Angle between principal stress and shear stress

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chetzread
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Homework Statement


I know that an element that is subjected to max shear stress is 45 degree away from position of an element that is subjected to principal stress.I couldn't understand why the θ s= θ p -45 degree?
Cant it be θ s= θ p +45 degree ?

Homework Equations

The Attempt at a Solution


IMO, it can be both θ s= θ p -45 degree and θ s= θ p +45 degree [/B]
 
Attachments
  • Worked example of plane stress on a square element: sigma x = 50 MPa, sigma y = -10 MPa, tau xy = 40 MPa, with the principal stress formulas and results sigma max = 70 MPa and sigma min = -30 MPa.
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  • Worked solution for principal and maximum shear stress: tan 2θp = 2τxy/(σx − σy) = 80/60, θp = 26.6°, τmax = 50 MPa, θs = θp − 45° = −18.4°, σave = 20 MPa, beside a diagram of a rotated stress element with σmin = 30 MPa and σmax = 70 MPa.
    339.jpg
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