**Title: Understanding Mohr's Circle for Stress Analysis****Problem Statement:**For the state of stress shown in the following figure, if Mohr's circle is to be plotted, and if the diameter of the Mohr's circle is \(d\) and the principal stresses are \(p\) and \(q\) (magnitudes only), the values of \(d\), \(p\), and \(q\) (in MPa units) respectively are:**Diagram Explanation:**A rectangular element is depicted with the following stresses:- A normal stress of 10 MPa acting vertically downward at the top.- A normal stress of 40 MPa acting horizontally to the right on the left side.- A normal stress of 50 MPa acting horizontally to the right on the right side.**Options for the values of \(d\), \(p\), and \(q\):**(a) 50, 70, 30 (b) 100, 70, 30 (c) 90, 70, 30 (d) 100, 100, 30 (e) 100, 40, 0 ---**Graphical Interpretation:**To solve this problem using Mohr's circle, one would typically:1. Identify the normal and shear stresses on the element.2. Use the normal stress values to determine the center and radius of Mohr's circle.3. Calculate the principal stresses which correspond to the maximum and minimum normal stresses on the Mohr's circle. 4. The diameter \(d\) of Mohr’s circle is the difference between the maximum and minimum principal stresses.The principal stresses, \(p\) and \(q\), represent the extremities on the normal stress axis of Mohr's circle. By solving these steps with the given stress values, one should determine which set of values corresponding to \(d\), \(p\), and \(q\) is correct.

For the state of stress shown in the following figure, if Mohr's circle is to be plotted. If the i diameter of the Mohr's circle is d and the principal stresses are p and q (magnitude es only), the values of d, p & q (in MPa units,) respectively are: 10 MPa

For the state of stress shown in the following figure, if Mohr's circle is to be plotted. If the i diameter of the Mohr's circle is d and the principal stresses are p and q (magnitude es only), the values of d, p & q (in MPa units,) respectively are: 10 MPa

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Methods to Determine Vertical Stress

The load applied to the soil is transferred to the underground. The presence of water at soil pores and solid grains above the soil are the primary components that are responsible for the effective load transfer. Due to the load acting, the internal component of the soil or the underground formations undergoes deformations or a tectonic shift. The amount of deformation depends upon the amount of load acting on the soil surface, which indeed, depends on the weight of everything present above the soil. Due to this, the underground soil element develops internal stresses which try to resist the tectonic changes.

Question

**Title: Understanding Mohr's Circle for Stress Analysis**

**Problem Statement:**

For the state of stress shown in the following figure, if Mohr's circle is to be plotted, and if the diameter of the Mohr's circle is \(d\) and the principal stresses are \(p\) and \(q\) (magnitudes only), the values of \(d\), \(p\), and \(q\) (in MPa units) respectively are:

**Diagram Explanation:**

A rectangular element is depicted with the following stresses:

- A normal stress of 10 MPa acting vertically downward at the top.
- A normal stress of 40 MPa acting horizontally to the right on the left side.
- A normal stress of 50 MPa acting horizontally to the right on the right side.

**Options for the values of \(d\), \(p\), and \(q\):**

(a) 50, 70, 30
(b) 100, 70, 30
(c) 90, 70, 30
(d) 100, 100, 30
(e) 100, 40, 0

---

**Graphical Interpretation:**

To solve this problem using Mohr's circle, one would typically:

1. Identify the normal and shear stresses on the element.
2. Use the normal stress values to determine the center and radius of Mohr's circle.
3. Calculate the principal stresses which correspond to the maximum and minimum normal stresses on the Mohr's circle.
4. The diameter \(d\) of Mohr’s circle is the difference between the maximum and minimum principal stresses.

The principal stresses, \(p\) and \(q\), represent the extremities on the normal stress axis of Mohr's circle.

By solving these steps with the given stress values, one should determine which set of values corresponding to \(d\), \(p\), and \(q\) is correct.

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