Page 96 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
74
According to the force equilibrium and force-deflection relationships, the forces in
the bolt and in the clamped members are calculated by
{
ΔF =Δ k b
F −ΔF =Δ k
m
From these equations, we then have
k b
⎧
⎪ ΔF = F
k + k
⎪ b m
⎨
k m
F −ΔF = F
⎪
k + k
⎪
b m
⎩
Therefore, the total load in the bolt is
k b
Q = Q + F (3.18)
p
k + k
b m
The total load in the bolt includes the initial preload due to tightening, and a partial
of subsequently applied operating force, which tends to separate the clamped members.
And the resultant load in the clamped members is
k m
′
Q = Q − F (3.19)
p p
k + k
b m

where k b is the relative stiffness of the joint. Since gaskets are usually inserted at the
k b +k m
interface between bolted members, the relative stiffness depends on the material of gas-
kets. For a metal gasket, it is approximately 0.2–0.3; for leather 0.7; for asbestos, 0.8 and
for rubber, 0.9.
The total load in the bolt depends greatly on the relative stiffness. If k ≫ k ,wehave
m
b
Q ≈ Q + F; while for k ≪ k ,wehave Q ≈ Q . Therefore, when a bolted joint carries a
m
p
p
b
relatively large load, high stiffness gaskets should be used.
To prevent the separation of joint, the resultant load in the clamped members Q ′ p
should be greater than zero, that is,
′
Q ≥ 0 (3.20)
p
′
For ordinary bolted joints subjected to a stable load, select Q = (0.2–0.6) F; for ordi-
p
nary bolted joints subjected to a variable load, Q ′ = (0.6–1.0) F;for asealing case,
p
′
′
Q = (1.5–1.8) F and for anchor bolt joints, Q ≥ F [8].
p p
The static strength of a preloaded bolt subjected to a combined preload and static axial
loads is then
1.3Q
= ≤ [ ] (3.21)
ca 1
d 2 1
4
3.5.3.4 Preloaded Tension Bolts Subjected to Combined Preload and Variable Axial
Loads
When a preloaded tension bolt is subjected to a variable load fluctuating between zero
and an upper extreme F, the total load in a bolt varies from Q to Q, as indicated in
p