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1、毕业外文文献翻译Determination of effective stress range and its applicationon fatigue stress assessment of existing bridges院、系（部） 专业及班级 学 号 姓 名 指 导 教师 日 期 Determination of effective stress range and its applicationon fatigue stress assessment of existing bridges Abstract This paper presents a unified approa
2、ch on determination of the effective stress range based on equivalent law of strain energy and fatigue damage model, so as to provide an efficient approach for accurately assessing effective fatigue stress of existing bridge under traffic loading. A new theoretical framework to relate variable- and
3、constant-amplitude fatigue is proposed in this paper. Different formulation for calculating effective stress range can be derived by the proposed theory, which include the effective stress range by the root mean square, by Miners law and a new effective stress range based on the nonlinear fatigue da
4、mage model. Comparison of the theoretical results of fatigue damage under the effective stress range of the variable-amplitude stress spectrum and experimental data of fatigue damage under realistic traffic loading has confirmed the validity of the proposed theory. As a way to relate variable-amplit
5、ude fatigue data with constant-amplitude data, the effective stress range provides the most convenient way for evaluating fatigue damage under variable-amplitude loading. The proposed theory is then applied to provide an efficient approach for accurately assessing fatigue damage of existing bridges
6、under traffic loading, in which online strain history data measured from bridge structural health monitoring system is available. The proposed approach is applied to evaluate the effective stress range for the purpose of the fatigue analysis of a deck section of a long-span steel bridgethe Tsing Ma
7、Bridge in Hong Kong. 2002 Elsevier Science Ltd. All rights reserved.5. Efficient approach of bridge fatigue analysis and its application The effective stress range provides a link between the variable-amplitude fatigue loading that actually occur on bridges and the constant-amplitude fatigue data an
8、d allowable-stress ranges that are commonly used in fatigue design and evaluation of bridges. It will be applied to fatigue evaluation for bridges with online health monitoring data in this section.5.1. Approach of fatigue analysis under blocked cycles of traffic loading Fatigue analysis and life pr
9、ediction of the bridge-deck section for bridges with online health monitoringdata can be carried out by use of the strain-time history data measured by the health monitoring system.The strain-time history data have been shown to be approximately a block repeated cycles in which thecycles are daily r
10、epeated (Li et al., 2001b). Therefore, it can be represented by a blocked repeated cycles.The stress spectrum of the block, called the representative block of cycles, can be obtained by rain-flow counting cycles of the strain history and statistical analysis on daily samples of strain spectrum. The
11、approach of fatigue analysis for deck sections of bridges with the health monitoring system was provided by Li et al. (2001a). Based on the proposed theory, the approach can be further improved by use of the effective stress range. The effective stress range for the variable-amplitude spectrum at a
12、given location is a quantitative description of fatigue stress and fatigue resistance (class of the welded details, fatigue stress limit,etc.) of the member under consideration. Therefore it can be considered as a representative value of fatigue behavior at the location. On this point of view, the f
13、atigue analysis of bridge-deck sections should be carried out only for the critical location on the section where the effective stress range is comparatively large at the section. The improved approach based on this idea is as shown in Fig. 4, in which the fatigue analysis iscarried out for the crit
14、ical location instead of being done for each of the locations. The most critical location is determined by the value of the effective stress range.5.2. Variation and distribution of effective stress range in a bridge-deck section In this section, the approach proposed above is applied to evaluate th
15、e effective stress range of the bridge-deck section for the purpose of fatigue analysis of Tsing Ma Bridge. The Tsing Ma Bridge of 2.2 km total length with a main span of 1377 m is the longest suspension bridge in the world carrying both highway and railway traffic. As the main part of the Lantau Li
16、nk, a combined highway and railway transport connection between Tsing Yi Island and Lantau Island, it forms an essential part of the transport network for the new airport of Hong Kong. The Bridge was commissioned on May 22, 1997. In order to ensure user comfort and bridge safety, a structural monito
