Issue 52
M. Fouzia et alii, Frattura ed Integrità Strutturale, 52 (2020) 281-298; DOI: 10.3221/IGF-ESIS.52.22
By noting (
) moy
l
being the mean shear stress deformation of the adhesive,
the mean shear displacement of the
A moy
A
adhesive,
A G the adhesive shear modulus and φ the diameter of the fixations, we have:
(
)
(
)
2
=
bL n −
A f
/
/ 4
(4)
moy
and
) ( A
)
) ( A
)
(
(
2
2
=
bL n −
=
bL n −
=
f
/ 4
G
/ 4
A moy
A moy
(5)
(
) ( /
)
(
)
2
=
e bL n −
( G l
/ 4
A
moy A
The authors considering that the bolts are deformed only by shearing at the joint plane. Noting G B the shear modulus if the bolt, T B the uniform stress of the bolt and Δ l B the shear deformation of the bolt we have:
2
B B f =
/ ( ( n
) / 4)
(6)
and
(
)
2
n
B
(
)
2
=
=
(7)
f
l
/
en
/ 4
B
moy
B
4
by noting:
( ) l
) B
=
k
(8)
(
l
moy
A
we obtain:
(
)
(
) 2
(
)
=
G k l
e n
(9)
f
)/
/ 4
B B
moy
A
Thus:
(
)
(
)
(
)
(
)
2
2
( = l
e G bL n −
+
(10)
f
1/
/ 4
kG n
/ 4
moy
A
B
A
By defining α as the tress concentration factor expressed by:
(
)
/ total l = l
(11)
moy
A
and considering
(
)
/ = = A total G l e
(12)
G
max
A moy A
A
where ( τ max ) A is the maximum stress at the adhesive, we obtain :
(
)
(
)
(
)
2
2
=
e G bL n −
+
(13)
f
1/
/ 4
kG n
/ 4
l
A
B
total
286
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