Civil Engineering Reference
In-Depth Information
200 lb
18 in.
6 in.
2 in.
1 in.
400 lb/in.
Figure P4.13
500 lb
200 lb
10 in.
8 in.
8 in.
D
400 in.-lb
D
2
1.0 in.
D
1
1.5 in.
Figure P4.14
2 in.
200 lb
300 lb
10 in.
20 in.
10 in.
2 in.
0.25 in.
Figure P4.15
4.16
The tapered beam element shown in Figure P4.16 has uniform thickness
t
and
varies linearly in height from
2
h
to
h
. Beginning with Equation 4.37, derive the
strain energy expression for the element in a form similar to Equation 4.39.
y
2
h
h
x
L
Figure P4.16
Use the result of Problem 4.16 to derive the value of component
k
11
of the
element stiffness matrix.
4.17
The complete stiffness matrix for the tapered element of Figure P4.16 is given by
4.18
−
243
243
156
L
87
L
Eth
3
60
L
3
56
L
2
−
42
L
2
156
L
156
L
[
k
]
=
−
243
−
156
L
243
−
87
L
87
L
42
L
2
−
87
L
45
L
2
