Page 172 - Marine Structural Design
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148 Part 11 Ultimate Strengrh
For beam-columns under combined external pressure, compression, and bending moments, the
ultimate strength interaction equation may be expressed as:
(8.39)
where the ultimate axial strength PuQ and the plastic moment capacity M, (considering the
effects of hydrostatic pressure) are used to replace the parameters in Eq.(8.37) in which the
effect of hydrostatic pressure has not been accounted for in calculating PuLT and M,, .
8.2.4 Alternative Ultimate Strength Equation - Initial Yielding
For a beam-column with initial deflection and eccentric load, as discussed in Section 8.2.2, an
ultimate strength equation may be derived by using an initial yielding condition:
(8.40)
where, u,, is given by Eq. (8.31). Hughes (1988) extended Perry-Robertson Formula to
beam-columns under combined axial compression and lateral pressure as follows:
(8.41)
where
(8.42)
In Eq.(8.42), The maximum moment and lateral deflection due to lateral pressure may be
obtained as follows,
Mqrnax = s and 5q14 (8.43)
ql
Wq,, =-
384EI
where q is the lateral pressure per unit length of the beam-column. It should be pointed out
that the effect of boundary condition on beam-column strength under combined compression
and lateral pressure is significant, and may be accounted for using the maximum moment and
lateral deflection derived for the boundary conditions of concern. The general solution for
elastic deflection of beam-columns under combined axial force, lateral pressure and end
moments may be found in Part 2 Chapter 9 of this book.
8.3 Plastic Design of Beam-Columns
8.3.1 Plastic Bending of Beam Cross-section
When a beam cross-section is in filly plastic status due to pure bending, M,, the plastic
neutral axis shall separate the cross-sectional area equally into two parts. Assuming the
distance from the plastic neutral axis to the geometrical centers of the upper part and lower
part of the cross-section is yu and yL , we may derive an expression for M, as below:
