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Overview

1 Introduction

2 Theoretical Background

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

$v_{E d, f} = \frac{∆ F_{d, f}}{h_{f} \cdot ∆ x_{f}}$

where

Table 2.1
h_f	flange thickness at junction
Δx_f	considered length
ΔF_d,f	longitudinal force difference in flange over length Δx

The maximum value that may be assumed for the length Δx_f 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 F_d,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 M_z,Ed

Table 2.1
$F_{d, i =} (\frac{M_{y, Ed}}{z} - \frac{N_{Ed}}{z} \cdot z_{s}) \cdot \frac{b_{eff, i}}{b_{eff}}$	for compression flanges
$F_{d, i} = (\frac{M_{y, Ed}}{z} - \frac{N_{Ed}}{z} \cdot z_{s} + N_{Ed}) \cdot \frac{A_{s, a}}{A_{s}}$	for tension flanges

where

Table 2.1
z_s	distance between centroid of cross-section and tension reinforcement
z	lever arm of internal forces 0.9 d
b_eff,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)
b_eff	flange width
A_sa	reinforcement exposed in connected tension flange
A_s	total area of tension reinforcement

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

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

$a_{sf} \geq \frac{v_{Ed, f} \cdot h_{f}}{\cot θ_{f} \cdot f_{yd}}$

where

Table 2.1
1.0 ≤ cot θ_f ≤ 2.0	inclination of concrete compression strut for compression flanges
1.0 ≤ cot θ_f ≤ 1.25	inclination of concrete compression strut for tension flanges
f_yd	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:

$v_{E d} \leq ν_{1} \cdot f_{c d} \cdot \sin θ_{f} \cdot \cos θ_{f}$

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

where

Table 2.1
f_cd	design value of concrete strength
ν₁	reduction factor for concrete strength in case of shear cracks

Parent section

2.1 Ultimate Limit State Design