Civil Engineering Reference
In-Depth Information
Finally, if a member is connected to a support, but is free to rotate at
the support, a modified member stiffness factor can be used. In this mod-
ified method, the support joint is moment balanced then carried over and
no further calculations are performed at that joint.
3
4
K
K
′ =
Example 4.13
Moment-distribution method
Determine the moments in the beam shown in Figure 4.25 by the
moment-distribution method.
The modulus of elasticity,
E
, and moment of inertia,
I
, are constant
for the beam.
Since
E
and
I
are constant, the member relative stiffness factor can be
used and we can use a unit value for
I
.
I
L
1
20
K
===
AB
005
.
AB
AB
I
L
1
10
BC
K
===
010
.
BC
BC
At fixed support
A
, the distribution factor for member
AB
is 0 and at the
roller support
C
, the distribution factor for member
BC
is 1. For the inter-
nal roller, the distribution factor for each member must be calculated.
K
KK
005
005010
.
D
=
AB
=
=
0 333
.
FAB
+
.
+
.
AB
BC
K
KK
01
005
.
BC
D
=
=
=
0 667
.
FBC
+
.
+
010
.
AB
BC
Z
8 kips
1.2 kips/ft
8 kips
X
A
B
C
20ft
5ft
5ft
Figure 4.25.
Example 4.13 Moment-distribution.
