Abstract
This study concerns the safety factor and the reliability calculation for structural codes. The Eurocodes are used as a reference. Safety factor calculation is a demanding task which necessitates using an appropriate root-solving algorithm with a sufficient numerical accuracy. This article introduces a simple algorithm to calculate the safety factors directly, as previously there has been no means to control the accuracy. Presently, the safety factors are defined indirectly through the reliability index. The basic safety factor calculation is presented here in six different equations with the same outcome but differences regarding the numerical calculation, which provides a method to check the accuracy and select a proper equation for the root solver. The safety factor calculation for the permanent and the variable load in the Eurocodes is based on the independent, i.e., random, load combination and single load pairs. The current approach of safety factor calculation applied in the Eurocodes is disclosed here. Simple analytical equations based on the convolution equation are presented. Those can be used instead of the computer programs applied currently.
Highlights
This study concerns safety factor calculation for structural codes
The primary assumption of this method is the independent load combination where a load reduction occurs. It is implemented by sensitivity factors αE and αR, which decrease the target reliability as in this load combination it is improbable that the highest permanent load and the highest variable load occur simultaneously
In the independent load combination (8.13a,b), load reduction of approximately 10% occurs which means that the lines of Figure 5 lie about 10% higher when the load consists of equal permanent and the variable load, i.e., in this load combination, the lines are almost straight between the cases when the permanent load or the variable load is acting alone
Summary
This study concerns safety factor calculation for structural codes. The structural codes and articles regarding codes are divided into three accuracy levels: I, II, and III [1,2,3,4,5]. The Eurocodes were earlier based on level I, i.e., on deterministic, historic, and empiric methods. The safety factors of the current Eurocodes are based on level II, i.e., on the first order reliability method. The primary assumption of this method is the independent load combination where a load reduction occurs. It is implemented by sensitivity factors αE and αR , which decrease the target reliability as in this load combination it is improbable that the highest permanent load and the highest variable load occur simultaneously.
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