Problem 6 Given: A plane element in a body is acted upon by combined stresses as shown below: 40 MPa 10 MPa 15 MPa →30 MPa Required: a) Determine the Principal stresses. b) What is the maximum shear stress? c) What is the angle between the original plane of stress and the maximum principal stress?
Problem 6 Given: A plane element in a body is acted upon by combined stresses as shown below: 40 MPa 10 MPa 15 MPa →30 MPa Required: a) Determine the Principal stresses. b) What is the maximum shear stress? c) What is the angle between the original plane of stress and the maximum principal stress?
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![**Problem 6**
**Given:** A plane element in a body is acted upon by combined stresses as shown below:
[Diagram Explanation]
- The diagram shows a square plane element with various stresses applied.
- On the top side, a compressive stress of 40 MPa is acting vertically downwards.
- On the right side, a tensile stress of 30 MPa is acting horizontally to the right.
- On the left side, a compressive stress of 15 MPa is acting horizontally to the left.
- On the bottom side, a tensile stress of 10 MPa is acting vertically upwards.
- Additionally, a diagonal shear stress arrow appears on the element, indicating a complex stress state.
Axes are labeled as x (horizontal), y (vertical), and z (perpendicular to the plane).
**Required:**
a) Determine the Principal stresses.
b) What is the maximum shear stress?
c) What is the angle between the original plane of stress and the maximum principal stress?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb54c94dc-8fa5-45f1-a08b-382951c33f95%2Fb8571da2-51fe-4325-bb35-872592bab83c%2Fwehf1hs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 6**
**Given:** A plane element in a body is acted upon by combined stresses as shown below:
[Diagram Explanation]
- The diagram shows a square plane element with various stresses applied.
- On the top side, a compressive stress of 40 MPa is acting vertically downwards.
- On the right side, a tensile stress of 30 MPa is acting horizontally to the right.
- On the left side, a compressive stress of 15 MPa is acting horizontally to the left.
- On the bottom side, a tensile stress of 10 MPa is acting vertically upwards.
- Additionally, a diagonal shear stress arrow appears on the element, indicating a complex stress state.
Axes are labeled as x (horizontal), y (vertical), and z (perpendicular to the plane).
**Required:**
a) Determine the Principal stresses.
b) What is the maximum shear stress?
c) What is the angle between the original plane of stress and the maximum principal stress?
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