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4. Considering the state of stress at a certain location of a structure, as shown in Figure 4, a) determine the center, C, the reference point, A of the Mohr's circle, draw the Mohr's circle (clearly indicate points A and C, the radius R, the reference axis, and o & Taxes with units) and determine R, Using the Mohr's circle you have drawn, b) determine the principal stresses ₁ and 2 and their respective angles, p1 and 8p2, and show them on the Mohr's circle. c) determine the in-plane maximum shear stress, T max, the inplane associated normal stress, and the angle 051, d) determine the absolute maximum shear stress Tabs, max e) draw the principal stress element (2D) with its respective orientation as measured from the reference axis drawn horizontally and f) maximum in-plane shear stress element with its appropriate orientations as measured from the reference axis 140 MPa Figure 4 40 MPa 60 MPa

4. Considering the state of stress at a certain location of a structure, as shown in Figure 4, a) determine the center, C, the reference point, A of the Mohr's circle, draw the Mohr's circle (clearly indicate points A and C, the radius R, the reference axis, and o & Taxes with units) and determine R, Using the Mohr's circle you have drawn, b) determine the principal stresses ₁ and 2 and their respective angles, p1 and 8p2, and show them on the Mohr's circle. c) determine the in-plane maximum shear stress, T max, the inplane associated normal stress, and the angle 051, d) determine the absolute maximum shear stress Tabs, max e) draw the principal stress element (2D) with its respective orientation as measured from the reference axis drawn horizontally and f) maximum in-plane shear stress element with its appropriate orientations as measured from the reference axis 140 MPa Figure 4 40 MPa 60 MPa

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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**Problem 4: Considering the State of Stress at a Certain Location of a Structure** Given the state of stress shown in Figure 4: a) Determine the center, \( C \), the reference point, \( A \) of the Mohr's circle. Draw the Mohr's circle (clearly indicate points \( A \) and \( C \), the radius \( R \), the reference axis, and \( \sigma \) & \( \tau \) axes with units) and determine \( R \). Using the Mohr's circle you have drawn: b) Determine the principal stresses \( \sigma_1 \) and \( \sigma_2 \) and their respective angles, \( \theta_{p1} \) and \( \theta_{p2} \), and show them on the Mohr's circle. c) Determine the in-plane maximum shear stress, \( \tau_{\text{inplane}}^{\text{max}} \), the associated normal stress, and the angle \( \theta_{s1} \). d) Determine the absolute maximum shear stress \( \tau_{\text{abs}}^{\text{max}} \). e) Draw the principal stress element (2D) with its respective orientation as measured from the reference axis drawn horizontally and f) Draw the maximum in-plane shear stress element with its appropriate orientations as measured from the reference axis drawn horizontally. --- **Figure 4 Description:** The diagram in Figure 4 shows a 3D rectangular element subjected to stresses. The element has the following stresses: - A normal stress of 140 MPa in the positive \( y \)-direction. - A shear stress of 40 MPa. - A normal stress of 60 MPa in the negative \( x \)-direction.
Transcribed Image Text:**Problem 4: Considering the State of Stress at a Certain Location of a Structure** Given the state of stress shown in Figure 4: a) Determine the center, \( C \), the reference point, \( A \) of the Mohr's circle. Draw the Mohr's circle (clearly indicate points \( A \) and \( C \), the radius \( R \), the reference axis, and \( \sigma \) & \( \tau \) axes with units) and determine \( R \). Using the Mohr's circle you have drawn: b) Determine the principal stresses \( \sigma_1 \) and \( \sigma_2 \) and their respective angles, \( \theta_{p1} \) and \( \theta_{p2} \), and show them on the Mohr's circle. c) Determine the in-plane maximum shear stress, \( \tau_{\text{inplane}}^{\text{max}} \), the associated normal stress, and the angle \( \theta_{s1} \). d) Determine the absolute maximum shear stress \( \tau_{\text{abs}}^{\text{max}} \). e) Draw the principal stress element (2D) with its respective orientation as measured from the reference axis drawn horizontally and f) Draw the maximum in-plane shear stress element with its appropriate orientations as measured from the reference axis drawn horizontally. --- **Figure 4 Description:** The diagram in Figure 4 shows a 3D rectangular element subjected to stresses. The element has the following stresses: - A normal stress of 140 MPa in the positive \( y \)-direction. - A shear stress of 40 MPa. - A normal stress of 60 MPa in the negative \( x \)-direction.
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