2005 Research Reports No R844-R863

Abstract
This report describes the experimental investigation of cold-formed, thin-walled stainless steel sections subject to distortional buckling under compression. Austenitic 304, ferruruc 430 stainless steel and ferritic-like 3Cr12 chromium weldable steel sheets were brake-pressed into simple-lipped channels and lipped channels with low proportionality stress and low n-parameter, anisotropy and yield strength enhancements up to 2.33 times due to cold-forming. A total of 19 channel sections were tested and failed by distortional buckling at average ultimate stresses greater than the proportionality stress, and hence were influenced by material nonlinearity, with greater nonlinearity evident for sections with intermediate stiffener. This paper presents comprehensive procedures to determine stainless steel mechanical properties and procedures to investigate the distortional buckling mode of cold-formed section. Experimental data required to calibrate finite element models and assess current design guidelines for distortional buckling of stainless steel compression members are provided herein.

Keywords
Stainless steel, distortional buckling, cold-formed sections, corner compression coupons, enhanced corner strength, nonlinear stress-strain relation, low proportionality stress, anisotropy, lipped channels, intermediate stiffeners.

Abstract
This report describes the numerical investigation of cold-formed, thin-walled stainless steel sections subject to distortional buckling under compression. Austenitic alloy 304 and ferritic alloys 430 and 3Cr12 were considered. A finite element model calibrated to the data gathered in a recent experimental programme (Lecce and Rasmussen 2005) shows that material anisotropy can be ignored and that an accurate calibration model can be achieved provided nonlinear yielding and enhanced corner properties are included in the model. FE analyses of more than 570 simple lipped and lipped channels with intermediate stiffeners covering a distortional buckling slenderness range 0.47 ≤ λd ≤ 3.64 reveal that enhanced corner properties may become significant for stocky sections with a large corner area (λd <1 with a corner area of at least 10%). The experimental and FE test data were used to evaluate the Australian, North American and European codes for stainless steel and cold-formed carbon steel. The evaluation reveals that both the effective width area approach and direct strength methods are generally inadequate for the design of stainless steel sections. Modified resistance factors are recommended for the effective width approach of current design codes to meet limit states design criteria. Direct strength design curves are developed for austenitic and ferritic stainless steel alloys.

Keywords
Stainless steel, distortional buckling, cold-formed sections, effective width design, enhanced corner strength, direct

Abstract
This paper explores a number of situations where columns with out-of-tolerance crookedness or which have been damaged may still be designed, despite the implications of many codes that they must be replaced, and suggests rules for their design.

The case of a column whose crookedness is out-of-tolerance is first examined, and two design methods are suggested.  In the first method, the column is treated in a similar way to that used for the basis of the BS5950 column design method by allowing for the excess crookednesses.  In the second method, the column is designed as a straight beam-column with design moments equal to those resulting from the first-order analysis of an imperfect structure whose geometry includes the excess crookednesses.

Following this, the case is considered of a column damaged by unexpected bending which leaves an out-of-tolerance permanent set.  It is concluded that the residual stresses caused by the damaging bending moments may often be ignored, in which case the damaged column can be designed for its increased crookedness by using either of the methods proposed for columns with out-of-tolerance crookedness.  The straightening of the damaged column is also considered.  It is found that the residual stresses which follow relaxation after straightening may also be ignored and the column designed in the usual way.

Finally, the case is analysed of a force-fitted column which has excessive crookedness locked in during its connection to other members of a structure.  It is found that the force-fitting deflection can be regarded as an initial crookedness, so that the column can be designed as an out-of-tolerance column.

Keywords
Buckling, columns, crookedness, damage, design, imperfection, steel.

Abstract
This report describes an experimental investigation of stainless steel roof sections under pure bending. The results of this experimental investigation are provided herein and serve as a basis for future finite element analyses and the development of design procedures. Two commercially available roof sheeting profiles named Monoclad and Megaclad provided by Stramit Building Industries have been tested. A total of nine tests were conducted successfully. The test rig allowed essentially constant, pure bending moment to develop with little influence of shear and axial forces. A detailed description of the rig and moment evaluation are provided. All tests achieved ultimate moments greater than the proportionality yield moment and the average ultimate moment to yield moment ratio ranged from 0.87 to 1.16. The effects of material nonlinearity was evident in the test results, shown by the considerable loss of stiffness before reaching the ultimate load. A greater loss of stiffness is exhibited for those specimens which have the wide flange in compression and this may be due to the influence of flange curling. Data are now available for the development of a finite element model calibration and parametric studies.

