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Pages 53-77

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From page 53...
... 53 C H A P T E R 4 Development of the Guidelines- Probabilistic Approach for Strength Evaluation As an improvement on the methods used in NCHRP Report 534, the Random Field Method is adopted to calculate the strength of a suspension bridge main cable. In this section, the method is described in detail, and compared with those used in NCHRP Report 534.
From page 54...
... 54 The RT feels that the Random Field methodology is a significant improvement as it considers a large amount of corrosion stage data that is currently recorded, but not utilized, by the NCHRP 534 methodology. It is anticipated that in some cases the Random Field methodology will yield cable strength results similar to those of NCHRP 534.
From page 55...
... 55 Table 3. Corrosion Stage Variation Along Observed Wire Ring # Corrosion Stage Variation along Wire (Wedge 1, left side)
From page 56...
... 56 Figure 24. Corrosion Map of Cable (with Broken Wire Locations)
From page 57...
... 57 To build the empirical CDF of the wire strength for the different corrosion stages, it is necessary to have the experimental results of ultimate tension tests on wire specimens of length 𝑙𝑙𝑠𝑠. As specified in the section on sampling/wire splicing of the Guidelines, a sufficient number of wire specimens is recommended in order to have reliable CDF curves.
From page 58...
... 58 Once the CDFs are available, they can be used to obtain different random realizations of the spatial variation of the wire strength along the entire effective length of the panel. Simulating The Variation Of The Wire Strength Along The Effective Panel Length This process for determining the variation in corrosion stage along the wire outlined in the section on CDFs for different corrosion stage wires has to be repeated for each wire in the exposed 16 faces at the wedged openings (note that a full table of results is presented in the worked example in Chapter 7)
From page 59...
... 59 Figure 26. How to Obtain the Values of Οƒ_u from the CDF The procedure is repeated for each single wire segment to obtain values of the πœŽπœŽπ‘’π‘’.
From page 60...
... 60 Table 4. Ultimate Stresses Determined from CDF Segment Corrosion Stage πˆπˆπ’–π’– ksi 3 226.9 3 252.7 3 251.1 3 236.1 3 243.2 2 238.7 2 215.0 (Minimum)
From page 61...
... 61 Based on the example provided in Chapter 7 using data from a typical suspension bridge, Method 1 provides an approximately 7% lower value of the calculated cable strength. Upon further evaluation of these two methods by the research team, it was decided to carry forward Method 2 for use in the Guidelines.
From page 62...
... 62 The total number of broken wires in the evaluated panel, 𝑁𝑁𝑏𝑏1, consists of both observed broken wires and estimated broken wires. The number of broken wires in each corrosion stage is proportioned from the observed broken wires from the same corrosion stage: (𝑁𝑁𝑏𝑏1)
From page 63...
... 63 where 𝑁𝑁𝑏𝑏𝑑𝑑 is the number of broken wires in the 𝑖𝑖 βˆ’th panel, 𝑁𝑁𝑏𝑏1 is the number of broken wires in the evaluated panel; and 𝐢𝐢𝑑𝑑𝑑𝑑 is the redevelopment factor in the 𝑖𝑖 βˆ’th panel. It is then suggested to remove all the estimated equivalent broken wires on the basis of the same proportion as the observed broken wires.
From page 64...
... 64 2) Divide this force by the number of effective wires in the cross-section to find the force carried by a single wire, 𝐹𝐹0,𝑑𝑑: 𝐹𝐹0,𝑑𝑑 = 𝐹𝐹0 𝑁𝑁𝑒𝑒𝑒𝑒𝑒𝑒 (10)
From page 65...
... 65 Carlo simulations and the process stops when the COV drops below a pre-specified value (e.g.
From page 66...
... 66 The FOS is determined by dividing the calculated capacity by the demand forces, Fi , in the evaluated panel (the calculation of cable force is not covered in this report)
From page 67...
