PSI - Issue 64

Cedric Eisermann et al. / Procedia Structural Integrity 64 (2024) 1224–1231 Eisermann et al./ Structural Integrity Procedia 00 (2019) 000–000

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in the cross-sectional area of the top and bottom slab result in an average increase in the moment of inertia of 3.12%. Further studies are needed to quantify effect of the increased stiffness on the structural behavior.

Table 1. Comparison of cross-section component dimensions X d X i Avg. absolute deviation

Avg. relative deviation

Designation of the geometry parameters

17 cm 13.7 to 20.0 cm -0.47 cm -2.76% 25 cm 24.0 to 27.3 cm +0.72 cm +2.88% 35 cm 33.5 to 36.6 cm -0.10 cm -0.22% 37 cm 34.5 to 38.4 cm -0.10 cm -0.19%

t ts1 t ts2 t w1 t w2 A ts A w A bs t bs

variable 3.623 m² variable variable

variable

+2.55 cm +7.10%

3.493 to 4.006 m²

+0.154m² -0.058m² +0.105m²

+4.25% -1.16% +7.08%

variable variable

3.4. Calculation of partial safety factors The variance σ 2 for the geometry can be determined using Equation (6), based on the calculated cross-sectional areas. As the cross-section of the Nibelungen Bridge varies over its length, each as-is area A i,i has its own expected value A d,i The variance σ 2 is 0.0474 (m²)², and the standard deviation is 0.2178 m². 2 = 1 � ( − ) 2 =1 = 1 �� , − , � 2 =1 (6) The coefficient of variation, which is a standardized measure of relative dispersion, can be calculated from the standard deviation σ using Equation (7). To normalize the standard deviation, the smallest cross-sectional area A d,min is used. This yields a coefficient of variation of 2.91%. Assuming a model uncertainty factor γ Ed,G of 1.07 and a reliability index β of 3.8, the coefficient of variation for new structures is 9.84%. By equally dividing the variation between weight and geometry, the coefficient of variation for geometry is calculated to be 6.75%. This demonstrates that geometry-related uncertainties can be significantly reduced through precise in-situ measurements. = , (7) The coefficient of variation for the concrete density is estimated using empirical values from the literature as in situ measurements were not conducted. According to Rackwitz (1996), a coefficient of variation of 4% is recommended for concrete strength classes below C20/25 and 3% for classes above C40/50. Braml and Wurzer (2012) suggest a coefficient of variation of 2.5% for reinforced concrete, regardless of its strength class. Boros (2019) analyzed the density scatter of almost 100 samples from five bridges built between 1949 and 1971. The mean coefficient of variation was 2.1%. For the subsequent determination of the partial safety factor, a rather conservative coefficient of variation of 4% is initially used. According to Equation (3), the coefficients of variation for geometry and density result in a coefficient of variation for the dead load of 4.95%. For a reliability level of β = 3.8, the modified partial safety factor γ G for dead load is calculated as 1.211 (DVM) and 1.207 (APFM), as per Equations (1) to (4). If the calculations are performed using a reduced coefficient of variation of 2.1% for the concrete density, a further reduction to 1.172 (DVM) and 1.168 (AFPM) is possible.