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001022
Hedi Boukraa, B.Sc.
2023-05-24

VE 1022 | Design of a Flat Slab According to DIN EN 1992-1-1 with NA: Slab Internal Forces and Bending Design Under Full Load

Description

The model is based on the example 4 of [1]: Point-supported slab.

The flat slab of an office building with crack-sensitive lightweight walls is to be designed. Inner, border and corner panels are to be investigated. The columns and the flat slab are monolithically joined. The edge and corner columns are placed flush with the edge of the slab. The axes of the columns form a square grid. It is a rigid system (building braced with wall plates).

The office building has 5 floors with a floor height of 3.0 m. The environmental conditions to be assumed are defined as "closed interior spaces". There are predominantly static actions.

Reinforced Concrete Slab Supported by Concrete Columns
01 Reinforced Concrete Slab Supported by Concrete Columns

The focus of this example is to determine the slab moments and the required reinforcement above the columns under full load.

Material Concrete C35/45 Modulus of Elasticity E 34000 N/mm2
Design value of concrete compressive strength fcd 19.8 N/mm2
Reinforcing Steel B500S(B) Characteristic yield strength fyk 500.000 N/mm2
Design yield strength fyd 435.000 N/mm2
Geometry Flat slab Slab thickness h 240 mm
Span of a panel in y-direction leff,y 6.750 m
Span of a panel in z-direction leff,z 6.750 m
Column cross-section Width b 450 mm
Height h 450 mm
Load Permanant loads Reinforced concrete slab 6.000 kN/m2
Covering and suspended ceiling 1.250 kN/m2
Total characteristic value gk 7.250 kN/m2
Total design value gd 9.790 kN/m2
Variable loads Live load 2.000 kN/m2
Partitions aggregate 2.000 kN/m2
Total characteristic value qk,1 3.25 kN/m2
Total design value qd 4.880 kN/m2

Verification Example 1022 | Slab Designed According to DIN EN 1992-1-1 with NA
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Verification Example 1022 | Slab Designed According to DIN EN 1992-1-1 with NA

The approximation method used in [1] is not suitable as a reference solution for the FE calculation. As an alternative, the reference solution is established as a range of solutions derived from various FE calculations, as documented in the EvaDAT website. The acceptable range of results is limited to a +/- 10% deviation from the median of the available results.

RFEM Settings

  • The columns are modeled as nodal supports with a vertical spring constant Cu,Z of 2295000 kN/m and a torsion spring constant CΦ of 232368 kNm/rad in x- und y-direction.
  • The target length of the finite elements lFE is 0.450 m.
  • In addition, a FE mesh refinement is applied to each nodal support. The mesh refinement type is circular with a radius R=0.700 m, an inner target FE length LFE,i=0.100 m and an outter target FE length LFE,o=0.300 m.
  • The evaluation of the moments takes place on the column periphery
  • The first reinforcement layer is assumed to have a concrete cover of d1 = 3.0 cm and a bar diameter of 20 mm. This results in an effective depth dx = 200 mm and dy = 180 mm.

    • Results

    In the following tables, the results of RFEM 6 are compared with the reference solution.

