Benchmark 5: Interaction curve
Project file: CCD_Benchmark_C2.esa
SCIA Engineer Version R21.1
Introduction
Benchmark document: Composite Structures according to Eurocode 4 - Dujmović / Androić / Lukačević (2014)
Benchmark C2 given by the publication (pages 419-444) covers Composite column with concrete-filled circular hollow section subject to axial compression, verified using European buckling curves and using second-order analysis taking into account member imperfections.
The column (4.5 meters long) is loaded by a compression force NEd of 6000 kN.
The cross-section has the following dimensions:
with:
| Structural steel | Reinforcing steel | Concrete |
| fy = 355 MPa | fs = 460 MPa | fck = 40 MPa |
| Ea = 210000 MPa | Es = 210000 MPa | Ecm = 35000 MPa |
| Gamma_M = 1.00 | Gamma_s = 1.15 | Gamma_c = 1.50 |
Reference results
The reference gives following results:
Cross-section properties
| Structural steel | Reinforcing steel | Concrete |
| Aa = 124.5 cm2 | As = 20.1 cm2 | Ac = 1153 cm2 |
| Ia = 24476 cm4 | Is = 1591 cm4 | Ic = 107834 cm4 |
Compression check
| χ | Npl,Rd | UCN |
| 0.90 | 8302 kN | 0.80 |
Interaction curve N+My
SCIA Engineer results
Cross-section properties
Compression check
Interaction curve N+My
Comments
Differences explained:
- page 423 - minor differences in steel section and concrete areas caused by the polygonal shape of CHS section
Aa = 124.5 cm2 compared to 124.4 cm2 in SEN
Ac = 1153 cm2 compared to 1151 cm2 in SEN
- page 424+425 - minor differences in moment of inertia for all components
Is = 1591 cm4 compared to 1629 cm4 in SEN (reference is not using central moments of inertia for reinforcment bars)
Ia = 24476 cm4 compared to 24414 cm4 in SEN (circular shape)
Ic = 107834 cm4 compared to 107518 cm4 in SEN (circular shape)
These changes projects through the whole example resulting in a differences at the end.
- page 430 - Npl,Rd = 8302 kN compared to 8289 kN in SEN (circular shape)
- page 434 - in the reference the European buckling curves method is used to pre-check the axial force which leads to unity of 0.8. This method should in general be only used for linear analysis and pure compression. In SEN for the given case we perform the standard section check (no chi in 6.44 formula) instead together with interaction N+My.
This lead to a difference of unity 0.8 compared to UCN = 0.72 in SEN
- page 440 - slight difference in the constructed diagram mainly caused by using the real curve diagram from SEN solver but also caused by area and moment of inertia differences
This lead to a difference of 315 kNm compared to MN,y,Rd = 411 kNm in SEN. This projects to μd and result in final difference in unity of 0.41 compared to UCN+My = 0.31 in SEN.