Civil Engineering Reference
In-Depth Information
Centre of rotation
(
y
r
, z
r
)
M
x
δ
y
V
y
z
δ
x
V
y
Centre of
rotation
(
y
r
, z
r
)
x
M
y
δ
x
N
x
r
i
A
i
(
y
i
, z
i
)
A
i
y
V
vi
(
y
i
, z
i
)
N
xi
z
Typical
connector
Typical connector
Connection plane
M
z
z
(a) In-plane joint
(b) Out-of-plane joint
Figure 9.11
Joint forces.
equilibriumoftheconnectorforces
V
vi
thattheaxisofrotationliesatthecentroid
of the connector group. The moment exerted by the connector force is
V
vi
r
i
, and
so the total moment
M
x
is given by
A
i
r
i
.
M
x
=
k
v
δθ
x
(9.2)
i
If this is substituted into equation 9.1, the connector force can be evaluated as
V
vi
=
M
x
A
i
r
i
.
(9.3)
A
i
r
i
i
However,therealbehaviourofin-planemomentjointsislikelytobesomewhat
different,justasitisfortheforcejointsdiscussedinSection9.4.1.Thisdifference
is due to the flexibility of the plates, the inelastic behaviour of the connectors at
higher moments, and the slip due to the clearances between any bolts and their
holes.
Welded moment joints may be analysed by making the same assumptions as
forboltedjoints[12].Thusequations9.2and9.3maybeused, withtheweldsize
substituted for the bolt area, and the summations replaced by integrals along the
weld.
Thesimplifyingassumptionsofelasticconnectorsandrigidplatesaresometimes
also made for joints with moments acting normal to the plane of the connectors,
as shown in Figure 9.12b. It is shown in Section 9.9.2 that the connector tension
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