Keywords
Stainless steel, roof sheeting, distortional buckling, local buckling, flange curling, pure bending.

Abstract
The finite strip method has proved to be an accurate and efficient tool for the analysis of structures having regular cross-section and mechanical proprieties along the longitudinal axis. The spline finite strip method has furthermore proved to be a more flexible tool for the analysis of structures with general support conditions and, utilising the isoparametric mapping, structures with a geometry varying along the longitudinal direction, such as curved slab bridges. In this report, the isoparametric spline finite strip method is applied to the analysis of plate containing cut-outs of different shape and subjected to in-plane stresses.

The mapping technique and the theory for the general in-plane stress condition are outlined, as is a novel method for assembling the strips in order to model the particular case of a cut-out.

To prove the reliability of the isoparametric spline finite strip method, three different shapes perforation in rectangular plates in traction are analysed. The shapes of the cut-outs presented are a circular, a rectangular and a key shaped hole. The result are compared with exact solutions and finite element analyses.

Keywords
Isoparametric spline finite strip method, perforations, numerical analysis, thinwalled elements, plates, in-plane stress.

Abstract
This report describes a set of bearing tests on a new range of cold-formed steel sections, LiteSteel™ Beam (LSB™), subjected to concentrated bearing load. LSB sections are manufactured using a unique dual resistance welding process which forms a channel section with hollow flanges. The tests were performed under interior one flange loading (IOF) and exterior one-flange loading (EOF) conditions. The IOF and EOF bearing loads were applied at the top flange at the centre of the beam and at the bottom flange at both ends of the beam respectively. Some different stiff bearing lengths were selected.

Two flange filled tests were conducted to investigate the failure mode of IOF. This confirmed that the bearing failure mode was associated with web crippling, rather than hollow flange crushing.

The test strengths are compared with the design strengths obtained using current and proposed versions of AS/NZS 4600. All tests show capacities well above those predicted by either the current AS/NZS 4600 or the draft DR 03518 (overstrength 96% or 40% respectively for IOF loading condition and overstrength 49% or 43% respectively for EOF loading condition).

Keywords
Steel, Hollow section, SSHS, Channel, Web crippling, Buckling, Hollow flange, LiteSteel Beam; Bearing, Interior loading, Exterior loading.

Abstract
This report describes the experimental and theoretical analysis of flange curling deformations. Flange curling of two commercially available roof sheeting profiles named Monoclad and Megaclad provided by Stramit Building Industries have been examined. The results show that a true representation of the wide-flange support condition provided by the web is essential to obtain reasonable agreement with experimental tests and that models used in the past are generally inadequate. The iterative theoretical flange curling model which represents the changing geometric and loading conditions shows that a 5-15% reduction in yield moment due to reduced section modulus can occur and this is otherwise ignored by the simplified flange curling models used in the past. Stresses in the wide flange can vary considerably, with the most drastic nonlinear behaviour exhibited by the Megaclad section where the center-pan stress was only 9% of the web/flange junction stresses. The analysis of section stresses shows that yield develops first at the short flanges and webs and that, for the sections considered, the wide flange stresses remain below the yield stress.

Keywords
Stainless steel, roof sheeting, local buckling, nonlinear flange curling, pure bending, stress distributions, section modulus, yield moment.

Abstract
This report describes the influence of flange curling on cross-sectional properties and critical elastic buckling stresses of two wide-flanged roof sections (commercially available Monoclad and Megaclad). Results show that modified geometries due to flange curling can cause an increase of critical buckling stress ranging from 1.10 to 3.41 times that based on original geometries ignoring flange curling. Furthermore, the section modulus can be lowered from 6% to 16.9% due to flange curling deformations for the sections investigated. Flange curling was most significant for the more slender Megaclad section. The current proposed DSM design curve for the distortional buckling of stainless steel sections (Lecce and Rasmussen 2005a) and the Winter curve for local buckling are generally more conservative than the current North American Standard Appendix 1 (2004) DSM formulations. The design moment capacities alter due to flange curling and for distortional buckling there was an increase of up to 10.6% but a net decrease of up to 12.2% for local buckling. Given the current data, it would be prudent to ignore the effects of flange curling for distortional buckling but it would be necessary to consider them for local buckling.

