Understanding Shear Stress Theories: Moors Circle & McGraw Hill

In summary, the conversation discusses a discrepancy between the solution provided by McGraw Hill Connect and the information presented in the professor's powerpoint. The powerpoint states that sigma1 is equivalent to the yield strength, while sigma(x), sigma(y), and sigma(z) are designated as sigma1, sigma2, and sigma3, respectively. However, the McGraw Hill solution contradicts this information by stating that sigma(x) is 100 MPa, which is not possible if the yield strength is 350 MPa. The conversation also mentions the use of Mohr's circle and provides two scenarios for determining the maximum shear stress.
  • #1
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Homework Statement
A ductile hot-rolled steel bar has a minimum yield strength in tension and compression of 350 MPa. Using the distortion-energy and maximum-shear-stress theories, determine the factors of safety for the following plane stress states.

σx = 100 MPa and σy = 100 MPa
Relevant Equations
NA
Hello:)
Our homework is done through mcgraw hill connect. I am able to see the solution to the problem and it contradicts what the book and powerpoint says.

according to the powerpoint given by my professor, moors circle, sigma1 = Sy or yield strength. Powerpoint also states that sigma(x) is sigma1, sigma(y) is sigma2 and sigma(z) is sigma3.

If the powerpoint is correct, then there is no way that sigma(x) from the mcgraw hill assignment IS 100, because Sy is 350. The solution states sy is 350 as well. see attached file

n=sy/Tmax

Tmax we know is half of sy based on moors circle so 350/175 = n

view attached files to see what i mean
 

Attachments

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  • #2
Based on the Mohr's circle, if the maximum principal stress is 350 Mpa and the other principal stresses are 0 MPa, what is the maximum shear stress?

If the three principal stresses are 100 MPa, 100 MPa, and 0 MPa, what is the maximum shear stress?
 

1. What is shear stress and how is it measured?

Shear stress is the force per unit area that acts parallel to the surface of an object. It is measured in units of force divided by area, such as pounds per square inch (psi) or newtons per square meter (N/m²). It can be measured using a variety of instruments, such as a shear stress sensor or a rheometer.

2. What is the Moors Circle method for understanding shear stress?

The Moors Circle method is a graphical approach for analyzing shear stress and strain in a material. It involves plotting the principal stresses on a circle and using the radius of the circle to determine the maximum shear stress at a given point. This method is commonly used in materials science and engineering to understand the behavior of materials under different loading conditions.

3. How does the McGraw Hill theory explain shear stress?

The McGraw Hill theory, also known as the Mohr-Coulomb theory, is a mathematical model that describes the relationship between shear stress and shear strain in a material. It states that the shear stress at a point is directly proportional to the shear strain and is also affected by the cohesion and internal friction of the material. This theory is commonly used in geotechnical engineering to analyze the stability of soil and rock structures.

4. What are some real-world applications of understanding shear stress theories?

Understanding shear stress theories is essential in many fields, including materials science, engineering, and geology. In materials science, it is used to design and test the strength and durability of various materials. In engineering, it is crucial for designing structures that can withstand different types of loading, such as bridges, buildings, and airplanes. In geology, it is used to analyze the stability of slopes, landslides, and other natural hazards.

5. How can understanding shear stress theories impact everyday life?

Shear stress theories have a significant impact on everyday life. They are used in the design and construction of buildings, bridges, and other structures that we use daily. They also play a crucial role in the development of new materials and technologies that make our lives easier and more efficient. Additionally, understanding shear stress theories is essential for ensuring the safety and stability of natural and man-made structures, which can prevent accidents and disasters.

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