LSBs with their flanges fastened to supports. Thirty nine web crippling tests were conducted under two flange load cases (End Two Flange (ETF) and Interior Two Flange (ITF)). Test results showed that for ETF load case the web crippling capacities increased by 50% on average while they increased by 97% for ITF load case when flanges were fastened to supports. Comparison of the ultimate web crippling capacities from tests showed that AS/NZS 4600 and AISI S100 web crippling design equations are conservative for LSB sections with flanges fastened to supports under ETF and ITF load cases. Hence new equations were proposed to determine the web crippling capacities of LSBs with flanges fastened to supports. This paper presents the details of the experimental study into the web crippling behaviour of LSB sections with their flanges fastened under ETF and ITF load cases, and the results.

Shear tests 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 channel beams. It is a monosymmetric channel section made by intermittently rivet fastening two torsionally rigid rectangular hollow flanges to a web plate. This process enables the end users to choose an effective combination of different web and flange plate sizes to achieve optimum design capacities. Recent research studies focused mainly on the shear behaviour of the most commonly used lipped channel beam and welded hollow flange beam sections. However, the shear behaviour of rivet fastened RHFCB has not been investigated. Therefore a detailed experimental study involving 24 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 shear capacities 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. Such enhancements to the shear behaviour and capacity were achieved with a rivet spacing of 100 mm. Improved design rules were proposed for rivet fastened RHFCBs based on the current shear design equations in AISI S100 and the direct strength method. This paper presents the details of this experimental investigation and the results.

Experimental and numerical studies of hollow flange channel beams subject to web crippling under ETF and ITF load cases

This paper presents the details of experimental and numerical studies on the web crippling behaviour 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. 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 consisting of 28 tests were first conducted in this research to assess the web crippling behaviour and strengths of LSBs under two flange load cases (ETF and ITF). Experimental web crippling capacity results were then compared with the predictions from AS/NZS 4600 and AISI S100 design rules, which showed that AS/NZS 4600 and AISI S100 design equations are very unconservative for LSBs under ETF and ITF load cases. Hence improved equations were proposed to determine the web crippling capacities of LSBs. Finite element models of the tested LSBs were then developed, and used to determine the elastic buckling loads of LSBs under ETF and ITF load cases. New equations were proposed to determine the corresponding elastic buckling coefficients of LSBs. Finally suitable design rules were also developed under the Direct Strength Method format using the test results and buckling analysis results from finite element analyses.

Numerical modelling of rivet fastened rectangular hollow flange channel beams subject to shear

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. 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 experimental and numerical studies were undertaken to investigate the shear behaviour and strength of rivet fastened RHFCBs. In this research finite element models of rivet fastened RHFCBs were developed to investigate their nonlinear shear behaviour including their buckling characteristics and ultimate shear strength. This paper presents the details of the finite element models of rivet fastened RHFCBs and the results. Both finite element analysis and experimental results showed that the current design rules are very conservative for the shear design of rivet fastened RHFCBs. Appropriate improvements have been proposed for the design rules of shear strength of rivet fastened RHFCBs within the Direct Strength Method format.

Shear tests of rivet fastened rectangular hollow flange channel beams with web openings

The rivet-fastened rectangular hollow flange channel beam (RHFCB) is a new cold-formed hollow section proposed as an alternative to welded hollow flange steel beams. No research has been undertaken on the shear behaviour and strength of rivet fastened RHFCBs with web openings. Hence a detailed experimental study involving 30 shear tests was undertaken to investigate the shear behaviour and strength of rivet fastened RHFCBs with web openings. Experimental results showed that the current design rules are inadequate for the shear design of Rivet fastened RHFCBs with web openings. Improved design equations have been proposed for the shear strength of rivet fastened RHFCBs with web openings.

Web crippling tests of rivet fastened rectangular hollow flange channel beams under two-flange load cases

The rivet-fastened rectangular hollow flange channel beam (RHFCB) is a new cold-formed hollow section proposed as an alternative to welded hollow flange steel beams. To date, no investigation has been conducted on their web crippling behaviour and strengths. Hence an experimental study was conducted to investigate the web crippling behaviour and capacities of rivet fastened RHFCBs under End Two Flange (ETF) and Interior Two Flange (ITF) load cases. Experimental results showed that the current design rules are unconservative for rivet fastened RHFCB sections under ETF and ITF load cases. Hence new equations were proposed to determine the web crippling capacities of rivet fastened RHFCBs.