<p>The research work of this thesis is concerned with the local buckling behaviour and the post-local buckling strength of perforated cold-formed steel (CFS) members subjected to axial compression loading.</p> <p>Cold-formed steel sections are widely used nowadays as primary and secondary framing members in low-rise steel buildings. Although CFS members are essentially thin-walled framing elements, with a major susceptibility to local buckling, these members maintain a considerable reserve of post-local buckling strength prior to yielding. The post-local buckling strength of CFS members is largely affected by the sectional non-uniform material properties after the forming operation, the initial imperfections, the large deformation behaviour after buckling, and the possibility having utility perforations in the plate components of the members.</p> <p>A finite element-based analytical model has been developed in this thesis to investigate the post-local buckling behaviour and the ultimate strength of non-performated and perforated CFS compression members. A large deformation degenerated shell finite element was used to model the surface of CFS sections. The kinematic formulation of the degenerated shell element was enhanced using the method of "assumed strain fields", to eliminate any locking program problem of the element. Special consideration was given in the finite element model to the geometric imperfections and the loading technique of CFS compression members.</p> <p>Tensile coupon tests and residual stress tests were performed on CFS channel sections, in order to determine the effects of the cold forming operation on the distribution of the material properties across CFS sections. based on the results of these tests, analytical models for the stress-strain relationship, the yield strength distribution, and the residual stress distribution across CFS sections were developed and incorporated in the finite element model of CFS compression members.</p> <p>A seris of CFS channel stub-column tests was performed to verify the deformation and ultimate strength predictions of the proposed finite element model. The tests were also used to investigate the effects of perforations on the behaviour and load capacity of CFS members in compression. The finite element model was then used to assess the axial stress distribution and the effective design width of perforated plates of CFS compression members. This assessment was performed through a parametric study on the perforation and the plate parameters.</p> <p>Two effective design width equations for stiffened compression plates with square and elongated perforations were developed, based on the analysis of the finite element results. The ultimate load predictions of the two equations were compared to the stub-column test results of this thesis, and several other test results from the literature. The proposed equations proved to give accurate and safe predictions for the effective design width and the ultimate strength of perforated CFS compression members.</p> / Doctor of Philosophy (PhD)

<p>Cable-stayed bridges have been gaining popularity in the last few decades as a viable, efficient, economical and aesthetically appealing design for spanning medium to long crossings. The construction of these bridges in seismic regions has created a need to more fully understand their dynamic behaviour and seismic response.</p> <p>The objectives of this research work are to: (1) define a dynamic modal analysis procedure suitable for cable-stayed bridges, and (2) use the developed procedure to study seismic response characteristics of cable-stayed bridges.</p> <p>The research program was divided into four main stages: (1) development of analytic models for estimating frequencies of two of the main structural systems of cable-stayed bridges (i.e. deck and tower); (2) a 3-D model of Quincy Bayview Bridge was used as a prototype structure to study the modal characteristics of cable-stayed bridges and investigate the effect of major geometric parameters on the modal characteristics of cable-stayed bridges; (3) eigenvectors and load dependent Ritz vectors were examined to compare their appropriateness as bases for modal transformation of the equation of motion of cable-stayed bridges. A seismic response study was conducted of the Quincy Bayview Bridge in each vector basis to judge which is more appropriate for dynamic and seismic analysis of cable-stayed bridges. Frequency cut-off criteria were proposed that would ensure the inclusion of all important modes in a dynamic analysis; and (4) the proposed criteria were applied in a seismic response study that used a 3-D finite element model of the Quincy Bayview Bridge. The study investigated the effect of frequency content of ground motion on the seismic response of cable-stayed bridges with different deck supports.</p> <p>The results of the study showed that modal characteristics of cable-stayed bridges are most affected by the cable arrangement, the tower shapes, and deck supports. Almost the same number of eigenvectors or Ritz vectors are required to ensure the inclusion of all important modes in a modal analysis. To ensure the inclusion of all important modes, it is proposed to calculate an upper limit frequency using the developed analytic models, generate modal vectors up to the set limit and then check the effective modal mass of these vectors to meet a pre-set percentage of the total mass. The study showed that seismic response of a cable-stayed bridge is strongly dependent upon the deck support condition, and the frequency content of input motion. It also showed that towers are less sensitive to changes in frequency content of the ground motion than the deck.</p> / Doctor of Philosophy (PhD)

