For each of the elements shown below, draw Mohr’s circle and determine the principal stresses (σ₁, σ₂, and σ₃). In addition, determine the maximum shear stress (τ_max).### (a)**Diagram Description:**- A square element labeled "E" is subjected to shear stress.- The element is experiencing equal shear stress on all four sides: τₓᵧ and τᵧₓ = 150 MPa.- The shear stress vector is pointing to the right on the top face and downwards on the right face.### (b)**Diagram Description:**- A square element labeled "E" is subjected to normal stress σₓ.- The element is experiencing a normal stress of σₓ = 110 psi on the left and right sides of the element.- The stress vector is pointing inward on the left side and outward on the right side.### (c)**Diagram Description:**- A square element labeled "E" is subjected to normal stresses σₓ and σᵧ.- The element is experiencing a normal stress of σₓ = 300 MPa on the left and right sides.- The element is experiencing a normal stress of σᵧ = 150 MPa on the top and bottom sides.- The stress vector for σₓ is pointing to the right, and for σᵧ it is pointing upwards.### (d)**Diagram Description:**- A square element labeled "E" is subjected to normal and shear stresses.- The element is experiencing a normal stress of σₓ = 62 psi on the right side.- The element is experiencing a normal stress of σᵧ = 85 psi on the top side.- The element is experiencing shear stress τₓᵧ = 37 psi on the right side.- The shear stress vector points to the right on the top face.For each of these stress elements, Mohr's circle can be constructed to find the principal stresses and maximum shear stress. Mohr's circle provides a graphical representation of the state of stress at a point and helps determine the principal stresses and the maximum shear stress experienced by the element.

Answered: Image /qna-images/answer/06f708fb-28b3-49f3-ad31-93a6941e4e6a.jpg

For each of the elements shown below, draw Mohr's circle and determine the principal stresses (0₁, 02 and 03). In addition, determine the maximum shear stress (Tmax). (a) Tyx = Txy E Txy = 150 MPa (b) (c) (d) 0x E E E Oy = 150 MPa 0x = 110 psi x = 300 MPa Ty = 85 psi Txy = 37 psi 0x = 62 psi

For each of the elements shown below, draw Mohr's circle and determine the principal stresses (0₁, 02 and 03). In addition, determine the maximum shear stress (Tmax). (a) Tyx = Txy E Txy = 150 MPa (b) (c) (d) 0x E E E Oy = 150 MPa 0x = 110 psi x = 300 MPa Ty = 85 psi Txy = 37 psi 0x = 62 psi

Elements Of Electromagnetics

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ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Concept explainers

Stress transformation

The term stress indicates the measure of internal forces that develop due to an external force's application on an object. When a specific external force is applied to an object, internal stress generates in the material. The value of stress can obtain by taking the ratio of the externally applied force and cross-sectional area of the object. There are different types of stress depending on the type of external force.

Question

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For each of the elements shown below, draw Mohr’s circle and determine the principal stresses (σ₁, σ₂, and σ₃). In addition, determine the maximum shear stress (τ_max).

### (a)
**Diagram Description:**
- A square element labeled "E" is subjected to shear stress.
- The element is experiencing equal shear stress on all four sides: τₓᵧ and τᵧₓ = 150 MPa.
- The shear stress vector is pointing to the right on the top face and downwards on the right face.

### (b)
**Diagram Description:**
- A square element labeled "E" is subjected to normal stress σₓ.
- The element is experiencing a normal stress of σₓ = 110 psi on the left and right sides of the element.
- The stress vector is pointing inward on the left side and outward on the right side.

### (c)
**Diagram Description:**
- A square element labeled "E" is subjected to normal stresses σₓ and σᵧ.
- The element is experiencing a normal stress of σₓ = 300 MPa on the left and right sides.
- The element is experiencing a normal stress of σᵧ = 150 MPa on the top and bottom sides.
- The stress vector for σₓ is pointing to the right, and for σᵧ it is pointing upwards.

### (d)
**Diagram Description:**
- A square element labeled "E" is subjected to normal and shear stresses.
- The element is experiencing a normal stress of σₓ = 62 psi on the right side.
- The element is experiencing a normal stress of σᵧ = 85 psi on the top side.
- The element is experiencing shear stress τₓᵧ = 37 psi on the right side.
- The shear stress vector points to the right on the top face.

For each of these stress elements, Mohr's circle can be constructed to find the principal stresses and maximum shear stress. Mohr's circle provides a graphical representation of the state of stress at a point and helps determine the principal stresses and the maximum shear stress experienced by the element.

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