预制板的连续组合双肋桥的裂缝控制英文文献和中文翻译(4)
Fig. 17(a) shows the momentary closure of crack width occurring at O-1 and O-2 duringthe repeated loading. This phenomenon illustrates the tensionstiffening effect that slows down the increase of width bythe development of new cracks in the vicinity of the crackedsection. It is suggested that the propagation of crack width forO-1 and O-2 will remain within the allowable crack width evenafter one million cycles. Crack widths O-3 and O-4 measuredat the proximity of the center of the deck above the internalsupport were also observed to remain below the allowable crackwidth (Fig. 17(b)). From the results, it is considered that crackwidths were controlled appropriately within an allowable crackwidth [9] in the decks and transverse joints of the compositebridge with prefabricated slabs. On the contrary, large crackwidths occurred at the bottom of the deck in the loaded area.In particular, the developed transverse cracks were comparableto the longitudinal cracks considered during the design of thedeck. Following this, the moment developed at the bottomof the deck should be considered for both longitudinal andtransverse directions for the design of the deck. Especially,attention should be paid to the fact that crack width propagationunder static and repeated loading may be larger in the decks atloaded section than near the internal support. This feature issupposed to be also correlated with the ratio of the deck spanto the bridge span. The occurrence of such phenomenon seemsparticularly highly probable in long-span decks of bridges witha limited number of girders. O-5 corresponds to crack widthmeasured in the deck joint nearest to the bottom of the deckin the loaded section. The crack width measured by O-5 underinitial repeated load was negligible but, after 1000 cycles ofloading, the crack width was suddenly increased. This showsthat the action of repeated loading may suddenly magnify crackwidths although crack widths measured in the loop joints (O-5)were observed to be smaller than the ones measured inside thedeck (O-6).Fig. 18 displays the relative slip between the deck andthe girder with the number of loading cycles. Similar to thedeflection and crack width, relative slips were also provedto increase with the number of loading cycles. The relativeslip (SL1–SL6) between deck and girder has been measuredlongitudinally at regular intervals from the extremities of thebridge to the internal supports (Fig. 3(c)). As can be seenin Fig. 18(a), SL1, SL2 and SL3 were increased with theincreasing cyclic loading number, and the increasing trendfor SL2 and SL3, corresponding to relative slips measuredin the negative moment region, can be observed clearly. Even if the occurrence of relative slip was verified, themaximum relative slip occurring after one million cyclesdid not exceed 0.14 mm (Fig. 18(a)). Since the prototypebridge was designed as full shear connection using strengthdesign, the level of relative slip may be assumed as fullcomposite action, and the strength formula related to studshear connections applied in precast decks and the designproposal for shear connections can be considered as valid alsounder repeated loading [6,7].The longitudinal distribution of relative slip can be verifiedin Fig. 18(b). Also, it can be easily observed that thelongitudinal relative slip increases with the number of repeatedloading cycles. As relatively large relative slips occurred in thenegative moment region, future researches will be performed toestablish the relationship between cracks developed in concretedecks and relative slips in the negative moment region.The increasing ratios of displacement, crack width and slipafter fatigue test were presented in Fig. 19. Due to the cyclicloading of one million times, displacement increased by amaximum, of about 45% of initial displacement and crackwidth increased by a maximum, of about 40% of initial crackwidth. Since the relative slip was very small initially, theincreasing ratio was so large, but still the quantity is not aproblem after fatigue test as mentioned above.Moment curvature relationship of the bridge model afterfatigue test was also observed as shown in Fig. 20. In spite ofone million cyclic loading, only slight change of the stiffnesswas observed in both maximum positive and negative momentsections. Accordingly, even though the one million cyclicloading was applied, the composite section behaviour of theprefabricated slab with loop joints was confirmed.3.3. Static inelastic behaviour after repeated loadingAfter the repeated loading test was performed with onemillion loading cycles, static loading test was performed byapplying load up to 900 kN at the same loaded points. The curvedesignated as “Analysis” in Fig. 21 is the load–deflection curvecomputed using the 3D finite element model, and correspondsto the elastic deflection of the bridge relative to the uncrackedcomposite section. Following this, the difference between thiscurve and the experimental curves expresses the stiffnessreduction factors for the occurrence of cracks in concrete due tothe action of static and repeated loads, the compressive materialnonlinearity of concrete and the relative slip.Fig. 22 plots the crack widths measured in the static loadingtest performed up to 900 kN after repeated loading test ofone million cycles. The crack widths progressing inside thedeck and in the deck transverse joint near the internal support remained below 0.2 mm until 670 kN (Fig. 22(a)). This loadis 2.7 times the design rear wheel load considering impact [9].Thus, it is considered that in negative moment regions, controlof crack widths within 0.2 mm can be done for compositebridges with prefabricated slabs under service loads. O-1 andO-3 did not exceed 0.3 mm under 900 kN while O-4 exhibited sudden increase of crack width at the proximity of 700 kN, toexceed 0.3 mm near 900 kN. On the other hand, the presence ofresidual crack widths made O-6 to exceed 0.3 mm at 300 kN toreach an extremely large crack width of 0.8 mm at 900 kN.Fig. 23 presents the curves expressing the relationshipbetween the crack width (O-1 or O-2) measured in the deckjoint cast interface at internal support and the reinforcementstress calculated from the strain of the reinforcement.Comparison is also done with the crack widths proposed in ACIcode (Gergely–Lutz equation), CEB-FIP code and Eurocode tocontrol crack width [1–4]. It is seen that crack width occurringin the joint cast interface is initially larger than the onescalculated according to foreign codes. With increasing steelstress, crack widths of the test girder, O-1 and O-2 becameless than that evaluated by Eurocode 2.