## 4 Maximum Strength of Masonry-Infilled Frames  
### Strength of Masonry Infills  
In ASCE 41 [25], which is a representative standard used for the seismic performance evaluation of buildings, the shear strength of masonry was defined as the sum of cohesion and friction. \[V_{max}=P_{inf}^{grav}\times\mu+A_{w}\times C \tag{3}\]  
where \(\mu\) is the friction coefficient, \(A_{w}\) is the horizontal cross-sectional area of an infill, and \(C\) is cohesion of the brick-mortar interface, which is equal to the shear strength when no axial stress is applied. \(P_{inf}^{grav}\) is the axial load supported by the infill caused by gravity distributed between the infill and the columns based on their relative axial stiffnesses assuming full contact between the infill and the beams. In the case of the specimen in this paper, \(P_{inf}^{grav}\) was ignored as the masonry wall was constructed after the frame was completed so that no vertical load was applied. Therefore, the strength of the masonry wall is determined by the cohesion only. The strength of the specimen calculated using only the adhesive strength obtained through material testing is 270.3 kN for single wythe and 371.9 kN for double wythe. Table 5 shows a comparison between the calculated strength and the strength from the tests. It can be seen that the prediction for IFS-0.5, which has a single wythe wall with a gap, was accurate, but predictions for the rest of the specimens were underestimated. This result implies that frictional force should be considered. In FEMA 306 [24], the masonry shear strength \(\tau_{m}\) is described as the sum of the bond strength \(v_{m}\) between the masonry unit and the mortar, and the frictional force, which is the \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Drift Ratio (\%)**} & \multicolumn{2}{c}{**Effective Stiffness (kN/mm)**} & \multirow{2}{*}{**(IFS-0.5)/(IF-0.5)**} \\ \cline{2-3} \cline{5-5}  & & **IF-0.5** & & **IFS-0.5** \\ \hline
0.10 & 42.73 & 98.23 & 2.30 \\
0.25 & 49.72 & 46.44 & 0.93 \\
0.50 & 37.20 & 30.26 & 0.81 \\
0.75 & 29.32 & 20.78 & 0.71 \\
1.00 & 20.62 & 15.14 & 0.73 \\
1.50 & 15.12 & 9.72 & 0.64 \\
2.00 & 9.91 & 7.37 & 0.74 \\
2.50 & 7.97 & 6.12 & 0.77 \\ \hline
**Drift Ratio (\%)** & **IF-1.0** & **IFS-1.0** & **(IFS-1.0)/(IF-1.0)** \\ \hline
0.10 & 199.86 & 163.79 & 0.82 \\
0.25 & 115.67 & 95.90 & 0.83 \\
0.50 & 81.40 & 63.65 & 0.78 \\
0.75 & 58.50 & 36.51 & 0.62 \\
1.00 & 41.34 & 22.81 & 0.55 \\
1.50 & 24.19 & 15.99 & 0.66 \\
2.00 & 14.98 & 11.98 & 0.80 \\
2.50 & 10.09 & 9.31 & 0.92 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Effective stiffness estimated from the test results. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Specimen ID** & _Bond Stress_ & _V\_* Equation (\%)_ & _2V\_* Equation (\%)_ & _P\_*app (Prediction)_ & _P\({}_{\pi}^{*}\) (Test)_ & _P\({}_{\pi}^{*}\) (Test)_ & _P\({}_{\pi}\)_**-(Test)** & _P\({}_{\pi}\)_**-(Test)** \\ \hline IF-0.5 & 0.462 MPa & 91.5 kN & 178.8 kN & 270.3 kN & 360.5 kN & –317.24 kN & 0.75 & 0.85 \\ \hline IFS-0.5 & 0.462 MPa & 91.5 kN & 178.8 kN & 270.3 kN & 288.33 kN & –253.76 kN & 0.94 & 1.07 \\ \hline IF-1.0 & 0.462 MPa & 193.1 kN & 178.8 kN & 371.9 kN & 590.1 kN & –530.6 kN & 0.63 & 0.70 \\ \hline IFS-1.0 & 0.462 MPa & 193.1 kN & 178.8 kN & 371.9 kN & 468.7 kN & –399.9 kN & 0.79 & 0.93 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Prediction of maximum force by ASCE 41.  
product of the friction coefficient and normal stress applied to the masonry, as shown in Equation (4). Here, the normal stress \(N\) can be calculated from the curvature shortening associated with lateral displacement of the frame, as shown in Equation (5). \[\tau_{m}=v_{m}+\mu N \tag{4}\]  
\[N=E_{m}\theta^{2} \tag{5}\]  
where \(\mu\) is the friction coefficient, \(E_{m}\) is the modulus of elasticity of the masonry, and \(\theta\) is the rotation angle of the column in radians.