RF-CONCRETE Surfaces Version 5

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RF-CONCRETE Surfaces Version 5

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2.4.3 Determination of Statically Required Reinforcement

Determination of Statically Required Reinforcement

The stress-strain relations for concrete and reinforcing steel described in chapter 2.4.2 together with the possible range of strain distributions (limit strains) represent the basis for the determination of the required longitudinal reinforcement for the previously determined design moments. This process is also documented in the design details.

Figure 2.39 Design details: Required longitudinal reinforcement

The first subentries for the required longitudinal reinforcement are top surface and bottom surface of the plate. The entries Bottom surface (+z) and Top surface (-z) contain further details for each reinforcement direction.

Figure 2.39 shows that the reinforcement directions 2 and 3 require only very little or no reinforcement at the plate's bottom surface.

The Reinforcement Direction 1 is to be designed for the design bending moment mend,+z,φ1 = 35.89 kNm/m. The strains provide information about the determination of the longitudinal reinforcement.

We will check the example shown in Figure 2.39 for a dimensionless design procedure by means of a design table. The following input parameters are given:

  • Cross-section [cm]: rectangle w/h/t = 100/20/17
  • Materials: concrete C20/25 B 500 S (A)
  • Design internal forces: MEds = nsend, +z, φ1 = 240.005 ⋅ 0.161 = 38.64 KNm/m
    NEd = 0.00 kNm/m

fcd = α · fckγc = 0,85 · 2,01,5 = 1,13 kN/cm2 

μEds = MEdsb · d2 · fcd = 3864100 · 172 ·1,13 = 0,1183 

For μEds = 0.1183, the following values can be interpolated from the design tables (for example [3] Annex A4):

ω1 = 0,1170 + (0,1285 - 0,1170) · (0,1183 - 0,11)0,12 - 0,11 = 0,1265 

σsd = 45,24 + (45,40 - 45,24) · (0,1183 - 0,11)0,12 - 0,11 = 45,37 kN/cm2 

With these values, the required longitudinal reinforcement can be determined:

As1 = ω1 · b · d · fcd + NEdσsd =0,1265 · 100 · 17 · 1,13 + 045,37 = 5,36 cm2/m 

Literatur
[3] Deutscher Beton-Verein e.V.: Beispiele zur Bemessung von Betontragwerken nach EC2. Bauverlag, Wiesbaden/Berlin, 1994.