Keywords
Stainless steel, roof sheeting, local buckling, nonlinear flange curling, pure bending, distortional buckling, section modulus, yield moment, direct strength method.

Abstract
Although steel single angle sections are commonly used as beams to support distributed loads which cause biaxial bending and torsion, their behaviour may be extremely complicated, and the accurate prediction of their strengths very difficult. Further, many design codes do not have design rules for torsion, while some recommendations are unnecessarily conservative, or are of limited application, or fail to consider some effects which are thought to be important.

This paper is one of a series on the behaviour and design of single angle section steel beams. Two previous papers have studied the biaxial bending and torsion of restrained beams, a third has studied the lateral buckling of unrestrained beams, a fourth the biaxial bending of unrestrained beams, and a fifth and sixth the buckling and torsion of unrestrained beams. In each paper, simple design methods have been developed.

In this present paper, an approximate method of predicting the second-order deflections and twist rotations of steel equal angle section beams under biaxial bending and torsion is developed. This method is then used to determine the approximate maximum biaxial bending moments in such beams, which are then used with the section moment capacity proposals of the first paper of the series and the lateral buckling proposals of the third paper to approximate the member capacities.

Keywords
Angles, beams, bending, buckling, design, elasticity, member capacity, moments, section capacity, steel, torsion.

Abstract
In this paper, dynamic response of a circular tunnel with prefabricated piecewise lining embedded in a porous medium subjected to seismic waves is studied. The surrounding saturated porous medium of the tunnel is described by Biot’s theory. The piecewise tunnel lining consists of several lining pieces connected by joints. Both the lining pieces and the joints are treated as curved beams. The scattered wave field in the porous medium is obtained by the wave function expansion approach. The differential equations governing the vibration of a curved beam is discretized by the General Differential Quadrature (GDQ) method. The domain decomposition method is used to establish the global discrete dynamic equations for the piecewise lining. In terms of the boundary least square collocation method, the coupled problem is solved by the stress and displacement continuation conditions between the porous medium and the tunnel lining. Numerical results demonstrate that the stiffness difference between the liner piece and joints can enhance the internal forces of the piecewise liner significantly, which is crucial for the design of a piecewise tunnel liner.

Keywords
Biot’s theory; tunnel; lining; curved beam; porous media; General Differential Quadrature (GDQ) method

Abstract
In the last decades, considerable efforts have been devoted to the phenomenon of wave-induced liquefactions, because it is one of the most important factors for analysing the seabed and designing marine structures. Although numerous studies of wave-induced liquefaction have been carried out, comparatively little is known about the impact of liquefaction on marine structures. Furthermore, most previous researches have focused on complicated mathematical theories and some laboratory work. In the present study, a data dependent approach for the prediction of the wave-induced liquefaction depth in a porous seabed is proposed, based on a multi-artificial neural network (MANN) method. Numerical results indicate that the MANN model can provide an accurate prediction of the wave-induced maximum liquefaction depth with 10% of the original database. This study demonstrates the capacity of the proposed MANN model and provides coastal engineers with another effective tool to analyse the stability of the marine sediment.

Keywords
Wave-induced liquefaction, Artificial neural networks, Multi-artificial neural network.

Abstract
The mechanism of flow around a pier structure is so complicated that, it is difficult to establish a general empirical model to provide accurate estimation for scour. Interestingly, each of the proposed empirical formula yields good results for a particular data set. In this study, an alternative approach, artificial neural networks (ANN), is proposed to estimate the equilibrium and timedependent scour depth with numerous reliable data base. Numerous ANN models, multi-layer perceptron using back propagation algorithm (MLP/BP) and radial basis using orthogonal least-squares algorithm (RBF/OLS), Bayesian neural Network (BNN) and single artificial Neural Network (SANN) were used. The equilibrium scour depth was modeled as a function of five variables; flow depth, mean velocity, critical flow velocity, mean grain diameter and pier diameter. The time variation of scour depth was also modeled in terms of equilibrium scour depth, equilibrium scour time, scour time, mean flow velocity and critical flow velocity. The training and testing data are selected from the experimental data of several valuable references.

Keywords
Neural networks; Bridge pier; Back propagation algorithm; Orthogonal least square algorithm, Scour depth.

