Civil Engineering Reference
In-Depth Information
Example 4.14
Moment-distribution
Determine the moments in the beam shown in Figure 4.25 by the modified
moment-distribution method.
There are two primary differences when using this method. First, use
a modified member stiffness factor for member BC.
=
()
=
3
K
301
4
.
K
′ =
BC
0 075
.
BC
4
The modified factor must be used to recalculate the distribution factors.
K
KK
005
005075
.
AB
D
=
=
=
040
.
FAB
+
.
+
.
AB
BC
K
KK
0 075
00
.
. 550075
D
=
BC
=
=
060
.
FBC
+
+
.
AB
BC
Second, the fixed-end moment at the pinned support is balanced then car-
ried over to the far end before the moment-distribution process begins.
The process is shown in Table 4.2.
Table 4.2.
Example 4.14 Moment-distribution
0.00
0.400
0.600
1.00
Distribution
Factor
−
40.00
40.00
−
10.00
10.00 Fixed
-
end
Moment
−
5.00
−
10.00
Balance @ C
0.00
−
10.00
−
15.00
Distribution
1
−
5.00
0.00
0.00
Carry
-
over
1
−
45.00
30.00
−
30.00
0.00
Final Moments
4.10
ELAStic MEMbER StiffnESS, X-Z SYStEM
The stiffness method for analyzing building structures is widely used by
engineers and commercial computer structural analysis programs. The
method was developed 1934 and 1938 by Arthur Collar (Lewis et al.
1939). The basic definition of
stiffness
is the force due to a unit deforma-
tion.
Flexibility
is the reciprocal or inverse of stiffness and is defined as
the deformation due to a unit force. Either of these principles can be used
to find the behavior of structural members due to motion and loads. In this
section, the
elastic member stiffness
for a linear element will be derived.
