“…Note that the factor a R significantly affects the partial factor c Rd [44]. Further information on derivation of the partial factors in the semi-probabilistic framework can be found elsewhere [6,49]. Note that the model uncertainty factors are here differentiated with respect to the shear strength q w f yw only as the previous studies indicated less significant effect of other shear parameters (such as d or q l ) on the model uncertainty.…”
Section: For Deterministic Reliability Verifications En 1990mentioning
Resistance of civil engineering structures is primarily dependent on material properties, geometry and uncertainties related to an applied model. While materials and geometry can be relatively well described, the resistance model uncertainty is not yet well understood. The present paper improves the general concept for the model uncertainty from the Probabilistic model code of the Joint Committee on Structural Safety. Influences affecting results obtained by tests and models and effects of actual structural conditions are overviewed. Statistical characteristics of the uncertainties in resistance of reinforced concrete members are then provided considering simple engineering formulas based on EN 1992-1-1 models and effects of deterioration. To facilitate practical applications the partial factors for the model uncertainties are derived using a semi-probabilistic approach. It appears that the model uncertainties are substantial for shear resistances while they are less significant for the well-established models used for bending resistance and axial compression without buckling. Uncertainty in test procedures seems to be less important in common cases. The effect of the resistance uncertainties on structural reliability seems to be more significant for corrosion-damaged structures than for sound structures. Consequently the quantification of the model uncertainties is a key issue when assessing corrosion-damaged reinforced concrete structures. Further research should be focused on model uncertainties related to the models for shear and corrosion-damaged structures considering the fib Model Code 2010.
“…Note that the factor a R significantly affects the partial factor c Rd [44]. Further information on derivation of the partial factors in the semi-probabilistic framework can be found elsewhere [6,49]. Note that the model uncertainty factors are here differentiated with respect to the shear strength q w f yw only as the previous studies indicated less significant effect of other shear parameters (such as d or q l ) on the model uncertainty.…”
Section: For Deterministic Reliability Verifications En 1990mentioning
Resistance of civil engineering structures is primarily dependent on material properties, geometry and uncertainties related to an applied model. While materials and geometry can be relatively well described, the resistance model uncertainty is not yet well understood. The present paper improves the general concept for the model uncertainty from the Probabilistic model code of the Joint Committee on Structural Safety. Influences affecting results obtained by tests and models and effects of actual structural conditions are overviewed. Statistical characteristics of the uncertainties in resistance of reinforced concrete members are then provided considering simple engineering formulas based on EN 1992-1-1 models and effects of deterioration. To facilitate practical applications the partial factors for the model uncertainties are derived using a semi-probabilistic approach. It appears that the model uncertainties are substantial for shear resistances while they are less significant for the well-established models used for bending resistance and axial compression without buckling. Uncertainty in test procedures seems to be less important in common cases. The effect of the resistance uncertainties on structural reliability seems to be more significant for corrosion-damaged structures than for sound structures. Consequently the quantification of the model uncertainties is a key issue when assessing corrosion-damaged reinforced concrete structures. Further research should be focused on model uncertainties related to the models for shear and corrosion-damaged structures considering the fib Model Code 2010.
“…(2). The semi-probabilistic (Level I) method according to EN 1990:2002 (for details see [8]) leads to a partial factor for lognormal X i with a unit characteristic value:…”
Historic structures are made of various types of masonry with significantly different material properties and different degrees of degradation. As a rule the information on mechanical properties of masonry components has to be obtained by testing. Estimation of masonry strength from measurements with respect to relevant uncertainties may be a key issue of the reliability assessment. The probabilistic model of masonry strength is developed considering uncertainties in basic variables and testing procedures. It appears that the characteristics of masonry strength can be well estimated using fundamental statistical methods. The attached case study indicates that the design value of masonry strength obtained by the probabilistic approach may be about double of the value obtained deterministically.
“…Taking into account the limited amount of data, the following recommendations are provided on the basis of the results given in Table 2: -Model uncertainty characteristics µ θ ≈ 1.2 and V θ ≈ 0.15 should be considered when compressive strength is decisive in Equation (2), -µ θ ≈ 1.25 and V θ ≈ 0.15 should be considered when tensile strength is governing resistance of a cast-iron column. These characteristics can be directly applied when deriving model uncertainty factor for assessments using the partial factor method as provided in EN 1990:2002 for basis of structural design [16,17]. Figure 4 shows variation of model uncertainty values with slenderness ratio for solid cylindrical columns.…”
Section: Statistical Evaluation Of Model Uncertaintymentioning
Numerous processing and manufacturing mills, workshops, warehouses, bridges and other industrial buildings belong to industrial heritage. Their origin dates back to the 19th and 20th century when cast iron became a widely used construction material. It has been recognised that existing structures including cast-iron structures do not fulfil requirements of present codes of practice. A key step of reliability assessment is modelling of resistance of load-bearing members made of cast iron. The present paper investigates several empirical or physical models for resistance of historic cast-iron columns. Outcomes of the models are critically compared with experimental results obtained for solid and hollow cylindrical, and square columns from English grey cast iron. Imprecision of the models is expressed by means of model uncertainty for which appropriate probabilistic models are proposed. As tensile strength of cast iron is considerably lower than compressive strength, it dominates resistances of columns centrically loaded in compression with slenderness ratio over 60. In such cases model uncertainty can be described by a two-parameter lognormal distribution with the mean of 1.25 and coefficient of variation of 0.15. For columns with lower slenderness ratios compressive strength is decisive and the mean of model uncertainty decreases to 1.2.
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