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5. DC EC 06: 2nd order effect in a column

# DC EC 06: 2nd order effect in a column

## Description

KRUIPFACTOR?!

Geometry Load Cross-section: Column height: Material: C25/30 Concrete cover: Reinforcement distribution: Identical Only upper and lower Design forces: EN 1992-1-1 [- -]
How to model a column in Diamonds that can be compared with handcalculations
• Diamonds always looks for the most economical reinforcement ratio. This is not always neat according to the local axes of the rod, but often according to the main axes of inertia. While in hand calculations the load is placed along a local axis and the calculation is also performed in that direction. To impose that behavior in Diamonds, you must choose only top and bottom reinforcement.
By choosing an ‘identical’ reinforcement distribution, you ask him to choose the top and bottom reinforcement equally. This is a reinforcement distribution for which graphs/tables are suitable for manual calculations.
• In this example we want to focus on the 2nd order effects. Therefor we set the additional eccentricity to zero.
• By default, Diamonds will apply the 2nd order eccentricity in different directions, only keeping the worst direction. Since the cross section is not a square, and the loads are applied around the strong axis, we can already predict that the worst direction for the 2nd order effect, will be around the weak axis. When that happens, we have bi-directional bending. Something we don’t want in this example.
So to force Diamonds into applying the 2nd order effect into the same direction as the already present bending moment, we deselect the buckling verification around the weak axis.
• According to Eurocode 2, reinforcement is required for the forces in ULS, possibly increased with additional reinforcement to limit the stresses in SLS. It is not known in advance whether additional reinforcement will be required for SLS. Since we are only doing a ULS calculation in this example, we turn off the stress limits in SLS in Diamonds (by making a copy of C25/30 and editing the copy).

## Results

Handcalculation
Eurocode 2 offers simplified methods (EN 1992-1-1 §5.8.7 and §5.8.8) to include 2nd order effects and imperfections into the results. The method based on nominal curvature (EN 1992-1-1 §5.8.8) is implemented in Diamonds. This method results in an increased bending moment.

#### Is a 2nd order calculation required? (EN 1992-1-1 §5.8.3.1)

This column has the same ULS loads has validation example  DC EC 05. So we just reuse the reinforcement amounts:

Because is bigger than , second order effects need to be taken into account.

Note: these intermediar results cannot be consulted in Diamonds at the moment. However, we’re working on a solution (expected in Diamonds 2025).

#### Magnitude of 2nd order eccentricity (EN 1992-1-1 §5.8.3.2)

Correction factor depending on the axial force (this factor is sometimes called ):

Correction factor depending on the axial force (this factor is sometimes called ):

#### Magnitude of design bending moment (2nd order effect included)

The additional moment for 2nd order effects equals:

The total design moment becomes:

#### Reinforcement calculation

The principle for entirly the same as for has validation example  DC EC 05. Only differs:

Graph 10.2a from Gewapend beton: numeri (click here to open the graph) shows as a function of and . Using this graph and the results above, we can deduct:

Note: The intermediar results as calculated above, cannot be consulted in Diamonds at the moment. However, we’re working on a solution (expected in Diamonds 2025).

Longitudonal reinforcement calculated by Diamonds (EN 1992-1-1 [- -])
The reinforcement due to ULS is shown using a thin line, the reinforcement due to ULS + SLS + buckling with a thick line. Because  the SLS verification were turned off, the thick line represents the reinforcement for ULS + buckling.

Results Independent reference Diamonds Difference
Longitudonal reinforcement 593mm² 593mm² 0%

## References

• Tested in Diamonds 2024r01.