Page 493 - Marine Structural Design

Chapter 26 Reliability-Based Design and Code Calibration 469

penalty function for deviations from the target reliability. Several possible choices for the
penalty function exist. One that penalizes over and underdesign equally on the p scale may be

in which M denotes the penalty, W[j,k,l is the weighting factor for the design case identified by
the index set (i,j,k,l), and PIJ,~,~ the reliability index that is obtained for the design case by
is
design according to the code. This expression for the penalty function M may be interpreted as
the expected squared deviation from the target reliability over the scope of design cases.
A prime requirement to the calibration of a common set of safety factors for the entire scope of
code is then that, over the scope of code, the calibrated set of safety factors shall lead to
designs with safety levels as close as possible to the target. The common set of safety factors
is therefore determined as the set y that minimize the penalty function M
Minimize{M 1 (26.1 1)

subject to : pijkr 2 Plrdn (26.12)
over the scope of the code.
In which Pmin is the minimum acceptable reliability index. This can be achieved by means of
an optimization technique, and this applies also if another choice of penalty function is made,
such as one that is more heavily biased against under-design than against over-design.
26.4.3 Code Calibration Procedure

Combining the calibration principles outlined above with a practical design consideration, the
following steps should be in general be considered as the proper reliability based code
calibration procedure.
Step 1 : Identify the failure modes for the considered design case

Step 2: Define design equation
Step 3: Form Limit State Function (LSF)
Step 4: Measure uncertainties involved in all random variables in LSF
Step 5: Estimate failure probability
Step 6: Determine target safety level
Step 7: Calibrate safety factors
Step 8: Evaluate the results
26.4.4 Simple Example of Code Calibration
To demonstrate the code calibration principles and procedure, a simple example is given
below.
Problem
Assume that a strength design check for ship structural details in terms of a
resistance R and load effect S is given by
R, >y.S,