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Opl = op2 = Tmax= (a) Enter the principal stresses and the magnitude of the maximum in-plane shear stress Tmax acting at the point. Enter a positive value for Tmax. 0p = Gavg i Tabsmax i 4.2 69 i i Txy (b) On a piece of paper, show these stresses on an appropriate sketch. For the sketch, calculate, the angle between the x axis and the first principal stress orientation. Enter a positive value for 0, for a counterclockwise rotation from the x axis to the direction of o,1, or a negative value for a clockwise rotation. Also, calculate avg, the normal stress on planes of maximum in-plane shear stress. Enter 0, and oavg i ksi ksi ksi y ksi (c) Enter the absolute maximum shear stress at the point. -X ksi

Opl = op2 = Tmax= (a) Enter the principal stresses and the magnitude of the maximum in-plane shear stress Tmax acting at the point. Enter a positive value for Tmax. 0p = Gavg i Tabsmax i 4.2 69 i i Txy (b) On a piece of paper, show these stresses on an appropriate sketch. For the sketch, calculate, the angle between the x axis and the first principal stress orientation. Enter a positive value for 0, for a counterclockwise rotation from the x axis to the direction of o,1, or a negative value for a clockwise rotation. Also, calculate avg, the normal stress on planes of maximum in-plane shear stress. Enter 0, and oavg i ksi ksi ksi y ksi (c) Enter the absolute maximum shear stress at the point. -X ksi

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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Consider a point in a structural member that is subjected to plane stress. Normal and shear stresses acting on horizontal and vertical planes at the point are shown. (a) Determine the principal stresses and the maximum in-plane shear stress acting at the point. (b) Show these stresses on an appropriate sketch (e.g., see figures below). - **Figure Description:** - The diagram illustrates a stress element under plane stress conditions. - Two principal stress axes are defined: σp1 and σp2, with the principal plane P aligned with these axes. - Shear stresses τxy act on the element. - Angles θs and θp define the orientation of the principal plane and shear plane, respectively. - Stress magnitudes are labeled on arrows. (c) Compute the absolute maximum shear stress at the point. Note that the horizontal direction has been taken as the x-direction, and the vertical direction has been taken as the y-direction. Assume the stress magnitudes are |σx| = 9.9 ksi, |σy| = 12.5 ksi, and |τxy| = 4.0 ksi. The directions of these stresses are indicated in the figure below.
Transcribed Image Text:Consider a point in a structural member that is subjected to plane stress. Normal and shear stresses acting on horizontal and vertical planes at the point are shown. (a) Determine the principal stresses and the maximum in-plane shear stress acting at the point. (b) Show these stresses on an appropriate sketch (e.g., see figures below). - **Figure Description:** - The diagram illustrates a stress element under plane stress conditions. - Two principal stress axes are defined: σp1 and σp2, with the principal plane P aligned with these axes. - Shear stresses τxy act on the element. - Angles θs and θp define the orientation of the principal plane and shear plane, respectively. - Stress magnitudes are labeled on arrows. (c) Compute the absolute maximum shear stress at the point. Note that the horizontal direction has been taken as the x-direction, and the vertical direction has been taken as the y-direction. Assume the stress magnitudes are |σx| = 9.9 ksi, |σy| = 12.5 ksi, and |τxy| = 4.0 ksi. The directions of these stresses are indicated in the figure below.
### Problem Statement on Shear and Principal Stresses #### Diagram Explanation: The diagram presents a stress element with labeled forces acting on it. It includes the following notations: - \(\sigma_x\), \(\sigma_y\): Normal stresses in the x and y directions. - \(\tau_{xy}\): Shear stress. The stress element is oriented in a 2D plane with an x-y coordinate system shown to the right of the element. #### Tasks: (a) **Principal Stresses and Maximum Shear Stress** - **Objective**: Enter the principal stresses and the magnitude of the maximum in-plane shear stress (\(\tau_{\text{max}}\)) acting at the point. - **Instruction**: Provide a positive value for \(\tau_{\text{max}}\). - \(\sigma_{p1} =\) [Enter value] ksi - \(\sigma_{p2} =\) [Enter value] ksi - \(\tau_{\text{max}} = 4.2\) ksi (b) **Sketching Stresses and Calculations** - **Objective**: On a piece of paper, sketch these stresses for a visualization. - **Instructions**: - Calculate \(\theta_p\), the angle between the x-axis and the direction of the first principal stress orientation. - **Note**: Enter a positive value for \(\theta_p\) if the rotation is counterclockwise from the x-axis to the direction of \(\sigma_{p1}\), or a negative value if it is a clockwise rotation. - Calculate \(\sigma_{\text{avg}}\), the normal stress on planes of maximum in-plane shear stress. - **Enter values**: - \(\theta_p =\) [Enter value] ° - \(\sigma_{\text{avg}} =\) [Enter value] ksi (c) **Absolute Maximum Shear Stress** - **Objective**: Enter the absolute maximum shear stress at the point. - \(\tau_{\text{abs max}} =\) [Enter value] ksi Follow these instructions to solve and successfully sketch the stress state as described.
Transcribed Image Text:### Problem Statement on Shear and Principal Stresses #### Diagram Explanation: The diagram presents a stress element with labeled forces acting on it. It includes the following notations: - \(\sigma_x\), \(\sigma_y\): Normal stresses in the x and y directions. - \(\tau_{xy}\): Shear stress. The stress element is oriented in a 2D plane with an x-y coordinate system shown to the right of the element. #### Tasks: (a) **Principal Stresses and Maximum Shear Stress** - **Objective**: Enter the principal stresses and the magnitude of the maximum in-plane shear stress (\(\tau_{\text{max}}\)) acting at the point. - **Instruction**: Provide a positive value for \(\tau_{\text{max}}\). - \(\sigma_{p1} =\) [Enter value] ksi - \(\sigma_{p2} =\) [Enter value] ksi - \(\tau_{\text{max}} = 4.2\) ksi (b) **Sketching Stresses and Calculations** - **Objective**: On a piece of paper, sketch these stresses for a visualization. - **Instructions**: - Calculate \(\theta_p\), the angle between the x-axis and the direction of the first principal stress orientation. - **Note**: Enter a positive value for \(\theta_p\) if the rotation is counterclockwise from the x-axis to the direction of \(\sigma_{p1}\), or a negative value if it is a clockwise rotation. - Calculate \(\sigma_{\text{avg}}\), the normal stress on planes of maximum in-plane shear stress. - **Enter values**: - \(\theta_p =\) [Enter value] ° - \(\sigma_{\text{avg}} =\) [Enter value] ksi (c) **Absolute Maximum Shear Stress** - **Objective**: Enter the absolute maximum shear stress at the point. - \(\tau_{\text{abs max}} =\) [Enter value] ksi Follow these instructions to solve and successfully sketch the stress state as described.
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