## 1 Introduction  
Ultra-high-performance concrete (UHPC) is a relatively novel fibrous cementitious composite. It is characterized by its ultra-high compressive strength, low water to cement content (usually less than 25%), superior packing density, impact resistance, flowability, and long-lasting characteristics [1, 2, 3]. The generally acknowledged minimum compressive strength level of UHPC is 150 MPa. However, it is practical to allow for the broader domain of UHPC's strengths, as investigators employ various standardized methods for strength assessment [4]. The compact microstructure of UHPC is obtained by optimizing its packing density. The latter significantly affects the compressive strength and waterproofness (i.e., enhances the permanency features) [2]. UHPC normally incorporates steel fibers to enhance its ductility response to tensile forces [5]. The technology for developing UHPC involves properly mixing Portland and other types of cement with an optimized aggregate size distribution, fibrous reinforcement, and employment of chemical admixtures (superplasticizers) [6, 7]. The scientific community has devoted significant efforts to explore the applicability of UHPC in various structures (e.g., slab on grade, highway bridges, abutments, super-ductile structural elements, rehabilitation of existing structures, etc.) [8, 9, 10]. UHPC, in addition to its superior compressive strength, has a higher Young's modulus than conventional concrete that enables the design of slender structural elements. The high tensile and flexural strength of UHPC obtained by the inclusion of fibrous systems enable its potential usage in special structural features. In previous research, many investigators have studied the use of UHPC in beam elements due to its remarkable merits with regard to entire mechanical responses. It is worth noting that the balanced reinforcement area for the UHPC beam is significantly larger than the comparable high-performance concrete, due to the higher strength class. This behavior results in a more ductile flexural response in the condition of ultimate loading and increased bar reinforcement conditions [11; 12]. The use of discontinuous fibers in UHPC can cause improved cracking resistance and therefore higher tensile and flexural strength. Fractured UHPC has the capacity to resist higher loading, with strain-hardening (multiple cracking) responses [13]. Research evidence has shown that the use of fiber reinforcement in UHPC increases its tensile strength. It reduces the amount of mild steel bars needed and the total cost of materials [14]. Additionally, the higher strength-to-weight ratio of UHPC generates a substantial decrease in the dead-weight of UHPC elements. Under analogous loading conditions, the use of UHPC instead of normal strength concrete to design a structural element reduces the dead load of structures by 50-67% [15]. In light of these aspects, UHPC has received attention from builders who strive to develop slenderer structures, especially in bridges, to provide cost-effective construction. Therefore, UHPC has been extensively used in various structural members (e.g., precast girders, deck (infill) connections, railway slab systems, tiny elements, deck sheets, permanent formwork, and functionally categorized materials) for road and walkway bridges [16; 17; 18; 19; 20; 21; 22]. The guidelines for designing normal concrete structures have been successfully developed by many building codes such as ACI (American Concrete Institute), IBC (International Building Code), Eurocode, etc., which have been utilized in design practice for many years [10]. Nevertheless, these guidelines do not apply for recently developed UHPC structural members, since its intrinsic mechanical properties (i.e., tensile, compressive, and fracture energy) are quite different from normal concrete. It is noteworthy that some references on the prediction of the ultimate moment of UHPC structural elements are available in [23; 24; 25]; however, these methods have not yet been adopted in the international design codes.