Test-based calibration of safety factors for capacity models

A simple procedure to calibrate the safety factor of capacity models is presented. The calibration can be carried out based on any available database of experimental tests, even of limited size. The procedure aims to assess the model capability of predicting the test results and tocalibratethesafety factorsothatthecapacity equationmeetsthetargetreliabilitylevelrequired bythecodeorsoughtbythecalibrator. Afterpredictingeachtestofthedatabasewiththecapacity equationunderconsideration,thetest-predictionpairsarecheckedfortheproperty oflinearity,andtherelativeerrorforthepropertiesofhomoscedasticityandnormality.Oncethesepropertiesarefulfilled—whichmayrequire a nonlinear transformationof thetest valuesand/or the predictions—the closed-form equationproposedinthis paper isemployedtocompute a target design value. The model safety factor is finally obtained by comparing such target designvalue with the design value obtained from the code. The paper also proposes two approximate analytical equations tocompute the tolerance factor, used to attain any given fractile, as a function of the (even small) number of tests, with any assigned confidence level. A fundamental outcome of the procedure is that it yields an objective indicator of the model accuracy, measured by the standard deviation of its error, which may be regarded as a parameter useful for selecting the most reliable model among different competing ones. In the long run, the application of the proposed procedure will allow achievingauniform reliability levelthroughoutallcapacity models usedincodesandguidelines.Afurther advantageisthatthepartial safety factors so derived can be straightforwardly updated when more experiments become available. As an example, the proposed procedure is herein applied to the ACI 318 shear design capacity equation for concrete members unreinforced in shear. DOI: 10.1061/(ASCE)ST.1943541X.0001571. © 2016 American Society of Civil Engineers.