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C-1 CONTENTS APPENDIX C ILLUSTRATIVE EXAMPLES.....................................................................................C-1 C.1 INTRODUCTION ......................................................................................................................................C-2 C.2 EXAMPLE 1 SIMPLIFIED MODEL ......................................................................................................C-3 C.2.1 Simplified model assuming that adjacent panels are perfect.........................................................C-4 C.3 EXAMPLE 2 BRITTLE-WIRE MODEL, ONE PANEL INSPECTED...............................................C-5 C.4 EXAMPLE 2A (EXAMPLE 2 - CONDENSED FORMAT)...................................................................C-6 C.5 EXAMPLE 3 BRITTLE WIRE MODEL, ENTIRE EFFECTIVE LENGTH INSPECTED .............C-7 C.6 EXAMPLE 3A (EXAMPLE 3 - CONDENSED FORMAT)...................................................................C-8 C.7 SUMMARY.................................................................................................................................................C-9 C.8 EXPLANATION OF STEP NUMBERING...........................................................................................C-10 C.8.1 Inspection (I) ....................................................................................................................................C-10 C.8.2 Data Reduction (D). .........................................................................................................................C-10 C.8.3 Estimation of Cable Strength (S)....................................................................................................C-10 C.8.3.1 Simplified Model (Steps 2 and 3 not used) ......................................................................C-10 C.8.3.2 Brittle-Wire Model ...........................................................................................................C-10
C-2 C.1 INTRODUCTION Three different calculations for estimating the strength of a cable panel on the Centennial Bridge are presented in Appendix C. The bridge and the data are entirely fictional, although the same level of deterioration has been found in some real inspections. The events are reported as if they had actually occurred (e.g., so many samples taken, so much deterioration found, etc.). The number of samples was deliberately reduced to limit the size of the tables, but obtaining less than the recommended number of samples can be defended as reasonable, considering that this is only the first internal inspection. Three locations on each cable were selected for inspection, following the recommendations in Article 2.2.5.1. Ten Stage 1 and 15 Stage 2 wires were sampled. After a significant number of Stage 4 wires were found in two of the panels, 20 Stage 3 and 30 Stage 4 wires were also sampled. Table 24.3.5.1-1 requires even more samples: 35 Stage 3 and 60 Stage 4, but opening only 6 panels reduced the number of samples that could be removed. It is expected that more samples will be obtained during the next scheduled inspection, when more panels are opened. The strength of each opened panel was calculated using the Simplified Model presented in Article 5.3.3.1, which excludes broken and cracked wires. It was determined from these calculations that the lowest cable strength occurred at the low point of the south cable in Panel 77-78. In the third sample calculation, it is assumed that the owner was concerned enough about the apparent low strength of this panel to open up additional panels for inspection. The other two examples are based on the original plan of 6 locations. Calculations for the estimated strength of this panel are presented as follows: ⢠Example 1: Simplified Model, with all panels in the effective development length assumed alike, since adjacent panels were not inspected (Article 5.3.3.1) ⢠Example 2: Brittle-Wire Model, with same assumptions (Articles 5.3.3.2, 5.3.4 and 5.3.2.4) ⢠Example 3: Brittle-Wire Model, with all panels in the effective development length inspected, using a more elaborate method for determining the effects of deterioration in adjacent panels (Articles 5.3.3.2, 5.3.4 and Appendix B). In all three examples, the results are often given to more significant figures than is necessary, implying an accuracy that does not exist. For instance, the mean tensile strength of wires is shown to 1 decimal place, while the nearest integer is sufficient for the calculation. This is also true of the standard deviation. The cable strength is shown to the nearest integer, implying that it is known to 5 significant figures, whereas 3 figures, or the nearest 1%, are sufficient. Various methods for checking the accuracy of the calculations are part of the reason for retaining significant figures beyond their apparent effectualness. For example: ⢠The number of wires in each ring, when added together, should result in exactly the total number of wires in the cable. This is a check on the formulas entered into the cells of the spreadsheet. If the total is not exact, the error should be found. This is one of the reasons that the number of wires in each ring is not rounded. ⢠On Page EX1-12, the number of wires that are less than Stage 1 or greater than Stage 4 must be exactly zero, or the data are incorrect. ⢠The total number of wires in each stage must add up exactly to the number of wires in the cable, or there is an error. It is primarily for these checks that the calculations are shown with so much seeming accuracy. The results should be rounded in the final summary. As stated above, 1% is close enough.
