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The primary objective of this investigation was to study the behavior of reinforced concrete beams subjected to combined loading with particular regard to their behavior at failure. The experimental phase of this investigation consisted of testing 34 reinforced concrete beams. Twenty two beams were subjected to various combinations of bending and torsion and twelve were subjected to various combinations of bending, torsion and shear. All beams had a nominal cross section of 6" x 12" and a nominal concrete strength of 5000 psi. Both longitudinal and transverse reinforcement in various combinations was provided in all beams. The testing equipment that was designed and fabricated for this investigation permitted independent application of the twisting and transverse loads. The ratio between the twisting moment and the bending moment could be changed at any time during a test. All beams were tested to failure by applying the load in a series of increments. Each increment consisted of increasing to a predetermined level the transverse load or the twisting load or both, depending on the type of test. In the cases where both types of load were applied in the same increment, the transverse load was applied first. Twenty nine beams were subjected to loads such that for any one test the ratio of twisting moment to bending moment at the end of each increment was a constant. For the other five beams this ratio was different at the end of each increment and four of these beams were subjected to various sequences of load. Based on the observations made in the experimental phase of this investigation three idealized failure surfaces have been presented, two of which were first suggested by Lessig. Equations for the ultimate torsional strength of a beam based on each of the three failure surfaces have been developed and their method of solution has been presented. These equations have also been simplified and an interaction diagram consisting of three straight lines has been presented along with the applicable equations. The correlation between the experimental results of 109 beams and the theoretical results obtained from both the simplified analysis and the more comprehensive analysis has been given. Of these beams, 34 are the beams tested in this investigation and 75 are beams that have been tested by other investigators. The observations and test results indicate that reinforced concrete beams that are subjected to bending, torsion and moderate amounts of transverse shear can fail by three different modes. These modes of failure are characterized by the formation of a hinge adjacent to one face of the beam and yielding of the reinforcement adjacent to the face opposite to the hinge. The modes of failure predicted by the analysis agree with the observed modes of failure.
Ultra High Performance Concrete (UHPC) is characterized by a very high compressive strength which may reach more than 200 MPa. The behavior of this material under tension and compression actions has been established to be very brittle in nature. Discontinuous fibers (normally steel fibers) are usually added to the UHPC mix to introduce ductility. In order to investigate the beneficial effects of using fiber reinforced UHPC in structural members subjected to torsion, a series of experimental tests on 17 UHPC beams subjected to pure torsion were carried out. The test beams consisted of plain UHPC beams, UHPC beams reinforced with steel fibers only, UHPC reinforced with steel fibers and different combinations of traditional longitudinal and transverse reinforcement. The plain UHPC beams showed very brittle behavior, whereas the UHPC beams with steel fibers only showed a post cracking ductile behavior. The addition of little steel fiber volume (e.g. 0.5 %) to the plain UHPC beams enhanced the ductility. The enhancement at the ultimate capacity amounts to about 20 %. Meanwhile, the steel fibers with 0.9 % by volume showed much enhanced ductility and a maximum enhancement of the torsional carrying capacity up to 32 %. The addition of moderate steel fiber volume (e.g. 0.9 %) to one type of traditional reinforcement (either longitudinal or transverse) accomplished an effective post cracking torsional carrying mechanism. The steel fibers shows a tendency to replace the missing type of traditional reinforcement, however this should be confirmed by more tests and by using higher steel fiber volumes. A series of experimental tests on fiber reinforced UHPC prisms to investigate the post cracking shear strength and stiffness of the used UHPC mix (e.g. M3Q) was conducted. The results of these tests revealed that this fine grained UHPC mix has a weak post cracking shear behavior. The results of these tests were used later in the Finite Element (F.E) model. An analytical model based on the well known thin-walled tube analogy was developed in order to estimate the torsional carrying capacity of beams under pure torsion having different combinations of steel fibers and traditional reinforcement. The comparison between the test and model results showed very good agreement for all cases. A finite element model based on calibrated small scale tests was developed using ATENA F.E. package to predict the full load-deformation behavior of the test beams. The predictions of the model show very good agreement with the test results.
Sets out basic theory for the behavior of reinforced concrete structural elements and structures in considerable depth. Emphasizes behavior at the ultimate load, and, in particular, aspects of the seismic design of reinforced concrete structures. Based on American practice, but also examines European practice.
In recent years both free-standing and geometric staircases have become quite popular. Many variations exist, such as spiral, helical, and elliptical staircases, and combinations of these. A number of researchers have come forward with different concepts in the fields of analytical and numerical design and of experimental methods and assessments. The aim of this book is to cover all these methods and to present them with greater simplicity to practising engineers. Staircases is divided into five chapters: Specifications and basic data on staircases; Structural analysis of staircases – Classical methods; Structural analysis of staircases – Modern methods; Staircases and their analysis – A comparative study; Design analysis and structural detailing. Charts and graphs are included and numerous design examples are given of freestanding and other geometric staircases and of their elements and components. These examples are related to the case studies which were based on staircases that have already been constructed. All examples are checked using various Eurocodes. The book includes bibliographical references and is supported by two appendices, which will be of particular interest to those practising engineers who wish to make a comparative study of the different practices and code requirements used by various countries; detailed drawings are included from the USA, Britain, Europe and Asia. Staircases will serve as a useful text for teachers preparing design syllabi for undergraduate and post graduate courses. Each major section contains a full explanation which allows the book to be used by students and practising engineers, particularly those facing the formidable task of having to design/ detail complicated staircases with unusual boundary conditions. Contractors will also find this book useful in the preparation of construction drawings and manufacturers will be interested in the guidance given.
This book comprises the proceedings of the Annual Conference of the Canadian Society of Civil Engineering 2021. The contents of this volume focus on specialty conferences in construction, environmental, hydrotechnical, materials, structures, transportation engineering, etc. This volume will prove a valuable resource for those in academia and industry.