*Article* **A New Analytical Model for Deflection of Concrete Beams Reinforced by BFRP Bars and Steel Fibres under Cyclic Loading**

**Haitang Zhu 1,2, Zongze Li 2,\*, Qun Chen 2, Shengzhao Cheng 3,4, Chuanchuan Li <sup>2</sup> and Xiangming Zhou <sup>5</sup>**


**Abstract:** Basalt-fiber-reinforced plastic-bars-reinforced concrete beams (i.e., BFRP-RC beams) usually possess significant deformations compared to reinforced concrete beams due to the FRP bars having a lower Young's modulus. This paper investigates the effects of adding steel fibers into BFRP-RC beams to reduce their deflection. Ten BFRP-RC beams were prepared and tested to failure via four-point bending under cyclic loading. The experimental variables investigated include steel-fiber volume fraction and shape, BFRP reinforcement ratio, and concrete strength. The influences of steel fibers on ultimate moment capacity, service load moment, and deformation of the BFRP-RC beams were investigated. The results reveal that steel fibers significantly improved the ultimate moment capacity and service load moment of the BFRP-RC beams. The deflection and residual deflection of the BFRP-RC beams reinforced with 1.5% by volume steel fibers were 48.18% and 30.36% lower than their counterpart of the BFRP-RC beams without fibers. Under the same load, the deflection of the beams increased by 11% after the first stage of three loading and unloading cycles, while the deflection increased by only 8% after three unloading and reloading cycles in the second and third stages. Finally, a new analytical model for the deflection of the BFRP-RC beams with steel fibers under cyclic loading was established and validated by the experiment results from this study. The new model yielded better results than current models in the literature.

**Keywords:** cyclic loading; deflection; BFRP-RC beams; steel fiber; analytical model
