2015 Research Reports No R952-R960

Abstract
This report describes the design and functions of a new experimental facility built in the School of Civil Engineering at the University of Sydney used for the investigation of flocculation-related processes. This facility was uniquely designed to replicate physical (hydrodynamic processes and sediment load), chemical (nutrients and contaminants) and biological (micro-organisms) processes in natural aqueous environment; hence, it allows for investigating the effects of these processes on the flocculation dynamics of suspended particle matter (SPM) through a fully controllable laboratory-based research. It consists of five major components, including a smallscale settling column, a turbulence generating system, a water quality mea-suring system, a μPIV system, and a micro-controlling system. Measurements, either imaging data of settling SPM or water quality readings, can be acquired automatically with any ar-bitrary scheduling. The innovation of this facility is the integration of physical, chemical and biological aquatic processes into one framework to explore the complexity of the interactions be-tween these processes and SPM dynamics. One of its major contributions to the advancement in sediment dynamics studies is the direct detection of possible repercussions the increased anthropogenic stresses has on the microbial population and the aggregation kinematics and statistics of suspended particles in aqueous ecosystem. Ultimately, this facility is expected to contribute to a comprehensive understanding of how all possible interactions in natural water bodies affect each other and consequently, how these interactions affect SPM flocculation and transport.

Keywords
Aggregation, Settling column, μPIV, Suspended particle matter Biological flocculation

Abstract
Compared with austenitic or duplex stainless steels, ferritic stainless steels have no or very low nickel content. Therefore, their cost is lower and more stable than those of austenitic and duplex stainless steels, providing a more viable alternative for structural applications. Existing stress−strain models, however, are less accurate in predicting stress−strain curves of ferritic stainless steels than for austenitic and duplex stainless steels, since ferritic stainless steels behave more similarly to plain carbon steel. A wide range of tensile test data were collected for ferritic stainless steel coupons, either cut from steel sheets or cold-formed hollow sections. Using the three basic Ramberg-Osgood parameters, stress−strain models are developed for both flat and corner ferritic stainless steels. The accuracy of the proposed models is verified by comparing their predictions with experimental stress−strain curves.

Keywords
Stainless steel; Ferritic stainless steel; Stress−strain relation; Cold-formed; Corner effects.

Abstract
This document describes the functioning principles and practical use of BRTSim framework at its version 1 stage of development.

BRTSim (BioReactive Transport Simulator) is a general‐purpose multiphase and multicomponent computational solver for biogeochemical reaction‐advection‐dispersion processes in porous and non‐porous media. BRTSim finds suitable applications to describe water flow in soils and geophysical media, to track transport and dispersion of aqueous and gaseous chemicals, as well as to assess their chemical equilibrium and their decomposition rates in both chemical and biochemical reactions. For these characteristics, BRTSim is an extraordinary computational tool in soil physics and biogeochemistry, soil and water quality assessment and prediction, soil bio‐ and phyto‐remediation potential estimation, and in all environmental engineering contexts where physical, chemical and biological processes co‐exist and affect each other with complex nonlinear feedbacks.

BRTSim allows defining a geophysical domain with an arbitrary number of grid elements nodes that may be heterogeneous in their physical and hydraulic properties; BRTSim allows full control of initial and boundary conditions, and allows defining a biogeochemical system with an arbitrary number of primary aqueous species, secondary aqueous species, gaseous and mineral species (in chemical equilibrium with primary species), and biological microbial functional groups with any specific metabolic requirement. Chemical and biochemical reactions can be defined for any kinetics framework and order.

BRTSim version 1 bases on solvers that have been largely tested, but because of its potentiality, it is under continuing development and improvement in numerical accuracy, robustness, reliability, and computational performance. It is to be noted that, although all methods used to solve physical and chemical processes follow recommendations and methods largely accepted in the scientific literature, the integration of diverse processes, each one requiring time scales that may largely vary from any other, may have potential defects. BRTSim, as a consequence, is also a platform where newly developed algorithms are implemented and tested to improve older and less performing algorithms. Iteration number and tolerances can be set for the various processes but it is practically impossible to exhaustively cross‐check mutual compatibility. The BRTSim framework is therefore designed to allow the user to correct potential instabilities, which depend on the specific problem to be solved, and set the numerical solvers to converge by criteria with an arbitrary level of accuracy.

Abstract
There have been comparatively few studies of the elastic lateral buckling of braced or continuous tapered beams, and these are limited in their application. Lateral buckling is affected by the separate effects of moment distribution, taper, and restraints between adjacent segments.

Moment distribution effects are commonly allowed for in design codes by using Cbm factors to multiply the classic lateral buckling moments Mu of simply supported uniform beam segments in uniform bending.

Taper effects for linearly web tapered beam segments may conveniently be allowed for by multiplying the segment lateral buckling moments Cbm Mu computed using the mid-segment section properties by taper factors Cbt. Values of Cbt for a number of different segment moment distributions have been determined using a finite element computer program for the buckling of tapered beam structures.

Lateral buckling of a braced or continuous beam is also affected the interaction between the segments into which it is divided by its braces and supports. One segment will be more critical than its neighbours, which will restrain the critical segment and increase its buckling resistance. The effects of restraints on buckling are commonly allowed for by using effective length factors to multiply the segment length used in the formulation of the elastic lateral buckling moment Mu of a uniform segment in uniform bending. Methods of determining the critical segment and of approximating its increased resistance developed for uniform beams have been adapted for web-tapered braced and continuous beams.

This paper shows how these effects can be allowed for separately to develop good approximations for the elastic lateral buckling resistances of tapered braced and continuous beams. The accuracy of the approximations is demonstrated by comparisons with the predictions of the finite element computer program for the buckling of tapered beam structures.

Keywords
Beams, Braces, Buckling, Continuity, Interaction, Steel, Structures, Taper

Abstract
Shear stress distributions in tapered web I-beams are incorrectly predicted by the conventional beam analysis method used for uniform beams. More accurate predictions are obtained by adopting the finding for wedges that the normal stress trajectories are radial instead of parallel.

The shear stress distributions in web-tapered I-beams are influenced by the vertical components of the inclined flange forces (which are zero in uniform beams), as well as by the normal stress gradients in the flanges. The net web shear equal to the difference between the external shear and the vertical components of the inclined flange forces is resisted by the resultant of the vertical components of the normal stresses and the circumferential shear stresses.

The circumferential shear stresses have linear components due to axial force and parabolic components due to moment and shear. The magnitudes of these stresses are controlled by the normal stress gradients at the flange-web junctions and by the requirement that the web shear resistance must equal the net web shear force.
Keywords
Bending, deflections, elasticity, force, I-beam, normal stress, shear, shear stress, tapered web, edge

Abstract
Shear stress distributions in mono-symmetric tapered I-beams are incorrectly predicted by the conventional beam analysis method used for uniform beams. More accurate predictions are obtained by assuming that the normal stress trajectories vary linearly between plate edges, instead of parallel to the centroidal axis.

Transverse shear stresses at the flange-web junctions of mono-symmetric tapered I-beams of constant depth are induced by gradients of the forces in the tapered flanges. The transverse shear stress distributions caused by axial force, moment, and shear force are constant, linear, and parabolic, respectively.

Axial force induces non-zero principal axis shear stresses, while shear force induces non-zero normal stresses acting parallel to the centroidal axis.

Keywords
Bending, deflections, elasticity, force, I-beam, mono-symmetry, normal stress, shear, shear stress, tapered flange, edge