Help drawing Mohr's circle with rotated axis

In summary, the conversation discusses using Mohr's Circle to find stress values in an xy-plane, with given values for σx, σy, and τxy. The conversation also mentions the use of equations for R and center, and the attempt at finding points on the Mohr's Circle using a textbook. The conversation ends with the person solving the problem on their own.
  • #1
Blugga
22
0

Homework Statement



Plane stress in xy-plane. Use Mohr's Circle to find σx1 σy1 and τx1y1 if the XY axis is rotated counterclockwise θº

I want to do my HW problem myself so I'll just put some sample values. If i know how to get this one, i'll know how to do the HW problem(s).
(Units won't matter for this)

σx = -45
σy = -15
τxy = -20 which makes τyx = 20
θ = 100°

Homework Equations


τmax=R
R = √((σxy)/2)2xy2
center=σave= (σxy)/2


The Attempt at a Solution


center=σave= {[(-45)+(-15)]/2} = -30
R=25
Point A (-45,-20)
Point B (-15,20)
Using my book (Gere 8th), i was only able to get this far. Not sure if this is on the right track or not, but I'm stuck at this point. Don't know how to continue...
How can I get σx1 σy1 and τx1y1 from here?
33awgld.jpg
 
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  • #2
Problem Solved. I did it all by myself!
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1. What is Mohr's circle and how is it used in engineering?

Mohr's circle is a graphical representation of stress and strain in a material. It is commonly used in engineering to analyze and understand the behavior of materials under different loading conditions.

2. How do you draw a Mohr's circle with rotated axis?

To draw a Mohr's circle with rotated axis, you first need to determine the principal stresses and their directions. Then, using the equations for rotated stresses, you can calculate the new stresses at any desired angle. Finally, plot the new stresses on the circle with the corresponding angles.

3. What are the benefits of using a rotated axis in Mohr's circle?

Using a rotated axis in Mohr's circle allows for easier visualization and analysis of stresses at different angles. It also simplifies the calculations for stress transformations, making it a more efficient and accurate method for analyzing stress in materials.

4. Can Mohr's circle be used for both 2D and 3D stress analysis?

Yes, Mohr's circle can be used for both 2D and 3D stress analysis. In 2D analysis, it represents stresses on a plane, while in 3D analysis, it represents stresses on a point.

5. What are some practical applications of Mohr's circle in engineering?

Mohr's circle is commonly used in structural engineering to analyze the strength and stability of different structures, such as buildings and bridges. It is also used in geotechnical engineering to analyze soil and rock stability. Additionally, it is used in material science to study the behavior of various materials under different loading conditions.

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