## 1 Introduction  
The percentage of steel reinforcement controls the behavior and failure process in reinforced concrete members. This failure can be of steel yielding followed by crushing of concrete in the case of under-reinforced beams and crushing of concrete in the case of over-reinforced beams. Hence, minimum ductility requirements should be satisfactorily met while designing reinforced concrete beams. This can be attained by providing an adequate amount of tensile reinforcement. If a beam is provided with less steel than required, the failure becomes brittle. This stimulates instability in the overall response of a beam. Before concrete cracking, the load-deflection response of a plain cement concrete beam and a reinforced concrete beam is of equal order. When the ultimate strength generated with the provided reinforcement is less than the flexural cracking strength, immediate crack growth is created. Therefore, a certain amount of minimum tension reinforcement is necessary for ductile behavior. While the percentage of flexural reinforcement increases, the ultimate strength, and ductility of reinforced concrete beams increase [1]. However, provisions for minimum flexural reinforcement specified by most codes of practice are based on empirical approaches. The criteria for evaluating minimum reinforcement consider that a beam should not fail instantly upon concrete crushing. To meet this condition, the ultimate capacity of a reinforced concrete beam should be greater than, or equal to, its cracking moment. Most codes use flexural strength to evaluate cracking stress in beams [2; 3; 4; 5; 6; 7; 8; 9]; however, large-scale specimens have less cracking bending strength than flexural strength. In the traditional design method, cylinder split tensile test, compression test, and modulus of rupture tests are used to define concrete properties, which cannot completely characterize the behavior of concrete [10]. Damage assessment plays an important role in the evaluation of the stability and strength of a structure, which is significant for both existing structures and those under construction [11]. The flexural strength of normal-strength concrete members is commonly designed using rectangular stress block parameters. Current design codes provide rectangular stress block parameters for a simplified design methodology. However, these stress blocks are determined by tests of reinforced concrete columns, which have apparent limitations. A rectangular stress block can be used because the shape of the stress-strain relation of concrete is analogous to the trapezoid. However, the shape of the stress-strain relationship of concrete changes into a triangle as the compressive strength of concrete increases. For this reason, rectangular stress block parameters depend on the compressive strength of concrete [12]. In design practice, when the deflection of a reinforced concrete beam is calculated, according to standards, two states are analyzed: the cracked state and the uncracked state. The flexural stiffness of a reinforced concrete beam changes from an uncracked state to a cracked state. The equation for the effective moment of inertia used to calculate a moment of inertia somewhere between the uncracked moment of inertia and the cracked moment of inertia depends on the applied load. As the load increases, the initial distribution of stiffness of the element changes, and the number of cracks varies non-deterministically. The distribution of strains and stresses in concrete and steel, along the axis of the element, is irregular. The resulting effective moment of inertia can be used in elastic deflection equations to approximate actual deflections. Enhancing the physical properties of the concrete can increase the shear strength and flexural strength of the beam [13]. In a previous study, [PERSON] et al.