<p>In this dissertation research, grey mathematical programming (GMP) and grey fuzzy mathematical programming (GFMP) methods have been developed for the first time for decision making under uncertainty, and applied to case studies for municipal solid waste (MSW) management planning in the Regional Municipality of Hamilton-Wentworth (RMHW), Ontario, Canada.</p> <p>The GMP/GFMP approaches have improved upon existing mathematical programming methods, such as fuzzy mathematical programming, stochastic mathematical programming, and interval mathematical programming, by introducing concepts of grey systems and grey decisions into ordinary mathematical programming (MP) and fuzzy mathematical programming (FMP) framework. The developed methods allow uncertain information (presented as grey numbers) to be effectively communicated into the optimization processes and resulting solutions, such that feasible decision alternatives can be generated through the interpretation and analysis of the grey solutions according to projected applicable system conditions. Moreover, the proposed GMP/GFMP solution algorithms do not lead to more complicated intermediate models, and thus have lower computational requirements and are applicable to practical problems.</p> <p>Four GMP (grey linear programming (GLP), grey quadratic programming (GQP), grey integer programming (GIP), and grey dynamic programming (GDP)) and four GFMP (grey fuzzy linear programming (GFLP), grey fuzzy quadratic programming (GFQP), grey fuzzy integer programing (GFIP), and grey fuzzy dynamic programming (GFDP)) methods have been developed. The GFMP improved upon the GMP through the introduction of concepts of fuzzy decisions and FMP into the GMP frameworks to better reflect system uncertainties and generate grey solutions with higher certainty and improved applicability. The use of the GFMP approaches may be particularly pertinent for GMP problems with model stipulations fluctuating within wide intervals but the related membership function information for admissible violations of system objectives and constraints is known. The GMP/GFMP pairs are all directly linked (GLP-GFLP, GIP-GFIP, and GDP-GFDP) except for the GFQP which is not linked to the GQP but instead is linked to and improves upon the GFLP since it enables the modelling of constraints with independent uncertain characteristics. In comparison, the GQP was formulated by including the effects of economies of scale within the GLP modelling framework. In terms of the difference between the GIP/GFIP and GDP/GFDP, the GIP/GFIP methods provide a "one step" optimization process which is convenient for modelling formulation and solution, but may require computers with high capacities and speeds when large scale problems with a multitude of variables and time stages are to be solved, while the GDP/GFDP methods could potentially solve such a problem by dividing the planning horizon into several stages, but may require more effort for the dynamic analysis and computation of the stage submodels. The effectiveness of the methods and their solution algorithms have been demonstrated through a series of comparisons between the MP/GMP/GFMP solutions, as well as related sensitivity analyses.</p> <p>The GMP and GFMP methodologies were applied to case studies of short term waste flow allocation and long term facility expansion for the waste management system in the RMHW. Through examining the relationships and conflicts between different system components, a GLP model was formulated for the waste flow allocation planning problem, and a GIP model was formulated for the facility expansion planning problem. The grey solutions provided optimal and stable ranges for system objective function values and decision variables, which could be used for generating decision alternatives through adjusting/shifting the decision variable values within their solution intervals and making relevant tradeoffs between different system objectives/restrictions according to projected applicable conditions. Generally, the short term waste flow allocation solutions were useful for adjusting or justifying the existing waste flow allocation patterns, and the long term capacity planning solutions provided optimal times, sizes and locations of the waste management facility developments/expansions. Sensitivity analyses of the effects of system condition variations on the model solutions were also conducted.</p> / Doctor of Philosophy (PhD)

