Downstand Beams, Ribs, T-Beams: Minimum Reinforcement for Partial Cross-Sections According to 7.3.2

Technical Article

According to Section 7.3.2 (2), the standard EN 1992‑1‑1 [1] states: ‘In profiled cross‑sections like T‑beams and box girders, minimum reinforcement should be determined for the individual parts of the section (webs, flanges).’

In the case of a T‑beam with a T‑section, the minimum reinforcement should be determined for both the chord and the web if the corresponding partial cross‑sections are in the tension area. Figure 01 shows the cross‑section classification.

Figure 01 - Partial Cross-Sections with Example of Distribution of Mean Concrete Stress

Depending on whether a web or a chord is concerned, the coefficient kc, which takes into account the influence of the stress distribution within the partial cross‑section, is determined as follows:
$$\mathrm{Formula}\;7.2\;\mathrm{for}\;\mathrm{web}:\;{\mathrm k}_\mathrm c\;=\;0.4\;\cdot\;\left[1\;-\;\frac{{\mathrm\sigma}_\mathrm c}{{\mathrm k}_1\;\cdot\;{\displaystyle\frac{\mathrm h}{\mathrm h^\ast}}}\;\cdot\;{\mathrm f}_{\mathrm{ct},\mathrm{eff}}\right]\;\leq\;1$$
and
$$\mathrm{Formula}\;7.3\;\mathrm{for}\;\mathrm{chord}:\;{\mathrm k}_\mathrm c\;=\;0.9\;\cdot\;\frac{{\mathrm F}_\mathrm{cr}}{{\mathrm A}_\mathrm{ct}\;\cdot\;{\mathrm f}_{\mathrm{ct},\mathrm{eff}}}\;\geq\;0.5$$

In the case of pure tensile stress, kc = 1 applies for the entire cross‑section as well as the individual partial cross‑sections.

The mean concrete stress σc affecting the examined part of the cross‑section is determined using the concrete stress distribution applying the crack moment due to fct,eff, at the shear point of the respective partial cross‑section (see Figure 01 σc).

Options in RF-CONCRETE Members

The partial cross‑sections are determined automatically, depending on the underlying cross‑section. The RF‑CONCRETE Members add‑on module provides the following control options, which have an effect on the minimum reinforcement of the partial cross‑sections.

Figure 02 - Options for Minimum Reinforcement in RF-CONCRETE Members

By selecting the minimum reinforcement layout, you specify at the same time on which side of the cross‑section the concrete tensile stress fct,eff is applied or in which direction the crack moment acts.

Figure 03 - Layout of Minimum Reinforcement

The corresponding options for stress distribution within the section prior to cracking control the distribution of the mean concrete stress.

Figure 04 - Options for Stress Distribution, Factor kc

If you select kc = 1.0, fct,eff acts constantly over the cross‑section. If you select kc = 0.4 or kc = variable depending on the defined load, the mean concrete stress distribution is determined due to bending about y or due to bending about y and the axial force. The minimum reinforcement is arranged in the partial cross‑sections where the stress fct,eff is reached.

If fct,eff is not reached on any cross‑section fibre in some partial cross‑sections, but nevertheless a wedge is formed, then the tensile force of the partial cross‑section is assigned to the governing tension side.

Results in RF-CONCRETE Members

Window 4 shows the governing design and the detailed results of the minimum reinforcement for the individual partial cross‑sections. For each partial cross‑section, the coefficient kc for considering the influence of the stress distribution, the area of the tension zone Act, and the absolute value of the maximum allowable steel stress are displayed, among other results.

Figure 05 - RF-CONCRETE Members: Results of Minimum Reinforcement

Under ‘Design’, you can see the resulting design with the highest criterion. This is confronted with the calculated minimum reinforcement in the partial cross‑section of the provided reinforcement (Figure 07).

Figure 06 - RF-CONCRETE Members: Design of Minimum Reinforcement

Figure 07 - RF-CONCRETE Members: Provided Longitudinal Reinforcement

Reference

[1]  Eurocode 2: Design of concrete structures - Part 1‑1: General rules and rules for buildings; EN 1992‑1‑1:2004 + AC:2010
[2]  Zilch, K. & Zehetmaier, G. (2010). Bemessung im konstruktiven Betonbau - Nach DIN 1045‑1 (Fassung 2008) und EN 1992‑1‑1 (Eurocode 2) (2nd ed.). Berlin: Springer.

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