Question

9-15. The state of stress at a point is shown on the element. Determine (a) the principal stress and (b) the maximum in-plane shear stress and average normal stress at the point. Specify the orientation of the element in each case. Show the results on each element. 80 MPa 50 MPa 60 MPa

          9-15. The state of stress at a point is shown on the element.
Determine (a) the principal stress and (b) the maximum
in-plane shear stress and average normal stress at the point.
Specify the orientation of the element in each case. Show
the results on each element.
80 MPa
50 MPa
60 MPa

9-15. The state of stress at a point is shown on the element.
Determine (a) the principal stress and (b) the maximum
in-plane shear stress and average normal stress at the point.
Specify the orientation of the element in each case. Show
the results on each element.
80 MPa
50 MPa
60 MPa

Added by Aaron A.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Shaiju T

06/17/2022

Step 1

The principal stresses can be calculated using the formula: σ1,2 = (σx + σy)/2 ± √((σx - σy)/2)^2 + τxy^2 Substitute the given values: σ1 = (50 + 60)/2 + √((50 - 60)/2)^2 + 30^2 σ1 = 55 + √((-5)^2 + 30^2) σ1 = 55 + √(25 + 900) σ1 = 55 + √925 σ1 ≈ 55 + 30.41 σ1 ≈ Show more…

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9-15. The state of stress at a point is shown on the element. Determine (a) the principal stress and (b) the maximum in-plane shear stress and average normal stress at the point. Specify the orientation of the element in each case. Show the results on each element. σx = 50MPa σy = 60MPa τxy = 30MPa