# Shear between web and flanges: the transverse reinforcement per unit length `A`_{sf}/`s`_{f} and crushing of the compressive structs in the flanges

_{sf}

_{f}

## Eurocode 2 part 1-1: Design of concrete structures 6.2.4 (3)

• The transverse reinforcement per unit length, `A _{sf}`/

`s`, may be determined as follows (see Figure 6.7):

_{f} (A⋅_{sf}f / _{yd}s) ≥ _{f}v⋅_{Ed}h / cot_{f}θ _{f} | (6.21) |

where:

`v`_{Ed}- is the longitudinal shear stress at the junction between one side of a flange and the web. It is determined by the change of the normal (longitudial) force in the part of the flange considered:
`v`= Δ_{Ed}`F`/ (_{d}`h`⋅_{f}`Δ`)`x`(6.20) with

`h`_{f}- the thickness of flange at the junctions
- Δ
`x` - the length under consideration.

The maximum value that may be assumed for Δ`x`is half the distance between the section where the moment is 0 and the section where the moment is maximum. Where point loads are applied the length Δ`x`should not exceed the distance between point loads - Δ
`F`_{d} - the change of the normal force in the flange over the length Δ
`x`.

`θ`_{f}- is the angle between the concrete compression strut and the beam axis, see § 6.2.4 (4)
`f`_{yd}- is the design yield strength of the reinforcement,
`f`=_{yd}`f`/_{yk}`γ`,_{S}

see § 2.4.2.4 (1), § 2.4.2.4 (2) for the values of`γ`,_{S}

see § 3.2.2 (3)P for the uper limit of`f`,_{yk}

see Figure 3.8 for the design stress-strain diagrams of the reinforcing steel.

• To prevent crushing of the compression struts in the flange, the following condition should be satisfied:

v ≤ _{Ed}ν f sin_{cd}θ cos_{f}θ _{f} | (6.22) |

where:

`ν`- is a strength reduction factor for concrete cracked in shear, the recommended value of
`ν`is`ν`= 0,6(1 -`f`/250) (Expression 6.6N in § 6.2.2 (6))_{ck} `f`_{cd}- is the design compressive strength of concrete, see § 3.1.6 (1)P.

This application calculates
the reinforcement per unit length `A _{sf}`/

`s`from your inputs. Intermediate results will also be given.

_{f}