A lot of assumptions,simplifications and approximations are made in the
deterministic design of structures in the process of substituting a real physical system,
whose behaviour is inherently random, with a mathematical model. Resort is therefore
often made to the application of safety factors and allowable limits which in reality
represent factors of ignorance of actual operating conditions and true performance
capabilities of a structure. Recognising that safety involves a consideration of random
variables, it is obvious that the approach to the analysis of structural safety is through the
use of probabilistic methods.
The deterministic and probabilistic methods of analyses are both employed to
check the performance of the roof truss of a multi-purpose indoor sports hall in Bauchi
which failed during construction. In the deterministic analysis, real physical systems are
substituted with deterministic equations which do not contain terms corresponding to
random forces. The probabilistic method takes into account the variabilities in material
properties and random nature of loading.
The results show that although the design of the truss satisfies the determinsitic
requirements, the probabilistic check invalidates the adequacy of the design. The actual
axial stress on the most loaded truss member is 119.85N/mm2 while the permissible
stress is 123N/mm2. The probability of failure is 0.456 corresponding to a safety index
of 0.110. This level is grossly inadequate on the basis of the level stipuated for this class
It is therefore concluded that the collapse of the roof could have been initiated by
the failure of the most loaded member.
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