Civil Engineering Reference
In-Depth Information
EI= 1.0
r
A=420.0
1.0
1.0
1.0
Figure 11.24
5. A simply supported beam of length,
L
=
1 and properties
EI
=
1
.
0,
ρA
=
3
.
7572 is
subjected to a constant transverse force,
48, which moves across the beam from
the left to right support with a constant velocity,
P
=
1. By discretising the beam
into 4 elements, compute the time dependent response of the centreline of the beam.
Show that the centreline deflection reaches a maximum value that is approximately
1.743 times the deflection that would have been obtained if the load had been placed
statically at the centre of the beam. Use equivalent fixed end moments and reactions
to model the effect of the moving load at four locations within each element.
Compare your result with the analytical solution at the centreline given by:
U
=
sin
2
PL
3
π
cω
1
t
−
c
sin
ω
1
t
v
=
4
EI
1
−
c
2
where
EI
ρA
2
ω
1
=
π
πU
ω
1
L
and
c
=
L
2
References
Bathe KJ 1996
Numerical Methods in Finite Element Analysis
, 3rd edn. Prentice Hall, Englewood
Cliffs, N.J.
Key SW 1980 Transient response by time integration: A review of implicit and explicit operators. In
Advances in Structural Dynamics
(ed. Donea J). Applied Science, London, pp. 71-95.
Smith IM 1984 Adaptability of truly modular software.
Eng Comput
1
(1), 25-35.
Warburton GB 1964
The Dynamical Behaviour of Structures
. Pergamon Press, Oxford.
Wong SW, Smith IM and Gladwell I 1989 PCG methods in transient FE analysis Part II: Second
order problems.
Int J Numer Methods Eng
28
(7), 1567-1576.
