Page 193 - Marine Structural Design

Chapter 9 Buckling and Local Buckling of Tubular Members 169

9.3 Theory of Analysis
9.3.1 Simplified Elasto-Plastic Large Deflection Analysis
In this section, an analytical model, which simulates the e-sto-plastic large deflection
behavior of a tubular member, is proposed taking into account the influence of local buckling.
The material is assumed elastic-perfectly plastic. It is also assumed that local buckling takes
place after plastification occurs.

Pre-Analysis of Local Buckling
A tubular member is assumed to be accompanied by the initial deflection of a sinusoidal form:

m
wo = czo sin-
I
where, I = Length of a tubular member
= Magnitude of initial deflection
an

The equilibrium equation of a beam-column may be written as:
d4 d2w
El-(w- wo)+ P- = q (9.2)
dr4 dx2
where, w = Total deflection P = Axial force (positive in compressive)
E = Young's modulus I = Moment of inertia of a cross-section
The general solution of Eq. (9.2) is expressed as follows:

w=a, coskx+a,sinkx+a,x+a, +Q'sinmfl+ f(q)

where,
k = m

Q' = a. PE APE - P)

INITIAL DEFLECTION : w. = a. sin

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Figure 9.12 Beam-Column Member Under External Loads