Understanding Shearing Strain: Explanation and Examples

In summary, the shearing strain is positive when the angle formed by two surfaces closest to the origin and oriented along positive y and x axes decreases. This means that when one face is sheared to the right and the other face is sheared to the left, the angle between them will increase.
  • #1
chetzread
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Homework Statement


In the notes , refer to the circled part . It 's stated that the shearing strain is positive when the angle formed by two surfaces oriented along positive y and x axes decreases ..

Homework Equations

The Attempt at a Solution


. As we can see from the figure( paralleogram ) , one of the angle increases , while another angle decreases , am i right ? Why the author said angle decreases ?
 
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  • #2
Here it is
 

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  • #3
is the notes wrong
?
 
  • #4
chetzread said:
...angle formed by two surfaces oriented along positive y and x axes decreases ..
I think that could be stated more clearly. Obviously there are two surfaces oriented along each axis. To match the description to the diagram, try rewording it to:

"...angle formed by two surfaces closest to the origin and oriented along positive y and x axes decreases .."
 
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  • #5
Tom.G said:
closest to the origin
what do you mean by it ? Can you explain further ?
 
  • #6
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  • #7
Tom.G said:
"...closest to the origin..."

closest to the origin of the graph as shown in the image of your post #2.
-or-
the two faces closest to and facing the X-Z and Y-Z planes.
https://www.physicsforums.com/attachments/img_20161015_102808-jpg.107454/
if the downwrads plane is sheared to the right , and the upper planes sheared to the left , then the angle formed by two surfaces closest to the origin and oriented along positive y and x axes will increase , right ?.
 
  • #8
Right!
 
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1. What is shearing strain?

Shearing strain is a measure of the deformation or distortion that occurs in a material when it is subjected to a force that is applied parallel to its surface. It is a type of strain that results in the material changing shape without changing its volume.

2. How is shearing strain calculated?

Shearing strain is calculated by dividing the amount of distortion or displacement that occurs in a material by its original length or size. It is often represented by the Greek letter gamma (γ) and has no units as it is a ratio of two lengths.

3. What are some examples of shearing strain?

Shearing strain can be observed in a variety of everyday situations, such as when cutting a piece of paper with scissors, sliding a book across a table, or twisting a piece of clay. It is also an important consideration in engineering and construction, where it can affect the stability and strength of structures.

4. How does shearing strain differ from other types of strain?

Shearing strain is different from other types of strain, such as tensile or compressive strain, in that it involves forces acting parallel to the surface of a material rather than perpendicular to it. This results in a different type of deformation and can lead to different properties and behaviors in materials.

5. Why is understanding shearing strain important?

Understanding shearing strain is important in various fields, including material science, engineering, and geology. It allows us to predict how materials will behave under different forces and can help us design more efficient and durable structures. It also plays a role in understanding natural phenomena, such as earthquakes and landslides.

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