Stress and Deformation Analysis

Stress and Deformation Analysis - Stress and Deformation...

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1 Stress and Deformation Analysis Material in this lecture was taken from chapter 3 of Mot , Machine Elements in Mechanical Design, 2003 Representing Stresses on a Stress Element ± One main goals of stress analysis is to determine the point within a load-carrying member that is subjected to the highest stress level. ± The orientation of the stress element is critical, and it must be aligned with specified axes on the member, usually called x, y, and z. Representing Stresses on a Stress Element con’t ± Tensile and compressive stresses, called normal stresses, act perpendicular to the opposite faces of the stress element. ± Tensile stresses pull on the element. ± Compressive stresses crush the element.
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2 Stress Elements for 3 Types of Stresses Mot , Machine Elements in Mechanical Design, 2003 Representing Stresses on a Stress Element con’t ± Shear stresses are created by direct shear, vertical shear in beams, or torsion. ± There is a tendency to cut the element by exerting a stress downward on one face while simultaneously exerting a stress upward on the opposite, parallel face. Sign Convention for Shear Stresses ± Positive shear stresses rotate the element in a clockwise direction. ± Negative shear stresses rotate the element in a counterclockwise direction. ± A double subscript notation is used to denote shear stresses in a plane. For example, drawn for the y-z plane, the pair of shear stresses, τ yz , indicates a shear stress acting on the element face that is perpendicular to the y-axis and parallel to the z-axis. ± So, τ yx acts on the face that is perpendicular to the y- axis and parallel to the x-axis. In this example, τ yz is positive and τ yx is negative.
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3 Direct Stresses: Tension and Compression ± Stress = the internal resistance offered by a unit area of a material to an externally applied load. Normal stresses ( σ ) can be tensile (positive) or compressive (negative). ± The magnitude of the stress can be calculated from the direct stress formula: ± σ = force / area = F/A ± (US Units) lb / in 2 = psi ; (SI Units) N / m 2 = pascal = Pa Mot , Machine Elements in Mechanical Design, 2003 Direct Stresses: Tension and Compression con’t ± The conditions on the use of the previous equation are as follows: 1. The load-carrying member must be straight 2. The line of action of the load must pass through the centroid of the cross-section of the member
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Stress and Deformation Analysis - Stress and Deformation...

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