Civil Engineering Reference
In-Depth Information
=
1
in. Determine (a) the required values of forces
F
2
and
F
4
, (b) displacement
of node 2, and (c) the reaction force at node 1.
F
2
k
1
k
2
k
3
1
2
3
4
F
4
k
1
k
3
30 lb./in.
k
2
40 lb./in.
Figure P2.5
Verify the global stiffness matrix of Example 2.3 using (a) direct assembly and
(b) Castigliano's first theorem.
2.6
Two trolleys are connected by the arrangement of springs shown in Figure P2.7.
(a) Determine the complete set of equilibrium equations for the system in the
form
[
K
]
{
U
}={
F
}
.
(b) If
k
=
50
lb./in.,
F
1
=
20
lb., and
F
2
=
15
lb., compute
the displacement of each trolley and the force in each spring.
2.7
F
1
2
k
F
2
k
2
k
k
Figure P2.7
Use Castigliano's first theorem to obtain the matrix equilibrium equations for the
system of springs shown in Figure P2.8.
2.8
F
2
F
3
F
4
1
2
3
4
5
k
1
k
2
k
3
k
4
Figure P2.8
2.9
In Problem 2.8, let
k
1
=
k
2
=
k
3
=
k
4
=
10
N/mm,
F
2
=
20
N,
F
3
=
25
N,
F
4
=
40
N and solve for (a) the nodal displacements, (b) the reaction forces at
nodes 1 and 5, and (c) the force in each spring.
2.10
A steel rod subjected to compression is modeled by two bar elements, as shown
in Figure P2.10. Determine the nodal displacements and the axial stress in each
element. What other concerns should be examined?
0.5 m
0.5 m
12 kN
1
2
3
E
207 GPa
A
500 mm
2
Figure P2.10
