# Effect of Aggregate Type on the Shear Behavior of Reinforced Lightweight Concrete Beams
## 3 Existing Design Guidelines for Reinforced Lightweight Concrete Beams  
The equations selected for this study, which predict the shear strength of LWAC beams, were derived from existing structural design guidelines and include modification or reduction factors to account for the lower strength of LWAC compared to NWC. Table 1 summarizes the requirements of LWAC based on concrete compressive strength measured at 28 days and/or density and the modification or reduction factors suggested by each design code [23; 24; 25; 26; 32; 33; 34; 35]. It should be noted that the strength and density outlined in Table 1 do not necessarily imply suitability for structural applications as they can be tailored to meet the specific requirements of the project and the types of structures involved. ACI 318-11 [24] presents equations to estimate the shear capacity of LWAC beams, accounting for the lower modulus of elasticity and sometimes reduced tensile strength of LWAC compared to NWC. These equations specifically include the cylindrical compressive strength, the tensile reinforcement ratio, and the shear span to effective depth ratio (_a/d_). As indicated in Equation (2) below, ACI 318-11 also recommends using a modification factor, \(\lambda\), particularly for LWAC, based on the measured splitting tensile strength, \(f^{\prime}_{sp}\). If \(f^{\prime}_{sp}\) is unavailable, default values of 0.75 for ALWAC and 0.85 for LWAC are recommended. \[V_{c}=\left(0.16\lambda\sqrt{{f_{c}}^{\prime}}+17\rho_{s}\frac{V_{u}d}{M_{u}} \right)b_{w}d\leq 0.29\lambda\sqrt{{f_{c}}^{\prime}}b_{w}d \tag{1}\]  
\[\lambda=\frac{{f_{sp}}^{\prime}}{0.56\sqrt{{f_{c}}^{\prime}}}\leq 1.0 \tag{2}\]  
where \(V_{c}\) represents the shear resistance of the reinforced LWAC beam, \(f_{c}^{\prime}\) denotes the cylindrical compressive strength, \(\rho_{s}\) is the tensile reinforcement ratio, \(V_{u}\) indicates the factored shear force, \(d\) is the effective depth of the beam, \(M_{u}\) refers to the factored shear moment, \(b_{w}\) is the section width, and \(f_{sp}\)' is the splitting tensile strength. BS 8110 [26] suggests an empirical equation that considers important parameters, such as the reinforcement ratio, _a/d_, and cubical compressive strength, to determine the shear capacity of reinforced LWAC beams (see Equation (3)). \[V_{c}=\frac{0.79}{\gamma}\left[\left(\frac{100A_{s}}{b_{w}d}\right)^{\frac{1} {3}}\left(\frac{400}{d}\right)^{\frac{1}{3}}\left(\frac{f^{\prime}_{cube}}{25 }\right)^{\frac{1}{3}}\right]b_{w}d+\frac{A_{v}f_{y}d}{s} \tag{3}\]  
where \(V_{c}\) is the shear strength of the reinforced LWAC beam, \(\gamma\) is the partial factor of the materials, \(A_{s}\) is the area of tensile reinforcement, \(b_{w}\) is the beam section width, \(d\) is the effective depth of the beam, \(f_{cube}\) represents cubical compressive strength, \(A_{v}\) is the cross-sectional area of the stirrup, \(f_{y}\) is the yield strength of the stirrup, and \(s\) is the spacing of the stirrup. It should be noted that BS 8110 adopts the use of cubical compressivestrength rather than cylindrical compressive strength. Additionally, the cube strength must range between 25 MPa and 40 MPa. The CSA [34] recommends equations that consider a reduction factor of 0.75 or 0.85 for LWAC. According to the CSA, diagonal compression struts are thought to spread in a spiral pattern around the specimen, with the inclination angle varying depending on the loading conditions and the level of reinforcement.