Downstand Beams, Ribs, T-Beams: Shear Between Web and Flanges

Technical Article

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In order to ensure the effects of panels, which should act as tensile or compression chords, it is necessary to connect them to the web in a shear-resistant manner. This connection is obtained in a similar way as the shear transfer in the joint between concreting sections by using the interaction between compressive struts and ties. In order to ensure the shear resistance, it must be verified that the compressive strut resistance is given and the tie force can be absorbed by the transverse reinforcement.

Design According to EC2-1-1

It must be proven that the acting shear force v Ed does not exceed the resisting shear forces vRd, max and vRd, s:
${\mathrm v}_\mathrm{Ed}\;\leq\;{\mathrm v}_{\mathrm{Rd},\max}\;\mathrm{and}\;{\mathrm v}_\mathrm{Ed}\leq\;{\mathrm v}_{\mathrm{Rd},\mathrm s}$

The longitudinal shear force v Ed is determined by the relation $ {\ mathrm v} _ \ mathrm {Ed} \; = \; \ frac {{\ mathrm {ΔF}} _ \ mathrm d} {{\ mathrm h} _ \ mathrm f \; \ cdot \; \ mathrm {Δx}} $. ΔF d corresponds to the longitudinal force difference which occurs in a one-sided chord section on the length Δx. To determine this longitudinal force difference, the compression flange force F cd, a and the tension belt force F sd, a are required. For Δx, it is allowed to assume a maximum of half the distance between the moment zero point and the moment maximum. When single loads act, the length Δx must not be greater than the distance between the single loads.

Figure 01 - Notations for Connection Between Flange and Web (Source: [1])

The reinforcement for absorbing the tensile forces in the plate that is transverse to the web is determined as follows:
$(\frac{{\mathrm A}_\mathrm{sf}\;\cdot\;{\mathrm f}_\mathrm{yd}}{{\mathrm s}_\mathrm f})\;\geq\;\frac{{\mathrm v}_\mathrm{Ed}\;\cdot\;{\mathrm h}_\mathrm f}{\cot\;{\mathrm\theta}_\mathrm f}$

Furthermore, it must be demonstrated that the load-bearing capacity of the compression strut (A in Figure 01) in the chord is not exceeded. This is done with the equation $ {\ mathrm v} _ \ mathrm {Ed} \; \ leq \; \ mathrm \ nu \; \ cdot \; {\ mathrm f} _ \ mathrm {cd} \; \ cdot \; \ sin \; {\ mathrm \ theta} _ \ mathrm f \; \ cdot \; \ cos \; {\ mathrm \ theta} _ \ mathrm f $.

If there is simultaneous loading due to transverse bending of the slab and longitudinal shear between web and chords, the larger steel cross-section resulting from both designs for the top layer in the slab must be arranged. This also means that the upper transverse bending reinforcement can be completely compensated for the upper position of the shear reinforcement.

Considering Shear Between Web and Flange in RF-CONCRETE Members

The shear joints can be considered in RF-CONCRETE Members in Window 1.6 Reinforcement under the "Shear Joint" tab.

Figure 02 - Activating Consideration of Shear Between Web and Flange in RF-CONCRETE Members

Results of Shear Joint Design

Windows 2.1 to 2.4 show the resulting required reinforcement. These results can be displayed by cross‑section, by set of members, by member, or by x‑location.

Figure 03 - Results of Shear Joint Design

The output of the required reinforcement for the shear joint is given by the output of the transverse reinforcement per section length a sf . In the "Intermediate Results" window, you can see some intermediate values for the shear design between the chords and the web. These intermediate values are listed under the result branch "Shear Forces Between Beam and Web".

Reference

[1]  Fingerloos, F.; Hegger, J.; Zilch, K.: Eurocode 2 für Deutschland - Kommentierte Fassung (2nd ed.). Berlin: Beuth, 2016
[2] Manual RF‑/CONCRETE Members . Tiefenbach: Dlubal Software, October 2017. Download

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