Flexural behavior is an important characteristic of concrete bridges. Research has shown that prestressed UHPC girders demonstrate excellent ductility, cracking resistance, and flexural deformation capacity [3] due to the use of fibers, which significantly improve the strength, toughness, and durability of UHPC. The flowability of UHPC mixtures is significantly reduced due to the use of steel fiber [4], while the compressive strength and flexural properties are considerably improved with increase in steel fiber content [5,6]. However, when the content exceeds 2%, the effect on strength and toughness is limited [7]. Due to the addition of steel fibers, the entire stress failure process of reinforced UHPC beams under flexural load is different from that of normal concrete (NC) and can be roughly divided into three stages [8,9]. The first is the elastic stage in which the bending moment in the pure bending section is small, the stress is basically the same as that of a uniform elastic body, and the load-deflection curve is a straight line. After an initial crack in UHPC, a crack development stage occurs in which the original tensile force carried by the UHPC is transferred to the steel fiber and the tensile longitudinal reinforcement. The slope of the deflection curve decreases gradually. In the later stage of damage, the longitudinal tensile reinforcement yields, and the compressive zone gradually starts to enter the stage of elasticity. The cracks in the purely bending span develop rapidly along the height of the beam and increase in width, the section reaches its ultimate load, the slope of the load-deflection curve gradually tends to zero, and an obvious main crack appears. The ratio of the elastic stage to the entire failure process of the UHPC beam is greatly increased and the ratio of the cracking load to the yield load is also increased [10].
In recent years, a considerable amount of experimental research has been undertaken on the flexural behavior of NC-UHPC composite beams, including that reported in [14,15,16,17,18]. In [14], the bond strength between UHPC and NC was found to be very high. When a flexural load was applied, an initial crack was observed to occur diagonally in the mid-depth of the shear span of the NC layer. Additional diagonal cracks were formed within the shear span as the applied load increased. Failure occurred when the concrete was crushed at the NC layer [14]. The initial and yield stiffnesses, as well as the peak and ultimate loads, were found to be enhanced by increasing the thickness of the UHPC layer, enabling expression of its high strength and ductility characteristics [15]. Compared with an NC beam, the numbers of cracks in a UHPC-NC composite beam was found to be significantly reduced [16]. NC-UHPC composite beams were shown to exhibit three failure patterns, including typical flexural failure, a hybrid of debonding and NC overlay flexural failure, and a hybrid of debonding and NC overlay shear failure [17]. The interfacial zone of a UHPC-NC composite beam does not affect the cooperative performance of the concrete beam and the UHPC layer before the failure stage. Therefore, the concrete beam and the UHPC layer can be understood to operate closely together. However, at the ultimate stage, due to a large number of fine cracks in the interfacial zone, the concrete will be softened, and the stiffness of the interfacial zone will be reduced, which represents one of the main failure modes of the composite structure [18].
Jbridge 15 Crack
Based on Figure 10, and the loading process of the beam, it can be seen that: (i) at stage I, the load level was low, the internal force of the beam section was small, and the beam body was not yet cracked; (ii) at stage II, when the load increased to the cracking load, the first micro-crack appeared near the bottom of each beam section, and the load continued to increase. The micro-crack slowly extended upward, but the crack did not expand horizontally and more micro-cracks appeared near the first micro-crack; (iii) at stage III, when the load continued to increase to the crack development load, the first crack at the bottom of the beam gradually became the main crack and gradually developed and penetrated to the NC-UHPC joint surface. The crack width increased, a large number of new cracks appeared and the beam flexed and deformed. As the speed increased, the sound of the steel fiber being pulled out could be heard; (iv) at stage IV, the load increased slowly, the main crack extended to the flange plate and developed horizontally at the height of the joint surface. New cracks were no longer generated, the load barely increased and the deflection increased sharply, indicating that the steel strand had yielded and the beam had reached the ultimate bearing state.
