P12.026
The stresses shown act at a point on the free surface of a machine component. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are Sx = 17.9 ksi, Sy = 2.3 ksi, and Sxy = 7.4 ksi. Assume β=30∘. Determine the normal stresses σx and σy and the shear stress τxyat the point.
I tired those number and gave me wrong answers
x = 16.21 and 20.40
y = -10.81 and -0.2
xy = -20.91 and -3.054
Homework Answers
From Mohr's circle
we can transform stress tensors from S frame to xy frame
given beta = 30 deg
so, let area of the side of the cube be A
then
From mohr's circle
sigma-x = 0.5(Sx + Sy) + 0.5(Sx - Sy)*cos(2*beta) +
Txy*sin(2*beta)
and
Tn = -0.5(s-x - s-y)*sin(2*beta) + Txy*cos(2*beta)
given values
Sx = 17.9 ksi, Sy = 2.3 ksi, Sxy = 7.4 ksi, beta = 30 deg
Sigma-x = 0.5(17.9 + 2.3) + 0.5(17.9 - 2.3)*cos(60) +
7.4*sin(60)
sigma-x = 20.408587988004 ksi
and
Tn = -0.5(17.9 - 2.3)*sin(60) + 7.4*cos(60)
Tn = -3.0549981495 ksi
hence, sigma-x = 20.408587988004 ksi
sigma-y = 0 ksi
Txy = -3.0549981495 ksi
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P12.026
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compressive) and τ (magnitude only) at this point on the inclined
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used to obtain normal strain data at a point on the free surface of
a machine component. Given the values εa= -185 με, εb= -150 με, εc=
55 με, E = 10,800 ksi, and v = 0.33,
determine
(a) the stress components σx, σy, and τxy at the point.
(b) the principal stresses and the maximum in-plane shear stress at
the point; on paper, show these stresses on an appropriate sketch
that indicates the orientation...
P12.037 The stresses shown act at a point on the free surface of a stressed body. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are Sy = 98.00 MPa 20 MPa, and Sxv = 72 MPa. Assume B = 57. Determine the normal stresses on and ot and the shear stress Int at this point if they act on the rotated stress element shown. 5 Su 15 Answers: On= MPa o MPа Int =...
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