CIV E 270 Lab #8 - University of Alberta Department of...

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University of Alberta Department of Civil and Environmental Engineering Civ E 270 Laboratory 8 Name: I.D.: Date: Mark: Lab Section: TRANSFORMATION OF STRESS – MOHR'S CIRCLE 8.0 INTRODUCTION This laboratory session treats the problem of transformation of stress at a point in a body. Only the case of plane stress is covered, that is, σ z = τ xz = τ yz = 0. (Refer to Fig. 7.1 in the textbook for nomenclature). This means that two faces of the general infinitesimal cubic element are free of stress. Section 8.1 of this write-up reviews the transformation equations and Section 8.2 introduces the Mohr's circle representation of these equations. Section 8.3 sets out the exercise to be performed by the student. The reference material in the text is Chapter 9. An engineer calculates the stresses at a point in a member subjected to tensile, compressive, torsional, or bending forces using principles developed in a course like Civ E 270. This is done in the most convenient way, that is, an element is chosen for investigation in a way that suits the analysis. For example, the stresses in a bar under axial tension are calculated on a face normal to the longitudinal axis of the member. However, such a calculation does not necessarily identify the conditions of maximum stress at the point. The maximum stress may occur on an element with a different orientation. Having made the initial calculations for stress, the engineer must have the "tools" that enable an examination of the stresses for elements at the same point, but which have other orientations. 8.1 TRANSFORMATION EQUATIONS Given: The state of stress is known at a certain location in a body (Fig. 8.1). These stresses have been obtained from an analysis of the structural member or element, starting with the forces acting on the member. The orientation of the element relative to the member is known and, as described above, is chosen in a way that is convenient for the analysis. Required: Establish the state of stress at the same point, but with the element rotated arbitrarily, as shown in Fig. 8.2. (A determination of the "critical" orientation will eventually be made.) In referring to the stresses on the faces of the original element, the subscripts x and y are used. For the stresses acting on the faces of the rotated element, the subscripts x' and y' are used.
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