The probabilistic characteristics for the above mentioned types of resistances are in general
rather different; however, some common features apply for their probabilistic modelling and
these will be discussed in the following. Detailed probabilistic models for a comprehensive
list of resistance variables are given in JCSS (2000) and (2001).
Geometrical Uncertainties
Geometrical characteristics relate to the dimensions of the considered component or system.
Typical examples are the concrete cover of reinforced concrete structures, out of straightness
of steel columns and the eccentricity of the loading of columns.
The most important aspect for the probabilistic modelling of uncertain geometrical quantities
is their spatial variability. Usually their time variation may be assumed to be of no relevance.
At the time of design the geometry is uncertain and design specifications together with
specifications for the control of the execution quality are the only available means for limiting
the uncertainty. On the basis of such specifications it is possible to set up prior probabilistic
models for the geometrical characteristics.
As the absolute value of the deviations of geometry relative to the specified values are
governed by tolerance specifications the uncertainties of geometrical quantities tend to have a
decreasing influence for increasing structural dimensions.
When the structure has been realised the geometry of the structure may be assessed by
measurements. Depending on the geometrical characteristic at hand the measurements may be
more or less associated with uncertainty them selves but measurements are valuable means of
updating the probabilistic model whereby a posterior probabilistic model may be achieved.
Material Resistances – the JCSS Probabilistic Model Code “Light”
Concrete Compressive Strength
According to the JCSS Probabilistic Model Code the concrete compressive stress can be
modelled by the following expression:
fcc 53 (, )tf(o (7.34)where ( , ) 53 t is a deterministic function, which takes into account the concrete age at the
loading time [days] and the duration of loading 3 [days]. ( is a factor taking into account the
difference between the compressive strength of the concrete as measured in-situ and the
strength according to standard tests on concrete cylinders. Finally fco is the concrete cylinder
compressive strength after 28 days.
It has been found that ( varies only insignificantly and may be assumed to have the value
(0.96. The concrete compressive strength fco can assumed to be Lognormal distributed.
As ( is close to one, the in-situ concrete compressive strength fc can assumed to be
Lognormal distributed with a coefficient of variation equal to 0.15.