EN 1992-1-1, 5.8.6
The second design case performs the design in accordance with the general design method of EC 2 for compression members according to the second-order analysis.
In order to compare the results, a new concrete case is created for EN 1992-1-1, 5.8.6. As we need to change only little input data, we simply copy the first design case on the RF-CONCRETE Members menu by selecting
- File → Copy Case.
In Window 1.1 General Data, we need to adjust the [Settings] for the calculation.
We select the general method for members in axial compression according to the second-order theory.
The nonlinear design of the ultimate limit state for compression elements according to EN 1992-1-1, 5.8.6 is based on a divided safety concept (see Chapter 2.4.7.2). Therefore, we also have to calculate with the average values of the material parameters for the approach of Tension Stiffening. The partial safety factor γc flows directly into the applied tensile strength: fct,R = α ⋅ fct / γc. This also applies for the concrete's modulus of elasticity.
The parameters of the Iteration Parameters tab remain unchanged.
In [14], a required reinforcement of As,tot = 51.0 cm2 is determined by using the similar design method according to DIN 1045-1, 8.6.1. In order to compare these results with the RF-CONCRETE Members calculation according to EN 1992-1-1, 5.8.6, we change the minimum reinforcement to As,top = As,bottom = 25 cm2 in Window 1.6 Reinforcement.
Now the modifications are complete and we can start the [Calculation].
With the selected reinforcement, we get a safety factor γ of 2.163 for the restrained location (in comparison: γ = 1.989 for the design according to EN 1992-1-1, 5.7).
The following figure compares the deformations determined according to the second-order analysis and both nonlinear calculation methods.
The results can be illustrated by a representation in the M-N interaction diagram. In addition to the cross-section resistance (verified quantile values), Figure 9.49 shows the capacity curves for calculation according to the linear static analysis and the second-order analysis for linear material behavior, as well as according to the second-order analysis for nonlinear material behavior.
For our slender compression element, the calculation according to the second-order analysis already deviates from the calculation according to the linear static analysis when applying a low load level. The physical nonlinearity becomes noticeable only for a higher load level, but then it proceeds very quickly. Finally, the column fails due to loss of stability because of the strong stiffness reduction occurring in this process.
If the material-dependent nonlinearity is not taken into account, the pure cross-section design of the CO1 internal forces according to the second-order analysis (physically linear) provides a required reinforcement of As,tot = 2 ⋅ 5.27 = 10.54 cm2.
Thus, the de facto required reinforcement is clearly underestimated. The design of moment and axial force from the physically nonlinear calculation would also lead to an under-designed reinforcement: The result for My = 195.22 kNm and N = −1059.39 kN would be a required reinforcement of As,tot = 2 ⋅ 7.15 = 14.30 cm2. The reason is that the internal forces are calculated depending on the provided reinforcement. However, the column fails before the ultimate load bearing capacity of the cross-section is reached. In our example, this happens for a moment of approximately 441.5 kN. In the interaction with the axial force, we get a required reinforcement of As,tot = 2 ⋅ 25.40 = 50.80 cm2.