17、ring system has been devised by the Highways Department of the Hong Kong SAR Government (Lau and Wong, 1997) to monitor the integrity, durability and reliability of the bridge. This monitoring system comprises a total of approximately900 sensors, including accelerometers, strain gauges, displacement
18、 transducers, level sensors, anemometers, temperature sensors and weigh-in-motion sensors, installed permanently on the bridges and the data acquisition and processing system. The strain gauges which were installed to measure strain in bridge-deck sections are shown in Fig. 5. The locations of strai
19、n gauges installed in the Tsing Ma Bridge include railtrack sections at CH 24662.50, bridge-deck trough section at CH 24664.75 and deck at tower and rocker bearing links at CH 23623.00. The most critical parts of the cross frames for fatigue damage have been identified during the design of the WASHM
20、S. Fig. 6 shows locations of all strain gauges, including two sets of rosette strain gauges and 42 linear strain gauges, in the cross frame at CH 24662.5. In the figure, thestrain gauge numbered by SSTLN-nn and SSTLS-nn represent the linear strain gauge set at the north and south of the cross frame
21、respectively, and SPTLN-nn and SPTLS-nn represent a pair of linear strain gauges SRTLS-01 are two set of rosette strain gauges in the north and south respectively. The location of each strain gauge in the cross frame can be better found from Table 2 together with Fig. 6. Strain histories measured by
22、 these strain gauges have been recorded since the bridge commissioned on May 22, 1997. As an example to show the nature of strain-time history, the strain-time history measured by the strain gauge SSTLS-01 and SPTLS-09 over an hour is shown in Fig. 7(a) and (b) respectively. The strain histories ove
23、r a longer time period have been discussed and then the stress spectrum was obtained by use of rain-flow counting in our previous works (Li et al., 2001a). The effective stress range at the location of the strain gauge SSTLN-01, calculated by using NFDM and Miner method respectively, is now carefull
24、y studied. The variation of the calculated effective stress range with the increase of service time in years for the bridge is shown in Fig. 8. It can be seen that, the effective stress range calculated by NFDM increases with the increase of service time, which is turn increases with the increase of
25、 accumulated fatigue damage, while that calculated by Miner method maintains its value as that at the beginning of service. Obviously, the result obtained by NFDM is more close to the actual situation of the fatigue occurred in bridges. It should also be noted that the effective stress range calcula
26、ted by NFDM has a very small variation at the beginning of service. Therefore it is valid and also efficient to calculate the effective stress range by Miner method at the initial stage of service when the fatigue damage in the bridge is very small, since the calculation of the effective stress rang
27、e by NFDM is complicated than that by Miner method.The distribution of the effective stress range at each location of strain gauges is listed in Table 2. The effective stress range at each location of linear strain gauge is calculated by using Eq. (19) where the coefficient (b t 3) is simply taken a
28、s the same value for all welded connections, and the calculation for the two rosette strain gauges are not included. The distribution of the effective stress range is given by a normalized ratio of Dref=Dr0 where Dr0 is the value of effective stress range at the location of the strain gauge SSTLN-01
29、. It is observed that, several critical locations of fatigue are found at SSTLN-01 on the Kowloon bound and SSTLS-05, SSTLS-12, SPTLS-09 and SPTLS-14 on the Airport bound respectively where the effective stress range has a comparatively large value. Now it is clear that fatigue damage assessment for
30、 the deck section CH 24662.5 of the Tsing Ma Bridge should be carried out for the weld connections near the strain gauges SSTLN-01 on the Kowloon bound and SSTLS-05, SSTLS-12, SPTLS-09 and SPTLS-14 on the Airport bound respectively. The assessment of fatigue damage and the prediction of residual ser
31、vice life can be made by Miners law or NFDM based on CDM. Details of the calculation may be found in our previous work on fatigue damage model and fatigue analysis of bridge-deck sections (Chan et al., 2001; Li et al., 2001b). The critical location of the deck section of the Tsing Ma Bridge will be
32、one of those locations with a comparable large value of the effective stress range. In the deck section at CH 24662.5, the critical location will be one of locations ofSSTLN-01, SSTLS-05, SSTLS-12, SPTLS-09 and SPTLS-14, as shown in Fig. 6. The effective stress range reaches its maximum at SPTLS-09