... 67 Comparison of Proposed Random Field Method with NCHRP 534 To allow for a meaningful comparison of the proposed Random Field Method with respect to the current NCHRP 534 report, Table 6 represents a summary of pertinent changes broken down by article number (both in the current NCHRP 534 report and within this report)
From page 68...
... 68 NCHRP NCHRP Report 534 Article Guidelines Article Description NCHRP 534 Methodology Random Field Methodology 2.2.5.2, 2.2.5.3 and 2.2.5.4 2.2.4.1 Second Internal Inspection β€’ 4 panels/cable (if Stage 1 or 2) β€’ 6 panels/cable (if Stage 3 or superficial Stage 4)
From page 69...
... 69 NCHRP NCHRP Report 534 Article Guidelines Article Description NCHRP 534 Methodology Random Field Methodology 2.4.3.1 2.2.5.1.3 and 3.2.1 Recording of corrosion stages Only the highest stage found along the length of the wire is used in the analysis of cable capacity (C2.4.3.1) in accordance with the "weakest link" theory Corrosion stage recorded in each segment is utilized in calculations in accordance with the Random Field theory.
From page 70...
... 70 NCHRP NCHRP Report 534 Article Guidelines Article Description NCHRP 534 Methodology Random Field Methodology 2.4.3.5.2.c 2.2.6.1.1 Percentages of Stage 3 and Stage 4 wires Specific percentages are provided The statistics for determining the number of specimens in each group is currently based on only one bridge where data is available. The RT reviewed new test data from two additional bridges to verify the information and benchmark the new methodology.
From page 71...
... 71 NCHRP NCHRP Report 534 Article Guidelines Article Description NCHRP 534 Methodology Random Field Methodology 3.2.1 3.1.1.2, 2.2.5.1.3 Specimen Preparation "All of the specimens from a given sample should be at the same stage of corrosion, but it is understood that this is not always possible" Variation of corrosion stage along the length of the wire is explicitly accounted for in the calculations. 3.2.1 3.1.1.2 Specimen Preparation "Before sample wires are cut into specimens of suitable length for testing, they should be inspected and assigned to the appropriate corrosion stage" Properties of specimens are assigned to the appropriate group based on the recorded corrosion stage (not that of the sample wire)
From page 72...
... 72 NCHRP NCHRP Report 534 Article Guidelines Article Description NCHRP 534 Methodology Random Field Methodology 4.4.1 4.2.2 Wire Properties - Groups Groups 1 - 4 and "cracked" wires in Group 5 Group 5 is eliminated as cracked wires are grouped according to their respective corrosion stage. 4.5.2 3.4.1 Effective Development Length and Redevelopment Coefficient No guidance for special areas, such as anchorages or unsupported backstays (with no cable bands)
From page 73...
... 73 NCHRP NCHRP Report 534 Article Guidelines Article Description NCHRP 534 Methodology Random Field Methodology 5.3.3 4.2 Strength of Unbroken Wires Weakest Link theory Random Field Theory. 5.3.3.1, 5.3.3.2 and 5.3.3.3 4.2 Simplified Strength Model, Brittle Wire Model and Limited Ductility Model Multiple models for strength calculation Cable strength is calculated using an iterative procedure whereby the load is increased incrementally in the cable (similar in concept to the Limited Ductility Model)
From page 75...
... 75 Figure 30. Inspection and Strength Evaluation Procedure Flowchart [Guidelines Figure 1.2.3-1]
From page 76...
... 76 Predicted Remaining Life The calculation of remaining life for a given main cable of a suspension bridge requires information not only on the rate of deterioration that controls the cable strength calculation to the present time, but how that deterioration rate will be affected by any maintenance or preservation actions. Without quality information in these areas, it will not be possible to develop an accurate estimate of remaining life.
From page 77...
... 77 The pairing of a quality cable investigation and strength evaluation program performed at a regular frequency, alongside a cable monitoring system, would appear to be the best option for an owner looking to establish the strength vs. time relationship for the cables on their bridge.

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