The arrangement of the testing apparatus (three-point or four-point bend, distance between supports, etc.) also influences the calculation of the beam mechanics. There are several methods, including using an old solution, constraint-based design, topological synthesis, Freedom, Actuation, and Constraint Topologies (FACT), and Transmission Theory (a major contribution from my Master's thesis.) FACT is an intuitive and powerful. The I term is the moment of inertia about the neutral axis. General: A beam is a structural member whose length is large compared to its cross. Flexure concepts can be generated once the kinematics have been identified. The y term is the distance from the neutral axis (up is positive). For example, rectangular specimens are treated differently than cylindrical ones. This equation gives the bending normal stress, and is also commonly called the flexure formula. The mechanics that dictate bending tests rely heavily upon the geometry of the specimen. In the case of bones, the complex structure and small defects within the specimen serve to concentrate stresses locally, effectively causing localized weaknesses and lower flexural strength values. The flexural strength would be the same as thetensile strength if the material were homogeneous. Most materials fail under tensile stress before they fail under compressive stress, so the maximum tensile stress value that can be sustained before the specimen fails is its flexural strength. At the convex face of the specimen (point B), the stress will be at its maximum tensile value. At the edge of the concave face of the specimen (point A), the stress will be at its maximum compressive value. When a specimen is bent, it experiences a range of stresses across its depth. Flexure 1 through Flexure 4 (included at the end of the chapter) were developed using this condition. Three and four point bend tests are commonly used to determine the flexural strength of a specimen. The flexural strength represents the highest stress experienced within the material at its moment of rupture.
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