RF-CONCRETE Members – Online Manual Version 5

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RF-CONCRETE Members – Online Manual Version 5

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9.3.2.1 EN 1992-1-1, 5.7

EN 1992-1-1, 5.7

The first design case performs the analysis according to the holistic concept of the European standard EC 2.

Data entered in RF-CONCRETE Members

The basic input is shown in the following figures.

Figure 9.33 General data for nonlinear calculation according to EN 1992-1-1, 5.7

The [Settings] for the nonlinear calculation must be defined as shown in the following figures.

We select the method with mean values of material strength and global partial safety factor. Plastic releases (plastic curvatures) are excluded.

Figure 9.34 Analysis method according to EN 1992-1-1, 5.7

To achieve results comparable to the calculation in [14], we have to modify the Tension Stiffening model according to Quast: As the calculation of the allowable compression stress fcR is based on a low quantile, fctk,0.05 is also used for the determination of the allowable concrete tension stress.

Figure 9.35 Effective tension stress of concrete for Tension Stiffening

As our structure is a statically determinate system, we can keep the damping factor set to 1.0.

For the nonlinear calculation of models prone to instability risks, the break-off limits ε1 and ε2 are important: If a calculation according to the linear static analysis converges steadily, it is possible that compression elements may see a "reversal point" where the deviations ε increase again. This effect occurs when the system can no longer compensate or absorb the increase of internal forces through the decreasing stiffnesses, caused by the increase of the deformation according to the second-order analysis. We keep ε1 = ε2 = 0.001 unchanged in our example.

Figure 9.36 Iteration parameters

To represent the distribution of stiffnesses with sufficient accuracy, we limit the target length of the FE mesh to 0.20 m.

Figure 9.37 FE mesh settings

In [14], a required reinforcement of As,tot = 66.10 cm2 is determined using the similar design method according to DIN 1045-1, 8.5. In order to compare these results with the RF-CONCRETE Members calculation according to EN 1992-1-1, 5.7, we still have to specify other settings.

The design is performed with a provided reinforcement that is actually available. Thus, some specifications for diameter, concrete cover, and reinforcement amount are still required in window 1.6 Reinforcement. In the Longitudinal Reinforcement tab, we define the diameter as 25 mm.

Figure 9.38 Specifying the rebar diameter

The concrete cover is selected as cnom = 27.5 mm in order to get a center distance of 40 mm.

Figure 9.39 Specifying the concrete cover

In order to perform the design with the specified reinforcement from [14], a minimum reinforcement of As,top = As,bottom = 32 cm2 is defined.

Figure 9.40 Specifying the minimum reinforcement

Now the input is complete and we can start the [Calculation].

Results of nonlinear calculation
Figure 9.41 Window 6.1.1 Ultimate Limit State for Nonlinear Calculation by Cross-Section

The interpretation of results is explained in the previous example (chapter 9.2).

With the safety factor γ = 1.995, the system apparently has sufficient reserves. However, we want to demonstrate that a small load increase will lead to the system's instability. In window 1.1 General Data, we select CO 14 for the design so that the loading is increased by 10%. According to the physically linear second order theory, there is no stability problem for this load combination.

Now the nonlinear [Calculation] is stopped by displaying a message telling us that it is not possible to design a sufficient resistance of the system with the selected reinforcement.

Figure 9.42 Break-off of calculation for CO 14 due to instability

Analyzing the model according to EN 1992-1-1, 5.8.6, described in the following chapter, shows that the column fails before the cross-section resistance is reached.

Literatur
[14] Kleinschmitt, Jörrit. Die Berechnung von Stahlbetonstützen nach DIN 1045-1 mit nichtlinearen Verfahren. Beton- und Stahlbetonbau 100 (02/2005)

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