Page 476 - Shigley's Mechanical Engineering Design

bud29281_ch08_409-474.qxd 12/16/2009 7:11 pm Page 451 pinnacle 203:MHDQ196:bud29281:0073529281:bud29281_pagefiles:

Screws, Fasteners, and the Design of Nonpermanent Joints 451
Point E
For the Gerber criterion, from Eq. (8–46), the safety factor is

1
2
2
Answer n f = S ut S + 4S e (S e + σ i ) − S − 2σ i S e
ut
ut
2σ a S e
1
2
2
= 120 120 + 4(18.6)(18.6 + 63.72) − 120 − 2(63.72)(18.6)
2(3.10)(18.6)
= 3.65
which is greater than n p = 3.43 and contradicts the conclusion earlier that the dan-
ger of failure is fatigue. Figure 8–22 clearly shows the conflict where point D lies
between points C and E. Again, the conservative nature of the Goodman criterion
explains the discrepancy and the designer must form his or her own conclusion.

8–12 Bolted and Riveted Joints Loaded in Shear 10
Riveted and bolted joints loaded in shear are treated exactly alike in design and
analysis.
Figure 8–23a shows a riveted connection loaded in shear. Let us now study the
various means by which this connection might fail.
Figure 8–23b shows a failure by bending of the rivet or of the riveted members.
The bending moment is approximately M = Ft/2, where F is the shearing force and
t is the grip of the rivet, that is, the total thickness of the connected parts. The bend-
ing stress in the members or in the rivet is, neglecting stress concentration,
M
σ = (8–52)
I/c
where I/c is the section modulus for the weakest member or for the rivet or rivets,
depending upon which stress is to be found. The calculation of the bending stress in
this manner is an assumption, because we do not know exactly how the load is dis-
tributed to the rivet or the relative deformations of the rivet and the members.
Although this equation can be used to determine the bending stress, it is seldom used
in design; instead its effect is compensated for by an increase in the factor of safety.
In Fig. 8–23c failure of the rivet by pure shear is shown; the stress in the rivet is
F
τ = (8–53)
A
where A is the cross-sectional area of all the rivets in the group. It may be noted that
it is standard practice in structural design to use the nominal diameter of the rivet
rather than the diameter of the hole, even though a hot-driven rivet expands and nearly
fills up the hole.

10 The design of bolted and riveted connections for boilers, bridges, buildings, and other structures in which
danger to human life is involved is strictly governed by various construction codes. When designing these
structures, the engineer should refer to the American Institute of Steel Construction Handbook, the American
Railway Engineering Association specifications, or the Boiler Construction Code of the American Society of
Mechanical Engineers.