C-3 C.2 EXAMPLE 1 SIMPLIFIED MODEL Each cable of the Centennial Bridge is composed of 9,990 galvanized steel parallel wires. Each wire is 0.196 inches in diameter, including the zinc coating. The nominal diameter of the wire before galvanizing is 0.192 inches. Three panels on each cable were selected for inspection, as shown in the Inspection Location Diagram on Page EX1-02. The condition of the wires in Panel 77-78 was found to be severe enough to warrant removal of the cable band at panel point 77 to facilitate inspection of the entire cable cross-section. The steps required for this representative inspection (prefixed I), data reduction and testing (prefixed D), and calculation of cable strength (prefixed SS) are described on the following pages, and then illustrated. The page numbers in the follow paragraphs refer to the calculation page numbers that can be found in the upper right corner of the calculation sheets, e.g., EX1-02. Step I-1 Prepare inspection forms. Prior to the preparation of inspection forms, the number of rings of wire in the cable and the number of wires in each ring were estimated. This calculation is shown on Page EX1-03. The relevant forms are shown in the next step, on Pages EX1-04 and EX1-05. Step I-2 Record the inspection observations. The condition of the wires at one of the inspected locations along the length of Panel 77-78, inside wedged opening No. 5 (at 6:00), was recorded on the Field Inspection Sheet shown on Page EX1-04; the conditions at other locations were similarly recorded, but are not shown in the example. Step I-3 Remove sample wires for testing and measure retraction of the cut ends. The separations of the ends of four wires, at the location of the first cut for removal of samples, were measured and recorded on another field inspection form showing the cable cross-section, along with the location of the sample wires and wires found broken in the cable. This inspection form is shown on Page EX1-05. Step D-1 Calculate the redevelopment coefficient and the effective development length. The effective development length is calculated on Pages EX1-06 and EX1-07, using the measurements of wire retraction made during the inspection. Step D-2 Test the sample wires and calculate the tensile strength distribution (mean and standard deviation) of each group of wires. Many sample wires were removed from the cable for testing. Ten Stage 1 and 15 Stage 2 wires were selected, as well as 18 Stage 3 and 30 Stage 4 wires. Although the deterioration of the cable was observed to be severe in Panel 77-78, the limited number of panels opened in this inspection was insufficient for a larger sampling of the wires. The condition of this panel shows that a more intense investigation is needed at the next internal inspection, during which at least 35 Stage 3 and 60 Stage 4 wires should be sampled. The results of tensile tests on these samples are shown on Pages EX1-08 to EX1-11; the test results on an individual specimen from one sample are shown on Page EX1-08, along with the calculation of the estimated minimum tensile strength in one panel length, or 41 feet. When a crack is present in one or more specimens, the calculation of the estimated minimum strength using Equation 4.4.3.2-1 is not valid, and the lowest strength found for a cracked specimen is used instead, as shown on Page EX1-09. These values are calculated for each sample, and the results carried to Pages EX1-10 and EX1-11, where the sample means and sample standard deviations of the tensile strengths for each stage of corrosion are calculated. The fraction of samples in each corrosion stage that contain one or more cracks is calculated on Page EX1-11. Step D-3 Determine the number of wires in each corrosion stage. The corrosion stage of each wire in the wedged openings is tabulated on Page EX1-12. Upon reviewing all inspection records for wedge line 5, in Panel 77-78, Stage3 and Stage 4 were found to extend one to two wires deeper into the cable at another panel segment than at the middle panel for which the example on Page EX1-04 is shown, and this is reflected in the data on Page EX1-12. There is one line on this spreadsheet for each ring in the cable, and the estimated number of wires is entered for each ring. Two columns represent each wedge, one for the left-hand side and one for the right-hand side of the opening formed by the wedge. The fraction of the circle corresponding to the arc subtended by each half-sector is given at the top of each column. The number of wires in each stage in each ring is calculated by formulas in the appropriate cells, and the totals for the entire cable given at the bottom of the spreadsheet.
