Civil Engineering Reference
In-Depth Information
Calculate the
X
and
Y
displacements of node 3 using the finite element approach
and the data given in Problem 3.1. Also calculate the force in each element. How
do your solutions compare to the results of Problem 3.1?
3.2
Verify Equation 3.28 by direct multiplication of the matrices.
3.3
Show that the transformed stiffness matrix for the bar element as given by
Equation 3.28 is singular.
3.4
Each of the bar elements depicted in Figure P3.5 has a solid circular cross-
section with diameter
d
=
1
.
5
in. The material is a low-carbon steel having
modulus of elasticity
E
3.5
10
6
psi. The nodal coordinates are given
in a global (
X
,
Y
) coordinate system (in inches). Determine the element stiffness
matrix of each element in the global system.
=
30
×
2
(5, 30)
2
(30, 30)
2
(30, 15)
Y
1
1
(0, 0)
1
X
(20, 10)
(0, 0)
(a)
(b)
(c)
(
20, 30)
2
(0, 0)
1
(40,
10)
(10, 10)
1
2
(d)
(e)
Figure P3.5
Repeat Problem 3.5 for the bar elements in Figure P3.6. For these elements,
d
3.6
=
40 mm,
E
=
69 GPa, and the nodal coordinates are in meters.
1
(0, 0)
2
(0.4, 0.2)
1
2
(0.1, 0.1)
(0.2,
0.2)
(a)
(b)
Figure P3.6
