## 5 Estimation Equation for Maximum Load Bearing Capacity Considering Buckling Position
### Applicability of Estimation Equations
#### 5.3.2 Comparison with Static Loading Experiments  
The estimation equations were tried to apply to the horizontal load bearing capacity obtained in static loading experiments on concrete-filled steel tubes. Four models from experimental samples of concrete-filled steel tubes with circular cross-sections was used, based on studies by [PERSON] et al. [8] and [PERSON] et al. [4] in the comparison. These samples were in the range of design parameters of Table 1, \(0.03\leq R\leq 0.12\), \(0.2\leq\lambda\leq 0.4\), \(0.1\leq n\leq 0.5\), and \(0.2\leq L_{\mathrm{c}}/L\leq 0.6\). Table 3 shows the various properties of each model. Note that these experiments were performed using cyclic loading, rather than monotonic lateral loading. According to Chapter 20 of the Guidelines for Stability Design of Steel Structures [16], the difference between monotonic and cyclic loading is not significantly large until maximum lateral loading is reached, but the number of cycles after peaking has been shown to have a large effect on the behavior of the members. Hence, the equations proposed in this study are deemed to also be applicable for estimating the maximum load bearing capacity under cyclic loading. To obtain the normalized horizontal load bearing capacity \(P/P_{\mathrm{u}}\), the horizontal load bearing capacity of the steel tube at \(L_{\mathrm{c}}/L=0\) and \(n=0\) must be calculated. Since this property was tested in this study, \(P_{\mathrm{u}}\) was obtained using the following equations [16; 17]. \[\frac{P_{\mathrm{u}}}{P_{\mathrm{y}}}=\frac{0.02}{\left(R\right)^{0.8}}+1.10 \tag{9}\]  
Figure 15: Difference between maximum load bearing capacity from numerical analysis and modified estimation equations: (**a**) \(L_{\mathrm{c}}/L=\)0.2; (**b**) \(L_{\mathrm{c}}/L=0.4\); (**c**) \(L_{\mathrm{c}}/L=0.6\). Here, Equation (9) shows the horizontal yield strength \(P_{\rm y}\) calculated taking the effect of axial force into account. The applicable range of Equation (9) is \(0.03\leq R\leq 0.11\) and \(0.25\leq\lambda\leq 0.5\). In [PERSON] et al. [8], static cyclic loading tests were conducted for varying diaphragm locations, concrete filling ratios, and loading methods in order to show their effects on horizontal bearing capacity and buckling position. Among the tested specimens are two models with diaphragms directly above the concrete, C-008-030 and C-009-032, which fit within the range of application of Equation (9), the horizontal load bearing capacity estimation equation for steel tubular columns with circular cross-sections. Model C-008-030 was subjected to three cyclic loadings and had a concrete filling ratio \(L_{\rm c}/L\) of 0.34. Buckling occurred at the base of the steel tube. Model C-009-032 was subjected to one cyclic loading and had a concrete filling ratio \(L_{\rm c}/L\) of 0.34. Buckling occurred at the base of the steel tube in that case as well. In [PERSON] et al. [4], quasi-static cyclic loading tests were conducted on concrete-filled circular steel tubular columns to show the effects of concrete filling ratio and the presence of a diaphragm installed directly above the concrete on the bearing capacity and deformation performance of the steel tubes. Among the tested specimens are two models with diaphragms, C-1.5D-S and C-2D-S, which satisfy the range of application of Equation (9), the horizontal load bearing capacity estimation equation for steel tubular columns with circular cross-sections. The concrete filling ratio \(L_{\rm c}/L\) was 0.27 for C-1.5D-S and 0.35 for C-2D-S. Both models were subjected to three cyclic loadings and buckling occurred at the base of the steel tube. Figure 16 summarizes the estimated and experimental values. Figure 16a plots the results when buckling position is not considered, while Figure 16b plots the results when buckling position is taken into consideration. The vertical axis shows the estimated values of \(P/P_{\rm u}\), while the horizontal axis shows the experimental values of \(P/P_{\rm u}\).