C-4 These numbers are carried to Pages EX1-14 and EX1-16. Page EX1-13 presents a corrosion map of the cable cross- section in the inspected panel. All data up to this calculation on Page EX1-14 are the same for all the examples, and these pages will not be repeated for Example 2 and Example 3. Step D-4 Determine the number of broken wires in the effective development length and the effective number of unbroken wires in the cable. In this inspection, broken wires were found only on the periphery of the cable, up to 6 wires from the surface. The spreadsheet for broken wires is therefore not needed. The number of broken wires and the number of unbroken wires in the cable are estimated directly on Page EX1-14. Equation 4.3.3.2-1 is used to estimate the number of broken wires, because no wires were found broken beyond the sixth ring. The depth at which no broken wires are found is 7 wires (i.e., broken wires were found 6 layers into the cable), and d0 equals 7. Of the 8 broken wires found, 6 were repaired. The number of broken wires in all the panels in the effective development length is assumed to be the same as in the inspected panel, because only that panel was inspected. It follows that only wires in the inspected panel were repaired. Step D-5 Determine the number of discrete cracked wires in the effective development length. The total fraction (and total number) of wires in each stage that are cracked in the effective development length is found using the graph in Figure 5.3.2.4.1-1. These calculations are shown on Pages EX1-15. This information is added to the summary sheet shown on Page EX1-16. Step SS-1 Determine the fraction of the cable in each group of wires. The fraction of the cable in each stage of corrosion, and the fraction represented by each group of wires, is calculated on Page EX1-16. The testing laboratory reported that 50% of Stage 4 wires and 5% of Stage 3 wires contained preexisting cracks (i.e., they were observed to be cracked before testing). The cracked wires represented by these fractions are subtracted from the total number of wires in the appropriate stages to determine the net number of wires per stage that are not broken or cracked. The cracked wires are added together to form Group 5. In the Simplified Model, broken and cracked wires are ignored, and thus Group 5 has no wires. Steps SS-2 (Weibull parameters) and SS-3 (Strength of broken wires) are not used in the Simplified Model. Step SS-4 Determine the combined distribution of the tensile strength of unbroken and uncracked wires. The mean and standard deviation of the tensile strength of the combined groups of wires are calculated on Page EX1-17 using Equation 5.3.3.1.1-1 and Equation 5.3.3.1.1-2; the coefficient of variation (standard deviation divided by the mean) is also calculated. Step SS-5 Estimate the cable strength. On Page EX1-18, the strength reduction factor for use in Equation 5.3.3.1.2-1 is found from Figure 5.3.3.1.2-1, and the cable strength is calculated as 38,968 kips. The result is rounded to 3 significant figures, or 39,000 kips. C.2.1 Simplified model assuming that adjacent panels are perfect The Simplified Model can be used to quickly and easily identify the worst of the inspected panels for more detailed analysis, by assuming that only the inspected panel is deteriorated and all other panels are perfect. This calculation is shown on Page EX1-19. Only broken and cracked wires in the evaluated panel are considered; the entire calculation can be made on a single sheet. The effective development length is taken to be 1 panel because there are no broken wires outside this panel to be redeveloped. The number of cracked wires in each corrosion stage is the fraction cracked multiplied by the number if wires in that stage. The calculations on Pages EX1-14, 16, 17 and 18 are shown on Page EX1-19; Calculation Page EX1-15 is not required.