<p>The finite element method has recently become a well established technique in solving geotechnical problems, and has in the past few years been applied in glaciology to stimulate ice mass flow problems. In fact, the models available have advanced much more rapidly than knowledge of the physical parameters and laws which describe ice needed in the simulation process. In this thesis, several functional flow laws are developed.</p> <p>These laws, it is hoped, will lead to a better flow simulation for ice masses. Parameters such as grain size, age, and fabric, though poorly controlled in the testing of ice, are very important to the flow characteristics of ice as can be shown from a consideration of dislocation movements. A more systematic treatment of these parameters is needed.</p> <p>The influence of initial stresses on flow behaviour not considered in previous finite element method simulations of glacier flow, is shown to be significant. Two finite element schemes are compared, and a scheme based on an implicit approach appears to be somewhat faster in computer time.</p> <p>The importance of temperature to glacier flow is considered in this thesis. It is shown that non-isothermal conditions significantly affect the flow of ice masses.</p> <p>The functional flow laws, and the non-isothermal temperature distribution are used to stimulate flow of the Barnes Ice Cap. The simulation is found to be poor compared to observed results. It is felt that a consideration of initial stresses, better temperature distribution data, and improved flow laws are needed before the finite element method simulation will lead to satisfactory results.</p> / Master of Engineering (ME)

<p>A finite element method that utilizes boundary conditions from wave propagation considerations is given for predicting the seismic response of a pile embedded in soil. The response of the system and the stress distribution in the soil adjacent to and beneath the pile are resolved, and these provide a means of appraising the behaviour of a soil-pile system during an earthquake. The three directional components of the earthquake excitation are considered. The soil-pile system is idealized as an axisymmetric structure subjected to nonsymmetric loading to simplify the computations.</p> <p>Records of ground motions during recent earthquakes have clearly demonstrated the significance of local soil conditions on the amplitude and frequency characteristics of seismic motions. For large epicentral distances, the usual assumption of energy transfer by means of vertically propagating shear waves is valid. However, for sites nearer to the source the direction of shear wave propagation may be inclined and surface waves also contribute to the ground motions. These aspects of the seismic motions are considered.</p> <p>The spatial variations in seismic motions are computed using wave propagation theory and assuming that the earthquake energy is transferred through the soil layers by shear waves and Rayleigh waves. Spatial variations in motion are compared for various epicentral distances and wave propagation assumptions. It is shown that the surface wave makes a significant contribution to the response at near sites, while the effect of inclining the shear wave propagation is of secondary importance. The method and programs are general so that they can be used for a variety of problems. Dimensions of the soil-pile system are adopted so that "free field" conditions can be assumed at the boundary. The seismic motion record for each boundary node of the discretized structure is computed and used as the input for the full finite element dynamic analysis which utilizes a step-by-step procedure.</p> <p>It was found that the single pile foundation considerably reduced the responses transferred to the structure. The method of analysis was used to consider the pore pressures developed in the case of saturated soils around a single pile. The behaviour of a pile-saturated sand system during the San Fernando Earthquake showed that the sand around the pile liquefied. When a pile-saturated clay system was subjected to the same earthquake, there was no sign of liquefaction. These results are in qualitative agreement with field observations.</p> / Doctor of Philosophy (PhD)

<p>This thesis deals with the modelling of the circulation and pollutant transport in the nearshore areas of lakes and their tributaries. An integrated hydrodynamic/pollutant transport model was developed which operates in an interactive environment and is equipped with powerful graphics. The model can predict: (a) the horizontal and vertical current structure in the lake under isothermal and stratified conditions for steady and variable wind conditions, (b) the spatial and temporal pollutant concentration distributions in the lake from multiple input pollutant sources such as creeks, sewer treatment plant outfalls (STPs) and combined sewer outfalls (CSOs) discharging in the lake, and (c) the particle trajectories released in different locations in the lake. The model was calibrated with extant laboratory data. The water level set-up and current structure in the Great Lakes were obtained under various wind conditions and in two cases, in Lake St. Clair and Lake Ontario, the model was verified with current meter and water elevation measurements, respectively. The model was successfully applied to the St. Clair River in Sarnia for a number of storm cases and was proven to be an effective tool in screening remedial options for mitigation of bacteriological pollution in the Bay. The field data collected during the 1990-1991 field season in Hamilton Harbour was analyzed and used to verify the model. The seiches of Lake Ontario and Hamilton Harbour were revealed for the first time in the water level data in the Harbour. The simulated and measured currents and drogue trajectories were in good agreement, indicating the presence of topographical eddies and mixing zones in the Harbour. Finally, a nested-grid model was developed and successfully applied in three nearshore areas of Hamilton Harbour to examine the impact of artificial islands by studying the changes in current patterns and concentration peak, exposure, and flushing time in different locations of concern.</p> / Doctor of Philosophy (PhD)

