Civil Engineering Reference
In-Depth Information
The second condition is an unstable beam. This occurs when both ends
are released for deflection or more than two of the four degrees of free-
dom are released. Table 5.1 summarizes all the flexural stiffness con-
ditions for the X-Z system. In this table, 1 indicates that the degree of
freedom is released and 0 indicates that the degree of freedom is not
released.
Table 5.1.
Release codes—X-Z system
Equation
∆
iz
q
iy
∆
jz
q
jy
0
0
0
0
4.33
1
0
0
0
5.2
0
1
0
0
5.3
0
0
1
0
5.4
0
0
0
1
5.5
1
1
0
0
5.6
1
0
1
0
Unstable
1
0
0
1
5.6
0
1
1
0
5.6
0
1
0
1
5.6
0
0
1
1
5.6
0
1
1
1
Unstable
1
0
1
1
Unstable
1
1
0
1
Unstable
1
1
1
0
Unstable
1
1
1
1
Unstable
5.2
MEMbER EnD RELEASES, X-Y SYStEM
The X-Y member stiffness can be derived in a similar manner to the X-Z
system. In general, only the sign of the moments will change. The result-
ing stiffness matrices for releasing ∆
iz
,
q
iy
, ∆
jz
, and
q
jy
are shown in Equa-
tions 5.7 through 5.10 with only the affected terms replaced with the new