According to Figure 11, the strain varied approximately linearly with height changes at lower load levels. The same applied to the concrete on the compressive side at higher load levels, while the strain on the tensile side varied abruptly with height changes. This was because cracks appeared in the concrete of the tension zone at higher load levels, causing deformation or damage to the strain gauges there, resulting in distortion of the strain gauge data which did not reflect the true strain of the beam. In general, the longitudinal strains in the mid-span sections of different beams were consistent with the flat section assumption, according to the basic assumptions presented in Section 2.2.
where Mum, Muc are the measured value and calculated value of the ultimate state bending moment, where Muc is calculated from Equation (3); γu is the strength safety factor; Mcrm, Mcrc are the measured value and calculated value of the cracking moment, where Mcrc can be calculated with equation (11); and γcr is the safety factor of the crack. Figure 13 shows a comparison of Muc, Mum, Mcrm and Mcrc.
As can be seen from Figure 13, the measured value and the design value both decrease with the height of the NC layer, indicating that the NC layer has a negative effect on the normal section strength. The resistance factor γu ranges from 1.7 to 1.9 and γcr ranges from 1.5 to 1.7, which demonstrates that the calculation formulas for the ultimate state bending moment and the cracking moment proposed in Section 2 are accurate and have a safety reserve. It should be noted that the strength of the beam depends on the dimensions of the specimens in the test. It has been shown that, as the size increases, the flexural strength of UHPC beams tends to decrease, but the size effect on the flexural strength is negligible due to the high ductility of UHPC [10,44]; therefore, the normal section strength and cracking moment discussed here are reasonable up to a point.
(2) The test results for flexural performance of six NC-UHPC composite beams showed that flexural damage to the NC-UHPC composite beams exhibited four different stages: an elastic stage, a uniform cracking stage, a crack development stage and a yielding stage.
Some researchers conducted destructive tests on structures to evaluate the load transfer performance of cracked shear keys. Wang et al. [7] carried out a static load test on a structure composed of six beams connected by concrete shear keys. They found that at a load level of 70 kN, two shear keys cracked with relative displacement across the shear key (RDSK) of approximately 0.02 and 0.04 mm, respectively. As the load increased, the crack in the shear keys propagated and eventually failed at a load level of 140 kN, twice the cracking load. Yuan et al. [8,9] conducted four tests on two-beam structures connected by transverse post-tensioning (PT) and partially or fully cracked shear keys, which were cast with nonshrink grout. Over millions of cycles, the load levels increased from 80 to 400 kN, and the PT force dropped from 445 to 0 kN. The results showed that when the transverse PT force decreases from 445 to 45 kN, the load can still be transferred effectively, and the RDSK remains stable. Miller et al. [10] carried out three cyclic loading tests on four-beam structures connected by transverse tie rods and shear keys, cast with nonshrink grout. In the first two tests, there were initial cracks at shear keys in the middle caused by temperature, and in the third test, there were initial cracks near the beam end. During the cyclic loading, the cracks in the first two tests propagated, while the cracks in the third test did not. They found that the load was effectively transferred, and the load distribution changed by no more than 1% during all three tests. However, according to the test result of Leng et al. [11], it may be due to the position of the load and crack. Leng et al. tested an eight-beam structure connected only by concrete shear keys. They set different crack lengths on the first and the fourth shear keys to assess the influence of crack length and transverse position on load distribution. They found that the crack at the first shear key had a significant impact on the load distribution, but that at the fourth did not. These destructive tests indicate that the cracking of shear keys does not mean load transfer failure, and the ultimate bearing capacity may be much larger than the cracking load. However, destructive tests are unsuitable for bridges in service to evaluate residual capacity; the finite element method is more appropriate.
In the SDS test, the displacement was applied at a rate of 0.02 mm/s until the specimen failed. The displacement field, cracks, associated cracking loads, and final failure mode were recorded during the test.
In the CFS test, the load varied linearly between 15 kN and the specified control force at a frequency of 1 Hz. In the first CFS test, the control force was set at approximately 60% of the cracking load obtained by the SDS test. This value was proposed on the assumption that the properties of the interface material are similar to concrete, for which 60% of the maximum tensile stress could be regarded as the elastic limit [46]. The control forces of the second and third CFS tests were determined based on the result of the last test. The controlled force increased if the specimen was uncracked in the previous test. Otherwise, it decreased. A total of 1400 cycles were applied in one test for two main reasons: (1) supposing that the structure was overloaded once a week over a 20-to-30-year period; and (2) too much data generated by DIC during the test, causing storage problems. An SDS test on the same specimen would follow if no cracks appeared after the CFS test. The displacement field and the failure mode were recorded during the test.
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