Database

0036-D-DBV-AK Software-Design of a flat slab in accordance with DIN EN 1992-1-1, including NA Part 1: Slab section dimensions and design for bending under full load

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

The example was created by

Dipl. Ing. (FH) Alexander Meierhofer, Dr.-Ing. Roland Sauer, Dr.-Ing. Casimir Katz, Dr.-Ing. Aleksandra Serafinska

and published on 25.03.2022 on

published. You can find it at https://evadat.com/en/bsp/0036/.

It was qualified on 02.11.2022.

title-image.png
Developed by Dipl. Ing. (FH) Alexander Meierhofer, Dr.-Ing. Roland Sauer, Dr.-Ing. Casimir Katz, Dr.-Ing. Aleksandra Serafinska
Published on: 25.03.2022 | Qualified on: 02.11.2022
DE EN
D0Classification
  • ClassD · Standards-based verification example
  • Structural system typePlane structure
  • MechanicsStatics
  • Material lawElastic
  • MaterialConcrete/reinforced concrete/prestressed concrete
  • Verification formatUltimate limit state verification
  • StandardDIN EN 1992
D1Problem description
This section was machine-translated by DeepL.

D1.1Task description

The terms of reference have been issued [1] Example 4: Based on a point-supported plate.

The flat slab of an office building with lightweight partition walls that are prone to cracking is to be assessed.

The following are being examined: the central, edge and corner sections. The columns and the flat slab are monolithically connected. Perimeter and corner columns are positioned flush with the edge of the slab. The column axes form a square grid. This is a non-displaceable system (a building reinforced by wall panels).

The office building comprises five storeys, each with a floor-to-ceiling height of 3.0 m. The assumed environmental conditions are defined as ‘enclosed interior spaces’. The loads are predominantly static.

This example focuses on determining the slab moments and the required reinforcement beneath the columns under full load, without load distribution across the spans. A subsequent example will deal with the punching shear analysis of the floor slab.

D1.2Theoretical foundations

Design of the floor slab for bending under the ultimate limit state in accordance with DIN EN 1992-1-1/NA:2013-04.

D1.3System

The following diagram shows the dimensions of the point-supported floor slab.

20220324_System.png

Concrete cover:

As a result of exposure class XC1, the concrete cover is cnom = 20 mm required. This results in a laying dimension of
cv,Bü = 20 mm for the brackets and
cv,l = 30 mm for the longitudinal reinforcement

D1.4Material

C35/45 concrete

fck = 35 N/mm², EC = 34,000 N/mm², = 0.20
\gammacc= 1.5; \alphacc = 0.85
fcd = 0.85 * 35 / 1.5 = 19.8 kN/mm²

B500B reinforcement

fyk = 500 N/mm², \gammaS = 1.15
fyd = 500 / 1.15 = 435 N/mm²

D1.5Effects

D1.5.1Characteristic values

Description of the loads

Characteristic value [kN/m²]

Continuous (self-weight):

- 240 mm solid reinforced concrete slab: 0.24 m ∙ 25 kN/m³
- Flooring and suspended ceiling
Total:

6.00
1.25
gk = 7.25

Variable:

- Payload
- Partition wall surcharge
Total:

2.00
1.25
qk,1 = 3.25

D1.5.2Design values in the limit states relating to load-bearing capacity

Effects

cheap

unfavourable

permanent
variable

γG = 1.0
γQ = 0

γG = 1.35
γQ = 1.50

gd = γG ∙ gk = 1.35 × 7.25 = 9.79 kN/m²
qd = γQ ∙ gk,1 = 1.5 ∙ 3.25 = 4.88 kN/m²

\Rightarrow ed = 14.67 kN/m²

D1.6Additional boundary condition for the FEM calculation

To ensure that the results from the individual FEM calculations are comparable, the following boundary conditions have been agreed for the FEM calculation:

  • The slab is modelled across its entire outline.

  • The columns are modelled as nodal supports. When determining the column stiffness for the support springs, the final state is considered and the restraint from the rising column is taken into account. This results in a vertical spring constant Cp = 2,295,000 kN/m and a torsional spring constant Cm = 232,368 kNm/rad.

  • The target length of the finite elements is 0.45 m

  • Moments are analysed at the column base

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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] Grasser, E.; Thielen, G.: Hilfsmittel zur Berechnung der Schnittgrößen und Formänderungen von Stahlbetontragwerken nach DIN 1045; Ausgabe Juli 1988. Köln: Beuth Verlag. 1991.
  3. [3] Katz, C.: Modellierung punktgestützter Platten. In: M. Bischoff, M. v. Scheven, B. Oesterle: Baustatik Baupraxis 14. Stuttgart: Universität Stuttgart. 2020. ISBN 978-3-00-064639-3.
Editors
Dipl. Ing. (FH) Alexander Meierhofer Dlubal Software GmbH (Tiefenbach, Germany)
–
Creator
Dipl. Ing. (FH) Alexander Meierhofer Dlubal Software GmbH (Tiefenbach, Germany)
RFEM (6.02) Dlubal Software GmbH
Editor 1
Dr.-Ing. Roland Sauer RIB Software GmbH (Stuttgart, Germany)
iTWO structure fem (22.0) RIB Software GmbH
Editor 2
Dr.-Ing. Casimir Katz SOFiSTiK AG (Garching, Germany)
SOFiSTiK FEA (2022-4) SOFiSTiK AG
Editor 3
Dr.-Ing. Aleksandra Serafinska FRILO Software GmbH (Stuttgart, Germany)
PLT Platten mit finiten Elementen (1/2023) FRILO Software GmbH
Editor 4
Dipl. Ing. (FH) Alexander Meierhofer Creator, Editor 1

Dlubal Software GmbH (Tiefenbach, Germany)

Software used: RFEM (6.02) Dlubal Software GmbH
Dr.-Ing. Roland Sauer Editor 2

RIB Software GmbH (Stuttgart, Germany)

Software used: iTWO structure fem (22.0) RIB Software GmbH
Dr.-Ing. Casimir Katz Editor 3

SOFiSTiK AG (Garching, Germany)

Software used: SOFiSTiK FEA (2022-4) SOFiSTiK AG
Dr.-Ing. Aleksandra Serafinska Editor 4

FRILO Software GmbH (Stuttgart, Germany)

Software used: PLT Platten mit finiten Elementen (1/2023) FRILO Software GmbH