Page 168 - Marine Structural Design

144 Part II Utimate Strength

The above equation may be written as:

OiLT -[.. +(l++)OE]Ou" +UEQY =o (8.17)

where,

Its solution is called the Perry-Robertson Formula and may be expressed as:

-- QULT J+rl+Y-JGnT (8.18)
CY 2Y
where,

In Perry-Robertson formula, the effect of initial deflection is explicitly included. Comparison
with more precise solutions such as finite element results demonstrates that the formula is
accurate when the initial deflection is at the range of fabrication tolerance. When the initial
deflection is due to in-service damages, which may be up to 1 per cent of the column length,
the formula may under-estimate ultimate strength. The formula may be extended to account
for the effect of residual stress explicitly. Perry-Robertson Formula has been frequently used
in European steel structure codes.
8.1.3 Johnson-Ostenfeld Formula
The effect of plasticity may be accounted for by correcting the Euler buckling stress using the
Johnson-Ostenfeld approach (see Galambos, 2000), Figure 8.2:

QULT = QE for Q, /cy S 0.5 (8.19)

(8.20)

1.0 g-- *
,A
4 PT
inelastic elastic
Figure 8.2 Johnson-Ostenfeld Approach Curve