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

### Technical Article

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 is necessary to verify that the effective shear force v_{Ed} does not exceed the absorbable shear forces v_{Rd,max} and v_{Rd,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 following 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 chord force F_{cd,a} and the tensile chord force F_{sd,a }are required. The maximum value that may be assumed for Δx is half the distance between the section where the moment is 0 and the section where the moment is maximum. If applying point loads, the length Δx should not exceed the distance between point 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 verified that the load-bearing capacity of the compressive strut (A in Figure 01) is not exceeded in the flange. For this, the following equation is applied:

${\mathrm v}_\mathrm{Ed}\;\leq\;\mathrm\nu\;\cdot\;{\mathrm f}_\mathrm{cd}\;\cdot\;\sin\;{\mathrm\theta}_\mathrm f\;\cdot\;\cos\;{\mathrm\theta}_\mathrm f$.

If there is transverse bending of the plate and longitudinal shear between the web and flange at the same time, you should use the larger steel cross-section, which results from the two designs for the upper position in the plate. 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

It is possible to consider shear joints 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 result of the required reinforcement for the shear joint is displayed together with the result of the shear reinforcement by section length a_{sf}. In the 'Detailed Results' table, you can see some intermediate values of the shear design between flange and web. These intermediate values are listed under the results of 'Shear Between Web and Flanges of T-Sections'.

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