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The direct displacement method is another technique that can be used to analyze
indeterminate
structures. This method can be generalized and is commonly used
in
structural analysis software.
In
this method, all degrees of freedom of a structure are restrained, i.e. "locked", and the
member fixed end forces are calculated due to any applied loads on the member. As in
moment distribution, each degree of freedom is then independently released, i.e."un
locked", and the member end forces are determined due to an application of a unit
displacement
that corresponds to each degree of freedom. This displacement can either be a
rotation or a translation. The actual member end forces are then calculated by satisfying
equilibrium conditions at each of the degrees of freedom.
The steps required to complete an analysis based on the direct displacement method are
illustrated in the following simplified example:
Given a structure:
1
l+ l'
A
i) Determine the kinematic degree of indeterminacy,
i.e,
the number of degrees of
freedom.
The
kinematic degree of freedom
is the number of independent joint
displacements
(rotations and translations).
This sample problem has two degrees of kinematic indeterminacy
since the
structure can undergo rotations at both joints Band C.
X.
,,,.
A
+
However, the moment at Joint C is determinate. However, since the moment
at C is zero, modified stiffness can be utilized for member BC. Modified
stiffness is used by not including the rotation at C as an unknown reaction.
This reduces the kinematic indeterminacy
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 Fall '10
 Hosteng
 Governing Authority, member end forces

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