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2.1.3 Shear Forces Between Web and Flanges of T-Beams

Shear Forces Between Web and Flanges of T-Beams

The longitudinal shear stress vEd,f at the junction between flange and web is determined by the longitudinal force difference Δ Fd,f in the flange's governing part according to EN 1992-1-1, clause 6.2.4 (3), equation (6.20).

vEd,f = Fd,fhf · xf 

where

Table 2.1

hf

: flange thickness at junction

Δxf

:considered length

ΔFd,f

: longitudinal force difference in flange over length Δx

The maximum value that may be assumed for the length Δ xf is half the distance between the maximum and the zero point of moments. Where concentrated loads are applied, the distance between the concentrated loads should not be exceeded.

The determination of Δ Fd,f is done optionally with a control available in the module details according to two different methods that are described below.

1. Simplified method via inner lever arm z = 0.9d without considering Mz,Ed

Table 2.1

for compression flanges

for tension flanges

where

Table 2.1

zs

: distance between centroid of cross-section and tension reinforcement

z

: lever arm of internal forces 0.9 d

beff,i

: width of adjacent flange (compression flange) or width of reinforcement distribution in adjacent flange (tension flange) considering the Distribute reinforcement evenly over complete slab width option (see Figure 3.30)

beff

: flange width

Asa

: reinforcement exposed in connected tension flange

As

: total area of tension reinforcement

2. Calculation of Fd from general stress integration in partial areas of cross-section

The required tension flange reinforcement due to shear forces per unit length asf may be determined according to equation (6.21).

asf  vEd,f · hfcot θf · fyd 

where

Table 2.1

1.0 ≤ cot θf ≤ 2.0

: inclination of concrete compression strut for compression flanges

1.0 ≤ cot θf ≤ 1.25

: inclination of concrete compression strut for tension flanges

fyd

: design yield strength of reinforcement

At the same time, the compression struts in the flange must be prevented from failing, which is ensured if the following requirement is met:

vEd  ν1 · fcd · sin θf ·cos θf 

Equation 2.6 EN 1992-1-1, Eq. (6.22)

where

Table 2.1

fcd

: design value of concrete strength

ν1

: reduction factor for concrete strength in case of shear cracks

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