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Learning Goal: To calculate the principal stresses and maximum in-plane shear stress for a plane state of stress. The normal and shear stresses for a state of stress depend on the orientation of the axes. For a general plane state of stress, there is one orientation where the two normal stresses are a maximum and minimum and the shear stresses on the faces of the element are zero. The two normal stresses 01 and 2 are known as principal stresses. The directions of the faces on which the principal stresses act are known as the principal planes. The principal stresses can be calculated using the following formula: 01,2 = σI + Oy 2 Tmax= ± OT The maximum in-plane shear stress occurs on a plane that is 45° away from the principal planes. The average normal stress on this plane is O₂ + Oy generally not zero, but is avg = . The 2 maximum shear stress is given by the following equation: 2 JI Ty 2 2 2 tiểu + Ty Once avg and Tmax are calculated, the principal stresses can be found very directly: 1,2 = avg Tmax. The state of stress at a point can be described by |0₂| = 22 MPa, oy = 52 MPa, and Try 9 MPa, acting in the directions shown (Figure 1). Part A - In-plane shear stress What is the maximum in-plane shear stress for the given state of stress? Express your answer with appropriate units to three significant figures. ► View Available Hint(s) Tmax in-plane= Submit UA Value Units Part B - Maximum normal stress magnitude uA What is the principal normal stress with the largest magnitude? Express your answer with appropriate units to three significant figures. ► View Available Hint(s) ? ?

Learning Goal: To calculate the principal stresses and maximum in-plane shear stress for a plane state of stress. The normal and shear stresses for a state of stress depend on the orientation of the axes. For a general plane state of stress, there is one orientation where the two normal stresses are a maximum and minimum and the shear stresses on the faces of the element are zero. The two normal stresses 01 and 2 are known as principal stresses. The directions of the faces on which the principal stresses act are known as the principal planes. The principal stresses can be calculated using the following formula: 01,2 = σI + Oy 2 Tmax= ± OT The maximum in-plane shear stress occurs on a plane that is 45° away from the principal planes. The average normal stress on this plane is O₂ + Oy generally not zero, but is avg = . The 2 maximum shear stress is given by the following equation: 2 JI Ty 2 2 2 tiểu + Ty Once avg and Tmax are calculated, the principal stresses can be found very directly: 1,2 = avg Tmax. The state of stress at a point can be described by |0₂| = 22 MPa, oy = 52 MPa, and Try 9 MPa, acting in the directions shown (Figure 1). Part A - In-plane shear stress What is the maximum in-plane shear stress for the given state of stress? Express your answer with appropriate units to three significant figures. ► View Available Hint(s) Tmax in-plane= Submit UA Value Units Part B - Maximum normal stress magnitude uA What is the principal normal stress with the largest magnitude? Express your answer with appropriate units to three significant figures. ► View Available Hint(s) ? ?

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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Learning Goal: To calculate the principal stresses and maximum in-plane shear stress for a plane state of stress. The normal and shear stresses for a state of stress depend on the orientation of the axes. For a general plane state of stress, there is one orientation where the two normal stresses are a maximum and minimum and the shear stresses on the faces of the element are zero. The two normal stresses 01 and 2 are known as principal stresses. The directions of the faces on which the principal stresses act are known as the principal planes. The principal stresses can be calculated using the following formula: σ1,2 = Tmax = O₂ + Oy 2 ± Figure The maximum in-plane shear stress occurs on a plane that is 45° away from the principal planes. The average normal stress on this plane is O₂ + Oy generally not zero, but is avg = maximum shear stress is given by the following equation: . The OT Ty 2 JI Ty 2 y Oy 2 + Tzu Once avg and Tmax are calculated, the principal stresses can be found very directly: 01,2 avg Tmax. 2 Txy tiểu < 1 of 1 > Ox X The state of stress at a point can be described by |0₂| = 22 MPa, oy = 52 MPa, and Try = 9 MPa, acting in the directions shown (Figure 1). Part A - In-plane shear stress What is the maximum in-plane shear stress for the given state of stress? Express your answer with appropriate units to three significant figures. ► View Available Hint(s) = Tmax in-plane 1 Submit Part B - Maximum normal stress magnitude max = Value Submit What is the principal normal stress with the largest magnitude? Express your answer with appropriate units to three significant figures. ► View Available Hint(s) Provide Feedback Units Value Part C Complete previous part(s) Units ? ? Review Next >
Transcribed Image Text:Learning Goal: To calculate the principal stresses and maximum in-plane shear stress for a plane state of stress. The normal and shear stresses for a state of stress depend on the orientation of the axes. For a general plane state of stress, there is one orientation where the two normal stresses are a maximum and minimum and the shear stresses on the faces of the element are zero. The two normal stresses 01 and 2 are known as principal stresses. The directions of the faces on which the principal stresses act are known as the principal planes. The principal stresses can be calculated using the following formula: σ1,2 = Tmax = O₂ + Oy 2 ± Figure The maximum in-plane shear stress occurs on a plane that is 45° away from the principal planes. The average normal stress on this plane is O₂ + Oy generally not zero, but is avg = maximum shear stress is given by the following equation: . The OT Ty 2 JI Ty 2 y Oy 2 + Tzu Once avg and Tmax are calculated, the principal stresses can be found very directly: 01,2 avg Tmax. 2 Txy tiểu < 1 of 1 > Ox X The state of stress at a point can be described by |0₂| = 22 MPa, oy = 52 MPa, and Try = 9 MPa, acting in the directions shown (Figure 1). Part A - In-plane shear stress What is the maximum in-plane shear stress for the given state of stress? Express your answer with appropriate units to three significant figures. ► View Available Hint(s) = Tmax in-plane 1 Submit Part B - Maximum normal stress magnitude max = Value Submit What is the principal normal stress with the largest magnitude? Express your answer with appropriate units to three significant figures. ► View Available Hint(s) Provide Feedback Units Value Part C Complete previous part(s) Units ? ? Review Next >
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