Downstand Beams, Ribs, TBeams: Minimum Reinforcement for Partial CrossSections 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 k_{c}, which takes into account the influence of the stress distribution within the partial cross‑section, is determined as follows:
$$\mathrm{Formula}\;7.2\;\mathrm{for}\;\mathrm{web}:\;{\mathrm k}_\mathrm c\;=\;0.4\;\cdot\;\left[1\;\;\frac{{\mathrm\sigma}_\mathrm c}{{\mathrm k}_1\;\cdot\;{\displaystyle\frac{\mathrm h}{\mathrm h^\ast}}}\;\cdot\;{\mathrm f}_{\mathrm{ct},\mathrm{eff}}\right]\;\leq\;1$$$$\mathrm{Formula}\;7.3\;\mathrm{for}\;\mathrm{chord}:\;{\mathrm k}_\mathrm c\;=\;0.9\;\cdot\;\frac{{\mathrm F}_\mathrm{cr}}{{\mathrm A}_\mathrm{ct}\;\cdot\;{\mathrm f}_{\mathrm{ct},\mathrm{eff}}}\;\geq\;0.5$$
In the case of pure tensile stress, k_{c} = 1 applies for the entire cross‑section as well as the individual partial cross‑sections.
The mean concrete stress σ_{c} affecting the examined part of the cross‑section is determined using the concrete stress distribution applying the crack moment due to f_{ct,eff}, at the shear point of the respective partial cross‑section (see Figure 01 σ_{c}).
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 RFCONCRETE Members
By selecting the minimum reinforcement layout, you specify at the same time on which side of the cross‑section the concrete tensile stress f_{ct,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 k_{c}
If you select k_{c} = 1.0, f_{ct,eff} acts constantly over the cross‑section. If you select k_{c} = 0.4 or k_{c} = 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 f_{ct,eff} is reached.
If f_{ct,eff }is not reached on any cross‑section fiber 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 RFCONCRETE 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 k_{c} for considering the influence of the stress distribution, the area of the tension zone A_{ct}, and the absolute value of the maximum allowable steel stress are displayed, among other results.
Figure 05  RFCONCRETE 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
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Figure 01  Partial CrossSections with Example of Distribution of Mean Concrete Stress

Figure 02  Options for Minimum Reinforcement in RFCONCRETE Members

Figure 03  Layout of Minimum Reinforcement

Figure 04  Options for Stress Distribution, Factor kc

Figure 05  RFCONCRETE Members: Results of Minimum Reinforcement

Figure 06  RFCONCRETE Members: Design of Minimum Reinforcement

Figure 07  RFCONCRETE Members: Provided Longitudinal Reinforcement