# Shear Performance for Prestressed Concrete Hollow Core Slabs
## 2 Shear Strength of HCS  
As shown in Equation (1), the Korea Concrete Institute Model Code (KCI 2017) [15] and American Concrete Institute Standard (ACI 318-19) [16] specify that the design shear strength of a prestressed concrete member must be equal to or greater than the factored shear strength.  
\[V_{u}\ \leq\phi V_{n} \tag{1}\]  
Here, \(V_{u}\) is the factored shear strength and \(V_{n}\) is the nominal shear strength.  
Depending on the two types of shear failure, the shear strength of an HCS member without transverse reinforcement can be classified into flexural-shear strength (\(V_{ci}\)) and web-shear strength (\(V_{cw}\)), given by Equations (2) and (3), respectively. According to the Code, the smaller of the two values should be used.  
\[V_{ci}=0.05\lambda\sqrt{f_{ck}}b_{w}d_{p}+V_{d}+\frac{V_{i}M_{cre}}{M_{max}} \geq 0.17\lambda\sqrt{f_{ck}}b_{w}d_{p} \tag{2}\]  
\[V_{cw}=\left(0.29\lambda\sqrt{f_{ck}}+0.3f_{pc}\right)b_{w}d_{p}+V_{p} \tag{3}\]  
Here, \(\lambda\) is the lightweight concrete factor, \(f_{ck}\) is the compressive strength of concrete, \(b_{w}\) is the web width, \(d_{p}\) is the distance from the compressive edge to the center of the tendon cross section, \(V_{d}\) is the shear force of the cross section due to fixed load, \(V_{i}\) is the factored shear force due to applied load,  
Figure 1: Extrusion method of hollow core slabs (HCS): (**a**) Casting by extrusion machine; (**b**) Extruded HCS.  
is the crack moment due to applied load, \(M_{max}\) is the maximum factored moment due to applied load, \(f_{pc}\) is the compressive stress of concrete in consideration of stress loss of prestress at the cross-sectional centroid that is in resistance to applied load, and \(V_{p}\) is the vertical component of jacking force where inclined tendons are used.  
In the case of HCS, thin webs are the most vulnerable structures due to the hollow cores, and shear strength is likely to be determined based on web-shear strength. Since the calculation of effective cross section is important in evaluating shear strength, Precast/Prestressed Concrete Institute (PCI) [17] recommends the use of web width in the calculation of design member force.  
For HCS, the formation of web-shear cracks should be prevented in the transfer length section, where effective prestress is not fully exhibited. If the decrease in effective prestress is reflected at dangerous cross sections, web-shear strength decreases by about 30% according to Equation (3). Equation (3) is based on the study of [PERSON] and [PERSON] [2], who found that using Equation (3) to derive the web-shear strength may overestimate the actual strength of HCS members with heights greater than 300 mm because the web-shear strength of HCS members exceeding 380 mm falls in the range of 58 to 85% [8]. KCI 2017 and ACI 318-19 specify that web-shear strength should be halved for thick HCS members exceeding 315 mm in height and not meeting the minimum requirement for transverse reinforcement.  
To ensure the continuity considering the floor diaphragm of slabs, topping concrete is placed on HCS, and the slabs are used in the form of composite cross-sections. As described by PCI, the web-shear strength of HCS members can be obtained by substituting topping concrete with a transformed section. Since topping concrete generally has a lower compressive strength than that of the concrete used in HCS members, the elastic modulus of concrete (\(n=E_{RC}/E_{HCS}\leq 1\)) is used when calculating web-shear strength based on a transformed section.