y
y
y
y
d
x
x
x
x
∆s
∆b
∆
w
b
a
c
d
Figure 9. The geometry and deformation of a joint seal in shear loading. (a) original
configuration, (b) shear component of total deformation, (c) bending component of
total deformation, and (d) total deformation, corresponding to solution of Rivlin and
Saunders (1949) for the shear behavior of rubber cylinders bonded at their ends.
effect of reducing the apparent shear modulus of
be used in the nominal stressstrain relation
the seal relative to the actual shear modulus of
the sealant. This is illustrated in Figure 10, which
ty = Ga γ a
depicts the relation of eq 12 in a nondimensional
∆
(13)
form. For example, at d/w = 1, the apparent shear
= Ga
w
modulus is 75% of the shear modulus. Like the
where ty denotes the nominal or average inter-
expressions of eq 1 and 5 for extension and com-
face shear stress that is generated by the trans-
pression loading, the shear loading relations of eq
verse joint displacement ∆, and γa = ∆/w is the
12 and 13 allow the use of the modulus of elastic-
corresponding apparent shear strain. The expres-
ity, measured as a function of temperature, in
sion for the apparent shear modulus can be de-
design calculations.
rived by assuming small shear and bending dis-
placements, ∆ s and ∆b, respectively, as the
CONCLUSION
superimposed components of the total displace-
ment. For the shear component, ∆s = γw, where γ
The relations reviewed here constitute the ba-
is the shear strain, and thus
sis of a practical analysis technique for evaluating
ty
load vs. deflection responses of rectangular joint
∆s =
(14)
w .
seals subjected to tension, compression, and shear.
G
The nominal stressstrain relations presented have
For the bending component, beam theory
yields
10
2
1 ty w
∆b =
w
(15)
3 G d
8
for a volume-incompressible material. Ga can
6
be found by substituting the displacement
∆ = ∆s + ∆b into eq 13. The plane strain shear
4
stiffness F/∆ that corresponds to Ga is
2
Fd
=
Ga
(16)
∆ w
0
1
2
3
4
5
where, for shear loading, F is the resultant
d/w
shear force at the interface per unit length
Figure 10. Ratio of the apparent shear modulus to the shear
along the seal.
A significant bending contribution has the
width ratio d/w.
8
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