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Part A - Normal Stresses, Shear, and Angles The stress element shown in the figure below is subjected to the indicated stresses of magnitude |0₂| = 35 MPa, |oy| = 57 MPa, and Tay = 25 MPa. 0₂ TH Ox Determine the principal normal stresses ₁ and 2, the maximum in-plane shear stress Tmax,in-plane, and the angles at which they occur relative to the given stress element. Follow the sign convention. Suppose that when the element is oriented at an angle 0p1 relative to the given stress element, the normal stress that acts along the x' axis of the element is equal to the maximum normal stress σ1. When the element is oriented at an angle 0,2 relative to the given stress element, the normal stress that acts along the x' axis of the element is equal to the minimum normal stress 02. When the element is oriented at an angle 8, relative to the given stress element, the shear stress that acts on the element is equal to the maximum in-plane shear stress Tmax,in-plane and is positive according to the sign convention. Express your answers, separated by commas, to three significant figures. Express angles in the range 0 € (-180°, 180°].

Part A - Normal Stresses, Shear, and Angles The stress element shown in the figure below is subjected to the indicated stresses of magnitude |0₂| = 35 MPa, |oy| = 57 MPa, and Tay = 25 MPa. 0₂ TH Ox Determine the principal normal stresses ₁ and 2, the maximum in-plane shear stress Tmax,in-plane, and the angles at which they occur relative to the given stress element. Follow the sign convention. Suppose that when the element is oriented at an angle 0p1 relative to the given stress element, the normal stress that acts along the x' axis of the element is equal to the maximum normal stress σ1. When the element is oriented at an angle 0,2 relative to the given stress element, the normal stress that acts along the x' axis of the element is equal to the minimum normal stress 02. When the element is oriented at an angle 8, relative to the given stress element, the shear stress that acts on the element is equal to the maximum in-plane shear stress Tmax,in-plane and is positive according to the sign convention. Express your answers, separated by commas, to three significant figures. Express angles in the range 0 € (-180°, 180°].

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
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Part A - Normal Stresses, Shear, and Angles The stress element shown in the figure below is subjected to the indicated stresses of magnitude |ox| 01, p1, 02 =, =, 0p2 = Tmax,in-plane Determine the principal normal stresses 0₁ and 02, the maximum in-plane shear stress Tmax,in-plane, and the angles at which they occur relative to the given stress element. Follow the sign convention. Suppose that when the element is oriented at an angle p1 relative to the given stress element, the normal stress that acts along the x' axis of the element is equal to the maximum normal stress 1. When the element is oriented at an angle 02 relative to the given stress element, the normal stress that acts along the x' axis of the element is equal to the minimum normal stress 02. When the element is oriented at an angle , relative to the given stress element, the shear stress that acts on the element is equal to the maximum in-plane shear stress Tmax,in-plane and is positive according to the sign convention. , 0 s Express your answers, separated by commas, to three significant figures. Express angles in the range 0 € (-180°, 180°]. ► View Available Hint(s) - ΑΣΦ = N Oy IN vec 35 MPa, |oy| = 57 MPa, and Tay| = 25 MPa. P 0x Your submission doesn't have the correct number of answers. Answers should be separated with a comma. No credit lost. Try again. ? MPa, °, MPa, °, MPa, °
Transcribed Image Text:Part A - Normal Stresses, Shear, and Angles The stress element shown in the figure below is subjected to the indicated stresses of magnitude |ox| 01, p1, 02 =, =, 0p2 = Tmax,in-plane Determine the principal normal stresses 0₁ and 02, the maximum in-plane shear stress Tmax,in-plane, and the angles at which they occur relative to the given stress element. Follow the sign convention. Suppose that when the element is oriented at an angle p1 relative to the given stress element, the normal stress that acts along the x' axis of the element is equal to the maximum normal stress 1. When the element is oriented at an angle 02 relative to the given stress element, the normal stress that acts along the x' axis of the element is equal to the minimum normal stress 02. When the element is oriented at an angle , relative to the given stress element, the shear stress that acts on the element is equal to the maximum in-plane shear stress Tmax,in-plane and is positive according to the sign convention. , 0 s Express your answers, separated by commas, to three significant figures. Express angles in the range 0 € (-180°, 180°]. ► View Available Hint(s) - ΑΣΦ = N Oy IN vec 35 MPa, |oy| = 57 MPa, and Tay| = 25 MPa. P 0x Your submission doesn't have the correct number of answers. Answers should be separated with a comma. No credit lost. Try again. ? MPa, °, MPa, °, MPa, °
Part B - Total State of Stress due to Two Independent Stresses A point on a thin plate is subjected to two successive states of stress. The stresses have magnitude |σx | = 31.5 MPa, |oy| = 45.5 MPa, and Ta'y' | = 20.5 MPa. 0x =, 0y=, Txy || Determine the resulting state of stress on the element on the right. The rotation angles on the left-hand side of the figure are in relation to the orientation of the element on the right. Express your answers, separated by commas, to three significant figures. ► View Available Hint(s) ΑΣΦ 60° ved 220% ? Txy MPa, MPa, MPa
Transcribed Image Text:Part B - Total State of Stress due to Two Independent Stresses A point on a thin plate is subjected to two successive states of stress. The stresses have magnitude |σx | = 31.5 MPa, |oy| = 45.5 MPa, and Ta'y' | = 20.5 MPa. 0x =, 0y=, Txy || Determine the resulting state of stress on the element on the right. The rotation angles on the left-hand side of the figure are in relation to the orientation of the element on the right. Express your answers, separated by commas, to three significant figures. ► View Available Hint(s) ΑΣΦ 60° ved 220% ? Txy MPa, MPa, MPa
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