    1. Slab Moment in x-direction

      moment [kNm/m] in x-direction
      Axis Result location RFEM Result Reference solution
      Median +/- 10% range
      Axis 1 Column C -73.0 -74.4 -67.0 -81.8
      Column B -93.4 -95.7 -86.1 -105.2
      Column A -76.9 -78.1 -70.2 -85.9
      Span C-B 37.3 37.5 33.8 41.3
      Span B-A 49.7 50.5 45.4 55.5
      Axis 2 Column C -115.5 -115.8 -104.2 -127.4
      Column B -143.6 -144.7 -130.2 -159.2
      Column A -98.5 -99.2 -89.2 -109.1
      Span C-B 34.1 34.6 31.1 38.1
      Span B-A 51.2 52.1 46.8 57.3
      Axis 3 Column C -101.0 -100.7 -90.6 -110.7
      Column B -130.2 -130.8 -117.7 -143.9
      Column A -91.2 -91.8 -82.6 -100.9
      Span C-B 31.3 31.6 28.4 34.7
      Span B-A 48.9 49.7 44.7 54.6
      Axis 1-2 Column C -6.7 -7.0 -6.3 -7.7
      Column B -11.8 -11.9 -10.7 -13.1
      Span C-B 22.0 22.0 19.8 24.2
      Span B-A 37.6 37.7 33.9 41.4
      Axis 2-3 Column C -10.7 -11.1 -9.9 -12.2
      Column B -17.6 -17.9 -16.1 -19.7
      Span C-B 19.4 19.5 17.5 21.4
      Span B-A 37.9 37.9 34.1 41.7
      Verification Example 1022 | Support and Panel Moment in x-Direction in Relevant Axes
      02 Verification Example 1022 | Support and Panel Moment in x-Direction in Relevant Axes


    2. Trosional Moment Trosional moment m_xy

      Trosional moment m_xy [kNm/m]
      Axis Result location RFEM Result Reference solution
      Average result +/- 10% range
      Axis 1 Column C 17.62 16.7 15.0 18.3
      Column B 20.4 19.1 17.1 21.0
      Column A 32.8 31.1 28.0 34.2
      Axis 2 Column C 2.45 2.4 2.1 2.6
      Column B 1.74 1.7 1.5 1.9
      Column A 2.64 2.7 2.4 3.0
      Verification Example 1022 | Torsional Moment in Relevant Axes
      03 Verification Example 1022 | Torsional Moment in Relevant Axes


    3. Support Forces

      Support Forces [kN]
      Column RFEM result Reference solution
      Median +/- 5% range
      C1=A3 300.8 300.9 285.9 316.0
      B1=A2 328.8 328.8 312.3 345.2
      A1 153.2 153.4 145.7 161.0
      C2=B3 707.1 707.0 671.7 742.4
      B2 787.3 787.0 747.7 826.4
      C3 624.4 624.5 593.3 655.7
      Verification Example 1022 | Support Forces
      04 Verification Example 1022 | Support Forces


    4. Required Reinforcement

      Required Reinforcement asx [cm2/m] in x-direction, dx = 200 mm
      Axis Result location RFEM results Reference solution
      Median +/- 10% range
      Axis 1 Column C 10.82 10.8 9.7 11.9
      Column B 13.95 13.8 12.4 15.2
      Column A 13.37 13.0 11.7 14.3
      Span C-B 4.51 4.5 4.1 5.0
      Span B-A 6.08 6.1 5.5 6.7
      Axis 2 Column C 14.5 16.1 14.4 17.7
      Column B 18.43 20.3 18.3 22.3
      Column A 12.2 12.5 11.3 13.8
      Span C-B 3.89 3.9 3.5 4.3
      Span B-A 5.91 5.9 5.3 6.5
      Axis 3 Column C 12.21 13.5 12.1 14.8
      Column B 16.29 17.8 16.0 19.5
      Column A 10.9 11.1 10.0 12.2
      Span C-B 3.56 3.6 3.2 3.9
      Span B-A 5.62 5.7 5.1 6.2
      Axis 1-2 Column C 0.8 0.8 0.7 0.9
      Column B 1.33 1.3 1.2 1.5
      Span C-B 2.53 2.5 2.2 2.7
      Span B-A 4.34 4.3 3.9 4.8
      Axis 2-3 Column C 1.19 1.2 1.1 1.3
      Column B 1.99 2.0 1.8 2.2
      Span C-B 2.2 2.2 1.9 2.4
      Span B-A 4.34 4.3 3.9 4.8

      Verification Example 1022 | Required Reinforcement in x-direction at the Top of the Slab
      05 Verification Example 1022 | Required Reinforcement in x-direction at the Top of the Slab

