This study is concerned with the minimum cost design of a multi-storey building. The building consists of rectangular steel plane frames which are evenly spaced and support identical floors and a roof. The frame spacing, the column positions within the frame, and the number of intermediate beams spanning between frames are optimized using Box's Complex method and the optimum solution verified by an exhaustive search procedure. Member sizes for the frame and floor system are determined by a fully-stressed design criterion, for the AISC code, within the limits of a discrete set of member properties. The optimum design for several frames with various widths and heights is determined and the influence of the above variables, and the effect of cost parameters on the optimum solution is illustrated and the results discussed. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

Elastic structures exhibit instabilities which arise through the occurrence of finite displacements even when constitutive properties remain linear. A non-linear analysis which recognizes rotations in the strain displacement relationship is formulated for analyzing three-dimensional framed structures. A finite element method is used whereby the rotations within each element are restricted in size by use of a local element reference frame attached to the element. Two such coordinate systems are developed. Then an incremental solution technique based on an instantaneous linearization of a Taylor series expansion of the forces about the displacement configuration at the beginning of each increment is developed. The snap-through buckling of shallow frames, arches and domes is studied with a view to documenting the effect on the equilibrium paths of the type of moving coordinate frame, the number of elements, and the size of the increment step. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

Two theories for the stability analysis of a spaceframe structure are presented: the first uses only Livesley stability functions, the second includes in addition the effects due to chord rotation and flexural end shortening of a member. The critical condition is defined by the load which makes the tangent stiffness matrix of the structure become singular. Three methods for obtaining the critical load are presented: determinant plot, Southwell plot, and load-deflection curves. The analysis is carried out for the plexiglass model of an actual conical spaceframe, made of glulam timber, and built for the storage of potash. The overall critical load for this structure is found to be in satisfactory agreement with the experimental results obtained in previous model tests. Some additional effects, such as geometric imperfections in the joint coordinates and different member end-fixity conditions are investigated. The concept of effective length for a member is introduced to present the results obtained by varying the height/span ratio of the structure. Finally some design suggestions are given for structures of this type. The analyses were made using spaceframe programs based on the stiffness method, modified to include stability effects. An IBM 360/67 computer was used for the calculations. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

A procedure is described for the redesign of undamped unforced linear structural systems to meet specified changes in natural frequency or mode shape. A baseline analysis is conducted using finite elements to obtain a subset of the natural frequencies and mode shapes. A two stage perturbation analysis is then used to obtain the structural changes required to meet the specified changes in natural frequency or mode shape. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

This thesis formulates an account of two language abilities shared by adult speakers of English. First, language users are able to recognize when a text is contiguous from utterance to utterance. Second, users are also able to decide when a discourse as a whole is well-formed. As previous work in either area has been minimal, a central problem becomes that of discovering and demonstrating how strong, and of what order, adequate theories of these intuitions must be. Thus, Part I, which takes up the first of the abilities above, attempts to revise and strengthen current models of conjunction, extending them to handle successive sentence decisions. Part II subsequently attempts to develop a theory of expository performance to handle the larger discourse intuitions. Part I begins with a large corpus of grammatical , but unacceptable, successive sentence pairs. After moving first from strictly syntactic constraints through progressively stronger criteria, until reaching pragmatics and context, it makes the case that only a context-sensitive theory is adequate to block the generation of sentence pairs with content anomalies. However, as Part II argues, content relations between sentences in a discourse are not the only meaning relations of which a reader must be aware. Each utterance also has its own force, by which we know what a speaker intended to do in uttering what he has. Through examples I show that force considerations are ultimately prime in all acceptability decisions. Content analysis inaccurately predicts that if content meaning relations can be found between its successive sentence pairs the discourse comprised of the pairs will be acceptable, and if not, then the discourse will be anomalous. Nevertheless, texts with apparently anomalous content relations between sentences may be acceptable, given certain performative intentions of the speaker, and texts which appear to be acceptable may fail on performative grounds. Part II also contains an analysis of the necessary organization and ordering of certain expository actions in written texts, given a speaker's expository intentions for his discourse as a whole. In particular, I look at the discourse action of arguing, which obligatorily involves making a claim and giving reasons for belief, as well as the optional actions of making distinctions, explaining, admitting, contradicting, and others. In the final chapter, I bring together the two parts of the thesis, showing that conjuncti or successive sentence relations must be consistent with a discourse's underlying performative structure, and are to some extent determined by that performative structure. / Arts, Faculty of / English, Department of / Graduate

Includes bibliographical references. . / A FEM-based parametric study is undertaken to investigate the buckling behavior of meridionally and circumferentially stiffened steel cylindrical and conical shell frustum subjected to different load cases. This situation arises in different steel shell applications such as storage vessels (liquid, solid and gas) and in certain configurations of industrial process facilities. The stiffeners are flat strips of rectangular section welded on to the outer surface of the shell, either over the whole length of the shell meridian or around the circumference of the shell. It is required to establish how the elastic buckling load and mode shapes vary with respect to certain key parameters of the problem. The parameters of interest in the study include the number of stiffeners around the shell circumference and along the meridian, the stiffener-depth to shell-thickness ratio, and the stiffener depth-to-width ratio. This thesis reports the findings of the parametric study and also presents some results of experimental tests on laboratory small-scale models of stiffened cylindrical and conical frusta.

