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Confirm the principal stress magnitudes from the formulae.

Confirm the principal stress magnitudes from the formulae.

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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Note: I have answers to part (a). Guidance on part (b) would be much appreciated!

Hi, I'm unsure how to approach this part of the problem with Mohr's Circle. I understand the concept but struggle to see how to apply it to all the questions asked in the attached image.

Thank you in advance!

Figure Q2 shows that state of stress at a point within a loaded body consists of a combination of two direct normal stresses: O = 65 MPa (tension) and oy =-40 MPa, complemented by a tangential shear stress Ty = 35 MPa. 65 MPa 35 MPa 40 MR Figure Q2 Construct a Mohr's circle to establish, with additional sketches in the physical plane, answers to each of the following: (a) (0) the direct and shear stress state upon the plane inclined at 45° shown (ii) the magnitudes of the major and minor principal stresses the orientations of the major and minor principal planes relative to the (ii) left vertical side of the element in Fig. Q2 (iv) the magnitude of the maximum shear stress with its normal stress the directions of the maximum shear planes relative to the principal planes. (v) Confirm the principal stress magnitudes from the formulae. Find the safety factors which apply to the principal stress state based upon the Rankine, Tresca and von Mises yield criteria given that the tensile yield stress is 200 MPa. (b)
Transcribed Image Text:Figure Q2 shows that state of stress at a point within a loaded body consists of a combination of two direct normal stresses: O = 65 MPa (tension) and oy =-40 MPa, complemented by a tangential shear stress Ty = 35 MPa. 65 MPa 35 MPa 40 MR Figure Q2 Construct a Mohr's circle to establish, with additional sketches in the physical plane, answers to each of the following: (a) (0) the direct and shear stress state upon the plane inclined at 45° shown (ii) the magnitudes of the major and minor principal stresses the orientations of the major and minor principal planes relative to the (ii) left vertical side of the element in Fig. Q2 (iv) the magnitude of the maximum shear stress with its normal stress the directions of the maximum shear planes relative to the principal planes. (v) Confirm the principal stress magnitudes from the formulae. Find the safety factors which apply to the principal stress state based upon the Rankine, Tresca and von Mises yield criteria given that the tensile yield stress is 200 MPa. (b)
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