Database

0025-D-DBV-AK Software-Design of a reinforced concrete column using the nominal curvature method

An example by the working group DBV-Arbeitskreis Software für Baustatik

The example was created by

Bert Ziems, Dr.-Ing. Roland Sauer, Dipl. Ing. (FH) Alexander Meierhofer, Dr.-Ing. Casimir Katz

and published on 19.09.2018 on

published. You can find it at https://evadat.com/en/bsp/0025/.

It was qualified on 16.07.2021.

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Developed by Bert Ziems, Dr.-Ing. Roland Sauer, Dipl. Ing. (FH) Alexander Meierhofer, Dr.-Ing. Casimir Katz
Published on: 19.09.2018 | Qualified on: 16.07.2021
DE EN
D0Classification
  • ClassD · Standards-based verification example
  • Structural system typeSpecial component
  • MechanicsStatics - first-order theory
  • Material lawElastic
  • MaterialConcrete/reinforced concrete/prestressed concrete
  • Verification formatUltimate limit state verification
  • StandardDIN EN 1992
D1Problem description
This section was machine-translated by DeepL.

The verification example corresponds to Example 10 in [1, S. 10-1 ff.]. The following section therefore largely omits details and background information. Only the relevant input values for the design are given.

D1.1Task description

A reinforced concrete cantilever support must be designed at normal temperature in accordance with the GZT (German Design Guidelines) as per DIN EN 1992-1-1/NA:2013-04. [2] based on DIN EN 1990/NA:2010-12 [3].

D1.2Theoretical foundations

The design shall be carried out in accordance with the method using nominal radii as set out in DIN EN 1992-1-1, Section 5.8.8, taking into account creep via φeff in accordance with Section 5.8.4.

D1.3System

The column is located within a three-span flat hall frame. The frame consists of four cantilever columns and three individual trusses hinged to them. The column in question is one of the two end columns.

20210429_p1.png

The frame effect is only taken into account for the horizontally acting wind load by applying previously determined coupling forces at the column head. In addition, horizontal column forces are applied for the vertical loads to compensate for the displacements at the column heads resulting from the eccentric application of loads at the column heads (symmetry of deformation).

20210429_p2.png

For the design analysis, the edge column is modelled as a single column: an elastically fixed cantilever column subjected to uniaxial loading in the transverse direction of the hall.
The column height is taken to be the height of the beam supports above the top of the foundation (lcol = 6.20 m). The overhang is taken into account by applying the appropriate loads from dead weight and wind.

20210429_p3.png

Foundation rotation is defined in [1, S. 10-1 ff.] approximated by increasing the buckling length coefficient to ß = 2.1 (instead of ß = 2.0). This corresponds to an elastic
Clamping at the base using a torsion spring Cρ = 340,000 kNm.

Cross-section:
Rectangle
450 x 400 mm
Reinforcement spacing
d1= 3.8 cm
Creep
φ∞ = 2.35 [EN 1992-1-1, 3.1.4.]

D1.4Material

Concrete
C30/37
Ecm = 33,000 N/mm2
fcd = 17 N/mm2
Reinforcing steel
B500B
fyk = 500 N/mm2
fyd = 435 N/mm2

D1.5Effects

Continuous loads (ΥG =1.35)

Gk1
Constant vertical live load on trusses
Vertical load at the truss support ey = 10 cm
VGk,1 = 400 kN
H-load at the level of the truss support (see 1.3)
HGk,1 = 9.67 kN
Gk2
Dead weight of support + overhang
Vertical load at the centre of gravity ey = 0
VGk,2 = 31 kN

Variable loads (ΥQ =1.5)

Qk,S
Snow Ψ0 = 0.5 (towns and villages up to 1,000 metres above sea level)
vertical support load, Binder ey = 10 cm
VQk,s = 68 kN
H-load at the level of the truss support (see 1.3)
HQk,s = 1.64 kN
Q k,W
Wind (Wind Zone IV) Ψ0 = 0.6, pressure and suction act alternately
→ horizontal line load over the height of the column
Suction
wk,s = -1.85 kN/m
Print
wk,d = 4.32 kN/m

→ Edge moment and edge load based on a cantilever length of h = 1.90 m

Suction
Hw, k, s = -3.5 kN
Mw, k, s = 3.33 kNm
Print
Hw,k,d = -8.20 kN
Mw,k,d = 7.8 kNm

Coupling force (see 1.3)

Suction
Fh, k, S = -2.22 kN
Print
Fh, k, d = 13.74 kN

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D5References
  1. [1] Deutscher Beton- und Bautechnik-Verein e. V.: Beispiele zur Bemessung nach Eurocode 2. Band 1: Hochbau. Berlin: Ernst & Sohn. 2011. ISBN 978-3-433-01877-4.
  2. [2] DIN EN 1992-1-1/NA:2013-04: Nationaler Anhang zu DIN EN 1992-1-1:2011-01 - Eurocode 2: Bemessung und Konstruktion von Stahlbeton- und Spannbetontragwerken - Teil 1-1: Allgemeine Bemessungsregeln und Regeln für den Hochbau.
  3. [3] DIN EN 1990/NA:2010-12: Nationaler Anhang zu DIN EN 1990:2021-10 - Eurocode: Grundlagen der Tragwerksplanung.
  4. [4] Kordina, K.; Quast, U.: Bemessung der Stahlbeton- und Spannbetonbauteile nach DIN 1045-1:2001-07 - Teil II: Bemessung von schlanken Bauteilen für den durch Tragwerksverformungen beeinflussten Grenzzustand der Tragfähigkeit - Stabilitätsnachweis. In: Josef Eibl: Beton-Kalender. Berlin: Ernst & Sohn. 2002.

Additional literature

  • DIN EN 1990:2010-12: Eurocode: Grundlagen der Tragwerksplanung.
Editors
Bert Ziems FRILO Software GmbH (Stuttgart, Germany)
–
Creator
Bert Ziems FRILO Software GmbH (Stuttgart, Germany)
B5+ Stahlbetonstütze (01/2019) FRILO Software GmbH
Editor 1
Dr.-Ing. Roland Sauer RIB Software GmbH (Stuttgart, Germany)
MOST (V16.0) RIB Software GmbH
Editor 2
Dipl. Ing. (FH) Alexander Meierhofer Dlubal Software GmbH (Tiefenbach, Germany)
RFEM (5.07.09) Dlubal Software GmbH
Editor 3
Dr.-Ing. Casimir Katz SOFiSTiK AG (Garching, Germany)
COLUMN (2018-5) SOFiSTiK AG
Editor 4
Bert Ziems Creator, Editor 1

FRILO Software GmbH (Stuttgart, Germany)

Software used: B5+ Stahlbetonstütze (01/2019) FRILO Software GmbH
Dr.-Ing. Roland Sauer Editor 2

RIB Software GmbH (Stuttgart, Germany)

Software used: MOST (V16.0) RIB Software GmbH
Dipl. Ing. (FH) Alexander Meierhofer Editor 3

Dlubal Software GmbH (Tiefenbach, Germany)

Software used: RFEM (5.07.09) Dlubal Software GmbH
Dr.-Ing. Casimir Katz Editor 4

SOFiSTiK AG (Garching, Germany)

Software used: COLUMN (2018-5) SOFiSTiK AG