Displacements of a body in Equilibrium

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    Body Equilibrium
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Discussion Overview

The discussion revolves around understanding the physical reasoning behind why displacements of a body in equilibrium are functions of spatial coordinates (x, y). Participants explore the implications of varying displacements in the context of deformation and stress analysis.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions why displacements are functions of x and y, seeking a physical rather than mathematical explanation.
  • Another participant explains that displacements vary at different points in an object, necessitating a mapping of displacement as a function of location.
  • A participant further inquires about the reasons for the variation in displacements from point to point.
  • It is noted that if displacements were uniform across the object, it would indicate translation rather than deformation, which involves changes in size and shape at different locations.
  • An example is provided where bending a wire results in different deflections along its length, illustrating the concept of varying displacements.
  • A participant suggests that displacements at any point in the material are cumulative, incorporating the displacements of previous points as one moves away from a reference point.
  • Another participant distinguishes between displacement and strain, indicating that strain is assessed locally while bending energy is distributed throughout the material.

Areas of Agreement / Disagreement

Participants express varying viewpoints on the nature of displacements and their implications for deformation, with no consensus reached on a singular explanation for the variation in displacements.

Contextual Notes

Some assumptions about the material properties and the nature of deformation are not explicitly stated, which may influence the understanding of the discussion.

koolraj09
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Hi everyone.
While analyzing for stresses and strains for a body in equilibrium we consider the displacements u(x,y);v(x,y). Why are these displacements functions of x,y? I've got to understand it physically not mathematically.
Thanks in Advance.
 
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The displacements aren't typically the same at every point, so we have the challenge of how displacement varies as we move about the object. One way to keep everything straight is to map or tabulate the displacement as a function of the location (x,y) of the original point. Thus, u and v are functions of x and y. Does this answer your question?
 
Hi Mapes. I wanted to know that why the displacements not the same at every point? I mean why they vary from point to point?
 
If the displacements were the same at every point, the object would be moving (specifically, translating) and not deforming. Deformation means that some part of the object is changing size and/or shape, and this implies that deformation is different in different locations.
 
If you bend a straight wire (clothes hanger thick) by pulling one end down with your hands. your deflection is not the same over the full length
 
Another way to look at it, at any point in the material, if you start at whatever point is "fixed" (or some reference), as you get farther away, that point's displacements has all of the displacements of the previous point built into it.
 
displacement is the amount of movement. Strain is looked at a local spot on the material. The best way to look at it is bending energy is distributed
 

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