We are currently witnessing the advent of a revolutionary new tool for biomedical research. Complex mathematical models of "living cells" are being arranged into representative tissue assemblies and utilized to produce models of integrated tissue and organ function. This enables more sophisticated simulation tools that allows for greater insight into disease and guide the development of modern therapies. The development of realistic computer models of mechanical behaviour for soft biological tissues, such as cardiac tissue, is dependent on the formulation of appropriate constitutive laws and accurate identification of their material parameters. The main focus of this contribution is to investigate a Proper Orthogonal Decomposition with Interpolation (PODI) based method for inverse material parameter optimization in the field of cardiac mechanics. Material parameters are calibrated for a left ventricular and bi-ventricular human heart model during the diastolic filling phase. The calibration method combines a MATLAB-based Levenberg Marquardt algorithm with the in-house PODIbased software ORION. The calibration results are then compared against the full-order solution which is obtained using an in-house code based on the element-free Galerkin method, which is assumed to be the exact solution. The results obtained from this novel calibration method demonstrate that PODI provides the means to drastically reduce computation time but at the same time maintain a similar level of accuracy as provided by the conventional approach.

The study looks at how the sectorial coordinate approach can be used to solve the problem of unique shear centre property of non-standard monosymmetric sections. In solving the unique shear centres, the behaviour of the shear centre with reference to the centroid is carefully studied as the geometry of the section is changed. The study shows investigations of the sections which are 152x152x30 UC H-section, the same H-section with 2/3 as well as 1/3 of the bottom flange width and a 203x178x30 T-section. Vertical plates of 8mm thickness are added to the ends of the upper flanges of the sections instigating increments of 12.5mm from 0 to 100mm height. From the computations done, the following is observed: • The difference between the sectorial coordinate approach results and those from Prokon is at most 3.1%. Also, as the end plate heights are increased, the difference in the results increases. • Shear centres change in position with reference to the centroids as a result of the change in geometry of the sections. • For the H-section the shear centre is initially with the centroid at zero plate height. It then moves upward (higher than the centroid) to a certain peak point, then decreases steadily, intersecting the centroid again and eventually ending up being lower than the centroid with upstanding plate height increases. • A similar pattern follows the H-sections with reduced bottom flange widths, with the only difference being that the shear centre is initially higher than the centroid. It slightly increases to a peak then gradually decreases, intersecting the centroid at a certain point and ending up lower than the centroid. • As for the T-section, the shear centre is initially at the highest point (furthest from the centroid) and decreases gradually, intersecting the centroid and ending up lower than the centroid. • The H-section with upstanding plates offers itself as a section that has an envelope (gap) between the shear centre and centroid when the shear centre is above the centroid which is much lesser than the other sections. With the usage of excel spreadsheets, the sectorial coordinate approach is an efficient and accurate method to find shear centres and related section properties.

In today’s fast paced construction industry, there is an ever present need to increase productivity and to complete projects as quickly as possible. Reinforced concrete is a popular and widely used construction material. However it has the unfortunate drawback in that the concrete requires time to set and gain sufficient strength before loads may be applied and the formwork and props can be removed. It is therefore desirable to keep propping times to a minimum. If the propping is removed too early, there is a risk of the member deflecting excessively and exceeding the maximum allowable limits, or in severe cases it could even lead to a structural failure or collapse. The SANS 2001 code provides recommended propping times for beams and slabs, which can be used as a guideline by building contractors and structural designers. These propping times present a universal approach, which does not consider all the factors that affect deflection. This simplified approach may be considered to be conservative as shorter propping durations could be possible without a loss in performance. The aim of this dissertation is to look into the effects of early propping removal on the longterm deflections of concrete members. This was done by modelling the deflection of a typical reinforced concrete beam at different ages of loading, using three code-based deflection calculation methods. The codes that were used are the South African National Standard (SANS), Eurocode (EC2) and American Concrete Institute code (ACI 318). A detailed literature-based investigation was conducted to determine the factors which affect deflection in reinforced concrete members, as well as the theory behind the code-based deflection calculation procedures. This was followed by the modelling of deflections using the abovementioned methods. Three case studies were performed to determine the effects of early propping removal under different scenarios. The first case study only deals with the effects of early age loading on long-term deflection. As an added point of interest, two different concrete mixes were used, made with two different types of cement. The second case study compares the effect that different levels of relative humidity have on the long term deflection at early ages of loading. Lastly, the effects of concrete strength on long-term deflections at early ages of loading was modelled. The results of the first case study indicated that a reduction in propping time is possible without causing excessive deflections. In the second and third case study is was observed that both the relative humidity and concrete strength respectively have an effect on the long term deflection and therefore also influence the propping time. The study concluded that based on the obtained estimated deflection values using the codebased methods, the propping times provided in the SANS 2001 code may in certain applications be conservative. According to the results obtained from the code-based deflection calculation procedures, it is possible to reduce the propping duration. It was suggested that an alternative method should be developed which would allow structural designers to determine the required propping time more accurately.

