### Problem 4: Stress Analysis Using Mohr's Circle**Objective:**Complete the following tasks related to stress analysis:**a. Draw Mohr’s Circle for the given element and label the axes.****b. Determine the following for the element:** - \(\sigma_1\) : Major principal stress - \(\sigma_3\) : Minor principal stress - \(\tau_{max}\) : Maximum shear stress**c. Calculate the stresses \((\sigma_n, \tau_n)\) on the plane shown.****d. Plot the point representing the plane with stresses \((\sigma_n, \tau_n)\) on the Mohr's circle.**### Diagram Description:- A stress element is shown with dimensions and forces labeled.- The normal force on the plane \(\sigma_n\) is applied at an angle of 40°.- Stress values: - Along the horizontal direction: \(+4, -4\) - Along the vertical direction: \(8, 5\)### Graph Information:- A grid is provided for plotting Mohr’s Circle.**Steps:**1. **Mohr’s Circle Construction:** - Use the stress element to plot the normal and shear stresses on the circle. - Label the normal stress axis (\(\sigma\)) and the shear stress axis (\(\tau\)).2. **Principal Stresses & Maximum Shear Stress:** - Calculate \(\sigma_1\), \(\sigma_3\), and \(\tau_{max}\) using the given stress values.3. **Stress Determination:** - Evaluate the plane’s stress components (\(\sigma_n, \tau_n\)) at a 40° angle.4. **Plotting:** - Represent (\(\sigma_n, \tau_n\)) on Mohr’s Circle.**Note for Students:**Ensure clarity in drawing and labeling the axes on Mohr’s Circle for accurate stress analysis.

Answered: 4. Complete the following a. Draw…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

ChapterB: Graphical Analysis Of Planar Trusses

Section: Chapter Questions

Problem 10P

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### Problem 4: Stress Analysis Using Mohr's Circle

**Objective:**
Complete the following tasks related to stress analysis:

**a. Draw Mohr’s Circle for the given element and label the axes.**

**b. Determine the following for the element:**
- \(\sigma_1\) : Major principal stress
- \(\sigma_3\) : Minor principal stress
- \(\tau_{max}\) : Maximum shear stress

**c. Calculate the stresses \((\sigma_n, \tau_n)\) on the plane shown.**

**d. Plot the point representing the plane with stresses \((\sigma_n, \tau_n)\) on the Mohr's circle.**

### Diagram Description:
- A stress element is shown with dimensions and forces labeled.
- The normal force on the plane \(\sigma_n\) is applied at an angle of 40°.
- Stress values:
- Along the horizontal direction: \(+4, -4\)
- Along the vertical direction: \(8, 5\)

### Graph Information:
- A grid is provided for plotting Mohr’s Circle.

**Steps:**

1. **Mohr’s Circle Construction:**
- Use the stress element to plot the normal and shear stresses on the circle.
- Label the normal stress axis (\(\sigma\)) and the shear stress axis (\(\tau\)).

2. **Principal Stresses & Maximum Shear Stress:**
- Calculate \(\sigma_1\), \(\sigma_3\), and \(\tau_{max}\) using the given stress values.

3. **Stress Determination:**
- Evaluate the plane’s stress components (\(\sigma_n, \tau_n\)) at a 40° angle.

4. **Plotting:**
- Represent (\(\sigma_n, \tau_n\)) on Mohr’s Circle.

**Note for Students:**
Ensure clarity in drawing and labeling the axes on Mohr’s Circle for accurate stress analysis.

Expert Solution

Step 1

Answer

Since we are not allowed to provide handwritten solution we have used Autocad to draw the Mohr's circle based on the given data. Follow the same steps while drawing on graph paper.

major compressive stress = -4

minor compressive stress = -8

shear stress = 4

(a) Take a point A at origin and mark a point B at distance = -4(left) and point C at a distance -8(left) from A.

Now draw perpendicular from B to D and C to E of distance 4.

Join D and E we get centre of Mohr circle O.

Now taking centre O and OE as radius draw the Mohr's circle as shown below.

Now draw BD and CE perpedicular equal to 4

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