Page 219 - Marine Structural Design

Chapter 9 Buckling and Local Buckling of Tubular Members 195

existing semi-submersible drilling unit, and their diameter to thickness ratio, D/t, is 78. The
D/t ratio of small-scale specimens varies between 40 and 97. Axial compression tests with
load eccentricity are carried out on both specimens, and pure bending tests on small-scale
specimens only. These experiments have shown that after the ultimate strength has been
attained, local buckling takes place at the area of maximum compressive strain. Two types of
buckling mode are observed, which are denoted as a cosine mode and a dent mode. The
buckling wave of a cosine mode spreads about a half circle in the circumferential direction,
and that of a dent mode about a quarter circle in the circumferential direction. Nevertheless, it
has a short wavelength in the axial direction in both modes.
The load canying capacity suddenly decreases due to the initiation of local buckling.
In the case of a cosine mode, the formation of local denting deformation follows at the foot of
the initial cosine-buckling wave. Other local denting deformations are formed adjacent to the
initial dent and in the case of dent mode buckling.
A simplified method is proposed to analyze the elasto-plastic behavior of a tubular member
subjected to axial compression, end moments, and distributed lateral loads. Two models are
proposed which simulate the post-local buckling behavior of a tubular member based on the
observed results of experiments. They are the COS and the DENT model.
Combining these models with the simplified method, a series of analyses have been performed
on the newly tested specimens and on those previously reported. The analyses results are
compared with experimental results, and the validity and usefulness of the proposed simplified
methods of analysis are demonstrated.
Furthermore, the Idealized Structural Unit model (element) is developed by incorporating the
proposed simplified method. Using this model, the ultimate strength is automatically evaluated
under axial compression. After the local buckling has started, its influence is reflected upon
the fully plastic strength interaction relationship through plastic nodal displacements of the
element. Some example calculations are performed by applying the newly developed element.
The calculated results are compared with those obtained using the finite element method and
the validity and usefulness of this element is demonstrated.
Research remaining for future work is:
Accurate estimates of plastic strain and curvature at a plastic node
Accurate evaluation of critical buckling strain
System analysis using the proposed Idealized Structural Unit model

9.6 Example
Example 9.1: Comparison of the Idealized Structural Unit Method and tbe Plastic Node
Methods
Problem:
Describe the differences and similarities between the Idealized Structural Unit Methods and
the Plastic Node Methods.
Solution:
The Plastic Node Methods, as described in Part I1 Chapter 12, is a generalization of the plastic
hinge methods that have been popular for plastic analysis of beams and framed structures. The