      Verification Example 1022 | Required Reinforcement in x Direction at Bottom of Slab
      06 Verification Example 1022 | Required Reinforcement in x Direction at Bottom of Slab

      Required Reinforcement asy [cm2/m] in y-direction, dx = 180 mm
      Axis Result location RFEM results Reference solution
      Median +/- 10% range
      Axis A Column 3 12.34 12.3 11.0 13.5
      Column 2 15.98 15.7 14.2 17.3
      Column 1 15.31 14.8 13.4 16.3
      Span 2-3 5.04 5.0 4.5 5.5
      Span 1-2 6.81 6.8 6.2 7.5
      Axis B Column 3 16.64 17.9 16.1 19.6
      Column 2 21.31 22.7 20.4 24.9
      Column 1 13.93 13.9 12.5 15.2
      Span 2-3 4.34 4.4 3.9 4.8
      Span 1-2 6.6 6.7 6.0 7.3
      Axis C Column 3 13.93 15.0 13.5 16.4
      Column 2 18.67 19.7 17.7 21.7
      Column 1 12.42 12.3 11.1 13.5
      Span 2-3 3.97 4.0 3.6 4.4
      Span 1-2 6.29 6.4 5.7 7.0
      Axis A-B Column 3 0.85 0.9 0.8 1.0
      Column 2 1.47 1.5 1.3 1.6
      Span 2-3 2.82 2.8 2.5 3.0
      Span 1-2 4.85 4.8 4.4 5.3
      Axis B-C Column 3 1.34 1.4 1.2 1.5
      Column 2 2.22 2.2 2.0 2.4
      Span 2-3 2.46 2.4 2.2 2.7
      Span 1-2 4.83 4.8 4.4 5.3


    The internal forces and the required reinforcement calculated by RFEM 6 are consistently within the defined result range of +/- 10% of the median value.

