To investigate the benefit induced by adding a small amount of bonded reinforcing steel into a fully unbonded prestressed concrete beam, two well-founded and straightforward approaches for predicting tendon stress are proposed. The primary approach utilizes a flexural analysis to calculate member deformation. The supplementary approach employs a truss model to consider the additional member deformation due to shear force. Both approaches use a simplified iterative method. With these two approaches, a systematic parametric study is conducted to investigate the effects of various factors. The results indicate that adding little bonded reinforcement does significantly increase the stress increment in unbonded tendons at ultimate state for one-point loading as expected. Moreover, a lower span-to-depth ratio, the use of high-strength concrete, and a smaller mechanical reinforcement ratio also raise the stress increment.

To investigate the benefit induced by adding a small amount of bonded reinforcing steel into a fully unbonded prestressed concrete beam, two well-founded and straightforward approaches for predicting tendon stress are proposed. The primary approach utilizes a flexural analysis to calculate member deformation. The supplementary approach employs a truss model to consider the additional member deformation due to shear force. Both approaches use a simplified iterative method. With these two approaches, a systematic parametric study is conducted to investigate the effects of various factors. The results indicate that adding little bonded reinforcement does significantly increase the stress increment in unbonded tendons at ultimate state for one-point loading as expected. Moreover, a lower span-to-depth ratio, the use of high-strength concrete, and a smaller mechanical reinforcement ratio also raise the stress increment.

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Master of Science / Department of Civil Engineering / Robert J. Peterman / Prestressed concrete is commonly used for bridges, pavement and railroad ties because of economic advantages in cost, sustainability service life, and environmental friendliness. In general concrete design standard, the ultimate moment strength in flexure design is computed by finding the equilibrium of the internal force in the section (the compressive force in concrete and tension force in the steel and reinforcement). To predict tension force in steel one generally applies the 7-wire low-relaxation prestressing strand equation from the PCI manual even though the design employed prestressing wires instead of strand. The other method is to use equations from the ACI Code which is over conservative. Considering both approaches are lack accuracy, this research will provide an accurate estimation of the stress in prestressing wires through an experimental program and analytical modeling. The real stress-strain curves are collected through experimental testing in 13 types of prestressing wire. Experimental results are then used for modeling existing equations. As a result a more precise estimation is achieved. Additionally, this research simplifies the procedure for utilizing the equations which offers convenience in practical application.

A large number of building inventory in Canada and elsewhere in the world consists of non-ductile reinforced concrete frames, with or without masonry infill panels. These structures suffer damage when seismic force demands are higher than their force capacities. Therefore, seismic retrofitting of such frame buildings for drift control remains to be a viable option for improved building performance. A retrofit methodology has been developed in the current research project, which involves diagonal bracing of frames with prestressing strands. An experimental research project has been conducted to assess the effectiveness of diagonal prestressing in non-ductile reinforced concrete frame buildings. The experimental program consists of two large-scale single-bay single-storey reinforced concrete frames, with a height of 3.0m and a span length of 3.5 m. The frames were designed and built to reflect the 1960’s practice in Canada, without the seismic requirements of current building codes, and hence are seismically deficient. They were retrofitted with diagonally placed prestressing strands, having two different areas of steel, prestressed to 40% of the strand capacity. One of the frames was retested after the failure of the strands, with a new set of strands without any prestressing, forming the third test. The results indicate that lateral bracing reinforced concrete frames with high-strength prestressing strands is an effective strategy for controlling lateral drift and hence potential damage in buildings during strong earthquakes. Prestressing of the strands increases initial stiffness, as compared to non-prestressed cables, and provide superior performance. The area of diagonally placed steel (including the number of strands) and the level of initial prestressing depend on the required level of upgrade in the building in terms of seismic force requirements. The design procedure recommended in this thesis may be employed for implementing the technology. The thesis presents the details of the experimental program, and the test results. It also provides analytical verification of the approach, with a step-by-step design procedure.

