The cylinder consists of spirally wrapped steel plates that are
welded at the seams in the orientation shown. Assume β = 30 ∘ . The
cylinder has an inside diameter of 31 in. and a wall thickness of
0.3125 in. The end of the cylinder is capped by a rigid end plate.
The cylinder is subjected to a compressive load of P = 115
kips and a torque of T = 255 kip-ft, which are applied to
the rigid end cap in the directions shown. Determine:
(a) the normal stress perpendicular to the weld seams.
(b) the shear stress parallel to the weld seams.
(c) the principal stresses and the maximum shear stress on the
outside surface of the cylinder.
part 1
(a) Determine the magnitude of the normal stress (report a
positive number) on an element whose sides are parallel to the x
and y axes caused by the axial load. Express your answers in
ksi.
Answer: σ = ksi.
part 2
(a) Determine the magnitude of the shear stress (report a
positive number) on an element whose sides are parallel to the
x and y axes caused by the torque.
Answer: τ = ksi.
(a) Determine the correct signs for the stresses using the sign
convention for stresses on an element. Also determine the normal
and tangent directions for the weld seam specifying the angle
θn (report only the positive angle) that
locates the n direction with respect to the x
direction.
Answer:
σx = ksi,
σy = ksi,
τxy = ksi,
θn = °.
part 4
Determine the normal stress (positive if tensile, negative if
compressive) perpendicular to the weld.
Answer: σn = ksi.
part 5
(b) Determine the shear stress (remember that the t
direction is perpendicular to n in the same sense that
y is perpendicular to x) parallel to the
weld.
Answer: τnt = ksi.
part 6
(c) Determine the principal stresses
(σp1 >
σp2 ) at the point.
Answers: σp1
= ksi, σp2
= ksi.
part 7
(c) Determine the maximum in-plane shear stress and its
associated normal stress at the point.
Answers: τmax = ksi,
σavg = ksi.
part 8
Determine the orientation (report the smallest rotation angle)
of the principal stresses.
Answer: θp = °.
The cylinder consists of spirally wrapped steel plates that are welded at the seams in the...
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