Model to describe the mode I fracture of steel fiber reinforced ultra-high performance concrete

Ultra-high performance fiber reinforced concrete (UHPFRC) has arisen from the implementation of a variety of concrete engineering and materials science concepts developed over the last century. This material offers superior strength, serviceability, and durability over its conventional counterparts. One of the most important differences for UHPFRC over other concrete materials is its ability to resist fracture through the use of randomly dispersed discontinuous fibers and improvements to the fiber-matrix bond. Of particular interest is the materials ability to achieve higher loads after first crack, as well as its high fracture toughness. In this research, a study of the fracture behavior of UHPFRC with steel fibers was conducted to look at the effect of several parameters related to the fracture behavior and to develop a fracture model based on a non-linear curve fit of the data. To determine this, a series of three-point bending tests were performed on various single edge notched prisms (SENPs). Compression tests were also performed for quality assurance. Testing was conducted on specimens of different cross-sections, span/depth (S/D) ratios, curing regimes, ages, and fiber contents. By comparing the results from prisms of different sizes this study examines the weakening mechanism due to the size effect. Furthermore, by employing the concept of fracture energy it was possible to obtain a comparison of the fracture toughness and ductility. The model was determined based on a fit to P-w fracture curves, which was cross referenced for comparability to the results. Once obtained the model was then compared to the models proposed by the AFGC in the 2003 and to the ACI 544 model for conventional fiber reinforced concretes.

Looking at the effectiveness of an earth science unit designed using the Understanding by Design process

This report shares my efforts in developing a solid unit of instruction that has a clear focus on student outcomes. I have been a teacher for 20 years and have been writing and revising curricula for much of that time. However, most has been developed without the benefit of current research on how students learn and did not focus on what and how students are learning. My journey as a teacher has involved a lot of trial and error. My traditional method of teaching is to look at the benchmarks (now content expectations) to see what needs to be covered. My unit consists of having students read the appropriate sections in the textbook, complete work sheets, watch a video, and take some notes. I try to include at least one hands-on activity, one or more quizzes, and the traditional end-of-unit test consisting mostly of multiple choice questions I find in the textbook. I try to be engaging, make the lessons fun, and hope that at the end of the unit my students get whatever concepts I‘ve presented so that we can move on to the next topic. I want to increase students‘ understanding of science concepts and their ability to connect understanding to the real-world. However, sometimes I feel that my lessons are missing something. For a long time I have wanted to develop a unit of instruction that I know is an effective tool for the teaching and learning of science. In this report, I describe my efforts to reform my curricula using the “Understanding by Design” process. I want to see if this style of curriculum design will help me be a more effective teacher and if it will lead to an increase in student learning. My hypothesis is that this new (for me) approach to teaching will lead to increased understanding of science concepts among students because it is based on purposefully thinking about learning targets based on “big ideas” in science. For my reformed curricula I incorporate lessons from several outstanding programs I‘ve been involved with including EpiCenter (Purdue University), Incorporated Research Institutions for Seismology (IRIS), the Master of Science Program in Applied Science Education at Michigan Technological University, and the Michigan Association for Computer Users in Learning (MACUL). In this report, I present the methodology on how I developed a new unit of instruction based on the Understanding by Design process. I present several lessons and learning plans I‘ve developed for the unit that follow the 5E Learning Cycle as appendices at the end of this report. I also include the results of pilot testing of one of lessons. Although the lesson I pilot-tested was not as successful in increasing student learning outcomes as I had anticipated, the development process I followed was helpful in that it required me to focus on important concepts. Conducting the pilot test was also helpful to me because it led me to identify ways in which I could improve upon the lesson in the future.