# Research on Mechanical Properties of Core-Filled Desulfurized Gypsum Masonry
## 5 Conclusions  
Through axial compressive strength tests on five groups of new high-precision desulfurized gypsum core-filled masonry and reinforced masonry, the test results were analyzed and studied, leading to the following conclusions:  
1. The calculation of the compressive strength of new high-precision gypsum core-filled masonry blocks and reinforced masonry blocks using the standard formula shows significant errors and tends to be unsafe. 2. Based on the test observations, the grouted masonry and reinforced masonry specimens undergo three main stages during the entire compression process: the elastic stage, the elastoplastic stage, and the softening stage. The failure process of grouted masonry and reinforced masonry exhibits distinct phases, with crack development and outer wall spalling being the key factors leading to the reduction in load-bearing capacity. The performance of the core column and steel reinforcement plays a decisive role in the final failure mode. 3. Based on the test results, this paper proposes the compressive strength calculation Formula (10) \(f_{c,m}=2.03f_{c,m}+0.39a_{c,m}\) for core-filled masonry and the compressive strength calculation Formula (11) \(N_{c,m}=\varphi 1.06f_{g,m}A+0.38f_{y}^{\prime}A_{s}^{\prime}\) for reinforced masonry. The calculated values from Formulas (10) and (11) are in good agreement with the experimental values, providing a new basis and reference for calculating the compressive strength of such masonry. This solves the problem of compressive strength design for new high-precision desulfurized gypsum masonry blocks combined with core-filled concrete when used in load-bearing walls. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{ \begin{tabular}{c} **Specimen** \\ **Group** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Specimen** \\ **Number** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Strain** \\ **\(\varepsilon_{c,m}\)** \\ **(\%)** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Compressive** \\ **Strength** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Axial Strain** \\ **of 0.4** \(\varepsilon_{0.4}\) **(\%)** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Test Value of** \\ **Elastic** \\ **Modulus** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Calculated** \\ **Value of** \\ **Elastic** \\ **Modulus** \(E\) \\ **(MPa)** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **E\({}_{c,m}\)/\(E\)** \\ **Modulus** \\ **(MPa)** \\ \end{tabular}  } \\ \hline \multirow{2}{*}{\ \begin{tabular}{c} C20 \\ C20 \\ C20-2-2 \\ C20-2-3 \\ C25-2-2 \\ C25-2-2-3 \\ C25-2-3 \\ C25-2-3 \\ C20-2-1 \\ C25-2-3 \\ C30-2-1 \\ C30-2-2-2 \\ C30-2-3 \\ C30-2-3 \\ C32-3 \\ C35-2-1 \\ C35-2-2-3 \\ C35-2-3 \\ C40-2-1 \\ C40-2-2-2 \\ C40-2-2-3 \\ C40-2-3 \\ C40-2-3 \\ C40-2-3 \\ C40-2-3 \\ C40-2-3 \\ C40-2-3 \\ C40-2-3 \\ C40-2-3 \\ C40-2-3 \\ \end{tabular}  &
\begin{tabular}{c} 0.16 \\ 6.90 \\ 0.047 \\ 0.15 \\ 6.94 \\ 0.10 \\ 0.15 \\ 0.15 \\ 0.16 \\ 0.17 \\ 0.16 \\ 0.14 \\ 0.16 \\ 0.14 \\ 0.16 \\ 0.14 \\ 0.16 \\ 0.16 \\ 0.16 \\ 0.14 \\ 0.14 \\ 0.16 \\ 0.14 \\ 0.13 \\ 0.16 \\ 0.16 \\ 0.16 \\ 0.16 \\ 0.17 \\  
Since there is no unified constitutive model for the compressive stress-strain relationship of masonry structures and research on the constitutive relationship of gypsum masonry is relatively limited, a regression analysis of the test data was conducted, resulting in the elastic modulus calculation Formula (18) \(E=\frac{d\sigma}{d\varepsilon}=\frac{1.158f_{cj}}{\epsilon_{cj}}+\frac{1.386f_{cj 04}}{\epsilon_{cj}^{2}}-\frac{258f_{cj}c_{cj}^{2}}{\epsilon_{cj}^{2}}\) for grouted masonry and the compressive strength calculation Formula (19) \(E=\frac{1514f_{cnn}}{\epsilon_{cnn}}+\frac{0.0084f_{cnn}\epsilon_{04}}{\epsilon _{cnn}^{2}}-\frac{1.506f_{cnn}\epsilon_{04}^{2}}{\epsilon_{cnn}^{2}}\) for reinforced masonry. The calculated values from Formulas (18) and (19) align well with the test values.