Page 204 - Marine Structural Design

180 Part II Ultimate Strength

where dKP , is the increment of plastic curvature at the center of a plastic region.
On the other hand, if dK, is assumed to be uniformly distributed along the plastic region 1, , as
indicated by Eqs. (9.10) thru (9.12), the change of plastic slope increment along the plastic
region ld may be expressed as:
(9.65)

Here, 1, is determined so that de; =de, . This is equivalent to the condition that the
integrated values of plastic curvature in the plastic regions are the same for both cases, which
reduces to:
I, = 1,/2 (9.66)
The above-mentioned procedure used to estimate 1, , is only an approximation. In Section
9.3.2, a more accurate procedure is described. To evaluate the actual plastic region size I,, for
the calculated deflection, the stress is analyzed at 100 points along a span, with equal spacing
and the bending moment at each point is evaluated. After local buckling has occurred, plastic
deformation will be concentrated at the locally buckled part. For this case, 1,is considered
equal to the tube's outer diameter, which may approximately be the size of the plastically
deformed region after local buckling.
9.3.2 Idealized Structural Unit Analysis

Pre-Ultimate-Strength Analysis
Throughout the analysis of a beam-column using the ordinary Idealized Structural Unit
Method, an element is regarded to be elastic until the fully pIastic condition and/or the
buckling criterion is satisfied. When the axial force is in tension, a relatively accurate ultimate
strength may be evaluated with the former condition along with the post-yielding calculation.
However, when the axial force is in compression, the ultimate strength evaluated by the latter
criterion is not so accurate, since the latter criterion is based on a semi-empirical formula. In
the present study, the simplified elasto-plastic large deflection analysis described in 9.3.1 is
incorporated in the Idealized Structural Unit (element) in order to accurately evaluate the
ultimate strength under the influence of compressive axial forces.
The Idealized Structural Unit Method uses the incremental analyses. The ordinary increment
calculation is performed until the initial yielding is detected. The initial yielding is checked by
evaluating the bending moment along the span of an element and the deflection expressed by
Eq. (9.9). After the yielding has been detected, the simplified method described in 9.3.1 is
introduced.
Here, it is assumed that calculation of the (n+l)-th step has ended. Therefore, the following
equilibrium equation is derived similar to Eq. (9.19):
P(we +w,)+dp(em +e,)+M, +Q=M (9.67)
where,
P = Axial force given by Eq. (9.17)
dp =p-xi (SAX;)