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

We now set the stress at point A (r A = 150 mm) equal to the 90 MPa allowable stress and
solve for the corresponding magnitude of load P:
P ⎡
− ⎤
90 MPa = +
6,250 mm ⎣
⎢ 1 (217.5 mm)(189.674 mm 150 mm)
2
(150 mm)(197.500 mm − 189.674 mm) ⎦
⎥
∴ P ≤ 67,359 N
Finally, we repeat this process for point B (r B = 275 mm) and solve for the corresponding
magnitude of load P:
P ⎡
− ⎤
90 MPa = +
6,250 mm ⎣
⎢ 1 (217.5 mm)(189.674 mm 275 mm)
2
(275 mm)(197.500 mm − 189.674 mm) ⎦
⎥
∴ P ≤ 73,788 N
This calculation demonstrates that the stress at point A, where tensile flexural stress
is combined with the tensile axial stress, is the most highly stressed point on Section A–B.
On the basis of this combination, the largest allowable load that can be applied to the
clamp is P allow = 67.4 kN.
Ans.
pRoBLEmS
p8.77 A curved bar with a rectangular cross section is subjected
to a bending moment M = 850 N ⋅ m as shown in Figure P8.77. Use
b = 35 mm, d = 60 mm, and r i = 100 mm. Determine the normal
stress at A and B.
M
ri
B
A
M
b
B
A
d
ri
p8.79 The curved member shown in Figure P8.79 has a rectangular
cross section with dimensions b = 2 in. and d = 5 in. The
inside radius of the curved bar is r i = 4 in. A load P is applied at a
distance a = 9 in. from the center of curvature, O. If the tensile and
compressive stresses in the member are not to exceed 24 ksi and
18 ksi, respectively, determine the value of the load P that may be
safely supported by the member.
a
P
d
O
FIGURE p8.77
p8.78 The steel link shown in Figure P8.78 has a central angle
β = 120°. Dimensions of the link are b = 6 mm, d = 18 mm, and
r i = 30 mm. If the allowable normal stress is 140 MPa, what is the
largest load P that may be applied to the link?
O
B
A
r i
O
b
B
b
B
d
FIGURE p8.79
A
A
p8.80 The outside and inside diameters of the tube elbow shown
P
β
P r i
in Figure P8.80 are D = 1.75 in. and d = 1.50 in., respectively, and
r c the inner radius of the elbow is r i = 1.50 in. Determine the stresses
O
O
acting at points A and B when the tube is loaded by a moment
FIGURE p8.78
M = 2,500 lb ⋅ in.
315