Civil Engineering Reference
In-Depth Information
4 in.
d
2 in.
d
1 in.
x
T
80
F
T
212
F
Insulated
Figure P5.11
the heat flux values at the element boundaries. Use Galerkin's finite element
method.
5.12
Consider a tapered uniaxial tension-compression member subjected to
an axial load as shown in Figure P5.12. The cross-sectional area varies as
A
=
A
0
(1
−
x
/
2
L
)
, where
L
is the length of the member and
A
0
is the area at
x
=
0. Given the governing equation
d
2
u
d
x
2
E
=
0
as in Equation 5.31, obtain the Galerkin finite element equations per
Equation 5.33.
x
2
L
A
0
(
1
)
A
A
0
x
L
Figure P5.12
5.13
Many finite element software systems have provision for a tapered beam
element. Beginning with Equation 5.46, while noting that
I
z
is not constant,
develop the finite element equations for a tapered beam element.
5.14
Use the results of Problem 5.13 to determine the stiffness matrix for the tapered
beam element shown in Figure P5.14.
y
2 in.
1 in
.
x
6 in.
Uniform thickness
t
0.75 in.
E
30
10
6
lb/in.
2
Figure P5.14
