Academic literature on the topic 'Strains and stresses – Analysis'

Thesis (Ph. D.)--West Virginia University, 1998.<br>Title from document title page. Document formatted into pages; contains x, 107 p. : ill. (some col.) Includes abstract. Includes bibliographical references (p. 104-107).

Bone is a composite material consisting of hydroxyapatite crystals deposited in an oriented manner on a collagen backbone. The arrangement of the mineral and organic phases provides bone tissue with the appropriate strength, stiffness, and fracture resistance properties required to protect vital internal organs and maintain the shape of the body. A remarkable feature of bone is the ability to alter its properties and geometry in response to changes in the mechanical environment. However, in cases of metabolic bone diseases or aging, bone can no longer successfully adapt to its environment, increasing its fragility. To elucidate the mechanisms of bone microdamage, this research project developed a specimen-specific approach that integrated 3D imaging, histological damage labeling, image registration, and image-based finite element analysis to correlate microdamage events with microstructural stresses and strains under compressive loading conditions. By applying this novel method to different ages of bovine and human bone, we have shown that the local mechanical environment at microdamage initiation is altered with age. We have also shown that formation of microdamage is time-dependent and may have implications in age-related microdamage progression with cyclic and/or sustained static loading. The work presented in this dissertation is significant because it improved our understanding of trabecular bone microdamage initiation and unlocked exciting future research directions that may contribute to the development of therapies for fragility diseases such as osteoporosis.

The displacements and stresses in layered rock above underground openings can be calculated using a beam model for the rock layers. The traditional approach assumes that interfaces between layers are frictionless and layers can slip past one another freely as they deflect. In contrast, the design of structural laminated beams has traditionally been based on the assumption that the interfaces between layers were welded, with no slip occurring there. In this work, the theory of composite laminated beams, which allows for partial slip on layer interfaces, is applied to the problem of predicting displacements and stresses in layered roof rock. The effects of rockbolt reinforcement are modeled by discrete shear and normal stiffnesses incorporated at locations in the model where the rockbolts cross layer interfaces. Published solutions and results for laminated composite beams are reviewed. Composite laminated beam theory provided a means of accounting for rockbolt reinforcement effects and provided a conceptual framework that was used to develop two FORTRAN programs; one, based on the force method of analysis, that automatically finds shear and tensile interface failures in the system, and the other a finite element program that employs beam elements, elastic interface elements, and rockbolt elements to model a rockbolted layered rock system. Published data together with results from these programs suggest that shear reinforcement may be more effective when placed near the ends of roof layers. The normal interaction between layers tends to be uniformly distributed unless rockbolt forces act on the layers or if partial delamination of layers has occurred. Both shear and normal reinforcement will cause stresses to be redistributed within the system of layers. Analysis of this redistribution of stresses requires that the sequence of interface failure be predicted which, in turn, requires that the properties of the individual layers, of the interfaces between layers, and of the rockbolts be properly taken into account. Laminated composite beam theory and programs based on this theory provide rational and efficient ways to study and analyze the behavior of layered roof rock.

Analysis and design of connections, such as beam-to-column connections, pose various complexities such as nonlinear behavior of material and geometric condition, irregularities in geometry and boundary condition. The main purpose of these types of connections is to provide adequate structural strength and a sufficiently stiff structure at working loads, and to possess sufficient ductility and strength at overloads such as may occur during a major earthquake. At present the design profession does not have established guidelines for estimating the ultimate moment and shear capacity of these connections. The assumption of linear elastic material behavior of the connections is no longer valid when the elements are stressed beyond the yield stress of the material. For such problems encountered in the design of typical structures, either the closed-form analytical solutions are extremely complex or cannot be obtained at all. Thus, numerical techniques such as finite difference, finite element and boundary integral methods are used. In this study, a finite element program is developed for plastic analysis of connections such as beam-to-column connection using a constitutive law of the material, a three parameter stress-strain relationship, which gives stress explicitly in terms of strain. One hundred and fifteen cases of beam-to-column connections subjected to moment are analysed with the finite element program developed in this study, and the results are compared with the existing approximate solution by yield line theory to propose a simple formula to correlate actual ultimate capacity to the approximate solution.

Prestressing a steel girder reduces the required structural steel weight, limits tension stresses in the section, increases the ultimate strength, and increases the fatigue resistance. The technique of prestressing with tendons can be used for strengthening of existing bridges as well as for construction of new bridges. This thesis presents an analytical study of the behavior of simply-supported and continuous prestressed composite girders and describes the benefits of prestressing steel in composite construction. Analytical models are developed and used as a basis for a computer program that calculates the stresses and displacements in the cables and the girder at discrete number of nodes along the length of the girder. The effects of design variables such as prestress force, tendon profile, eccentricity and tendon length are studied. The results indicate that prestressing is an effective means of increasing the load carrying capacity of simple-span as well as continuous composite girders.