Page 95 - Analysis and Design of Machine Elements

Detachable Joints and Fastening Methods
Although tightening torque generates combined tensile and shear stresses in a bolt, 73
we can simplify the analysis by calculate the tensile stress only, while increasing the value
by 30% to account for the effect of torsional shear stress.
When preloaded bolts carry transverse loads, friction between joint members resists
the external transverse loads. The bolt is subjected to preload only, not affected by the
transverse loads. The magnitude of preload is determined by Eq. (3.2), and the strength
for a preloaded tension bolt subjected to a transverse load is thus
1.3Q p
= ≤ [ ] (3.15)
ca
1 2
d 1
4
3.5.3.3 Preloaded Tension Bolts Subjected to Combined Preload and Static Axial
Loads
When an external static axial load is applied to a preloaded tension bolt, the bolt is
subjected to a combined preload and static axial loads. As shown in Figure 3.12, before
the joint carries an external load, the tightening torque initially applied to the nut or on
the head of bolt produce a preload load Q in the bolt. The preload Q exerts tension on
p p
the bolt and stretch the bolt by a deflection ; while the same amount of force Q on
b p
the clamped members compress the members by a deflection .Thestiffnessofabolt
m
is the ratio of the applied force to the corresponding deflection, expressed as
Q p
k = tan = (3.16)
b
b
b
Similarly, the stiffness of the connected members is
Q p
k = tan = (3.17)
m
m
m
When an external static axial load F is applied to a preloaded tension bolt, the bolt
will stretch further by Δ . Thus, the total deflection of the bolt is +Δ and the total
b
deflection on the clamped members is −Δ . The initial preload and the applied axial
m
′
load add to give resultant forces of Q and Q on the bolt and the clamped members,
p
respectively. Thus, only part of the applied force is carried by the bolt. The amount is
dependent on the relative stiffness of the bolt and the clamped members.
Figure 3.12 Force-deflection F F
relationships of bolt and connected ΔF
members. Q Q
Q p
Q p
F
k k
Qʹ p

θ m
θ b
O b O m
λ λ Δλ
Δλ
λ b λ m