Civil Engineering Reference
In-Depth Information
Figure 5.5
Classification of joints by initial stiffness
A
nominally pinned
joint has
S
j,ini
≤
0.5
E
a
I
b
/
L
b
(5.1)
where
E
a
I
b
is the rotational stiffness of the connected beam, of length
L
b
.
The value of
E
a
I
b
should be consistent with that taken for a cross-section
adjacent to the joint in global analysis of the frame. The significance
of this limit to
S
j,ini
can be illustrated by considering a beam of span
L
b
and uniform section that is connected at each end to rigid columns, by
connections with
S
j,ini
0.5
E
a
I
b
/
L
b
. It can be shown by elastic analysis
that for a uniformly-distributed load
w
per unit length, the restraining
(hogging) moments at each end of the beam are
=
(
wL
2
/8)/7.5
M
el
=
(5.2)
These end moments act also on the columns, the flexibility of which
would in practice reduce the moments below
M
el
. In design with the
pins on the column centre-line, it is being assumed that columns designed
for
M
el
=
0 are not 'adversely affected' by bending moment from the
joint.
A joint is
rigid
if
S
j, ini
≥
k
b
E
a
I
b
/
L
b
where
k
b
8 for a braced frame (defined in EN 1993-1-8).
The amount of redistribution of elastic moments caused by the flexibility
of a connection that is just 'rigid' can be quite significant. As an example,
we consider the same beam as before, with properties
E
a
I
b
and
L
b
, sup-
ported at each end by rigid columns, with uniform load such that both end
moments are 2
M
j,Rd
/3, when the joints have stiffness
S
j,ini
=
=
8
E
a
I
b
/
L
b
.