33、which is installed at lower bracing of the cross frame underneath the bridge and mass transit railway (MTR). This result suggests that the accumulative fatigue of the deck section may be dominated by the rail traffic loading.The effective stress range at the location of the strain gauge SSTLN-01, ca
34、lculated by using NFDM and Miner method respectively, is now carefully studied. The variation of the calculated effective stress range with the increase of service time in years for the bridge is shown in Fig. 8. It can be seen that, the effective stress range calculated by NFDM increases with the i
35、ncrease of service time, which is turn increases with the increase of accumulated fatigue damage, while that calculated by Miner method maintains its value as that at the beginning of service. Obviously, the result obtained by NFDM is more close to the actual situation of the fatigue occurred in bri
36、dges. It should also be noted that the effective stress range calculated by NFDM has a very small variation at the beginning of service. Therefore it is valid and also efficient to calculate the effective stress range by Miner method at the initial stage of service when the fatigue damage in the bri
37、dge is very small, since the calculation of the effective stress range by NFDM is complicated than that by Miner method. The distribution of the effective stress range at each location of strain gauges is listed in Table 2. The effective stress range at each location of linear strain gauge is calcul
38、ated by using Eq. (19) where the coefficient(b t 3) is simply taken as the same value for all welded connections, and the calculation for the two rosette strain gauges are not included. The distribution of the effective stress range is given by a normalized ratio of Dref=Dr0 where Dr0 is the value o
39、f effective stress range at the location of the strain gauge SSTLN-01. It is observed that, several critical locations of fatigue are found at SSTLN-01 on the Kowloon bound and SSTLS-05, SSTLS-12, SPTLS-09 and SPTLS-14 on the Airport bound respectively where the effective stress range has a comparat
40、ively large value.Now it is clear that fatigue damage assessment for the deck section CH 24662.5 of the Tsing Ma Bridge should be carried out for the weld connections near the strain gauges SSTLN-01 on the Kowloon boundand SSTLS-05, SSTLS-12, SPTLS-09 and SPTLS-14 on the Airport bound respectively.
41、The assessment of fatigue damage and the prediction of residual service life can be made by Miners law or NFDM based on CDM. Details of the calculation may be found in our previous work on fatigue damage model and fatigue analysis of bridge-deck sections (Chan et al., 2001; Li et al., 2001b). The cr
42、itical location of the deck section of the Tsing Ma Bridge will be one of those locations with a comparable large value of the effective stress range. In the deck section at CH 24662.5, the critical location will be one of locations of SSTLN-01, SSTLS-05, SSTLS-12, SPTLS-09 and SPTLS-14, as shown in
43、 Fig. 6. The effective stress range reaches its maximum at SPTLS-09 which is installed at lower bracing of the cross frame underneath the bridge and mass transit railway (MTR). This result suggests that the accumulative fatigue of the deck section may be dominated by the rail traffic loading.6. Conc
44、lusions The present work proposed a theoretical framework for the determination of the effective stress range based on equivalent law of strain energy and fatigue damage model, an efficient approach for accurately assessing effective fatigue stress range of existing bridges under traffic loading is
45、then presented based on the proposed theory. The following specific conclusions can be obtained from the present study: The proposed theory on the determination of the effective stress range provides a unified approach to derive different formulation for the calculation of the effective stress range
46、 for a variable-amplitude spectrum. It is based on the equivalence of strain energy and fatigue damage. The theory leads to a new formulation for the determination of the effective stress range with respect to the nonlinear fatigue damage model, which allows the fatigue damage and its influence on t
47、he state of stress to be considered in the calculation of the effective stress range. The effective stress range for a variable-amplitude stress spectrum, as a way relating variable-amplitude fatigue data to constant-amplitude data, provides the most convenient way for fatigue assessment of bridges
48、under actual traffic loading. The comparison of the theoretical and the experimental results for fatigue life of an existing under real traffic loading has confirmed the validity of the proposedmethod. The calculated result of the effective stress range by NFDM is more close to the actual situation of the fatigue damage developed in bridges. It is valid and also efficient to calculate the effective stress range by Miner method instead of NF