The performance of reinforced concrete (RC) structures, such as bridges in the heavy haul industry, may be severely impacted by fatigue when subjected to repeated cyclic loading. Fatigue not only reduces load carrying capacity and serviceability limit states (SLS), but it can cause structural failure even when the components are subjected to low stress range cyclic loading. Corrosion damage exacerbates fatigue related problems as chloride induced pitting corrosion facilitates the formation and gradual propagation of cracks under cyclic loading. A common rehabilitation and retrofitting approach that involves patch repairing and fibre reinforced polymer (FRP) strengthening has proven effective to not only restore structural capacity, but also to enhance infrastructure service life. The structural repair process involves the replacement of deteriorated cover concrete with a less permeable patch repair mortar. The patch repair only restores durability of the structure; to restore or enhance structural capacity the repair process further involves bonding of FRP laminates. Particularly in the case of FRP's with a low elastic modulus, the design is often guided by serviceability limit states as opposed to ultimate limit states (ULS), resulting in an over-reinforced structural member. In addition, the reinforcement area of commercially available FRP strengthening may exceed the design requirements, especially at low levels of corrosion damage. In both the abovementioned considerations the design may result in an over-reinforced section. At the time when this researched was proposed, the effect of increasing damage extent on fatigue behaviour of over-reinforced RC beams was not clear and merited further investigation. A scientific experimental approach was developed to investigate the long-term performance of fifteen (15) full-scale 40MPa RC beams with dimensions 155x254x2000mm and ultimate capacity of 62.3kNm. Accelerated corrosion damage was induced in varied extents which included 450mm, 800mm, 1300mm and 1800mm length to a constant degree of 10% on all specimens. Specimens from each damage extent were patch repaired using SikaCrete214 and subsequently strengthened with externally bonded with SikaCarboDurS512 carbon fibre reinforced polymer (CFRP) laminates. Four-point bending monotonic loading tests were conducted on one (1) specimen from each damage extent. The results obtained from the quasi-static tests were used to determine two (2) cyclic loading stress ranges at which the remaining 2 specimens from each damage extent would be tested under. Under the 40% and 60% stress ranges four-point bending cyclic loading tests were carried out at a test frequency of 4Hz. Information was acquired on key performance indicators that included fatigue life, crack development, failure mode and stiffness degradation, where stiffness was assessed in terms of midspan deflection, composite material strains and neutral axis shift. Information on these parameters were collected using strain gauges, linear variable differential transducers (LVDT), DEMEC strain targets and digital image correlation (DIC). Ultimate failure loads under monotonic loading showed that despite having the highest degree of corrosion, the 450mm damage extent specimen had the highest failure load of 325kN. The failure load gradually reduced to 290kN as the damage extent was increased to 1800mm and the 0mm (control) specimen failed at the lowest load of 274kN. In contrast to the static behaviour, the specimen fatigue life enhanced by 106.3% as the damage extent was increased from 450mm to 1800mm. As expected, the 40% stress range tests yielded much longer fatigue lives than their 60% stress range counterparts. Furthermore, the experimentally obtained fatigue lives were compared to three fatigue life prediction models and the Helgason and Hanson model yielded the closest correlation with the experimental results. IV ABSTRACT Crack densities were found to increase with a longer fatigue life. An increase in damage extent was found to positively affect crack development and overall stiffness of the specimen during longterm fatigue testing. This finding was further substantiated by an assessment of midspan deflection, compression concrete strain and carbon fibre strain results, which all suggested a lower neutral axis and a lower stiffness reduction rate under fatigue loading as the damage extent was increased from 450mm to 1800mm. Furthermore, the tension concrete cracks propagated gradually during longer fatigue tests periods, while the tension steel and carbon fibre were comparably less affected by the resultant internal forces. Unfortunately, the neutral axis strain measurements using DEMEC targets were unable to assess the relative effect of an increase in damage extent as well as the compression concrete and carbon fibre strains were able to. During this experimental period, it was established that the laboratory layout was not conducive for carrying out the DIC process of long-term cyclic loading tests. The area in which testing took place did not adequately protect the camera against the environment and therefore required daily storage of the equipment. Regular movement of the camera for storage purposes introduced measurement inaccuracies which accumulated over longer test periods of up 20 days. However, for the short-term tests that did not require movement of the camera, the DIC process yielded favourable results. It was possible to capture the crack patterns early in the test period when the crack growth rate and development of new cracks was high using DIC. It was found that the high strain cracks coincided with the points of maximum vertical deflection (obtained through DIC) and eventual failure location of the specimen. The points of maximum deflection obtained from the DIC process were often not at midspan, which in the absence of the DIC process, would not have been possible to predict accurately. The results have shown that the specimens with the longer damage extents exhibit improved fatigue performance than their shorter counterparts. This revealed a stark contrast to their monotonic loading performance which favoured shorter damage extents. Furthermore, DIC holds potential to predict failure location more accurately than conventional approaches used for structural health monitoring (SHS).