**1. Introduction**

With the development of high-rise buildings and the increasing span and space of concrete structures, the disadvantage of conventional concrete with great self-weight becomes more acute compared to the imposed loads. This promotes the research and development of structural lightweight concrete with different kinds of lightweight aggregates categorized as natural lightweight aggregates and artificial lightweight aggregates [1–4]. Except for the savings in dead load for structure and on foundation due to the self-lightweight, structural lightweight concrete presents many advantages, including the rising of strength/weight ratio, the reduced risk of earthquake damage to a structure, superior thermal and sound insulation, and better durability [3–5]. However, some problems, including greater brittleness than conventional concrete for the same compressive strength, prevent the wide application of structural lightweight concrete [6,7]. One way to resolve these problems is the use of steel fibers. Based on previous research, steel fiber reinforced expanded-shales lightweight concrete (SFRELC), with market-supply sintered expanded-shales for the fine and coarse aggregates, has excellent mechanical properties, especially those related to tensile performances [8–13]. Due to lower shrinkage and reliable bond behavior with the rebar, the SFRELC can be applied to concrete structures [14–17]. To highlight the peculiarities of the tensile performance of SFRELC and the compressive property of conventional concrete, the SFRELC superposed beams and slabs were innovatively developed. The sectional characterization of this kind of superposed flexural member is composite with tensile SFRELC and compressive conventional concrete [18,19], while the fabrication is the bottom-layer of SFRELC successively followed by up-layer conventional concrete [20–22]. Based on the experimental studies and numerical analyses, the design methods for the flexural performances, including cracking resistance, crack width, flexural stiffness, and bearing capacity, of the reinforced SFRELC superposed beams under static loading were built up [23–26].

Civil engineering concrete structures are always subject to the actions of repeated loads. For example, industry plant structures suffer from the vibration from machines, bridges bear the vibration of rolling vehicles, and ocean structures are subject to repeated waves. This raises an important topic of research on the normal serviceability and reliability of engineering concrete structures under fatigue actions. Normally, the key points are concerned with the fatigue behaviors of structural materials, including the fatigue compressive performance of concrete and the fatigue fracture of tensile rebars [27–31]. At the level of structural members under fatigue load, geometric shapes, sectional composites of concrete and reinforcement, and the sectional stress distribution with different fatigue characteristics are also main factors [32–40]. For the reinforced SFRELC superposed beams, the shear fatigue behaviors were confirmed [34]. Results show that the maximum fatigue load controls the initial diagonal crack width and initial stress amplitude of stirrups, which has a great influence on the fatigue life; with an increase of maximum fatigue load, the diagonal crack width grows quickly and the fatigue failure of the test beams takes place with a large possibility of the fracture of stirrups; overload during fatigue is one of the main reasons for fatigue failure, which results in the sudden increase of diagonal crack width and stirrup' stress amplitude. Except for shear fatigue performance, a study of the flexural fatigue performance is also essential for the engineering application of reinforced SFRELC superposed beams subjected to fatigue loads. As per the previous studies on the flexural fatigue behavior of steel fiber reinforced concrete (SFRC) beams [35–40], the presence of steel fibers could promote fatigue resistance to crack growth, decrease the deflection and increase the energy dissipation at failure, and prolong the fatigue life of reinforced SFRC beams. This is due to the beneficial effect of SFRC at the tensile zone in reducing the stress level of tensile rebars. Therefore, with the integrity of the horizontal interface between SFRELC and conventional concrete, good flexural fatigue behavior of the SFRELC superposed beams could be a good prospect.

Due to a lack of investigation on the flexural fatigue of SFRELC superposed beams, the experimental study was carried out in this paper. Nine beam specimens with rectangular sections were fabricated and tested by a four-point flexural test under a constant amplitude sinusoid at a frequency of 10 Hz with a fatigue characteristic value ρ<sup>f</sup> = 0.10. The main influence factors were the SFRELC depth change as 0.5, 0.6, and 0.7 times of the whole sectional depth, and the volume fraction of the steel fiber varied as 0.8%, 1.2%, and 1.6%. The upper limit of the fatigue load was taken as the load corresponding to the maximum crack width of 0.20 mm at the barycenter of the longitudinal rebar. This crack width is the limit for reinforced concrete structure cracks within the life of normal serviceability in normal environmental conditions [41]. Based on the experimental results, the crack distribution, crack width, mid-span deflection, failure patterns, and compressive strain of conventional concrete are discussed. Methods for prediction of the stress level, stress amplitude of the longitudinal tensile rebar, and flexural stiffness degeneration with fatigue life are proposed.
