Page 484 - Shigley's Mechanical Engineering Design

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Screws, Fasteners, and the Design of Nonpermanent Joints 459
(c) The channel is thinner than the bar, and so the largest bearing stress is due to the
pressing of the bolt against the channel web. The bearing area is A b = td = 10(16) =
2
160 mm . Thus the bearing stress is
F 21.0(10) 3
Answer σ =− =− =−131 MPa
A b 160
(d) The critical bending stress in the bar is assumed to occur in a section parallel to
the y axis and through bolts A and B. At this section the bending moment is
M = 16(300 + 50) = 5600 N · m
The second moment of area through this section is obtained by the use of the trans-
fer formula, as follows:

2
I = I bar − 2(I holes + d A)
¯
15(200) 3 15(16) 3 2 6 4
= − 2 + (60) (15)(16) = 8.26(10) mm
12 12
Then

Mc 5600(100)
3
Answer σ = = (10) = 67.8MPa
I 8.26(10) 6

PROBLEMS
8–1 A power screw is 25 mm in diameter and has a thread pitch of 5 mm.
(a) Find the thread depth, the thread width, the mean and root diameters, and the lead, pro-
vided square threads are used.
(b) Repeat part (a) for Acme threads.
8–2 Using the information in the footnote of Table 8–1, show that the tensile-stress area is

π 2
A t = (d − 0.938 194p)
4
8–3 Show that for zero collar friction the efficiency of a square-thread screw is given by the equation

1 − f tan λ
e = tan λ
tan λ + f
Plot a curve of the efficiency for lead angles up to 45 . Use f = 0.08.
◦
8–4 A single-threaded 25-mm power screw is 25 mm in diameter with a pitch of 5 mm. A vertical
load on the screw reaches a maximum of 5 kN. The coefficients of friction are 0.06 for the
collar and 0.09 for the threads. The frictional diameter of the collar is 45 mm. Find the over-
all efficiency and the torque to “raise” and “lower” the load.
8–5 The machine shown in the figure can be used for a tension test but not for a compression test.
Why? Can both screws have the same hand?