A large number of building inventory in Canada and elsewhere in the world consists of non-ductile reinforced concrete frames, with or without masonry infill panels. These structures suffer damage when seismic force demands are higher than their force capacities. Therefore, seismic retrofitting of such frame buildings for drift control remains to be a viable option for improved building performance. A retrofit methodology has been developed in the current research project, which involves diagonal bracing of frames with prestressing strands. An experimental research project has been conducted to assess the effectiveness of diagonal prestressing in non-ductile reinforced concrete frame buildings. The experimental program consists of two large-scale single-bay single-storey reinforced concrete frames, with a height of 3.0m and a span length of 3.5 m. The frames were designed and built to reflect the 1960’s practice in Canada, without the seismic requirements of current building codes, and hence are seismically deficient. They were retrofitted with diagonally placed prestressing strands, having two different areas of steel, prestressed to 40% of the strand capacity. One of the frames was retested after the failure of the strands, with a new set of strands without any prestressing, forming the third test. The results indicate that lateral bracing reinforced concrete frames with high-strength prestressing strands is an effective strategy for controlling lateral drift and hence potential damage in buildings during strong earthquakes. Prestressing of the strands increases initial stiffness, as compared to non-prestressed cables, and provide superior performance. The area of diagonally placed steel (including the number of strands) and the level of initial prestressing depend on the required level of upgrade in the building in terms of seismic force requirements. The design procedure recommended in this thesis may be employed for implementing the technology. The thesis presents the details of the experimental program, and the test results. It also provides analytical verification of the approach, with a step-by-step design procedure.

To achieve thinner and longer floor slabs, rapid construction, and tight control of inservice deflections, modern concrete structures increasingly use high-strength, posttensioned prestressing steel as reinforcement. The resulting structures are called posttensioned (PT) concrete. Post-tensioned concrete slabs are widely believed to benefit from ‘inherent fire endurance.’ This belief is based largely on results from a series of standard fire tests performed on simply-supported specimens some five decades ago. Such tests are of debatable credibility; they do not capture the true structural behaviour of real buildings in real fires, nor do they reflect modern PT concrete construction materials or optimization methods. This thesis seeks to develop a more complete understanding of the structural and thermal response of modern prestressing steel and PT concrete slabs, particularly those with unbonded prestressing steel conditions, to high temperature, in an effort to steer current practice and future research towards the development of defensible, performance-based, safe fire designs. An exhaustive literature review of previous experimentation and real case studies of fire exposed PT concrete structures is presented to address whether current code guidance is adequate. Both bonded and unbonded prestressing steel configurations are considered, and research needs are identified. For unbonded prestressing steel in a localised fire, the review shows that the interaction between thermal relaxation and plastic deformation could result in tendon failure and loss of tensile reinforcement to the concrete, earlier than predicted by available design guidance. Since prestressing steel runs continuously in unbonded PT slabs, local damage to prestressing steel will affect the integrity of adjacent bays in a building. In the event that no bonded steel reinforcement is provided (as permitted by some design codes) a PT slab could lose tensile reinforcement across multiple bays; even those remote from fire. Using existing literature and design guidance, preliminary simplified modelling is presented to illustrate the stress-temperature-time interactions for stressed, unbonded prestressing steel under localised heating. This exercise showed that the observed behaviour cannot be rationally described by the existing design guidance. The high temperature mechanical properties of modern prestressing steel are subsequently considered in detail, both experimentally and analytically. Tests are presented on prestressing steel specimens under constant axial stress at high temperature using a high resolution digital image correlation (DIC) technique to accurately measure deformations. A novel, accurate analytical model of the stresstemperature- time dependent deformation of prestressing steel is developed and validated for both transient and steady-state conditions. Modern prestressing steel behaviour is then compared to its historical prestressing steel counterparts, showing significant differences at high temperature. Attention then turns to other structural actions of a real PT concrete structure (e.g. thermal bowing, restraint, concrete stiffness loss, continuity, spalling, slab splitting etc.) all of which also play inter-related roles influencing a PT slab’s response in fire. A series of three non-standard structural fire experiments on heavily instrumented, continuous, restrained PT concrete slabs under representative sustained service loads were conducted in an effort to better understand the response of PT concrete structures to localised heating. To the author’s knowledge this is the first time a continuous PT slab which includes axial, vertical and rotational restraint has been studied at high temperature, particularly under localised heating. The structural response of all three tests indicates a complex deflection trend in heating and in cooling which differs considerably from the response of a simply supported slab in a standard fire test. Deflection trends in the continuous slab tests were due to a combination of thermal expansion and plastic damage. The test data will enable future efforts to validate computational models which account for the requisite complexities. Overall, the research presented herein shows that some of the design guidance for modern PT concrete slabs is inadequate and should be updated. The high temperature deformation of prestressing steel under localised heating, as would be expected in a real fire, should be considered, since uniform heating of simplysupported elements is both unrealistic and unconservative with respect to tensile rupture of prestressing steel tendons. The most obvious impact of this finding would be to increase the minimum concrete covers required for unbonded PT construction, and to require adequate amounts of bonded steel reinforcement to allow load shedding to the bonded steel at high temperature in the event that the prestressing steel fails or is severely damaged by fire.

