Can Mohr's Circle be Constructed with Only xx and yy Strain Values?

In summary, the conversation discusses using a strain rosette with two gauges at 0 and 90 degrees to find strain on a beam under force and plotting Mohr's circle. The xx and yy strain values are easily found, but the question is how to find the xy strain value needed to plot the circle. The conversation also mentions the relationship between the orientation of the gauges and the principal axes of strain, as well as the kinematics of bending. The conclusion is that the gauges are aligned with the principal directions and the readings on the gauges represent the principal strains.
  • #1
GBA13
73
0

Homework Statement


I have used a strain rosette with two gauges at 0 and 90 degrees to find strain on a beam under force and an trying to plot Mohr's circle for the problem. As the gauges are at right angles finding the xx and yy strain is easy but I am lost about how to find the xy strain, which I need to plot the circle. How can I find xy from the xx and yy strain values?

Homework Equations

The Attempt at a Solution



I have got xx and yy but I honestly have no idea how to find xy[/B]
 
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  • #2
How does the orientation of these gages relate to the principal axes of strain for this particular deformation? Do you know?

Chet
 
  • #3
Chestermiller said:
How does the orientation of these gages relate to the principal axes of strain for this particular deformation? Do you know?

Chet

Hi Chet, I'm not sure how to tell to be honest! All I know is that the gauges are put on a long beam, one parallel to the edge of the beam and the other perpendicular and then the beam was forced downwards on the unsupported end.

I'm also told to think of it has a simple, uniaxial stress in x direction if that makes any difference.
 
  • #4
Your gages are aligned with the principal directions. If you understand the kinematics of bending, then you will know why.

Chet
 
  • #5
Oh OK. Does that mean that the readings on the gauges are the principle strains?
 
  • #6
GBA13 said:
Oh OK. Does that mean that the readings on the gauges are the principle strains?
Sure..
 

Related to Can Mohr's Circle be Constructed with Only xx and yy Strain Values?

1. What is a strain rosette and how is it used in testing?

A strain rosette is a specialized instrument used to measure strains, or changes in shape or size, in a material. It consists of three or more strain gauges arranged at different angles, and is typically attached to a material being tested. By measuring the changes in electrical resistance of the strain gauges, the strain rosette can provide precise information about the strains at different angles, allowing for the calculation of material properties such as stress and strain.

2. What is Mohr's circle and how is it related to strain rosette?

Mohr's circle is a graphical representation of stress and strain relationships in a material. It is often used in conjunction with strain rosettes, as the information from the strain rosette can be plotted on Mohr's circle to determine the principal stresses and strains at a specific point in a material.

3. How is strain rosette data analyzed?

The data from a strain rosette is analyzed using mathematical equations, typically involving trigonometry and linear algebra. The strain measurements from the rosette are used to calculate the principal strains and stresses, as well as other material properties such as Poisson's ratio and Young's modulus.

4. What are the advantages of using a strain rosette over other strain measurement techniques?

One of the main advantages of using a strain rosette is its ability to measure strains in multiple directions. This allows for a more comprehensive analysis of a material's behavior under stress, as well as providing more accurate data for calculating material properties. Strain rosettes are also non-invasive, making them suitable for use in various testing environments.

5. Are there any limitations to using strain rosettes?

One limitation of strain rosettes is their sensitivity to temperature changes. As strain gauges are affected by temperature, they must be carefully calibrated and temperature compensation must be taken into account during analysis. Additionally, strain rosettes are typically only used for static measurements and may not be suitable for dynamic testing. They also require careful placement and attachment to the material being tested, which can be time-consuming and may introduce errors if not done properly.

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