Code calibration using normalized reliability#

Code calibration seeks factors that give suitable reliability across a representative range of designs. The normalized reliability approach expresses resistance and load contributions on dimensionless scales, so the study can vary load ratios without selecting a particular structural size for each case.

The workflow is to specify probability models and characteristic values, choose candidate factors, generate designs satisfying the code equation, evaluate their reliability and compare it with the target. Factor derivation from representative design values supplies candidate factors within this workflow; it does not replace the final reliability verification.

Normalized design and reliability equations#

Let \(a_g\) describe the self-weight share of permanent load and \(a_q\) the variable-load share of total demand. These ratios describe the representative normalized load contributions, while \(R,G,P,Q\) describe the normalized random variables. For resistance scale \(z\), the design rule is

\[\phi z r_k = (1-a_q)\left[a_g\gamma_g g_k +(1-a_g)\gamma_p p_k\right]+a_q\gamma_q q_k.\]

The corresponding reliability limit state is

\[g = \omega_R zR - \omega_S\left[(1-a_q) \left(a_gG+(1-a_g)P\right)+a_qQ\right].\]

The characteristic values \(r_k,g_k,p_k,q_k\) and probability models are inputs separate from the candidate factors. Model-error factors \(\omega_R,\omega_S\) have explicitly specified distributions. Normalized variables need not all have the same bias or coefficient of variation.

NormalizedReliabilityModel describes these inputs. CodeCalibration solves the code equation for each load-ratio pair and calls FORM on the resulting design. CodeCalibrationResult preserves each design and its reliability result, including nonconvergence and target margins.

Interpreting a calibration study#

A candidate set can meet the target for some ratios and fall below it for others. The reliability envelope shows that variation; choosing a final factor set also requires a stated selection or optimization criterion and representative design cases. The current normalized study evaluates supplied factor sets; it does not infer those policy choices or optimize the factors.

Reference periods and load-process assumptions belong in the input models. Changing a normalized load ratio does not by itself convert an annual load distribution into a service-life maximum.

Deriving and verifying partial factors#

For explicitly defined representative load cases, solve_designs obtains designs at a supplied target reliability. derive_factors uses those design values to produce candidate resistance, load and combination factors. select_factors records how the candidates are combined. Finally, design_with_factors and verify_designs check the designs obtained with the selected common factors across all cases.

The coefficient method uses design-value/characteristic-value ratios. The matrix method follows the leading-action effect convention of the cited load-combination work. Both require the documented separable resistance-scale design rule; their algebra is not a general decomposition of arbitrary nonlinear limit states.

Worked examples and sources#

Code calibration using normalized reliability demonstrates normalized reliability and candidate-factor comparisons.
Calibrating partial and combination factors demonstrates partial-factor derivation and verification, with the Sørensen and Caprani–Khan examples and references.
Load combinations and FBC processes explains the load-process assumptions.
The European Commission/JRC reliability background report describes design-value and code-optimization approaches in Eurocode calibration.

Use this method: Calibrating code factors · Code calibration using normalized reliability · Code calibration and load combinations

For coordinate conventions, see Notation and probability spaces.