Civil Engineering Reference
In-Depth Information
cHAPtER 5
A
dvAnced
s
tructurAL
s
tiffness
In this chapter, concepts learned in previous chapters are expanded and
applied to advanced structural stiffness. This method is applied in comput-
ers to solve complex structures that are statically determinate or statically
indeterminate. Matrices will be utilized to determine internal member
forces and displacements within a structure. Small pieces of the struc-
ture are analyzed and then compiled into a larger matrix in order to view
the structure as a whole. This procedure is the basis for finite element
analyses.
5.1
MEMbER EnD RELEASES, X-Z SYStEM
Joint stiffness is expressed in the master matrix for a structure, but two
situations exist that may cause them to vary. First, a joint that is being uti-
lized as a support may be released. For example, the support becomes slot-
ted or pinned. When looking at a joint release, the joint is fully designed as
a support before the release. This creates the reaction components. A sup-
port release is in the global system and is handled in the reduction of the
joint stiffness matrix. Second, a member can be physically released from a
joint for one or more of the six possible end displacements. When a mem-
ber release occurs, the member is released in some direction and the stiff-
ness contribution that member was making to the joint changes or goes to
zero. When a member is released in the local system, this release changes
the member stiffness matrix. Some of these released stiffness matrices will
be derived in the following examples. The order of the motions and forces
on the member's end are given by the deflections and rotations at the
i
-end
followed by the deflections and rotations at the
j-
end. The following is a
full list of stiffness values simplified from Equation 4.33:
