Understanding Deformation and Strain in Engineering
Deformation occurs when a force is applied to a body, causing changes in its shape and size. Normal strain refers to the elongation or contraction of a line segment per unit length, while shear strain is the change in angle between two originally perpendicular line segments. Cartesian strain components show how normal strains affect volume and shear strains affect shape. Small strain analysis is used in engineering design for nearly infinitesimal deformations.
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Presentation Transcript
Chapter 2 Strain
Deformation Whenever a force is applied to a body, it will undergo deformation (change the body's shape and size) The deformation can be highly visible, but is often unnoticeable Generally, the deformation of a body will not be uniform throughout its volume so the change in geometry of any line segment within the body may vary along its length To study deformational changes in a more uniform manner, lines will be considered that are very short and located in the vicinity of a point
Normal Strain The elongation or contraction of a line segment per unit of length is referred to as normal strain ( ) s s' = The average normal strain The normal strain at point A in the direction of n Approximate final length of a short line segment in the direction of n Normal strain is a dimensionless quantity (but often still use units representing the ratio of length, mm/mm or in/in) avg s lim s' s = B along A n s + (1 s s' )
Shear Strain The change in angle that occurs between two line segments that were originally perpendicular to one another is referred to as shear strain ??=? 2 ? The shear strain at point A that is associated with n and t axes If ' is smaller than /2 the shear strain is positive, if ' is larger than /2 the shear strain is negative Shear strain is measured in radians (rad)
Cartesian Strain Components Normal strains cause a change in volume of the element, whereas the shear strains cause a change in its shape
Small Strain Analysis Most engineering design involves applications for which only small deformations are allowed It is assumed in this text that deformations occurring within a body are almost infinitesimal, so that normal strains are very small compared to 1 ( <<1, referred to as small strain analysis) If is very small, can approximate (in radians) sin = , tan = , cos = 1 Problems pg 78
