Civil Engineering Reference
In-Depth Information
Table 5.2.
Release codes—X-Y system
Equation
∆
jy
q
iz
∆
jy
q
jz
0
0
0
0
4.33
1
0
0
0
5.1
0
1
0
0
5.2
0
0
1
0
5.3
0
0
0
1
5.4
1
1
0
0
5.5
1
0
1
0
Unstable
1
0
0
1
5.5
0
1
1
0
5.5
0
1
0
1
5.5
0
0
1
1
5.5
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
Table 5.2 summarizes all the flexural stiffness conditions for the X-Y sys-
tem. In this table, 1 indicates that the degree of freedom is released and 0
indicates that the degree of freedom is not released.
5.3
MEMbER EnD RELEASES, 3-D SYStEM
When member releases occur in both coplanar systems, X-Z and X-Y, the
member stiffness matrix should be created by combining the appropriate
conditions from each system. The process for creating the global joint stiff-
ness is the same as outlined in Section 4.13 with four modifications. First,
the released member stiffness matrix should be used for the appropriate
members in step one. Second, if a released member has a member load the
fixed-end forces and moments must be modified. These modified forces
and moments can be found in most structural analysis textbooks. Third, the
released member stiffness matrix should be used to solve for the local mem-
ber forces in step six. Lastly, the modified fixed-end forces and moments
must be added to the local member end forces and moments in step six. The
following example uses a released member to model a structure.
