tailieunhanh - Ebook Mechanics of materials (8th edition): Part 2

(BQ) Containing Hibbeler’s hallmark student-oriented features, this text is in four-color with a photorealistic art program designed to help students visualize difficult concepts. A clear, concise writing style and more examples than any other text further contribute to students’ ability to master the material. | Stress Transformation CHAPTER OBJECTIVES In this chapter we will show how to transform the stress components that are associated with a particular coordinate system into compone nts associated with a coordinate system having a different orientation Once the necessary transformation equations are established we will then be- able to obtain the maximum normal and maximum shear stress at a point and find the orientation of elements upon which they act. Plane-stress transformation will be discussed in the first part of the chapter since this condition IS most common in engineering practice At the end of the chapter we will discuss a method for finding the absolute maximum shear stress at a point when the matenal is subjected to both plane and three-dimensional states of stress. Plane-Stress Transformation It was shown in See I 3 that the general state of stress at a point IS characterized by . independent normal and shear stress components which act on the faces of an element of material located .Il the point. Fig. 9-1 . This state of stress however is not often encountered in engineering practice Instead engineers frequently make approximations or simplifications of the loadings on a body in order that the stress produced in a structural member or mechanical clement can be analyzed in a single plane. When I his is the case the material is said to be subjected Io planesưexx. Fig. 9-1 h. For example if there IS no load on the surface of a body then the normal and shear stress components will be zero on the face of an element that lies on this surface. Consequently the corresponding stress components on the opposite face will also be zero and so the material at the point will be subjected to plane stress This case occurred throughout the previous chapter 438 Chapim 9 Sirfss Tpansfchvaiion Plane MTCS h ÍÌR. 9-1 b Fig. 9-2 The general stale at plane stress .11 a point is therefore represented by a combination of two normal-stress Components ƠJ. at. and one .