# Research on Mechanical Properties of Core-Filled Desulfurized Gypsum Masonry
## 4 Elastic Modulus Calculation Formula
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Specimen** & **Specimen** & **Strain** & **Axial** & **Test Value** & **Average** & **Complexive** & **Calculated** & \\
**Group** & **Number** & **\(\varepsilon_{c,i}\)** & **Strain of** & **of Elastic** & **of Elastic** & **Strength** & **Value of** & **F** \\
**(\%)** & **Number** & **(\%)** & **(\%)** & **(\%)** & **Modulus** & **of Elastic** & **Strength** & **Elastic** & **E**\({}_{c,i}\)**/**\(E\)** \\ \hline C20 & C20-1 & 0.215 & 0.065 & 3675.34 & 3985.44 & 5.77 & 3597.46 & 1.02 \\  & C20-2 & 0.174 & 0.044 & 4754.55 & & 5.23 & 4034.93 & 1.18 \\  & C20-3 & 0.166 & 0.044 & 4966.14 & & 5.50 & 4450.29 & 1.12 \\ C20 & C20-4 & 0.177 & 0.067 & 2946.43 & 3985.44 & 4.94 & 3665.29 & 0.80 \\  & C20-5 & 0.182 & 0.050 & 4208.00 & & 5.26 & 3881.93 & 1.08 \\  & C20-6 & 0.215 & 0.069 & 3362.19 & & 5.82 & 3617.89 & 0.93 \\  & C25-1 & 0.136 & 0.049 & 4887.98 & & 6.00 & 5835.19 & 0.84 \\  & C25-2 & 0.147 & 0.047 & 5598.29 & & 6.42 & 5841.31 & 0.96 \\  & C25-3 & 0.126 & 0.053 & 4620.04 & & 6.11 & 6241.38 & 0.74 \\  & C25-4 & 0.125 & 0.057 & 4274.65 & & 6.07 & 6109.10 & 0.70 \\  & C25-5 & 0.112 & 0.052 & 4321.71 & & 5.69 & 6361.09 & 0.68 \\  & C25-6 & 0.126 & 0.049 & 4882.59 & & 6.03 & 6250.44 & 0.78 \\  & C30-1 & 0.130 & 0.044 & 6090.09 & & 6.41 & 6562.08 & 0.93 \\  & C30-2 & 0.145 & 0.048 & 5778.78 & & 6.68 & 6144.84 & 0.94 \\  & C30-3 & 0.138 & 0.037 & 7439.35 & & 6.9 & 6716.03 & 1.11 \\ C30 & C30-4 & 0.142 & 0.046 & 6315.79 & & 7.20 & 6778.21 & 0.93 \\  & C30-5 & 0.127 & 0.040 & 6870.00 & & 6.87 & 7239.39 & 0.95 \\  & C30-6 & 0.127 & 0.043 & 5967.36 & & 6.41 & 6722.29 & 0.89 \\  & C35-1 & 0.136 & 0.040 & 7344.91 & & 7.40 & 7299.71 & 1.01 \\  & C35-2 & 0.140 & 0.038 & 8461.54 & & 7.98 & 7656.30 & 1.11 \\  & C35-3 & 0.124 & 0.040 & 7450.00 & & 7.45 & 8029.41 & 0.93 \\ C35 & C35-4 & 0.125 & 0.043 & 6986.05 & & 7200.77 & 7.51 & 7988.69 & 0.87 \\  & C35-5 & 0.122 & 0.045 & 6642.70 & & 7.39 & 8001.25 & 0.83 \\  & C35-6 & 0.115 & 0.043 & 6319.44 & & 6.83 & 7812.55 & 0.81 \\  & C40-1 & 0.121 & 0.031 & 10,165.61 & & 7.98 & 8856.45 & 1.15 \\ C40 & C40-2 & 0.107 & 0.034 & 9478.01 & & 8.08 & 10,099.39 & 0.94 \\  & C40-3 & 0.114 & 0.065 & 10,684.21 & & 8.12 & 9567.16 & 1.12 \\  & C40-4 & 0.097 & 0.044 & 8923.08 & & 8.05 & 11,060.72 & 0.81 \\ C40 & C40-5 & 0.120 & 0.044 & 9829.55 & & 8.19 & 9158.68 & 1.07 \\  & C40-6 & 0.105 & 0.067 & 9104.05 & & 8.27 & 10,510.78 & 0.87 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison of test results and calculated values for the elastic modulus of grouted masonry. From Table 8, it can be observed that the ratio of the test values of the elastic modulus of grouted masonry to the calculated values from Formula (18) has an average of 0.94 and a coefficient of variation of 0.14. Overall analysis shows that the elastic modulus of grouted masonry calculated using Formula (18) aligns well with the test values. From Table 9, it can be seen that the ratio of the test values of the elastic modulus of reinforced masonry to the calculated values from Formula (19) has an average of 1.12. Overall analysis indicates that the elastic modulus of reinforced masonry calculated using Formula (19) aligns well with the test values.