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Consider the element in with Tay = 30 MPa. 80 MPa Part A Txy

Consider the element in with Tay = 30 MPa. 80 MPa Part A Txy

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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### Understanding Principal Stresses #### Problem Statement: Consider the element in with \( \tau_{xy} = 30 \, \text{MPa} \). #### Diagram Explanation: The diagram shows a two-dimensional stress element with the following details: - A central square representing the material element. - Vertical arrows labeled "80 MPa" indicating compressive normal stress acting on the top and bottom surfaces. - Horizontal arrows labeled "τ_{xy}" indicating shear stress of 30 MPa acting on the sides of the element. #### Part A: Determining Principal Stresses Your task is to determine the principal stresses. - Enter your answers in megapascals to three significant figures, separated by a comma. #### Input: - A field is provided to enter the two principal stresses \( \sigma_1 \) and \( \sigma_2 \). #### Action: - Click "Submit" to check your answers or "Request Answer" for assistance. --- This section helps students understand how to extract stress components from a diagram and calculate principal stresses, an important concept in mechanics of materials.
Transcribed Image Text:### Understanding Principal Stresses #### Problem Statement: Consider the element in with \( \tau_{xy} = 30 \, \text{MPa} \). #### Diagram Explanation: The diagram shows a two-dimensional stress element with the following details: - A central square representing the material element. - Vertical arrows labeled "80 MPa" indicating compressive normal stress acting on the top and bottom surfaces. - Horizontal arrows labeled "τ_{xy}" indicating shear stress of 30 MPa acting on the sides of the element. #### Part A: Determining Principal Stresses Your task is to determine the principal stresses. - Enter your answers in megapascals to three significant figures, separated by a comma. #### Input: - A field is provided to enter the two principal stresses \( \sigma_1 \) and \( \sigma_2 \). #### Action: - Click "Submit" to check your answers or "Request Answer" for assistance. --- This section helps students understand how to extract stress components from a diagram and calculate principal stresses, an important concept in mechanics of materials.
## Part B ### Task Specify the orientation of the principal plane. Choose the angle from the half-interval (-90°, 90°). ### Instructions Express your answer in degrees to three significant figures. #### Input Area - **Variable:** θ<sub>p1</sub> - **Input Box:** Allows for numerical input of the angle in degrees. **Buttons Available:** - `vec`: A button for function or operation selection. - Additional symbols and operations may be provided in the interface. #### Submission - **Submit Button:** Confirm your input after entering the angle. - **Request Answer:** Option to request the correct answer if unsure. ## Part C ### Task Determine the maximum in-plane shear stress and average normal stress. ### Instructions Enter your answers in megapascals to three significant figures separated by a comma. #### Input Area - **Variables:** - τ<sub>max in-plane</sub> - σ<sub>avg</sub> - **Input Box:** Allows for numerical input of the stresses, separated by a comma. **Buttons Available:** - `vec`: A button for function or operation selection. - Additional symbols and operations may be provided in the interface. #### Submission - **Submit Button:** Confirm your input after entering the stresses. - **Request Answer:** Option to request the correct answer if unsure.
Transcribed Image Text:## Part B ### Task Specify the orientation of the principal plane. Choose the angle from the half-interval (-90°, 90°). ### Instructions Express your answer in degrees to three significant figures. #### Input Area - **Variable:** θ<sub>p1</sub> - **Input Box:** Allows for numerical input of the angle in degrees. **Buttons Available:** - `vec`: A button for function or operation selection. - Additional symbols and operations may be provided in the interface. #### Submission - **Submit Button:** Confirm your input after entering the angle. - **Request Answer:** Option to request the correct answer if unsure. ## Part C ### Task Determine the maximum in-plane shear stress and average normal stress. ### Instructions Enter your answers in megapascals to three significant figures separated by a comma. #### Input Area - **Variables:** - τ<sub>max in-plane</sub> - σ<sub>avg</sub> - **Input Box:** Allows for numerical input of the stresses, separated by a comma. **Buttons Available:** - `vec`: A button for function or operation selection. - Additional symbols and operations may be provided in the interface. #### Submission - **Submit Button:** Confirm your input after entering the stresses. - **Request Answer:** Option to request the correct answer if unsure.
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