Page 93 - Analysis and Design of Machine Elements

and Detachable Joints and Fastening Methods 71
zQ p M
≈ − > 0 (3.9)
pmin
A W
where W is effective section modulus of the contact surface and A is theeffectivearea
of the contact surface.
In real engineering practice, the total load a multiply bolted joint is subjected to is usu-
ally the combination of the previously discussed cases. The basic approach to obtain the
load on each bolt is decomposition and superposition. The complex external load is first
decomposed into simple loading cases and the load each bolt carries under each sim-
ple loading condition is obtained by previous analyses. The vector sum of these results
forms the total load a bolt carries. Since all the bolts within a group are identical, we
only need to consider the bolt carries the maximum load. When the bolt that carries the
maximum load is identified, the strength of bolt can be determined by the methods to
be introduced next.

3.5 Strength Analysis

3.5.1 Potential Failure Modes

According to the previous force analysis, it is found that although multiply bolted joints
can carry various external loads, each individual bolt actually carries either tension loads
or shear loads. Correspondingly, they are termed tension bolts or shear bolts.
A tension bolt carries external axial loads, preload or the combination of both. Poten-
tial failure modes for a tension bolt may be elastic or plastic deformation. Machinery
constantly operate dynamically; accordingly, tension bolts usually have a small dynamic
load superimposed on a much larger static preload. The fluctuating load will cause
fatigue fracture failure in fasteners. A shear bolt is subjected to a transverse shearing
load. The potential failure modes may be the crushing or shearing of bolt shanks.
Other failure modes can also be observed depending on operating conditions, for
example, fretting fatigue due to small amplitude cyclic relative motions at the interface,
corrosion fatigue in corrosive environments, creep and thermal relaxation at elevated
temperatures in jet engines and nuclear reactors, wear in movable joints and so on.
Statistically, the distribution of typical bolt failure is about 15% at the fillet under head,
20% at the end of thread and 65% at the first thread engaged in a nut [9, 10]. These are
the locations of high stress concentration.

3.5.2 Strength Analysis for Shear Bolts
Shear bolts, usually used in precision bolted joints, are used to carry transverse loads,
as illustrated in Figure 3.8c. Since there is no clearance between the bolt shank and the
inner surface of hole, the transverse load is carried by bearing between the shank and
cylindrical hole and shear at the shank cross section. Assume that the bearing stress is
uniformly distributed over the projected contact area of the bolt shank, the crushing
strength is then [11]
F s
= ≤ [ ] (3.10)
p p
d L
0 min