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EML 4507 FEA & DESGN
Fall 2010
HW11
Solution
An external couple
C
2
is applied at Node 2 in the beam shown below.
When
EI
= 10
5
N.m
2
, the
rotations in radians at the three nodes are determined to be
1
= –0.025,
2
= +0.05,
3
= –0.025
a) Draw the shear force and bending moment diagrams for the entire beam.
b) What is the magnitude of the couple
C
2
applied at Node 2?
c) What is the support reaction
F
y
1
at Node 1?
Solution:
Note that this problem is like a problem in reverse engineering in the sense the displacements are given
and one has to determine the forces applied. In fact this problem is a legitimate problem and is called an
inverse problem. In some practical situations one may not know the loads but displacements can be
measured. Then one needs to estimate the forces from the displacements using inverse methods.
There are two methods to determine the reactions and the applied couple. The first method is straight
forward and uses the equation
s
s
s
K Q
F
. Since we know all DOFs,
F
s
can be calculated easily.

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