# Structural Performance of a Precast Concrete Modular Beam Using Bolted Connecting Plates
## 4 Experimental Results and Analysis
### Evaluation of the Applicability of Design Code  
For modular structures, a design guideline that can consider the characteristics of connection between modules should be proposed [7; 8; 9]. In the modular members which are connected with steel plates, the structural performance depends on connection length, embedment length, and amount of steel plates. Therefore, the steel plate should be considered when designing modular members. In this paper, the embedment length was considered to prevent pull-out failure, and it was determined as provided in KDS 14 20 52:2021 [22]. As per the test results, pull-out failure did not occur. In addition, connection length and the amount of steel were designed so that both modules had the same amount of steel reinforcement based on the midspan. Therefore, the flexural and shear strengths were calculated according to ACI 318-19 [19] without considering the contribution of connecting plates. The purpose of reinforcements in the compression zone was to provide support for the stirrups. Therefore, the number of reinforcements in the compression zone were fewer than the number of reinforcements in the tensile zone. The bending strength was calculated, neglecting the contribution of compression reinforcements. The design of the flexural and shear strengths of the RC beam presented in ACI 318-19 [19] are as follows:  
\[\varnothing M_{n,ACI}=\varnothing\Big{\{}A^{\prime}{}_{s}f_{y}\big{(}d-d^{ \prime}{}\big{)}+\big{(}A_{s}-A^{\prime}{}_{s}\big{)}f_{y}\Big{(}d-\frac{a}{2 }\Big{)}\Big{\}} \tag{1}\]  
\[\varnothing V_{n,ACI}=\varnothing(V_{c}+V_{s}) \tag{2}\]  
\[V_{c}=\frac{\lambda}{6}\sqrt{f^{\prime}{}_{c}}b_{w}d \tag{3}\]  
\[V_{s}=\frac{A_{v}f_{y}}{s}d \tag{4}\]  
where \(\varnothing\) is the strength reduction factor, \(A^{\prime}{}_{s}\) is the area of compression reinforcement, \(A_{s}\) is the area of non-prestressed longitudinal tension reinforcement, \(f_{y}\) is the yield strength for non-prestressed reinforcement, \(d\) is the distance from extreme compression fiber to centroid of longitudinal tension reinforcement, \(d^{\prime}\) is the distance from extreme compression fiber to the centroid of longitudinal compression reinforcement, \(a\) is the depth of the equivalent rectangular stress block, \(\lambda\) is the modification factor, \(b_{w}\) is the web width, and \(A_{v}\) is the area of shear reinforcement within spacing, \(s\).  
The experimental results showed that the moment of the MCF and PCF were 153.42 and 135.3 kNm, respectively, and they were approximately 114% and 101% of the design moment strength calculated through ACI 318-19 code. The shear strength of the MCS and PCS were 113.13 and 100.48 kN, respectively, and they were about 116% and 103% of the design shear strength of ACI 318-19. It was indicated that the proposed PC modular method  
Figure 13: Strains of shear test specimens: (**a**) strain of stirrup in MCS; (**b**) strain of stirrup in PCS.  
met the requirements of the current design code, ACI 318-19 [19], and the PC modular beam had a similar performance capacity to a general monolithic RC beam. Furthermore, since the flexural and shear capacity of the PC modular beam exceeded the design strength, as a result of the comparison, the structural capacity of the PC modular beam using the proposed connection method can be estimated reasonably by using a current design code without any consideration of connecting plates. It was indicated that the steel plate did not contribute to enhancing strength, but it did act to transfer stress from each module. Therefore, if a steel plate connection is applied for the purpose of stress transfer, it is judged that the ACI 318-19 code can be used. In addition, it was confirmed that the connection method using a bolted connecting plate can solve the problems observed in typical PC modular beams using grouted splice sleeves wherein the full strength of a member could not be exploited because the sleeve was not fully grouted.