<p>Although hollow structural sections (HSS) are an efficient structural member and have attractive architectural appearance, their use as columns in low or medium-rise moment-resisting steel frames has been limited. Some of the difficulties are due to the lack of a simple and practical field-bolted moment connection between a W-shape beam and an HSS column.</p> <p>The objectives of this research study are to develop a practical bolted moment connection between a W-shape beam and a square HSS column and to evaluate its behaviour experimentally under monotonic and cyclic loading. In addition, it is of interest to evaluate the effect of the developed connection response on the frame's overall behaviour, and provide guidelines and design rules for detailing the connection. In this research study, attention is focused on investigating the behaviour of bolted end-plate connections developed by blind fasteners. An experimental-analytical approach was used in this research program.</p> <p>The experimental program which was carried out on full scale beam-to-column connections involved three phases. First, three monotonic tests were conducted to examine the behaviour of such a connection using blind fasteners and to compare their response with a similar connection using high strength A325 bolts. Second, four tests were conducted on connections utilizing larger HSS columns and with different stiffening conditions to reveal different modes of failure. Third, two cyclic tests were performed to examine the effect of cyclic loading on such a connection.</p> <p>Based on the observations and results of the experimental program, an analytical model to predict the behaviour of the connection was developed. The sensitivity of the model was checked by comparing its predictions with the experimental results. The model was then incorporated into "Drain-2DX" computer program to be used in analyzing moment resisting frames. Based on both experimental and analytical results, a design procedure for the connection was proposed.</p> <p>The effect of connection flexibility on the response of a 4-storey steel moment frame was evaluated by comparing the response to that of a similar frame with rigid connections. The frames were analyzed statically under monotonically increasing loading and dynamically under two earthquake ground motions. It was concluded that, the flexibility of semi-rigid connections should be included in both static and dynamic analyses to determine a frame's structural response more realistically.</p> / Doctor of Philosophy (PhD)

<p>The central focus of research undertaken concerned the strength and behaviour of separated double chord rectangular hollow section (RHS) K-joints. Peripherally the concepts of the twin member shear beam is introduced as a simple and inexpensive bridging for revealing the intrinsic structural properties of such joints.</p> <p>The finite element method has been used to investigate the stiffness characteristics of the separated joint. The RHS chord member is idealized by a thin plate representing the inner web and a channel representing the top and bottom flanges and the outer web. The stiffening effect by the channel is incorporated through its condensation into a boundary stiffness matrix to be added to the inner web stiffness matrix.</p> <p>The proposed finite element formulation includes rectangular plate elements in the inner web plate and a variety of beam elements in the channel forming grillage. The formulation considers both bending and in-plane actions. Material nonlinearities of the joint are assumed to be adequately represented by the Von Mises yield criterion and the associated plastic flow rule. While geometric nonlinearities have been excluded, this was deemed reasonable for the range of displacements considered in this study.</p> <p>To verify the finite element model, a number of experiments were conducted on twin shear beams with the objective of making definitive statements about the joint performance to be anticipated for the finite element model. Twenty-four specimens were tested in the Applied Dynamics Laboratory of McMaster University. Test results showed a definite improvement in structural performances for both increased depth and a decrease in the gap.</p> <p>From experimental result, a local deflection limit criterion was suggested to define a range of permissible displacements in double chord joints. Such a criterion was based upon that presented in the literature for single chord joints.</p> <p>A verification of the finite element model was made using the experimental data of the twin shear beams and it exhibited good correlation. A model of sensitivity analysis was then carried out with the objective of furthering understanding of the behaviour of such structural components.</p> <p>The model was extended to the general model called EPAC-RHS (Elasto-Plastic Analysis of RHS Connections). In the process of this extension, triangular plane stress-plate bending elements were introduced to accommodate an arbitrary joint assembly of K and N configuration. In addition, member preloads were accounted for in EPAC-RHS.</p> <p>Theoretical results of simulated K-joint models were compared with experimental data of K-joints obtained from the literature. While strength predictions were somewhat conservative, very good agreement of elastic response was observed for all tests.</p> <p>A yield line theory was developed for which two strength models, trapezoidal and conical were proposed. Their predicted strengths were compared with experimental loads at the limiting deflections suggested. Good agreement with the tests was found particularly for the trapezoidal model. The twin shear beam models were then extended to be applicable to K-joints by taking into account both the reduction in strength due to chord axial preload and the horizontal component of the diagonal force. Theoretical results were compared with previous experiments on K-joints and exhibited reasonable correlation.</p> / Doctor of Philosophy (PhD)

