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Two-dimensional state of stress at a point in a plane stressed element is represented by a Mohr circle of zero radius. Then both principal stressesa)Are equal to zero b)Are equal to zero and shear stress is also equal to zeroc)Are of equal magnitude but of opposite signd)Are of equal magnitude and of same signCorrect answer is option 'D'. Can you explain this answer?
Ref: https://edurev.in/question/517117/Two-dimensional-state-of-stress-at-a-point-in-a-plane-stressed-element-is-represented-by-a-Mohr-circ
Mohr circle of different cases are given as:
For equal and same nature of principal stresses, Mohr's circle will be zero.
FAQs on MCQ: Mohr’s Circle, GATE
| 1. What is Mohr's Circle and how is it used in engineering? |  |
Mohr's Circle is a graphical method used to determine the stress state at a point in a material subjected to combined loading. It is commonly used in engineering to analyze and design structures. The circle provides a visual representation of stress components and their orientations, making it easier to determine the principal stresses, maximum shear stress, and other important parameters.
| 2. How is Mohr's Circle constructed? | |
To construct Mohr's Circle, we start by plotting the normal stress (σ) on the x-axis and the shear stress (τ) on the y-axis. Then, we plot the stress state at a given point as a point on the graph. By repeating this process for different points, we can create a series of points on the graph. Finally, we draw a circle that best fits these points, known as Mohr's Circle.
| 3. What is the significance of the radius of Mohr's Circle? | |
The radius of Mohr's Circle represents the maximum shear stress (τmax) at the point of interest. It is equal to half the difference between the maximum and minimum principal stresses (σmax and σmin). By measuring the radius, engineers can determine the magnitude of shear stress and evaluate the material's ability to withstand shear forces.
| 4. How can Mohr's Circle be used to determine the principal stresses? | |
The principal stresses can be determined by finding the x-coordinate of the points where the circle intersects the x-axis. These points correspond to the maximum and minimum principal stresses (σmax and σmin) at the point of interest. By measuring these values, engineers can assess the strength and stability of materials under different loading conditions.
| 5. What are the advantages of using Mohr's Circle in engineering analysis? | |
Mohr's Circle offers several advantages in engineering analysis. It allows engineers to visualize stress states and their orientations, making it easier to understand and interpret complex stress conditions. It also provides a clear representation of principal stresses, maximum shear stress, and other important parameters. Additionally, Mohr's Circle enables engineers to predict failure and design structures that can withstand various loading conditions, enhancing overall safety and efficiency.
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