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# Notes422 - Mech 422 Stress and Strain Analysis D.L...

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Mech 422 - Stress and Strain Analysis D.L. DuQuesnay (adapted from original text by R.J. Ferguson) σ yy xy zy yx xx zx yz xz zz x y z R 1 R 2 September 2002

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1 Chapter 1 Introduction 1. What is Stress Analysis? The aim of stress analysis is to take the geometry of a component or structure and the externally applied “loads” and determine the state of stress in the material. Subjects that encompass stress analysis include “strength of materials”, “solid mechanics”, mechanics of deformable solids” , etc. When the stresses in the body are known, the material properties are used in a failure theory to decide whether the body can withstand the design loads. If this is the case, then further analysis may be undertaken to determine the service life of the structure. In general, these analyses are accomplished by computation with a calculator or a computer. However, stress analysis may also be performed experimentally. Since the computer has invaded the design office, the importance of experimental stress analysis has waned in recent times. It is now mainly used in the determination of loads and stresses for in-service components or systems. The following definitions are important: Stress analysis : used to find the stresses in a loaded body. Exact solution : is one that satisfies the conditions of equilibrium, compatibility and meets the boundary conditions of the body and its loads. There are comparatively few exact solutions in stress analysis. Closed-form solution : involves mathematical relationships that can be manipulated by the ordinary operations of algebra and calculus to determine the stresses. Many closed-form solutions involve simplifying assumptions that may make the results invalid for some situations or for portions of a loaded body. Numerical solution : uses algorithms for equations that cannot be solved easily (or at all) by conventional algebraic means. Finite element method : is a computer-based method wherein the body is divided into discrete elements and equations solved on an element-by-element basis. Failure theories : are used with the state of stress, the geometry of the body and candidate materials to determine the potential for failure within the desired service life. Apart from comparing the stresses to the strength of the material, such theories consider fracture, impact, fatigue, creep, etc. 2. Computer Programs A multitude of computer programs exist for general purpose computation, stress analysis, and for solving specific problems. In this course, the basic principles of stress analysis
2 will be introduced and illustrated with some worked examples. The method of solution may include computer software to assist with computation. However, the emphasis is on the development of the analytical models and analogues, the assumptions and the limitations, and the stress analysis solutions for some typical structural systems that may be encountered in the field.

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Notes422 - Mech 422 Stress and Strain Analysis D.L...

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