1. Home
  2. Diamonds
  3. Validation
  4. Design
  5. DC EC 03: longitudonal reinforcement in column under pure compression

DC EC 03: longitudonal reinforcement in column under pure compression

Description

Geometry Cross-section: b=h=250mm
Material: C25/30
Load Design axial force: N_{Ed.ULS}=1700kN
Standard EN 1992-1-1 [- -] and [BE]

Results

According to EN 1992-1-1 [- -]

Handcalculation

    \[N_{Ed,ULS}=\left ( A-A_s \right )  \cdot f_{cd} + A_s\cdot f_{yd}\]

Deduct A_s:

    \[A_s=\frac{N_{Ed,ULS}-A \cdot f_{cd}}{-\cdot f_{cd}+f_{yd}}\]

Diamonds neglects - \cdot f_{cd}:

    \[A_s=\frac{N_{Ed,ULS}-A \cdot f_{cd}}{f_{yd}}\]

Because we have pure compression the compression strain is limited to \varepsilon=0.2% (EN 1992-1-1 Figure 6.1). Resulting in f_{yd}=\varepsilon \cdot E_s=0.2% \cdot 200000MPa = 400MPa.

    \[A_s=\frac{1700kN-(250mm)^{2}  \cdot 23.3MPa}{400MPa}=604mm^2\]

Divide reinforcement over 4 sides:

    \[A_{s, on each side}=\frac{604mm^2}{4}=151mm^2\]

Longitudonal reinforcement calculated by Diamonds (EN 1992-1-1 [- -])

Results Independent reference Diamonds Difference
Longitudonal reinforcement 151mm² 151mm² 0,00%

According to EN 1992-1-1 [BE]

Handcalculation

    \[N_{Ed,ULS}=\left ( A-A_s \right ) \cdot \alpha_{cc} \cdot f_{cd} + A_s\cdot f_{yd}\]

Deduct A_s:

    \[A_s=\frac{N_{Ed,ULS}-A\cdot \alpha_{cc} \cdot f_{cd}}{-\alpha_{cc} \cdot f_{cd}+f_{yd}}\]

Diamonds neglects -\alpha_{cc} \cdot f_{cd}:

    \[A_s=\frac{N_{Ed,ULS}-A\cdot \alpha_{cc} \cdot f_{cd}}{f_{yd}}\]

Because we have pure compression the compression strain is limited to \varepsilon=0.2% (EN 1992-1-1 Figure 6.1). Resulting in f_{yd}=\varepsilon \cdot E_s=0.2% \cdot 200000MPa = 400MPa.

    \[A_s=\frac{1700kN-(250mm)^{2} \cdot 0.85 \cdot 23.3MPa}{400MPa}=1151mm^2\]

Divide reinforcement over 4 sides:

    \[A_{s, on each side}=\frac{1151mm^2}{4}=288mm^2\]

Longitudonal reinforcement calculated by Diamonds (EN 1992-1-1 [BE])

Results Independent reference Diamonds Difference
Longitudonal reinforcement 288mm² 288mm² 0,00%

References

  • EN 1992-1-1: 2005 + AC: 2010
  • Van Hooymissen, L., Spegelaere, M., Van Gysel, A., & De Vylder, W. (2002). Gewapend beton. Academia Press, example on page 10.22
    Keep in mind that the calculations in this book are made done using the NBN B15-002 which is comparable to ENV 1992-1. We used EN 1992-1 in our verification example.
    But it still remains a good reference if you want to understand how reinforcement calculations work.
  • Tested in Diamonds 2023r01.

Article Attachments

Was this article helpful?

Related Articles

Need Support?
Can't find the answer you're looking for? Don't worry we're here to help!
CONTACT SUPPORT