# Research on Mechanical Properties of Core-Filled Desulfurized Gypsum Masonry
## 3 Compressive Strength Calculation Formula  
According to the test data, the compressive strength of the new high-precision desulfrized gypsum core-filled masonry is calculated using current national standard calculation Formula (2). \[f_{c,i}=\frac{1000P_{c,i}}{A} \tag{2}\]  
where \(f_{c,i}\) represents the compressive strength of the gypsum-filled masonry specimens and \(P_{c,i}\) represents the ultimate load of the gypsum-filled masonry. From Table 2, it can be seen that the ratio of the average compressive strength of each group of core-filled masonry to the code-specified value is less than 1. This indicates that Formula (2) is not suitable for calculating the compressive strength of reinforced masonry, as its calculated values tend to be unsafe. According to the test data, the compressive strength of the new high-precision desulfurized gypsum reinforced masonry is calculated with reference to Formulas (3) and (4) in the Code for Design of Masonry Structures. \[N_{c}=\varphi\Big{(}f_{g}A+0.8f_{y}^{\prime}A_{s}^{\prime}\Big{)} \tag{3}\]  
\[\varphi=\frac{1}{1+0.001\beta^{2}} \tag{4}\]  
where \(f_{g}\) represents the compressive strength of reinforced masonry (MPa). \(A\) represents the cross-sectional area of the masonry specimen, \(A_{s}^{\prime}\) represents the cross-sectional area of the masonry specimen, \(f_{y}^{\prime}\) represents the compressive strength of the vertical steel reinforcement; \(\varphi\) represents the stability coefficient and \(\beta\) represents the height-to-thickness ratio of the masonry. From Table 3, it can be seen that the ratio of the average compressive strength of each group of reinforced masonry to the standard value is less than 1. This indicates that Formula (3) is not suitable for calculating the compressive strength of reinforced masonry, as its calculated values tend to be unsafe. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Masonry Group**} & **Average Compressive Strength Test Value (MPa)** & \multirow{2}{*}{**Code-Specified Value (MPa)**} & **Ratio of the Average** \\  & & & **compressive Strength Test Value** \\ \hline C20 grouted masonry & 5.45 & 5.78 & 0.94 \\ C25 grouted masonry & 6.05 & 6.75 & 0.90 \\ C30 grouted masonry & 6.75 & 8.03 & 0.84 \\ C35 grouted masonry & 7.43 & 8.96 & 0.83 \\ C40 grouted masonry & 8.00 & 9.92 & 0.80 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison between the average test values of compressive strength of grouted masonry and the standard values. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Masonry Group**} & **Average Compressive Strength Test Value (MPa)** & \multirow{2}{*}{**Code-Specified Value (MPa)**} & **Ratio of the Average** \\  & & & **compressive Strength Test Value** \\ \hline C20 Reinforced Masonry & 6.90 & 8.40 & 0.82 \\ C25 Reinforced Masonry & 7.96 & 9.00 & 0.89 \\ C30 Reinforced Masonry & 8.57 & 9.68 & 0.88 \\ C35 Reinforced Masonry & 9.08 & 10.35 & 0.88 \\ C40 Reinforced Masonry & 9.72 & 10.92 & 0.89 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison between the average compressive strength test value of reinforced masonry and the code-specified value. The compressive strength of grouted masonry and reinforced masonry exhibits a generally linear relationship with the strength of the grouted concrete, as shown in Figure 6.  
Due to the regular increase in compressive strength of both grouted masonry and reinforced masonry as the strength of the grouted concrete increases, regression analyses were conducted separately for the compressive strengths of grouted masonry and reinforced masonry. In this context, let  
\[y=\frac{f_{ci,m}}{f_{ch,m}} \tag{5}\]  
\[x=\frac{\alpha f_{ci,m}}{f_{ch,m}} \tag{6}\]  
where \(f_{ci,m}\) is the average compressive strength of grouted masonry, \(f_{ch,m}\) is the average compressive strength of hollow masonry, and \(f_{cu,m}\) is the average compressive strength of grouted concrete.