Page 230 - Shigley's Mechanical Engineering Design

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Deflection and Stiffness 205
4–88 For the wire form shown, determine the deflection of point A in the y direction. Assume
R/h > 10 and consider the effects of bending and torsion only. The wire is steel with E =
200 GPa, ν = 0.29, and has a diameter of 6 mm. Before application of the 250-N force the wire
form is in the xz plane where the radius R is 80 mm.

y

x

Problem 4–88
R

z
90°
A

250 N
4–89 A 100-ft cable is made using a 12-gauge (0.1055-in) steel wire and three strands of 10-gauge
(0.1019-in) copper wire. Find the deflection of the cable and the stress in each wire if the cable
is subjected to a tension of 400 lbf.
4–90 The figure shows a steel pressure cylinder of diameter 5 in that uses six SAE grade 4 steel bolts
having a grip of 10 in. These bolts have a proof strength (see Chap. 8) of 65 kpsi. Suppose the
bolts are tightened to 75 percent of this strength.
(a) Find the tensile stress in the bolts and the compressive stress in the cylinder walls.
(b) Repeat part (a), but assume now that a fluid under a pressure of 500 psi is introduced into the
cylinder.

1
Six -in grade 4 bolts
2

1
= in
4
t

Problem 4–90
l c = 9 in D = 5 in l = 10 in
b

4–91 A torsion bar of length L consists of a round core of stiffness (GJ) c and a shell of stiffness (GJ) s .
If a torque T is applied to this composite bar, what percentage of the total torque is carried by
the shell?