1
CE 332  Introduction
to the Flexibility
Method
Please Read and Reference Chapter 10 from the Hibbeler text
Applying
the Flexibility
Method
to solve Linear
Elastic,
Statically
Indeterminate
Structures
Flexibility Method
(A.K.A)
•
Method of Consistent Deformations
•
Method of Super Position
•
Force Method
We will be solving
1 and 2 degree
externally
indeterminate
structures
by satisfying:
•
Equilibrium
•
Compatibility
The concept
of compatibility
is based
on the physical
reality
that the structure
must fit together.
There
can be no gaps or overlaps
within
the members
and the deflected
shape
must be consistent
with the
constraints imposed
by the supports,
When a
structure
is indeterminate,
it is said to have redundancy,
meaning there are additional reactions
present which are not necessary
to maintain stability.
Since equilibrium
must be satisfied,
there
must be
at least 3 reactions present and no geometric
instabilities.
Based
on this information,
the degree
of indeterminacy
will be equal
to the number
ofredundants
present.
Example 1
Determine
the reactions
and draw
the moment
diagram
for this structure.
EI
=
constant
___
.~
x
L
First, determine
the degree
of indeterminacy:
Reactions
=
4
Equations
of Equilibrium
=
3
Therefore,
there is one more unknown
than equations
of statics to evaluate for the reactions.
We need one additional
equation
which
will be based
on the compatibility
of the structure.
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 Fall '10
 Hosteng
 2 degree, 0 , flexibility method

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