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CHAP 4 Finite Element Analysis for Beams and Frames
213
2.
The deflection of the simply supported beam shown in the figure is assumed as
( )
(
1)
v x
cx x
, where
c
is a constant.
A force is applied at the center of the
beam.
Use the following properties:
EI
= 1000 Nm
2
and
L
= 1 m. First, (a) show
that the above approximate solution satisfies displacement boundary conditions, and
(b) use RayleighRitz method to determine
c
.
Solution:
(a) At
x
= 0 and 1,
v
(0) =
v
(1) = 0.
Thus, the approximate solution satisfies displacement
boundary conditions.
(b) The second derivative become: 2
c
.
Using the expression for strain energy in a beam
given in Eq. (4.17) we obtain
1
2
0
2
2
EI
U
c dx
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This note was uploaded on 08/22/2011 for the course EML 4500 taught by Professor Staff during the Fall '08 term at University of Florida.
 Fall '08
 Staff
 Finite Element Analysis

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