Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

For element A, the absolute maximum shear stress is τ abs max =
32 ksi.
The Mohr’s circle for element B is constructed in the accompanying
plot. This circle shows all possible combinations of σ and
τ that occur in the x–y plane.
The maximum in-plane shear stress for element B is equal to
the radius of Mohr’s circle; therefore, τ max = 18 ksi.
As with element A, the z face of element B is also a principal
plane, and therefore, σ z = σ p3 = 0.
Two additional circles can be constructed. The maximum
shear stress in the x–z plane is given by the radius of the Mohr’s
circle connecting points x and z, and the maximum shear stress in
the y–z plane is given by the radius of the circle connecting points
y and z.
By inspection, the larger of these two circles—the x–z circle—
has a greater radius than the x–y circle. Consequently, the absolute
maximum shear stress for element B is τ abs max = 25 ksi. For
element B, the absolute maximum shear stress is greater than the
maximum in-plane shear stress.
τ
τ
τ
y
(14, 0)
σ p2
R = 18
C
Element B
x σ
σ p1 (50, 0)
Element B
R = 25
z
σ p3
y
(14, 0)
σ p2
R =18
C
σ p1
x
(50, 0)
σ
τ
mecmovies
ExAmpLE
m12.13 Using Mohr’s circle, interactively investigate a
three-dimensional stress state at a point.
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