C-5 C.3 EXAMPLE 2 BRITTLE-WIRE MODEL, ONE PANEL INSPECTED In Example 2, the investigator seeks to estimate the lower bound of the cable strength by including the effect of adjacent panels. The condition in adjacent panels is assumed conservatively to be the same as in the inspected panel, because only the latter has been inspected. Pages EX1-02 to EX1-14 also apply to this example, and are not repeated. The example starts with Step D-4. Step D-4 Determine the number of broken wires in the effective development length and the effective number of unbroken wires in the cable. The number of broken wires and the number of unbroken wires in the cable are estimated directly on Page EX2-02. Equation 4.3.3.2-1 is used to estimate the number of broken wires, because no wires were found at a depth greater than 6 rings. This page is the same as Page EX1-15, but is included here because some of the data calculated on this page are required on the following pages. This information is added to the summary sheet shown on Page EX2-04. Of the 8 broken wires found, 7 were repaired. Step D-5 Determine the number of discrete cracked wires in the effective development length. The number of discrete cracked wires is calculated on Page EX1-15, as described previously. This information is added to the summary sheet shown on Page EX2-04. Step D-6 Determine the number of discrete cracked wires that can be redeveloped in the evaluated panel when they break in an adjacent panel. The effective fraction of discrete cracked wires that will be redeveloped in the evaluated panel if they break is found by using Figure 5.3.2.4.2-1, and their effective number is calculated for each corrosion stage. The total fraction of wires that can be redeveloped is calculated on Page EX2-03. This fraction is used in the calculation of the cable tension at a given stress, found on Page EX2-08, and in the calculation of the cable strength on Page EX2-09. Step BS-1 Determine the fraction of the cable in each group of wires. The fraction of the cable in each stage of corrosion and the number of wires represented by each group are calculated on Page EX2-04. The number of cracked wires is subtracted from the total wires one stage at a time to determine the net number of wires per stage that are not broken or cracked. Unlike the Simplified Model, broken and cracked wires are included in the calculation, and are used to form Group 5. Step BS-2 Determine the Weibull coefficients. Coefficients for the Weibull distribution of each Group of wires are calculated on Page EX2-05, using the method given in Article A.4.2, Appendix A. The Microsoft Excel Spreadsheet Program is used for this purpose, and the tool, âSolver,â is used to determine the values of the parameters. Step BS-3 Determine the force that can be redeveloped in wires found broken in adjacent panels. The maximum force that wires found broken in the effective development length can sustain in the evaluated panel because of friction among wires developed at the cable bands is calculated on Page EX2-06, using Equation 5.3.4-3. Step BS-4 Determine the cable force at a specific value of stress. This calculation is shown on two pages, and is divided into two steps as follows. Step BS-4A Develop the cumulative compound distribution of the tensile strength. The Weibull parameters calculated on Page EX2-05, along with the fractions for each group of wires, are applied on Page EX2-07, using Equation 5.3.3.2.1-1 to evaluate the cumulative compound distribution curve for the entire cable at a specific stress. The calculation on this page is for the value of the distribution at a stress of 220 ksi. Step BS-4B Determine the cable force at a specific value of stress. The cumulative distribution is calculated on Page EX2-07 (the calculations are shown again in condensed form). The capacity of redeveloped wires found broken in the cable from Page EX2-06 and the fraction of Stage 5 wires that have failed at Stress s (F35(s)) from Page EX2-07 are used on Page EX2-08 to determine the force in the cable when the stress is 220 ksi. Step BS-5 Determine the estimated cable strength. The estimated cable strength is calculated on Page EX2-09. The âSolverâ function is used to maximize the cable force by varying the wire stress. The cable strength is found to be 50,824 kips, which rounds to 50,800 kips.
