## 4 Analysis of the Test Results
Coefficient \(ks\) is defined by:  
\[ks=\frac{N_{u,Str}}{N_{u,RC}} \tag{1}\]  
where \(N_{u,Str}\) is the ultimate load force of the strengthened column, while \(N_{u,RC}\) is the ultimate load force of the plain reinforced concrete column. It can be seen from coefficients ks that RC columns coupled with steel tube filled with special high-strength concrete (Fill 3) have 3.2 times greater load-bearing capacity, while specimens filled with regular fine-grain concrete have 2.9 (Fill 2) and 2.7 (Fill 1) times higher ultimate load. A relatively small difference between the ultimate forces of all strengthened models yields the conclusion that the quality of fill concrete has a relatively low impact on increasing the column strength. A possible reason for such low impact is the similarity of Poisson's ratio for all of the used concrete; moreover, in all models, the steel tube was similar. Usage of high-mechanical characteristics concrete for the fill will not contribute to considerably higher strength compared to the usage of concrete that has similar characteristics as concrete of the unstrengthened column. In addition, the high mechanical properties will probably never be reached during exploitation; on the other hand, the brittleness of the structure would be unnecessarily increased. Axial force (Ni) applied on a column in one load increment is divided between its structural components. The theoretical force distribution on the column's cross-section parts can be determined from the equality of axial strains. The stress theory of composite structural elements assumes that all parts of the cross-sections have equal longitudinal deformations. Therefore, force in the individual part of the cross-section (\(P_{i}\)) is calculated as:  
Figure 14.0  
where \(E_{i}\), \(\varepsilon_{i}\), and \(A_{i}\) are elastic modulus, axial strain, and cross-section area of a single part, respectively. Since all parts have equal strains (\(\varepsilon_{1}=\varepsilon_{2}=\ldots=\varepsilon_{n}\)), the load distribution can be determined as a ratio:  
Figure 14.1  
The modified cross-section area of the individual part (\(\tilde{A_{i}}\)) and the ideal cross-sectional area of the composite section (\(A^{*}\)) are:  
Figure 14.2  
The comparative elastic modulus of the composite cross-section (\(E^{*}\)) is usually chosen to be the elastic modulus of concrete. Theoretical force distribution between three parts of the composite column is presented in Figure 16 in terms of load percentage. From the presented values, it can be observed that the fill concrete compressive strength has a significant influence on the load distribution. In the case of the specimens filled with low strength of concrete, the fill carries around 29% of the applied load. The increase of the compressive strength of fill concrete yields higher percentages (to 36% and 39%). For individually considered cases, the steel jacket and the core RC column shared a similar percentage of the axial load. During the experimental testing, the axial force was applied only to the core RC column, and the load was transferred on other column parts over the bond between materials. Because of that, longitudinal strains in steel, fill, and core RC column were not equal during all load phases. The individual axial loads carried by the steel jacket, core RC column, and concrete fill in strengthened short columns under compression are determined from measured longitudinal strains using Equation (2). Since strains were registered on the RC core column and on the outer part of the steel tube, the strains of the fill concrete were chosen to have the same values as strains of the steel jacket. The presented analysis is limited to the exploitation load states, which, in this case, are loads up to 1000 kN. The distribution of axial force between parts of the composite column is presented in Figure 17 in the values of load percentage (P\({}_{\text{i}}\)/Ni).