# Pushover Analysis on Infill Effects on the Failure Pattern of Reinforced Concrete Frames
## 3 Results and Discussions
### Shear Force of Columns  
The strut effect of infilled walls should be taken into account in the calculation of column shear force. The stress between the frame and the infilled wall is simplified as a rectangular shape. The contact length is equal to \(\alpha_{c}h\), where \(\alpha_{c}\) is the equivalent contact length factor and \(h\) is the net height of the column, and can be calculated by Equations (13)-(16). The computing model of column 5 is shown in Figure 7. Suppose the second-order effect of the column is ignored, the equations are shown in Equations (11) and (12).  
\[\left\{\begin{array}{l}\sigma_{c}tm\frac{m}{2}+V_{c}m=M_{c-top}\\ V_{c}(h-m)-(\alpha_{c}h-m)\sigma_{c}t(\frac{\alpha_{c}h-m}{2}+h-m)=M_{c-bot} \end{array}\right. \tag{11}\]  
\[\left\{\begin{array}{l}V_{c-top}=V_{c}+\sigma_{c}tm\\ V_{c-bot}=V_{c}-\sigma_{c}t(\alpha_{c}h-m)\end{array}\right. \tag{12}\]  
where, \(M_{c-top}\) and \(M_{c-bot}\) = the bend moments of top column and bottom column, respectively; \(t\) = the thickness of the infilled wall; \(V_{c-top}\) and \(V_{c-bot}\) = the shear forces of top column and bottom column, respectively; \(V_{c}\) = shear force at the inflection point; \(m\) = the distance between the column top and the  
Figure 6: Damage cloud chart. (**a**) Damage of the whole structure; (**b**) damage of the full-filled wall and the surrounding frame; (**c**) damage of the half-filled wall and the surrounding frame; and (**d**) damage of the slabs.  
location of the inflection point of the column; and \(\sigma_{c}\) = the equivalent stress of the infilled wall, and can be calculated by [26].  
In the case of the column with the half-filled wall, the strut acts on the middle part of the column. The computing model of Column 1 is shown in Figure 8. The equations are shown in Equations (13) and (14).  
The second-order effect of column is also ignored.  
\[\left\{\begin{array}{l}V_{c}m=M_{c-top}\\ V_{c}(h-m)-\alpha_{c}h\sigma_{c}t(a-\frac{\alpha_{c}h}{2})=M_{c-bot}\\ \end{array}\right. \tag{13}\]  
\[\left\{\begin{array}{l}V_{c-top}=V_{c}\\ V_{c-bot}=V_{c}-\alpha_{c}h\sigma_{c}t\\ \end{array}\right. \tag{14}\]  
where, \(a\) = the height of the infilled wall.  
Figure 8: The computing model of RC Column 1 with a half-filled wall.  
Figure 7: The computing model of RC Column 5 with a full-filled wall.  
The computing model of Column 2 and Column 6 is shown in Figure 9. The equations are shown in Equations (15) and (16).  
\[\left\{\begin{array}{l}V_{c}\cdot m=M_{c-top}\\ V_{c}\cdot(h-m)+\alpha_{c}h\sigma_{c}t\frac{\kappa h}{2}=M_{c-bot}\\ \end{array}\right. \tag{15}\]  
\[\left\{\begin{array}{l}V_{c}=V_{top}\\ V_{c}+\alpha_{c}h\sigma_{c}t=V_{bot}\\ \end{array}\right. \tag{16}\]  
Shear force of each columns calculated by Equations (11)-(16) are shown in Table 2. It can be seen that the results of the columns with infilled walls have large deviations compared to Chinese code [15], EC8 [13], and ASCE41-06 [14]. Chinese code [15] and ACI [27] code do not take infilled walls into consideration, and the computing model is shown in Figure 10. EC8 provision 5.9 defines the clear column length equal to the length of column not in contact with the infills, considering the height of the infills is smaller than the clear length of the adjacent column. ASCE provision 7.4.2 points out that the reduced column length should be taken into consideration. The values are 1.56 to 5.02 times larger than those calculated by the codes. Shear failure of the column may appear in frames with infilled walls and shall be considered in the design process.  
Figure 10: Computing model of column shear in the Chinese code.  
Figure 9: The computing model of RC Column 2 and Column 6 with a half-filled wall.