C-6 C.4 EXAMPLE 2A (EXAMPLE 2 - CONDENSED FORMAT) On Pages EX2A-01 to EX2A-09, the calculations detailed in Example 2 are given in condensed form on spreadsheets. Steps D-4, D-5, D-6, BS-1 and BS-2. Page EX2A-02 shows the data from the inspection and calculated values (from Pages EX2-02 to EX2-05) for use in the spreadsheets that follow. Steps BS-3 to 5. Page EX2A-03 is a calculation of cable strength using the technique on Pages EX2-07 to EX2-09, while Pages EX2A-04 to EX2A-07 illustrate the steps required to develop both the cable strength and cable force vs. strain curve. On these 4 pages, each line of the spreadsheet calculates the cable tension at one value of the stress, the same as on Page EX2A-03. The calculation of redeveloped cracked wires that break as the stress is increased uses Equation B.5-1 and Equation B.5-2, instead of Equation 5.3.3.2.3-1, for convenience. The stress-strain curve of the wires and tensile strength distribution curves are shown on Page EX2A-08; Page EX2A- 09 includes curves for cable force vs. stress and strain.
C-7 C.5 EXAMPLE 3 BRITTLE WIRE MODEL, ENTIRE EFFECTIVE LENGTH INSPECTED When all the panels in the effective development length have been inspected, it is possible to estimate cable strength more accurately than in Example 2, using the method in Appendix B. The example applies whenever the entire length of the cable is opened for inspection, for instance during a maintenance operation. In this instance, the panels adjacent to the worst panel were opened after a low strength estimate was found in one of the panels. The initial calculations on Pages EX1-02 to EX1-14 are the same, and are not repeated here. The effective development length, calculated on Page EX1-07, is 7 panels. Step D-4 Determine the number of broken wires in the effective development length and the effective number of unbroken wires in the cable. In this example, since all panels in the effective development length are inspected, the number of broken wires found in each panel is entered into the summary sheet on Page EX3-02. The number of broken wires in each panel is estimated separately, and the number of repaired wires is entered for each panel. Then, the number of unbroken wires in the cable is calculated, taking into account the number of broken wires that were repaired in each panel. Step D-5 Determine the number of discrete cracked wires in the effective development length, and Step D-6 Determine the number of discrete cracked wires that can be redeveloped in the evaluated panel when they break in an adjacent panel. The number of discrete cracked wires in the effective development length is calculated on the large spreadsheet shown on Pages EX3-08 to EX3-23. Each line of this spreadsheet compares the corrosion stages of a single cable segment along the entire effective development length, Le, determines where cracks are likely, assumes the location of a crack, and calculates the probable number of discrete cracks in that segment and how many will redevelop in the evaluated panel. Totals are made on the last page. A detailed calculation of a single line of the spreadsheet is shown on Pages EX3-05 to EX3-07. The number of discrete cracked wires, given at the bottom of Page EX3-23, is used to divide the wires into groups on Page EX3-24; the effective number of cracked wires that can be redeveloped in the evaluated panel, also calculated on Page EX3-23, is used on Page EX3-28 to calculate the fraction of wires that are redeveloped at a given stress level. Step BS(adj)-1 Determine the fraction of the cable in each group of wires. The fraction of the cable in each stage of corrosion and the number of wires represented by each fraction are calculated on Page EX3-24. The number of cracked wires is subtracted from the total wires in each stage to determine the net number of wires per stage that are not broken or cracked. Unlike the Simplified Model, broken and cracked wires are included in the calculation; cracked wires are used to form Group 5. Step BS(adj)-2 Determine the Weibull coefficients. The calculation of the parameters of the Weibull distribution is the same as in Example 2, repeated here on Page EX3-25. These parameters are used on Page EX3-27, along with the fraction of wires in each group, to develop the compound cumulative distribution of the tensile strength of the wires in the cable at a stress of 220 ksi. Step BS(adj)-3 Determine the force that can be redeveloped in wires found broken in adjacent panels. The force that can be resisted in the evaluated panel by the broken wires is calculated using Equation 5.3.4-2 on Page EX3-26. Step BS(adj)-4A Develop the cumulative compound distribution of the tensile strength. The Weibull parameters calculated on Page EX3-25, along with the fractions for each group of wires, are applied on Page EX3-27, using Equation 5.3.3.2.1-1 to evaluate the cumulative compound distribution curve for the entire cable at a specific stress. The example calculation on this page is for the distribution at a stress of 220 ksi. Steps BS(adj)-4B and 5 Determine the cable force at a specific value of stress and calculate the estimated cable strength. The cable tension at a stress of 220 ksi is calculated on Page EX3-28; the estimated cable strength is calculated on Page EX3-29 by varying the cable stress until a maximum cable tension is reached, resulting in a cable strength of 53,092 kips (which should be rounded to 53,100 kips).
