The effect of extreme response and non-extreme response styles on testing measurement invariance

Extreme and non-extreme response styles (RSs) are prevalent in survey research using Likert-type scales. Their effects on measurement invariance (MI) in the context of confirmatory factor analysis are systematically investigated here via a Monte Carlo simulation study. Using the parameter estimates obtained from analyzing a 2007 Trends in International Mathematics and Science Study data set, a population model was constructed. Original and contaminated data with one of two RSs were generated and analyzed via multi-group confirmatory factor analysis with different constraints of MI. The results indicated that the detrimental effects of response style on MI have been underestimated. More specifically, these two RSs had a substantially negative impact on both model fit and parameter recovery, suggesting that the lack of MI between groups may have been caused by the RSs, not the measured factors of focal interest. Practical implications are provided to help practitioners to detect RSs and determine whether RSs are a serious threat to MI

Second-Order Latent Growth Models with Shifting Indicators

Second-order latent growth models assess longitudinal change in a latent construct, typically employing identical manifest variables as indicators across time. However, the same indicators may be unavailable and/or inappropriate for all time points. This article details methods for second-order growth models in which constructs’ indicators shift over time

Using Finite Mixture Modeling to Deal with Systematic Measurement Error: A Case Study

Conventional methods and analyses view measurement error as random. A scenario is presented where a variable was measured with systematic error. Mixture models with systematic parameter constraints were used to test hypotheses in the context of general linear models; this accommodated the heterogeneity arising due to systematic measurement error

Stainless Steel Tubular Beams - Tests and Design

The paper presents tests on square and circular stainless steel tubular beams. An important part of the test programme was to quantify the increase in bending strength resulting from cold-work during the fabrication process. Tension and compression tests on coupons cut from finished tubes were also included in the test programme. Stress-strain curves for shear were obtained using the coupon test results and the concept of affinity factors. A design method is proposed for stainless steel tubular beams. The method incorporates the increase in strength produced by the cold-rolling process and is validated by comparing it to the test strengths. Design rules are proposed for the bending and shear strengths and for combined bending and shear. The paper describes a simple non-iterative method for calculating deflections of stainless steel tubular beams. The method is suitable for design. It is shown to produce deflections which agree closely with the tests and a comprehensive finite element analysis

Distortional Buckling Formulae for Thin Walled Channel and Z-sections with Return Lips

Cold-formed Channel- and Z-sections subject to both flexure and torsion may undergo distortional buckling where the flange and lip rotate about the flange/web junction. This mode of failure is prevalent in purlin sections when lateral deformation of the section is prevented and when the sections are manufactured from high strength steel. In an attempt to prevent distortional buckling, some manufacturers have added additional return lips to the flange lips to produce complex edge stiffeners. The Australian/New Zealand Standard for Cold-Formed Steel Structures includes design rules for determining the distortional buckling strength of cold-formed beam and column sections. These design rules require the computation of the elastic distortional buckling stress. Appendix D of ASINZS 4600 provides design rules for computing the elastic distortional buckling stress of general channels in compression, simple lipped channels in compression and simple lipped Channel- and Z-sections in bending about an axis perpendicular to the web. The paper describes general formulations for computing the elastic distortional buckling stresses of sections with return lips including those with sloping lips and return lips. The accuracy of the formulations is compared with the results for a large range of section geometries using a finite strip buckling analysis which can be regarded as providing accurate solutions for distortional buckling stress. Explicit expressions are presented in the paper for the flange properties

Compression Tests on Cold-formed Angles Loaded Parallel with a Leg

This paper describes a series of compression tests on cold-formed equal angles with slender cross-section. The angles were tested between pinned ends and loaded axially with eccentric load which caused bending parallel with a leg. The test data are compared with the design rules of the Australian and American specifications for cold-formed and hot-rolled steel structures, as well as the ASCE Standard for the Design of Latticed Steel Transmission Structures. The rules of the specifications for cold-formed steel structures (AS/NZS4600 and AlSI) are shown to be very conservative. The cause of the conservatism is explained and improved design rules are proposed