Links
References
  1. German Concrete and Structural Engineering Association E. V, examples for design according to Eurocode 2. Volume 1: Building construction, Berlin: Ernst & Sohn 2012, 1st prize corrected reprint of 1. Edition, 978-3-433-01877-4
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Consideration of Construction Stages in RFEM 6
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Most Frequently Asked Questions Answered by Dlubal Support Team
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Most Frequently Asked Questions Answered by Dlubal Support Team | May 2024
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Steel Structures in RFEM 6 \n Part 2: Combinations, Design, Documentation
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Most Frequently Asked Questions Answered by Dlubal Support Team | June 2024
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Online Training | English
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Videos
EN-US | Flag Event
Calculation of Reinforced Concrete Slabs in RFEM 6
Length: 01:09:36 min
EN-US | Flag Knowledge Base
KB 001821 | Defining Rib Widths of Downstand Beams Using Example of Two-Span Beam
Length: 00:00:50 min
EN-US | Flag Event
Webinar | Design of Massive RSECTION Sections in RFEM 6
Length: 00:47:34 min
FAQ 005388
EN-US | Flag FAQ
FAQ 005388 | How can I activate the design with steel fiber-reinforced concrete in the "Concrete Design" add-on...
Length: 00:01:00 min
KB|001838
EN-US | Flag Knowledge Base
KB 001838 | Design of Ribs, Folded Plate Structures, and Surfaces Using Result Members in RFEM 6
Length: 00:00:47 min
DE | Flag Knowledge Base
KB 001838 | Design of Ribs, Folded Plate Structures, and Surfaces Using Result Members in RFEM 6
Length: 00:00:00 min
DE | Flag Knowledge Base
KB 001838 | Design of Ribs, Folded Plate Structures, and Surfaces Using Result Members in RFEM 6
Length: 00:00:00 min
DE | Flag Knowledge Base
KB 001838 | Design of Ribs, Folded Plate Structures, and Surfaces Using Result Members in RFEM 6
Length: 00:00:00 min
DE | Flag Knowledge Base
KB 001838 | Design of Ribs, Folded Plate Structures, and Surfaces Using Result Members in RFEM 6
Length: 00:00:00 min
Models to Download
Model 004552 | Design Level 1 - Fatigue Design
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Model 004505 | Building with Inclined Reinforced Concrete Columns
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Single-Span Beam with Fiber-Reinforced Concrete as Surface Component or Frame Structure
KB 001838 | Design of Ribs, Folded Plate Structures, and Surfaces Using Result Members in RFEM 6
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Verification Example 1000 | 1
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Model 004503 | Model of Elevator Shaft
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KB 001842 | Slab with Automatic Surface Reinforcement as Supplement
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KB 001842 | Automatic Design Process of Provided Surface Reinforcement
Knowledge Base Articles
Spans Based on Figure 5.2 from [1]
In order to correctly design a downstand beam or a T-beam in RFEM 6 using the Concrete Design add-on, it is essential to determine the flange widths for the rib members. This article describes the input options for a two-span beam and the calculation of the flange dimensions according to EN 1992-1-1.
KB 001838 | Design of Ribs, Folded Plate Structures, and Surfaces Using Result Members
If you want to use a pure surface model, for example, when determining the internal forces and moments, but the structural component is still designed on the member model, you can take advantage of a result beam.
Axial Force Distribution (nx)
According to EN 1992-1-1 [1], a beam is a member of which the span is no less than 3 times the overall section depth. Otherwise, the structural element should be considered as a deep beam. The behavior of deep beams (that is, beams with a span less than 3 times the section depth) is different from the behavior of normal beams (that is, beams with a span that is 3 times greater than the section depth). However, designing deep beams is often necessary when analyzing the structural components of reinforced concrete structures, since they are used for window and door lintels, upstand and downstand beams, the connection between split-level slabs, and frame systems.
Critical Perimeter Around Column Considering One Opening
The punching shear design, in line with EN 1992-1-1, should be performed for slabs with a concentrated load or reaction. The node where the design of punching shear resistance is performed (that is, where there is a punching problem) is called a node of punching shear. The concentrated load at these nodes can be introduced by columns, concentrated force, or nodal supports. The end of the linear load introduction on slabs is also regarded as a concentrated load and therefore, the shear resistance at wall ends, wall corners, and ends or corners of line loads and line supports should be controlled as well.
Screenshots
Reinforced Concrete Slab Supported by Concrete Columns
Reinforced Concrete Slab Supported by Concrete Columns
Design Level 2 – Design Setting
Design Level 2 – Design Setting
Design Level 1 – Design Setting
Design Level 1 – Design Setting
Model 004552 | Design Level 1 - Fatigue Design
Model 004552 | Design Level 1 - Fatigue Design
Design Level 1 - Ultimate Configuration
Design Level 1 - Ultimate Configuration
Design Level 2 - Ultimate Configuration
Design Level 2 - Ultimate Configuration
Number of Cycles
Number of Cycles
Correction Factor λs
Correction Factor λs
Feature 002671 | Seismic Design of Reinforced Concrete Members According to EC 8
Result Filter for Seismic Design of Reinforced Concrete Members in RFEM
Product Features
Feature 002670 | Fatigue Design According to EN 1992-1-1, Chapter 6.8

With the Concrete Design add-on, you can perform the fatigue design of members and surfaces according to EN 1992‑1‑1, Chapter 6.8.

