# Evaluation of Shear Effect on Deflection of RC Beams
## 1 Introduction  
Excessive deflection or cracking interferes with the function of reinforced concrete (RC) structures and causes inconvenience for users even if the strength of the structure satisfies safety standards. Therefore, the serviceability of RC structures must be reviewed. Many structural standards, including the current ACI building code [1], are based on the ultimate strength design method. Because the ultimate strength design method uses the ultimate state of the materials in the design, serviceability review for deflection or cracking is recommended. Deflection, which is one of the serviceability factors that must be considered, should be designed to be within the allowable range recommended by structural standards for the working load conditions. RC structures can crack even under a working load, and the flexural rigidity of the member changes depending on the degree of cracking. In an experimental study that illustrates these characteristics, [PERSON] [2] proposed a relatively simple equation for the effective moment of inertia that uses the relationship between the bending moment at the time of cracking and the subsequent bending moment. This formula was adopted in the ACI building code from 1971 to 2018 and used for calculating the deflection of RC beams [3]. Recently, the equation proposed by [PERSON] [4] using a spring model has been applied to ACI 318-19 for the effective moment of inertia. Since the [PERSON] equation was proposed, many researchers have conducted studies on the deflection of RC beams. [PERSON] and [PERSON] [5] investigated the deflection of RC beams subjected to uniformly distributed loads. They proposed a simplified procedure for calculating the elastic deflection using the moment of inertia of the cracked section and a deflection calculation method that uses the flexural stiffness of uncracked concrete in the tension zone. [PERSON] [6] discovered that the effective moment of inertia is sensitive to change in moment ratio when the applied moment is small and modified [PERSON]'s formula to simplify the calculation of the effective moment of inertia. [PERSON] [7] proposed an effective moment of inertia obtained by considering the tension reinforcement ratio. [PERSON] and [PERSON] [8] studied the variation of the effective moment of inertia under non-uniformly distributed loads in contrast with [PERSON]'s formula, which was derived from experimental results under a uniform load. [PERSON] and [PERSON] [9] proposed an effective moment of inertia obtained by considering the tension reinforcement ratio and the moment distribution that varies according to the loading patterns to approximate the moment of inertia of the cracked section. [PERSON] [10] pointed out that the deflection calculated by the ACI method is accurate for short-term loads but inaccurate for long-term loads. [PERSON] and [PERSON] [11] modified the equation proposed by [PERSON] and [PERSON] using the concrete compressive strength and the shear span of beams as variables. [PERSON] and [PERSON] [12] reported that [PERSON]'s equation had a larger deviation in members with steel reinforcement ratios of 1% or less. [PERSON] and [PERSON] [13] recommended that cracking moment should be reduced to 2/3 in consideration of restraint and the reduction of the tensile strength of concrete during construction. [PERSON] et al. [14] recommended modifying [PERSON]'s formula based on flexural tests on the tension reinforcement ratio and load pattern. [PERSON] and [PERSON] [15] proposed a new equation of the effective moment of inertia of FRP-steel RC beams using [PERSON]'s formula. [PERSON] and [PERSON] [16] evaluated the accuracy of [PERSON] and [PERSON] equations for the minimum deflection of two-way slabs. [PERSON] [17] calculated the deflection of tilt-up concrete wall panels under service load. [PERSON] [18] also compared his own formula, adopted in ACI 318-19, with the approaches of [PERSON] and Europe. The deflection of RC beams is affected not only by bending but also by shear.