Compression Tests of Cold-reduced High Strength Steel Long Columns

This paper describes a series of compression tests performed on long columns fabricated from cold-formed high strength steel plates with nominal yield stress of 550 MPa (80 ksi). The steel is classified as G550 to Australia Standard AS1397. The test results presented in this paper are the second stage of an Australian Research Council research project entitled Compression Stability of High Strength Steel Sections with Low Strain-Hardening . A total of 28 long columns, which were made from two thicknesses of sheet steel (0.42 mm and 0.6 mm) (0.017 in. and 0.024 in.), were tested. A box shaped section was tested between pinned ends over a range of lengths. This paper shows the comparison of loads obtained experimentally with those predicted on the basis of AS/NZS4600 and the AISI specification including Supplement No.1, 1999. The finite element program, ABAQUS, was also used to simulate the column behaviour. For sections which undergo local instability at loads significantly less than the ultimate loads, the column design rules in AS/NZS 4600 and the AISI Specification are unconservative if used in their current form for G550 steel. Proposals for improved column design of high strength slender sections are proposed in this paper

Identifying Shear Buckling Coefficients for Channels with Rectangular Web Stiffeners using the Generalised cFSM

The Direct Strength Method (DSM) of design for cold-formed sections was recently extended in the North American Specification for Cold-Formed Steel Structural Members (NAS S100:2012) to include members in shear. The method has largely been developed on the basis of work done on lipped channel sections. To utilise the method requires the critical shear buckling load of the section, which may be determined from a minimum point on the signature curve for the section in pure shear. However when longitudinal web stiffeners are added to the channel a minimum may not exist, or may occur at half-wavelengths where the critical buckling mode is localised in the individual vertical portions of the web rather than involving the full web as an essentially continuous element, as occurs for a plain lipped channel in local shear buckling. This paper explores the application of the recently-developed generalised constrained finite strip method (cFSM) to determine critical shear buckling loads for lipped channels with rectangular web stiffeners, from which shear buckling coefficients may be back-calculated. The addition of the stiffener leads to new distortional modes, deemed web-distortional modes, that play an important role in the buckling behaviour of web-stiffened channels at half-wavelengths where buckling involves deformations of the web as a continuous element. Using the cFSM, combinations of pure local modes and the web-distortional modes are considered to produce modal solutions. These modal solutions always give a minimum regardless of section and these minima are used to identify critical buckling half-wavelengths. The critical shear buckling loads are then taken as those at the same half-wavelengths on the corresponding traditional FSM signature curves for the sections. The proposed method is appropriate for sections with small stiffeners, as are used in practice

The problem of underpowered rivers

This study has hypothesized that for many rivers the trade‐off between flow accumulation and the decrease in slope along channel length means that stream power increases downstream and, moreover, that given the low slope angles in headwater and low‐order streams, they would have insufficient stream power to erode let alone transport sediment. The study considered the stream power profile, the particle travel distances and the application of the Hjulström curve based on the velocity profile of nine, large UK catchments. The study showed that: Some rivers never showed a maximum in their longitudinal stream power profile, implying that some rivers never develop a deposition zone before they discharge at the tidal limit. Particle travel distances during a bankfull discharge event showed that for some rivers 91% of the upper main channel would not be cleared of sediment. Furthermore, while some rivers could transport a 2 mm particle their entire length in one bankfull event, for another river it would take 89 such events. The Hjulström curve shows that for three of the study rivers the upper 20 km of the river was not capable of eroding a 2 μm particle. The study has shown that for all rivers studied, erosion is focused downstream and deposition upstream. Many UK rivers have a dead zone where, on time scales of the order of centuries, no erosion or transport occurs and erosion only occurs in the lower courses of the channel where discharge rather than slope dominates – we propose these as underpowered rivers