Unbonded post-tensioned concrete slabs have been widely used in Canada and the United States since the 1960s, as they allow increased span-to-depth ratios and excellent control of deflections compared to non-prestressed reinforced concrete flexural members. The satisfactory fire performance of unbonded post-tensioned concrete slabs in North America was established by a series of standard fire tests performed in the United States during the 1960s. However, there is a paucity of data on the effect of elevated temperatures on cold-drawn prestressing steel, both in terms of post-fire residual mechanical properties and high-temperature stress relaxation, which can lead to significant prestress loss both during and after a fire. A detailed and comprehensive literature review is presented that provides background on the residual mechanical properties of prestressing steel, as well as on the creep-relaxation behaviour experienced at elevated temperatures under stress. The results of two test series are discussed; the first examining the effects of elevated temperatures on the residual mechanical properties of prestressing steel exposed to elevated temperatures. The second test series examines the irrecoverable and significant loss of prestress force that results from steel relaxation and other thermal effects experienced during heating. A preliminary analytical model is presented, capable of predicting the change in prestress force experienced by a stressed strand under transient heating. The model is then compared with experimental elevated temperature relaxation data. Finally, the analytical model developed and residual mechanical properties obtained through experimentation are used along with a pre-existing finite difference heat transfer model (developed for concrete slabs) to examine the effect of elevated temperature exposure on the residual flexural capacity of a typical unbonded post-tensioned example slab. Several parameters, such as heated length and concrete cover, are examined using the example structure. From this it was observed that, after one hour of exposure to a standard fire (ASTM E119), significant losses in effective prestress and moment capacity occurred even with the appropriate amount of concrete cover. This is a finding which is of the utmost practical importance to engineers engaged in the evaluation of fire damaged unbonded post-tensioned structures. / Thesis (Master, Civil Engineering) -- Queen's University, 2007-12-18 17:15:17.521 / Natural Sciences and Engineering Research Council of Canada, and the Department of Civil Engineering at Queen’s University

abstract: Most engineers may agree that an optimum design of a particular structure is a proposal that minimizes costs without compromising resistance, serviceability and aesthetics. Additionally to these conditions, the theory and application of the method that produces such an efficient design must be easy and fast to apply at the structural engineering offices. A considerable amount of studies have been conducted for the past four decades. Most researchers have used constraints and tried to minimize the cost of the structure by reducing the weight of it [8]. Although this approach may be true for steel structures, it is not accurate for composite structures such as reinforced and prestressed concrete. Maximizing the amount of reinforcing steel to minimize the weight of the overall structure can produce an increase of the cost if the price of steel is too high compared to concrete [8]. A better approach is to reduce the total cost of the structure instead of weight. However, some structures such as Prestressed Concrete AASHTO Girders have been standardized with the purpose of simplifying production, design and construction. Optimizing a bridge girder requires good judgment at an early stage of the design and some studies have provided guides for preliminary design that will generate a final economical solution [17] [18]. Therefore, no calculations or optimization procedure is required to select the appropriate Standard AASHTO Girder. This simplifies the optimization problem of a bridge girder to reducing the amount of prestressing and mild steel only. This study will address the problem of optimizing the prestressing force of a PC AASHTO girder by using linear programming and feasibility domain of working stresses. A computer program will be presented to apply the optimization technique effectively. / Dissertation/Thesis / Masters Thesis Civil Engineering 2016

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