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

p12.19 Two steel plates of uniform cross section are welded
together as shown in Figure P12.19. The plate dimensions are b =
5.5 in. and t = 0.375 in. An axial force P = 28.0 kips acts in the
member. If a = 2.25 in., determine the magnitude of
(a) the normal stress that acts perpendicular to the weld seam.
(b) the shear stress that acts parallel to the weld seam.
p12.22 The state of stress at a point in a solid component is
shown in Figure P12.22. The stress magnitudes are σ n = 80 MPa,
σ t = 40 MPa, and τ nt = 32 MPa, acting in the directions indicated in
the figure. Determine the normal and shear stress components acting
on plane AB for a value of β = 35°.
P
a
A
σ
t
t
FIGURE p12.19
p12.20 The cylinder in Figure P12.20 consists of spirally
wrapped steel plates that are welded at the seams. The cylinder has
an outside diameter of 280 mm and a wall thickness of 7 mm. The
cylinder is subjected to axial loads P = 90 kN. For a seam angle
β = 35°, determine
(a) the normal stress perpendicular to the weld seams.
(b) the shear stress parallel to the weld seams.
b
P
y
x
p12.23–p12.24 The stresses shown in Figures P12.23a and
P12.24a act at a point on the free surface of a stressed body. Determine
the normal stresses σ n and σ t and the shear stress τ nt at this
point if they act on the rotated stress element shown in Figures
P12.23b and P12.24b.
B
FIGURE p12.22
β
τ nt
σ
n
y
β
P
x
P
32 MPa
t
FIGURE p12.20
p12.21 A rectangular polymer plate of dimensions a = 150 mm
and b = 360 mm is formed by gluing two triangular plates as shown
in Figure P12.21. The plate is subjected to a tensile normal stress of
10 MPa in the long direction and a compressive normal stress of
6 MPa in the short direction. Determine
(a) the normal stress perpendicular to the glue seam.
(b) the shear stress parallel to the glue seam.
71 MPa
y
x
86 MPa
FIGURE p12.23a
54°
τ
FIGURE p12.23b
σ
nt
t
σ
n
n
σ
y
1,100 psi
t
σ
t
a
Seam
σ
x
y
x
1,750 psi
2,900 psi
τ
nt
σ
n
20°
n
b
FIGURE p12.21
FIGURE p12.24a
FIGURE p12.24b
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