Understanding Engineering Shear Strain: Formulas, Graphs, and Errors Explained

In summary, the conversation discusses the "Engineering Shear Strain" formulas and graphs from a specific website. The person is questioning the validity of the graph on the right, which shows the total shear strain by adding the deformations along the x and y axes. They are unsure how adding these two components is valid and are looking for clarification and references. One person suggests that this is similar to summing angular velocity components in mechanics and explains that the shear strain along a direction is a scalar, so it can be added. They also mention that the graph on the right is just a rotated version of the one on the left, showing that the shear strain remains the same.
  • #1
Bempel
Hello,

I have problems with the "Engineering Shear Strain" formulas from the following website :

http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/strain.cfm

I agree with the formulas and the graph on the left, but I don't with it on the right. On the left graph du/dy and dv/dx are separated. On the right graph (total shear strain) dv/dx and du/dy are put together on the x-axis. One can't simply add the deformation u along the y-axis to the deformation v along the x-axis. One can't change d(something)/dx by d(something)/dy or say its the same. Could anyone give me some explanation on this?

Note that there are some errors on the graphs with x's and y's exchanged.

Could anyone please help me on this? I am working on the subject and I want to understand. If you know some references of literature would be appreciated to

Best regards

Stephane
 
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  • #2
Well I agree that adding "strains" along different directions might not sound so physical, nevertheless I do not see why it is ok for you adding up du/dy and dv/dx in the graph on the left (to define the strain tensor components) while it is not ok to add them on the one on the right (to define total strain).

The only difference in the two graphs is a rotation of axis.

Remember here we are simply talking geometry, there is no dynamical concepts involved, we are simply describing how a certain distribution of points in space has changed; no forces!

Here we are simply adding infinitesimal "angles" of rotation pretty much as we do when we sum different component of angular velocity in mechanics.

I used "angles" because I am not sure how exactly angles and strains are related to each other...

I will bve happy to work it out together if you like...

Dario
 
  • #3
please read it through,it will help:

both dv/dx and du/dy are along the same direcdtion viz the z-direction.in other words,what we are doing is measuring how much the body's vertex angles have changed from initial 90 degrees.in many books i have seen a subscript 'z' instead of 'xy' with the shear strain which makes things clear.(the angles in a plane in any prob whatsoever are measued from an axis perpendicular to the plane.)

the shear strain along a direction (here z-direction)is a SCALAR because it is a componenet of a tensor(dont get bogged down by terms,this is true for more familiar vecors also,for example the horizontal componenet of velocity is scalar) .So we can add them up.

may be you have noticed it that on the right hand side the figure has just been rotated and you see that the shear starin suffered by the particle remains same.this provides proof for the shear strain along a direction being a scalar because scalars are invariant under transformation of axes.

cheers :smile:
bye
 

1. What is shear strain in engineering?

Shear strain in engineering refers to the measure of deformation or distortion in a material caused by an applied force that is parallel to the surface of the material. It is a measure of how much a material has been sheared or pushed sideways.

2. What are the common formulas used to calculate shear strain?

The most commonly used formula for calculating shear strain is the engineering shear strain formula, which is defined as the change in angle between two originally perpendicular line segments in a material. Another formula that is frequently used is the shear strain ratio formula, which is the ratio of shear strain to normal strain.

3. How are shear strain graphs used in engineering?

Shear strain graphs are used in engineering to visualize the relationship between shear strain and shear stress. These graphs often show a linear relationship, with shear strain on the x-axis and shear stress on the y-axis. They can also be used to determine the shear modulus, which is a measure of a material's resistance to shear stress.

4. What are some common errors associated with measuring shear strain?

One common error in measuring shear strain is the misalignment of the measuring device, which can result in inaccurate readings. Another error is the presence of external forces, such as friction or bending, which can affect the accuracy of the measurement. Furthermore, errors can also occur due to the material's properties, such as anisotropy or nonlinearity.

5. How can understanding shear strain be beneficial in engineering?

Understanding shear strain is crucial in engineering as it allows engineers to predict how materials will behave under shear stress and design structures that can withstand these forces. It also helps in identifying potential failures and determining the most suitable materials for a particular application. Additionally, understanding shear strain can aid in the development of innovative and efficient engineering solutions.

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