Abstract
In this study, we investigated the effect of beach slope for a coastal aquifer adja-cent to a low-relief estuary. The waste was suspected to discharge leachate towards the estuary. Field observations at various locations showed that tidally induced groundwater head fluctuations were skewed temporally. Frequency analysis suggested that the fluctuation amplitudes decreased exponentially and the phase-lags increased linearly for the primary tidal signals as they propagated inland. Flow and transport processes in a cross-section perpendicular to the estuary were simulated using SEAWAT-2000, which is capable of depicting densitydependent flow and multi-species transport. The simulations showed that the modelled water table fluctuations were in good agreement with the monitored data. The simulations showed that density difference and tidal forcing drive a more complex hydrodynamic pattern for the mildly sloping beach than the vertical beach, as well as a profound asymmetry in tidally induced water table fluctuations and enhanced salt-water intrusion. The simulation results also indicated that contaminant transport from the aquifer to the estuary was affected by the tide.

Keywords
SEAWAT-2000; Salt-water intrusion; Water table fluctuation; Numerical model; Submarine groundwater discharge

Abstract
In this study, dynamic response of a circular tunnel embedded in a porous medium and subjected to a moving axisymmetric ring load is investigated. To avoid treating Biot’s dynamic equations directly, two scalar potentials and two vector potentials are introduced to represent the displacements of the solid skeleton and the pore fluid. Based on Biot’s theory and the Fourier transformation, the frequency domain governing equations for the potentials are derived. Performing the Fourier transformation on the axial coordinate, general solutions of the potentials are derived from the governing equations of the potentials. Using the obtained general solutions and boundary conditions along the tunnel surface, the boundary value problem is formulated in the frequencywave-number domain. Solution of the boundary value problem yields the unknown constants of the potentials. The closed form solutions in the frequency-wave-number domain for the displacements, stresses and pore pressure are derived in terms of the obtained potentials. Analytical inversion of the Fourier transformation with respect to the frequency together with the numerical inversion of the Fourier transformation with respect to axial wave number leads to the numerical solutions of the displacements, stresses and pore pressure. For demonstration of our method, some numerical examples and corresponding analysis are given in the paper.

Keywords
Porous media; tunnel; moving loads; Biot’s theory; the Fourier transformation

Abstract
In this study, the frequency domain dynamic response of a pile embedded in a porous medium and subjected to SH seismic waves is investigated. The surrounding porous medium of the pile is described by Biot’s theory, while the pile embedded in the porous medium is treated as a beam and described by a beam vibration theory. Using the Hankel transformation method, the fundamental solution for a half-space porous medium subjected to a horizontal circular patch load is established. According to the fictitious pile methodology, the second kind of Fredholm integral equation for the pile is established in terms of the obtained fundamental solution and free wave field. The solution of the integral equation yields the dynamic response of the pile to plane SH waves. Numerical results indicate that the parameters of the porous medium, the pile and the incident wave have considerable influences on the dynamic response of the pile and the porous medium.

Keywords
Biot’s theory; pile; SH waves; Fredholm integral equation; porous media.

Abstract
The evaluation of wave-induced seabed response has been recognised as a dominant factor in analyzing the seabed instability in the vicinity of a breakwater. Most previous investigations for wave-induced pore water pressure have been limited to two-dimensions, which are not able to simulate the phenomenon around the head of a breakwater. In this study, a three-dimensional model for the wave-induced pore pressure around the head of a breakwater is established for both oscillatory and residual mechanisms. Numerical results conclude: (1) diffracted wave components significantly affect the distribution of pore water pressure and vertical effective normal stresses and liquefaction potential; (2) a liquefied hole occurs near the head of a breakwater; (3) incident wave angles do not only affect the pattern of liquefied regions, but also the maximum liquefaction depth; (4) the soil types significantly affect the distribution of soil response and liquefaction, and liquefaction only occurs in fine sand, not coarse sand.

Keywords
pore pressure, vertical effective normal stresses, marine sediment, breakwater, liquefaction.