<p>Equipment can be mounted on rigid floors by placing the equipment freely on the floor without fastening, fixing it tightly to the floor. This study investigates the rocking response of equipment resting freely on rigid floors and also the effect of restrained rocking on the response of partially fixed equipment under seismic excitations.</p> <p>Equipment which rests freely on rigid floors is simulated as a rigid rectangular block. The overturning of rigid blocks is studied under the effects of three types of base motion, namely, pulsive, critical, and harmonic excitations.</p> <p>When the effect of pulse shapes on the overturning potential of rigid blocks under pulsive excitations is examined. It is found that the rectangular pulse will require the least peak acceleration for a specified duration. Under critical excitations, it is found that the extent of response amplification depends on the coefficient of restitution and the initial angle of rotation in addition to the peak acceleration of the pulses. TO amplify the motion by a specified ratio, pulses with lower peak acceleration are required for cases of large initial angles and for cases with large values of the coefficient of restitution. Under harmonic excitation, the conditions for steady-state periodic motion is derived. It is also found that as the coefficient of restitution decreases, the system becomes more stable against overturning and can withstand higher accelerations.</p> <p>Also in this research, the response of partially fixed equipment resting on rigid floors under the effect of harmonic and earthquake excitations is investigated. For systems restrained by non-yielding bolts, it is found that the existence of gaps has the effect of decreasing the deformation of the mounted equipment relative to the base compares to the case of complete fixation. The existence of gaps also decreases the natural frequency of the system. In systems with yielding bolts, the presence of the gaps affects the deformation of the equipment more than is systems with non-yielding bolts. In the latter, the total rocking angle after all stretching takes place is not sensitive to the initial gap size and depends only on the level of excitation.</p> <p>Based on this study, it is recommended hat equipment systems be allowed to rock on their bases by providing gaps in their anchorage systems. This kind of mounting has the advantage of allowing the equipment to rock with out the rock without the risk of overturning. Also, larger gaps are recommended for higher floor acceleration levels.</p> / Doctor of Philosophy (PhD)

<p>Electric power transmission lines have been traditionally designed for wind and ice loads. The earthquake load has not been considered in the analysis of transmission lines. During recent earthquakes, there have been indications of damage to transmission lines. Due to the complex nature of the problem, there is a lack of research work in the area of seismic analysis of transmission lines. The objective of this study is to evaluate the response of transmission lines to earthquake ground motion in order to evaluate the current design code methodology. The scope of this research program includes: (1) Modelling of different parts of the transmission line to analyze its seismic response, (2) comparison between the forces generated in the transmission tower members by wind, ice and earthquake loads, and (3) analyzing the probabilistic characteristics of the cable response to earthquake ground motion in order to establish a seismic design procedure for transmission lines. An intermediate span of a typical transmission line is chosen for the analysis. The tower members are modelled as truss elements. The cables are modelled by two node elements that retain their geometric nonlinearity. The dynamic characteristics of different components of the line (towers and cables) are determined in order to obtain a better understanding of the line behaviour. The in-plane and out-of-plane vibrations of the line are analyzed. The transmission line response to multiple support as well as uniform support excitations is evaluated. A closed form analytical solution for the cable vibration is carried out for a more detailed study of the cable nonlinear behaviour. It is concluded from the analysis that earthquake ground motion may cause substantial displacements and internal forces in the transmission line elements. The forces in transmission tower members due to the earthquake load may exceed those caused by the wind loads specified by the National Electrical Safety Code (NESC, 1993). Seismic ground motion may cause large displacement in the transmission line cables. This suggests that the cable motion during earthquakes should be included in the design of the line clearances to avoid having cables touch each other, which may cause power failure.</p> / Doctor of Philosophy (PhD)