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If a point in a strained material is subjected to two mutually perpendicular stresses, σx = 100 MPa (T) and σy = 50 MPa (C), then what will be the magnitude of maximum shear stress?
- a)25 MPa
- b)50 MPa
- c)75 MPa
- d)150 MPa
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If a point in a strained material is subjected to two mutually perpend...
Given:
σx = 100 MPa (Tensile) and σy = - 50 MPa (Compressive)
Since it is a bi-axial state of stress ⇒ σ3 = 0
Now, maximum shear stress is given by
∴ τ2 = 75 MPa.
σx = 100 MPa (Tensile) and σy = - 50 MPa (Compressive)
Since it is a bi-axial state of stress ⇒ σ3 = 0
Now, maximum shear stress is given by
∴ τ2 = 75 MPa.
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If a point in a strained material is subjected to two mutually perpend...
The resultant stress at that point can be determined using the principles of vector addition. The resultant stress is obtained by adding the magnitudes of the two perpendicular stresses and the angle between them.
Mathematically, if the two perpendicular stresses are denoted as σ1 and σ2, the resultant stress (σr) can be calculated using the following equation:
σr = sqrt(σ1^2 + σ2^2 + 2σ1σ2cosθ)
where θ is the angle between the two perpendicular stresses.
This equation takes into account both the magnitudes of the two stresses and the angle between them. The resultant stress will be maximum when the two stresses are parallel (θ = 0) and minimum when they are perpendicular (θ = 90°).
It is important to note that this equation assumes that the material is linearly elastic and obeys Hooke's law. In reality, materials may exhibit non-linear behavior under certain conditions, and more complex equations may be required to accurately calculate the resultant stress.
Mathematically, if the two perpendicular stresses are denoted as σ1 and σ2, the resultant stress (σr) can be calculated using the following equation:
σr = sqrt(σ1^2 + σ2^2 + 2σ1σ2cosθ)
where θ is the angle between the two perpendicular stresses.
This equation takes into account both the magnitudes of the two stresses and the angle between them. The resultant stress will be maximum when the two stresses are parallel (θ = 0) and minimum when they are perpendicular (θ = 90°).
It is important to note that this equation assumes that the material is linearly elastic and obeys Hooke's law. In reality, materials may exhibit non-linear behavior under certain conditions, and more complex equations may be required to accurately calculate the resultant stress.
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If a point in a strained material is subjected to two mutually perpendicular stresses, σx = 100 MPa (T) and σy = 50 MPa (C), then what will be the magnitude of maximum shear stress?a)25 MPab)50 MPac)75 MPad)150 MPaCorrect answer is option 'C'. Can you explain this answer?
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