StressStrain_06_Strain

StressStrain_06_Strain - Section 3.6 3.6 Strain If an...

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Section 3.6 Solid Mechanics Part I Kelly 74 3.6 Strain If an object is placed on a table and then the table is moved, each material particle moves in space. The particles are said to undergo a displacement . The particles have moved in space as a rigid body . The material remains unstressed. When a material is acted upon by a set of forces, it changes size and/or shape , it deforms . In this section, the kinematics of materials is studied, that is, a number of tools and techniques are developed to describe the deformation of a material. 3.6.1 Strain at a Point Material deformation can be described by imagining the material to be a collection of small line elements. As the material is deformed, the line elements stretch, or get shorter, and rotate in space relative to each other. This movement of line elements is encompassed in the idea of strain : the “strain at a point” is all the stretching, contracting and rotating of all line elements emanating from that point, with all the line elements together making up the continuous material, as illustrated in Fig. 3.6.1. Figure 3.6.1: a deforming material element; original state of line elements and their final position after straining It turns out that the strain at a point is completely characterised by the movement of any three mutually perpendicular line-segments . If it is known how these perpendicular line- segments are stretching, contracting and rotating, it will be possible to determine how any other line element at the point is behaving, by using a strain transformation rule (see later). This is analogous to the way the stress at a point is characterised by the stress acting on three perpendicular planes through a point, and the stress components on other planes can be obtained using the stress transformation formulae. before deformation after deformation
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Section 3.6 Solid Mechanics Part I Kelly 75 3.6.2 Two Dimensional Strain Consider the two-dimensional case: two perpendicular line-elements emanate from a point and the material that contains the point is deformed. Then two things (can) happen: (1) the line segments will change length and (2) the perpendicular angle between the line-segments changes . The change in length of line-elements is called normal strain and the change in angle between initially perpendicular line-segments is called shear strain . The strains are now defined as follows: Normal strain in direction x : (denoted by xx ε ) change in length (per unit length) of a line element originally lying in the x direction Normal strain in direction y : (denoted by yy ) change in length (per unit length) of a line element originally lying in the y direction Shear strain : (denoted by xy ) (half) the change in the original right angle between the two perpendicular line
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This note was uploaded on 01/20/2012 for the course ENGINEERIN 1 taught by Professor Staff during the Fall '11 term at Auckland.

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StressStrain_06_Strain - Section 3.6 3.6 Strain If an...

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