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# Shear between web and flanges: the transverse reinforcement per unit length Asf/sf and crushing of the compressive structs in the flanges

## Eurocode 2 part 1-1: Design of concrete structures \$(document).ready(function () { var freeExample = \$("#freeExample").length; \$("#mainMenu li#nav-appCate, #mainMenu li#nav-appEC211").addClass("active"); var proUser = false === true || false === true || freeExample !== 0; if (!proUser) { \$('#Input input').keyup(function(){ \$('#AlertSubscribe').modal(); }); \$('#Input select').change(function(){ \$('#AlertSubscribe').modal(); }); }; var tempInput = \$("#tempInput").text(); if (tempInput != "") { \$("#Input").parent("form").deserialize(tempInput); if (proUser) { \$("#acceptBtn").trigger("click"); } }; });  6.2.4 (3)

• The transverse reinforcement per unit length, Asf/sf, may be determined as follows (see Figure 6.7):

 (Asf⋅fyd / sf) ≥ vEd⋅hf / cotθf (6.21)

where:

vEd
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:
 vEd = ΔFd / (hf⋅Δx) (6.20)

with

hf
the thickness of flange at the junctions
Δx
the length under consideration.
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. Where point loads are applied the length Δx should not exceed the distance between point loads
ΔFd
the change of the normal force in the flange over the length Δx.
θf
is the angle between the concrete compression strut and the beam axis, see § 6.2.4 (4)
fyd
is the design yield strength of the reinforcement, fyd = fyk/γS,
see § 2.4.2.4 (1), § 2.4.2.4 (2) for the values of γS,
see § 3.2.2 (3)P for the uper limit of fyk,
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:

 vEd ≤ ν fcd sinθf cosθf (6.22)

where:

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

This application calculates the reinforcement per unit length Asf/sf from your inputs. Intermediate results will also be given.

Input
kN
cm
cm
MPa
MPa

Output
θf
°
vEd
MPa (6.20)
ν fcd sinθf cosθf
MPa
Reinforcement per unit length Asf/sf
cm2/m (6.21)
Crushing of the compression struts
(6.22)