C-8 C.6 EXAMPLE 3A (EXAMPLE 3 - CONDENSED FORMAT) A condensed form of Example 3, using spreadsheets, is given on Pages EX3A-02 to EX3A-07. This is in the same form as Example 2A. The calculation for the effect of cracked wires in adjacent panels is the same as in Example 3 (Steps D(adj) 5 and 6, Pages EX3-08 to EX3-23) and is not repeated here. Steps D(adj)-4, BS(adj)-1 and BS(adj)-2. Page EX3A-02 shows the data from the inspection and calculated values (from Pages EX3-02 and EX3-24 to EX3-26) for use in the spreadsheets that follow. Steps BS-3 to 5. Page EX3A-03 is a calculation of cable strength using the technique on Pages EX3-27 to EX3-29, while Pages EX3A-04 to EX3A-07 illustrate the steps required to develop both the cable strength and cable force vs. strain curve. On these 4 pages, each line of the spreadsheet calculates the cable tension at one value of the stress, the same as on Page EX3-29. The stress-strain curve of the wires and tensile strength distribution curves are shown on Page EX3A-08; Page EX3A- 09 includes curves of cable force vs. stress and strain.
C-9 C.7 SUMMARY The initial strength of a new cable can be estimated using the Simplified Model by assuming that only Group 2 wires are present. This calculation, which is not shown, results in a cable strength of 66,400 kips, for the cable in these examples. A severely corroded condition was assumed in the examples to demonstrate more clearly the differences in the three calculations. The Simplified Model, as expected, results in very low cable strength, 39,000 kips. This is the result of assuming that all cracked and broken wires in the effective development length do not contribute to the cable strength; redevelopment of force in these wires is assumed to be zero. When the conservative assumption of all panels alike is made in Example 2, the predicted cable strength is 50,800 kips. The assumption that all panels are alike is reasonable, especially when the entire cable is not inspected and such a severe condition is found. The difference between the cable strengths predicted by Examples 1 and 2 would be smaller in a less deteriorated cable. Nevertheless, the Simplified Model is useful as a quick way of finding the worst inspected panel. Estimating the strength when all panels in the effective length have been inspected is far more complex, but it results in a higher strength of 53,100 kips. The conditions assumed for this example approximate those that were found in an actual cable; the evaluated panel was known to be the worst in the entire cable. As a quick and easy way to identify the weakest panel of those inspected, the adjacent panels can be assumed to be perfect in the Simplified Model, resulting in a strength of 53,600 kips. The similarity between this strength and that found using the Brittle-Wire Model when all panels in the effective development length are inspected (Example 3), is coincidental. Use of the Simplified Model (i.e., assuming adjacent panels are perfect), however, can provide a quick indication of the weakest inspected panel. Example 3, which is complex, should be reserved for the worst panel, and then it is only worth the effort when the cable strength is marginal. All other panels inspected can be evaluated using the method shown in Example 2, or when the cable is less deteriorated, by the Simplified Model shown in Example 1. When only a few panels are inspected, as in these examples, it is important to remember that it cannot be known whether there is a panel in worse condition elsewhere in the cable.