Abstract
The existing DnV Recommended Practice (RP E305) for pipeline on-bottom stability is mainly based on the Pipe-Soil Interaction Model proposed by Wagner et al. (1987) and the Wake Model by Lambrakos et al. (1987) to calculate the soil resistance and the hydrodynamic forces upon pipeline, respectively. Unlike the methods in the DnV Practice, in this paper, an improved analysis method is proposed for the on-bottom stability of a submarine pipeline, which is based on the relationships between and for various restraint conditions obtained by the hydrodynamic loading experiments, taking into account the coupling effects between wave, pipeline and sandy seabed. The analysis procedure is illustrated with a detailed flow chart. A comparison is made between the submerged weights of pipeline predicted with the DnV Practice and those with the new method. The proposed analysis method may provide a helpful tool for the engineering practice of pipeline on-bottom stability design.

Keywords
Submarine pipeline; Analysis method; On-bottom stability; Sandy seabed; Wave-pipe-soil coupling effect.

Abstract
Artificial neural networks (ANNs) have been used increasingly for modelling complex hydrological processes. In this paper, we present a self-organizing polynomial neural network (SOPNN) algorithm, which combines the theory of bio-cybernetic self-organizing polynomial (SOP) with the artificial neural network (ANN) approach. With the SOP feature of seeking the best combination of polynomial model parame-ters through optimal reduction of the partial polynomial nodes in the network and the ANN function of seeking minimum error at each layer of the network, the algorithm possesses superiority in nonlinear modelling of dynamic systems. The developed al-gorithm is applied to model a real-time rainfall-runoff process. The results demon-strate the capability of the SOPNN approach in addressing difficult issues of ANN modelling: selection of appropriate model inputs, optimization of the network struc-ture and error minimization. The comparison of modelling results shows that the SOPNN algorithm performs better in complex hydrological modelling than two other nonlinear approaches: the group method of data handling (GMDH) algorithm and the traditional back-propagation network (BPN) algorithm.

Keywords
Self-organizing polynomial; artificial neural network; GMDH algorithm, rainfall-runoff modelling

Abstract
In this study, a new analytic solution of the wave interaction with a porous structure over a sandy seabed is derived. A uniform water depth is assumed, and the layer of the rigid porous medium is placed over an infinite thickness of poro-elastic sand bottom. The potential theory with the inertial and damping effects in the porous flow is considered in the rigid porous region, while the soil consolidation theory is adopted in the sand region. A new complex dispersion relationship involving the parameters of the rigid porous and poro-elastic medium is obtained. The analytic solutions can be simplified to the special cases, such as the wave interaction with the porous structure over an impermeable bottom or only interaction with the poro-elastic medium. The results indicate that the wave decay is highly dependent upon the thickness of the porous structure, the soil stiffness and their permeability. The increase of the thickness of the porous structure will shorten the wave length of the surface waves regardless of the coarse or fine sand. The pore pressure of the fine sand is larger than that of coarse sand, both decay with the distance of the wave progressing. It is also found that the increase of the thickness of the porous structure will effectively reduce the pore pressure in the sand.

Keywords
wave interaction; porous structure; poro-elastic medium; complex dispersion relationship; wave decay; soil stiffness; permeability; pore pressure.

Abstract
The coupling of sandy beach aquifers with the swash zone in the vicinity of the water table exit point is investigated through simultaneous measurements of the instantaneous shoreline (swash front) location, pore pressures and the water table exit point. The field observations reveal new insights into swash-aquifer coupling not previously gleaned from measurements of pore pressure only. In particular, for the case where the exit point is seaward of the observation point, the pore pressure response is correlated with the distance between the exit point and the shoreline in that when the distance is large the rate of pressure drop is fast and when the distance is small the rate decreases. The observations expose limitations in the existing models describing exit point dynamics which is based only on the force balance on a particle of water at the sand surface and neglects both sub-surface pressures and shoreline proximity. A new modified form of the model is shown to significantly improve model-data comparison through a parameterisation of the effects of capillarity into the aquifer storage coefficient. Observations of the shoreward propagation of the swash-induced pore pressure waves ahead of the runup limit shows that the magnitude of the pressure fluctuation decays exponentially and that there is a linear increase in time lags, behaviour similar to that of tidally induced water table waves. The location of the exit point and the intermittency of wave runup events is also shown to be significant in terms of the shore-normal energy distribution. Seaward of the mean exit point, peak energies are small due to the saturated sand surface within the seepage face limiting pressure fluctuations. Landward of the mean exit point the peak energies grow before decreasing landward of the maximum shoreline position.

Keywords
Swash zone, beach groundwater, capillarity, water table exit point, seepage face, wave run-up