Chap8 (1) - M. Vable Mechanics of Materials: Chapter 8...

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M. Vable Mechanics of Materials: Chapter 8 8-1 Printed from: http://www.me.mtu.edu/~mavable/MoM2nd.htm Stress Transformation Transforming stress components from one coordinate system to another at a given point . Relating stresses on different planes that pass through a point . Learning Objectives Learn the equations and procedures of relating stresses (on different planes) in different coordinate system at a point. Develop the ability to visualize planes passing through a point on which stresses are given or are being found, particularly the planes of maximum normal stress and maximum shear stress. σ xx σ xx T T τ x θ τ θ x P P Aluminum Cast Iron
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M. Vable Mechanics of Materials: Chapter 8 8-2 Printed from: http://www.me.mtu.edu/~mavable/MoM2nd.htm Wedge Method The fixed reference coordinate system in which the entire problem is described is called the global coordinate system . A coordinate system that can be fixed at any point on the body and has an orientation that is defined with respect to the global coordinate sys- tem is called the local coordinate system . Plane stress problem: We will consider only those inclined planes that can be obtained by rotation about the z-axis. Horizontal plane Outward normal to inclined plane Inclined plane Vertical plane x x n ± ± ± n t t y y z z
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M. Vable Mechanics of Materials: Chapter 8 8-3 Printed from: http://www.me.mtu.edu/~mavable/MoM2nd.htm C8.1 In the following problems one could say that the normal stress on the incline AA is in tension, compression or can’t be determined by inspection. Similarly we could say that the shear stress on the incline AA is positive, negative or can’t be determined by inspection. Choose the correct answers for normal and shear stress on the incline AA by inspec- tion. Assume coordinate z is perpendicular to this page and towards you. Class Problem 1 A A σ 30 0 τ A A 60 0 (b) (a) x x y y A A τ 30 0 (c) (d) x y
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M. Vable Mechanics of Materials: Chapter 8 8-4 Printed from: http://www.me.mtu.edu/~mavable/MoM2nd.htm General Procedure for Wedge Method Step 1: A stress cube with the plane on which stresses are to be found, or are given, is constructed. Step 2: A wedge made from the following three planes is constructed: a vertical plane that has an outward normal in the x-direction, a horizontal plane that has an outward normal in the y-direction, and the specified inclined plane on which we either seek stresses or the stresses are given. Establish a local n-t-z coordinate system using the outward normal of the inclined plane as the n-direction. All the known and the unknown stresses are shown on the wedge. The diagram so constructed will be called a stress wedge.
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This note was uploaded on 04/20/2010 for the course E M 319 taught by Professor Rodin during the Spring '07 term at University of Texas.

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Chap8 (1) - M. Vable Mechanics of Materials: Chapter 8...

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