Civil Engineering Reference
In-Depth Information
Repeat Problem 3.11 assuming elements 1 and 4 are removed.
3.12
The cantilever truss in Figure P3.13 was constructed by a builder to support a
winch and cable system (not shown) to lift and lower construction materials. The
truss members are nominal 2
3.13
×
4 southern yellow pine (actual dimensions
10
6
psi). Using the direct stiffness method, calculate
1.75 in.
×
3.5 in.;
E
=
2
×
a.
The global displacement components of all unconstrained nodes.
b.
Axial stress in each member.
c.
Reaction forces at constrained nodes.
d.
Check the equilibrium conditions.
4
30
30
5
2
3
500 lb
Node
1
2
3
4
5
X
Y
0
96
96
151.4
96
0
0
96
96
192
(inches)
Y
45
X
1
Figure P3.13
Figure P3.14 shows a two-member plane truss supported by a linearly elastic
spring. The truss members are of a solid circular cross section having
d
3.14
=
20 mm
and
E
=
80 GPa. The linear spring has stiffness constant 50 N/mm.
a.
Assemble the system global stiffness matrix and calculate the global
displacements of the unconstrained node.
b.
Compute the reaction forces and check the equilibrium conditions.
c.
Check the energy balance. Is the strain energy in balance with the
mechanical work of the applied force?
3 m
15 kN
50
4 m
k
Figure P3.14
