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Answer :
Final answer:
The principal stresses for a two-dimensional stress state consisting of a tension of 76 MPa and a shear of 48 MPa are 100 MPa and -100 MPa.
Explanation:
To determine the principal stresses for a two-dimensional stress state consisting of a tension of 76 MPa and a shear of 48 MPa, we can use the concept of principal stresses. The principal stresses are the maximum and minimum stresses experienced in a particular stress state.
To find the principal stresses, we can use the equation:
σ1 = (σx + σy)/2 + √((σx - σy)/2)2 + τxy2)
σ2 = (σx + σy)/2 - √((σx - σy)/2)2 + τxy2)
Substituting the given values:
σx = 76 MPa, σy = 76 MPa, τxy = 48 MPa
Calculating the principal stresses:
σ1 = (76 + 76)/2 + √((76 - 76)/2)2 + 482)
= 100 MPa
σ2 = (76 + 76)/2 - √((76 - 76)/2)2 + 482)
= -100 MPa
Therefore, the principal stresses for this plane stress state are 100 MPa and -100 MPa.
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