C-10 C.8 EXPLANATION OF STEP NUMBERING The steps required in the evaluation of a cable are numbered in these examples sequentially. The letters indicate the phase of the investigation, the numbers indicate the order of the steps in the phase. Only those actions required for evaluating the strength of the cable are included. C.8.1 Inspection (I) Step I-1 Prepare inspection forms Step I-2 Record the inspection observations Step I-3 Remove sample wires for testing and measure retraction of the cut ends C.8.2 Data Reduction (D) In this phase, sample wires are tested and the data obtained are reduced for use in estimating cable strength. Other information obtained in the field is also reduced so that it is in the form required by the calculations. Whenever all panels in the effective development length are inspected, the suffix (adj) is added (e.g., D(adj)-5), signifying that the techniques given in Appendix B are used. Step D-1 Calculate the redevelopment coefficient and the effective development length Step D-2 Test the sample wires and calculate the tensile strength distribution (mean and standard deviation) of each group of wires Step D-3 Determine the number of wires in each corrosion stage Step D-4 Determine the number of broken wires in the effective development length and the effective number of unbroken wires in the cable Step D-5 Determine the number of discrete cracked wires in the effective development length Step D-6 Determine the number of discrete cracked wires that can be redeveloped in the evaluated panel when they break in an adjacent panel C.8.3 Estimation of Cable Strength (S) In this phase, the data obtained in Steps D-1 to 6 are used to estimate the strength of the cable. The steps are prefixed and suffixed by a letter indicating the model that is used in the analysis. The prefixes used are S for the Simplified Model and B for the Brittle-Wire Model. When all panels in the effective development length are inspected, the suffix (adj) is added (e.g., BS(adj)-1), signifying that the techniques given in Appendix B are used. C.8.3.1 SIMPLIFIED MODEL (STEPS 2 AND 3 NOT USED) Step SS-1 Determine the fraction of the cable in each group of wires Step SS-4 Determine the combined distribution of the tensile strength of unbroken and uncracked wires Step SS-5 Estimate the cable strength C.8.3.2 BRITTLE-WIRE MODEL Step BS-1 Determine the fraction of the cable in each group of wires Step BS-2 Determine the Weibull coefficients Step BS-3 Determine the force that can be redeveloped in wires found broken in adjacent panels Step BS-4A Develop the cumulative compound distribution of the tensile strength Step BS-4B Determine the cable force at a specific value of stress Step BS-5 Determine the estimated cable strength
CALCULATION PAGE EX1-06 EXAMPLE CALCULATION NO 1 PROJECT: REDEVELOPMENT COEFFICIENT CENTENNIAL BRIDGE EFFECTIVE DEVELOPMENT LENGTH CABLE ARTICLES 4.5.1 AND 4.5.2 SPAN PANEL STEP D-1 CALCULATION OF REDEVELOPMENT COEFFICIENT CALCULATION OF EFFECTIVE DEVELOPMENT LENGTH REDEVELOPMENT OF WIRE TENSION THROUGH FRICTION AT CABLE BANDS SOUTH EAST MAIN SPAN 77-78 1 panel X X X NT panels Panel Length, L Friction force Wire break (Force = 0)Panel NT Panel 1Panel n Cable bands Wire Wire tension fully restored T Friction force at last band is < or = X Band NT+1 Band NT Band n Band 1 Wire tension = nX Wire tension = X Measured Gap, dw Wire tension = NTX Friction force F F F NT = number of panels required to develop 95% of mean strength of Group 2 wires Evaluated panel Wire break outside Le (Force = 0) Cable bands Wire 95% of mean strength of Group 2 wires is redeveloped in evaluated panel when wire breaks outside Le F Effective development length, Le (symmetric about evaluated panel) WIRE BREAKS OUTSIDE EFFECTIVE DEVELOPMENT LENGTH (Number of bands = Nb = N + 1)T
