Civil Engineering Reference
In-Depth Information
Repeat Problem 3.14 if the spring is removed.
3.15
Owing to a faulty support connection, node 1 in Problem 3.13 moves 0.5 in.
horizontally to the left when the load is applied. Repeat the specified
computations for this condition. Does the solution change? Why or why not?
3.16
Given the following system of algebraic equations
3.17
−
10
10
0
0
x
1
x
2
x
3
x
4
F
1
F
2
F
3
F
4
−
−
10
20
10
0
=
0
−
10
20
−
10
0
0
−
10
10
and the specified conditions
x
1
=
0
x
3
=
1
.
5
F
2
=
20
F
4
=
35
calculate
x
2
and
x
4
. Do this by interchanging rows and columns such that
x
1
and
x
3
correspond to the first two rows and use the partitioned matrix approach of
Equation 3.45.
Given the system
3.18
−
50
50
0
0
U
1
U
2
U
3
U
4
30
F
2
40
40
−
−
50
100
50
0
=
0
−
50
75
−
25
0
0
−
25
25
and the specified condition
U
2
=
0.5, use the approach specified in Problem 3.17
to solve for
U
1
,
U
3
,
U
4
, and
F
2
.
For the truss shown in Figure P3.19, solve for the global displacement
components of node 3 and the stress in each element. The elements have cross-
sectional area
A
3.19
1.0 in.
2
and modulus of elasticity 15
10
6
psi.
=
×
4
72 in.
60
3
60
30
1
2
Figure P3.19
3.20
Each bar element shown in Figure P3.20 is part of a 3-D truss. The nodal
coordinates (in inches) are specified in a global (
X
,
Y
,
Z
) coordinate system.
Given
A
=
2 in.
2
and
E
=
30
×
10
6
psi, calculate the global stiffness matrix of
each element.
