Page 108 - Failure Analysis Case Studies II

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reinforcing buttresses, the occurrence of several crack arrest lines on the fracture surface indicated
that the crack extended after the initial fracture, either while fluid was still issuing from the tank,
or at a later stage when the crack was investigated by the firemen and others at the scene of the
accident. Simple hand pressure on the side panel revealed the fracture surface, the act of doing so
putting extra stress on the long crack which already existed.

8.2. Pressure conditions in the failure tank
The exact stress on the lower tank panel where fracture occurred can be calculated relatively
easily, since the volume of the contents is known and the height of the top level of the contents is
also known within reasonably close limits. Together with a knowledge of the density of the caustic
soda, the hydrostatic pressure acting on the panel at the failure locus can be determined from the
simple formula

pressure P = hpg (1)
where h is the height from the origin of the fracture to the top level of the liquid when fully loaded
just prior to the accident, p is the density of caustic soda at ambient temperature and g is the
gravitational constant (= 9.81 m s-’).
The thickness of the panel at the origin of fracture is about 12 mm, and the ratio to the radius
of the tank (of about 1.35 m) is 112.5, a figure well in excess of the figure of about 10 normally
regarded as the threshold ratio between thick and thin walled pressure vessels [4]. The failed
tank can therefore be regarded as a thin-walled vessel, subjected to simple hydrostatic pressure.
Neglecting for the moment the self weight of the vessel and any creep in the plastic wall, the
situation is that described by Roark [4] in his Table 28 (case Id). There is only one important stress
acting in the wall, the hoop stress, cH acting around the circumference of the wall. There is no
stress acting in a vertical direction. It is therefore a force tending to extend the circumference in
tension, and hence acting on the vertical welds. This hoop stress can be calculated at the origin of
the fracture using the simple formula

where P is the pressure as determined above, R is the radius of the tank, and t the wall thickness.
Taking the design height of the failed tank as 3.5 m and the measured height of the crack origin
from the base of the tank as 1.486 m, then the height, h of fluid lying above the origin of the critical
crack is 2.014 m. This assumes that the last load delivered of 22.32 t came up to the top of the
vertical section of the tank. In fact, there is an overflow valve fitted just below this junction, so the
estimate of 2.014 m is probably slightly exaggerated. A round figure of h = 2 m will be taken as a
reasonable estimate of the total height of caustic soda above the origin. The specific gravity of
aqueous caustic soda of 47% concentration lies between 1.4873 and 1.5065 [5], so that a mean
value of 1.4969 may be rounded to a density value of about 1.5 g (or 1500 kg m-3) at about
20°C. The pressure at the origin of fracture is therefore
P= 1500~2.0~9.81 29.4kPa
=
hence, from eqn (2),