Stress transform - Mohr's circle

In summary, for the beam and loading shown, the state of stress at point A can be found using the Cartesian coordinate system shown in the figure. Mohr's circle can then be used to determine the principal stress and principal plane, as well as the normal and shearing stresses acting on a plane oriented at 45°. The transformation from point A to point B follows the rotation of the plane at 45° clockwise, while the transformation to point D follows the rotation of the plane at 90° clockwise. Both points are acceptable solutions.
  • #1
yecko
Gold Member
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Homework Statement

For the beam and loading shown below,

(a) find the state of stress at point A in the Cartesian coordinate system indicated in the figure.

(b) use Mohr’s circle to determine (i) the principal stress and principal plane; (ii) the normal and shearing stresses acting on a plane oriented at 45 deg indicated in the figure.
upload_2018-5-15_18-8-53.png

Homework Equations


Solution:
upload_2018-5-15_18-9-4.png


The Attempt at a Solution


for part b, let me define the mohr's circle be like this:

upload_2018-5-15_18-9-35.png

Why not transform to point D but point B in the solution?
hMZ4jL4qGywdkFRhDxR80d5CMHh0d8l9DpejR09GzYahu3s5v5Abmj3swZ4O0fFzKBE1Md0EBdx9A&owa=outlook.office.jpg

hMZ4jL4qGywdkFRhDxR80d5CMHh0d8l9DpejR09GzYahu3s5v5Abmj3swZ4O0fFzKBE1Md0EBdx9A&owa=outlook.office.jpg

I think as the plane rotate 45 deg clockwise, so the point would follow point x then rotate 90 deg clockwise to point D i written.

So may I know if the answer is right for point B as the destination point, or should point D i written be right?
thanks.
 

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  • #2
Yes, your answer is correct. The point B in the solution follows from the transformation of the plane at 45° clockwise. The point D in the solution is the result of the transformation of the plane at 90° clockwise.
 

What is stress transform?

Stress transform, also known as Mohr's circle, is a graphical method used to determine the principal stresses and their orientation at a particular point in a material subjected to a complex state of stress.

Why is stress transform important?

Stress transform is important because it allows engineers and scientists to visualize and analyze complex stress states in materials. This information is crucial for designing structures and predicting their response to external forces.

How does stress transform work?

Stress transform works by plotting the normal and shear stresses on a circle, with the center of the circle representing the average stress. The radius of the circle represents the maximum stress, and the angle between the radius and the horizontal axis represents the orientation of the principal stress.

What is the difference between normal and shear stress?

Normal stress is a force applied perpendicular to a surface, while shear stress is a force applied parallel to a surface. In Mohr's circle, normal stress is represented by the x-axis, and shear stress is represented by the y-axis.

What are the applications of stress transform?

Stress transform is widely used in engineering and geology for analyzing the stress states in materials such as soil, rock, and concrete. It is also used in the design of structures, such as bridges and buildings, to ensure they can withstand the expected stresses.

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