Bridge System Safety and Redundancy (2014) / Chapter Skim
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From page 12... ...
12 2.1 Introduction Redundancy is defined as the capability of a bridge system to continue to carry load after the failure of one of its members. This means that the system has additional reserve strength such that the failure of one member does not result in the collapse of the entire structure or a significant portion of it.
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From page 13... ...
13 of reliability theory and its application for calibrating bridge design and safety assessment codes. Section 2.5 develops the reliability model used in this study for the probabilistic evaluation of bridge redundancy and the calibration of system factors.
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14 To perform the load capacity analysis, the bridge is first loaded by the dead load and then the transient load is incrementally applied. The first structural member will fail when the transient load reaches LF1.
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15 terms of defense/security considerations. However, the LRFD specifications do not explain how to identify which bridges have low and high redundancy or how to define low and high ductility.
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16 overdesigned or under designed. This makes the proposed measures valid for the evaluation of existing bridges as well as new designs.
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17 In structural analysis, safety may be described as the situation where capacity (member strength or resistance, the maximum strain that a structural material can take before rupturing or crushing, ductility capacity) exceeds demand (applied load, applied moment, applied stresses, applied strains, or ductility demand)
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From page 18... ...
18 values as high as 50% to values as low as 10-9 or lower without giving an intuitive understanding of the corresponding level of safety. The reliability index, b, defined in Equations 2.7 and 2.8 provides an exact evaluation of the probability of exceedance if R and S follow normal distributions.
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19 equations in determining the reliability index b. Saydam and Frangopol (2013)
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20 • In general, there will be considerable scatter in such computed reliability indices. A target b is selected to correspond to the average reliability index of the representative bridge sample set.
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21 to the capacity of the system and should be placed on the resistance side of the equation as is the norm in reliabilitybased LRFD codes. f is the member resistance factor, RN is the required resistance capacity of the member accounting for the redundancy of the system, gd is the dead load factor, Dn is the dead load effect, gl is the live load factor, Ln is the live load effect on an individual member, and I is the dynamic amplification factor.
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From page 22... ...
22 deterministic measures defined in Equation 2.1 that do not take into consideration the uncertainties in evaluating the system capacity and the loading. As explained in Section 2.4, the safety of a bridge member, that of the originally intact entire system, or that of a damaged system, should be assessed using reliability criteria.
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From page 23... ...
23 COV is the ratio of the standard deviation of LL75 divided by the mean value. The COV values in Table 2.2 also are taken from Nowak (1999)
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From page 24... ...
24 factor for first member failure LF1 can be calculated from the capacity of the most critical member of the bridge, R, the dead load effect on that member, D, and L1, which is the load effect on the member calculated due to the HS-20 trucks. Specifically, LF1 can be obtained from .
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From page 25... ...
25 the mean value of LF1, relates to the strength capacity of the member represented by the resistance R and the dead load D LL75 is the mean value of the maximum expected 75-year live load, including dynamic load allowance effect.
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26 Dbd that compare the reliability indices for the ultimate and damaged limit states to that of the most critical member. The reliability index margins Dbu, Dbd are defined as (2.17)
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27 that a system factor equal to 1.0 indicates that the bridge is sufficiently redundant and that the reliability index of the system is higher than that of the member by an amount equal to a target value. Following common reliability-based code calibration processes, the target values can be established by studying the reliability of bridge systems that have historically shown adequate levels of redundancy in the sense that one of their critical members has failed, and the system did not undergo collapse.
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From page 28... ...
28 reliability index margins Dbu and Dbd are lower than the target values Dbu target = 0.85 and Dbd target = -2.70, a system factor fs < 1.0 should be used in Equation 2.11. However, fs should serve to lower the reliability index for the member and the system when the available Dbu and Dbd are higher than the target values.
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From page 29... ...
29 The required member capacity can be inferred from the relationship established between LFu and LF1 for the typical bridge configurations analyzed in this study. For example, in NCHRP Report 406 it was observed that the ratio Ru = LFu/LF1 is approximately constant for I-girder bridges designed to exactly satisfy the AASHTO design specifications.
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From page 30... ...
30 Melchers, R
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