Page 317 - Marine Structural Design

Chapter I4 Offshore Structures Under Impact Loads 293

The first three examples are problems that can be solved assuming small displacements, but
the material has kinematic strain hardening. The last example is a clamped beam struck by a
mass, which involves both large displacements and strain hardening.
EXAMPLE 14.1: Fixed Beam Under a Central Lateral Impact Load
The dynamic elastic-plastic behavior of a rectangular beam, clamped at both ends, as shown in
Figure 14.2 (a) is analyzed.
The beam is subjected to a concentrated step load at the midspan, as shown in Figure 14.2 (b).
Symmetry allows only half of the beam to be modeled. In an analysis using the MARC FEM
program, five elements of element type 5 are used as illustrated in Figure 14.2 (c). The
element is a two-dimensional rectangular section of a beam-column element. In the evaluation
of the element stiffness, three Gaussian integration points are chosen along the axial direction
of the element. At each Gauss point, the cross-section is divided in to 11 Simpson integration
points. Only normal stresses are considered in the elastic-plastic analysis. Since this is a small
displacement problem, the axial sectional force will always be zero. Therefore, the plastic
yield condition used in the present analysis is taken to be:
M,/M, - 1 = 0 (14.21)

1- h : 0.004m
lbl b : 0.01m
376 7 -. L L 0.2m
to1 E I 2.106 I IO" N m-*
P o,r2.943rIO'Nm''
tC)
I 2 3 4 5 6 p:78001rpm-'
0 u = dotlut~(nat centre
00009
!- L I t lmsl

5-

t lmsl

Figure 14.2 Dynamic Elastic-plastic Behavior of a Clamped Beam under
Central Lateral Impact Load
a. Calculation model
b. Applied load-time relationship
c. FE model in MARC analysis
d. Time history of displacement at impact point