For the fatigue design, you can optionally select two methods or design levels in the design configurations:

  • Design Level 1: Simplified design according to 6.8.6 and 6.8.7(2): The simplified design is performed for frequent action combinations according to EN 1992‑1‑1, Chapter 6.8.6 (2), and EN 1990, Eq. (6.15b) with the traffic loads relevant in the serviceability state. A maximum stress range according to 6.8.6 is designed for the reinforcing steel. The concrete compressive stress is determined by means of the upper and lower allowable stress according to 6.8.7(2).
  • Design Level 2: Design of damage equivalent stress acc. to 6.8.5 and 6.8.7(1) (simplified fatigue design): The design using damage equivalent stress ranges is performed for the fatigue combination according to EN 1992‑1‑1, Chapter 6.8.3, Eq. (6.69) with the specifically defined cyclic action Qfat.
Feature 002671 | Seismic Design of Reinforced Concrete Members According to EC 8

The Concrete Design add-on allows you to perform the seismic design of reinforced concrete members according to EC 8. This includes, among other things, the following functionalities:

  • Seismic design configurations
  • Differentiation of the ductility classes DCL, DCM, DCH
  • Option to transfer the behavior factor from a dynamic analysis
  • Check of the limit value for the behavior factor
  • Capacity design checks of "Strong column - weak beam"
  • Detailing and particular rules for curvature ductility factor
  • Detailing and particular rules for local ductility
Feature 002654 | Design of Fiber-Reinforced Concrete

The Concrete Design add-on allows you to design fiber-reinforced concrete components according to the guideline "DAfStb Steel Fiber-Reinforced Concrete".

You can use this option for the design according to EN 1992‑1‑1. The design according to the DAfStb guideline is carried out once the concrete of the "Fiber Concrete" type has been assigned to the reinforced structural component.

Go to Explanatory Video
Feature 002652 | "Crosstie" Reinforcement Option for Design According to EN 1992-1-1

In the "Shear Reinforcement" tab, you can select the option "Cross-ties over free rebars with active selection in graphic". It allows you to arrange additional cross-ties on free rebars of the longitudinal reinforcement.

You can activate or deactivate the position of the cross-ties in the Info Graphic. The cross-ties are applied for the ultimate limit state design and the structural design checks. They are available for the design according to EN 1992‑1‑1.

Go to Explanatory Video
Frequently Asked Questions (FAQ)
How can I use graphic templates for multi printing of a reinforcement?
How can I activate the design with steel fiber-reinforced concrete in the "Concrete Design" add-on for RFEM 6?
Although all the member design checks have been fulfilled, I get the "Not Covered Reinforcement" result. What is the reason?
Where can I find the graphical results of punching shear in the concrete design? Especially the distribution of shear forces at the critical perimeter or the punching loads.
Can the RFEM 6 Concrete Design add-on automatically design member and surface reinforcement?
Can I define a different bar size in the RFEM 6 Concrete Design add-on other than the default bar sizes available in the drop-down? 
Customer Projects
Reinforced Concrete Elevator Shaft at Montluçon Station, France (© E.T.L Structures)
Reinforced Concrete Elevator Shaft at Montluçon Station, France
Pedestrian and Cyclist Bridge "Herzogsteg" in Eichstätt, Germany | © Bruno Klomfar
Pedestrian and Cyclist Bridge "Herzogsteg" in Eichstätt, Germany
Front View of Office Building with V-Shaped Steel Composite Columns | © Die Tragwerker GmbH
Office Building with Integrated Visitor Center and Parking Garage in Geiselbulach, Germany
Office Building of Stadtwerke Kirchheim unter Teck, Germany (Rendering) | © MEDIA 4D GmbH
Office Building of Stadtwerke Kirchheim unter Teck, Germany
Quai M, the New Concert Hall in La Roche-sur-Yon, France (© LCA Construction Bois)
New Concert Hall in La Roche-sur-Yon, France
Residential Buildings in Trieste, Italy
Residential Buildings in Trieste, Italy
Deformations of Airedale Swing Bridge in RFEM
Airedale Swing Bridge in Rodley, United Kingdom
Deformations in RFEM | © Baumruck + Oswald
AQUAtherm Indoor/Outdoor Swimming Pool in Straubing, Germany
Pedestrian Bridge "Am Freischütz" over Federal Highway 236 | © VIC Planen und Beraten GmbH | Photo: René Legrand
Freischütz Pedestrian Bridge, Germany
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