Question

EXAMPLE The state of plane stress at a point on a solid is represented on the element shown in the figure. Determine a) principal stresses, and b) the maximum in-plane shear stress and associated average normal stress. y 90 MPa $\sigma_x = -20$ MPa 20 MPa $\sigma_y = +90$ MPa X 60 MPa $\tau_{xy} = +60$ MPa

          EXAMPLE
The state of plane stress at a point on a solid is represented on the element shown
in the figure. Determine a) principal stresses, and b) the maximum in-plane shear
stress and associated average normal stress.
y
90 MPa
$\sigma_x = -20$ MPa
20 MPa
$\sigma_y = +90$ MPa
X
60 MPa
$\tau_{xy} = +60$ MPa

EXAMPLE
The state of plane stress at a point on a solid is represented on the element shown
in the figure. Determine a) principal stresses, and b) the maximum in-plane shear
stress and associated average normal stress.
y
90 MPa
= -20 MPa
20 MPa
= +90 MPa
X
60 MPa
τxy = +60 MPa

Added by Rachel L.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Rashmi Prakash

Step 1

The stress tensor is given by: σ = [σx τxy] [τxy σy] Substituting the given values, we have: σ = [-20 60] [60 90] Show more…

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I need this example solved but without having a sigma in the Y direction, Ïƒy=0, and Ïƒx=20 in tension instead of compression. Tau stays the same. Ï„xy=60 MPa. EXAMPLE The state of plane stress at a point on a solid is represented on the element shown in the figure. Determine a) principal stresses, and b) the maximum in-plane shear stress and associated average normal stress. Ïƒx = -20 MPa, Ïƒy = 90 MPa, Ï„xy = 60 MPa.