Shear reinforcement design on detailing provisions for beam
Minimal shear reinforcement according to detailing provisions for beam is calculated according to formula
Aswm,min = max(Asw,long,min; Asw,trans,min; Asw,ρ,min; Asw,tor,min)
where
| Asw,long,min | minimal area of shear reinforcement from maximum longitudinal spacing 9.2.2(6) |
| Asw,trans,min | minimal area of shear reinforcement from maximum transverse spacing 9.2.2(8) |
| Asw,ρ,min | minimal area of shear reinforcement from minimal ratio 9.2.2(5) |
|
Asw,tor,min) |
minimal area of shear reinforcement for torsion 9.2.3(3) |
Minimal area of shear reinforcement from maximum longitudinal spacing 9.2.2(6)
Based on maximum longitudinal spacing of shear links which is defined in clause 9.2.2(6).
Asw,long,min = 1 / sl,max ∙ π ∙ ϕ2 / 4 ∙ ns
where
| sl,max | Maximum longitudinal spacing of shear links according to clause 9.2.2(6) |
| ϕ | Diameter of shear reinforcement |
| ns | Number of cuts in one shear link |
Minimal area of shear reinforcement from maximum transverse spacing 9.2.2(8)
Based on formula 9.8N from EN 1992-1-1
sst,max,lim = min(Coeffst,max,A ∙ d; Coeffst,max,B)
Where
Final minimal area is calculated by
Asw,trans,min = 1 / sst,max,lim ∙ π ∙ ϕ2 / 4 ∙ ns
where
| sl,max | Maximum longitudinal spacing of shear links according to clause 9.2.2(6) |
| ϕ | Diameter of shear reinforcement |
| ns | Number of cuts in one shear link |
Minimal area of shear reinforcement from minimal ratio 9.2.2(5)
Based on formula 9.5N from EN 1992-1-1
ρw,min = Coeffρw,min ∙ √fck / fywk
where
| Coeffρw,min | Coefficient for minimal ratio, can be changed in National annex setting. Default value 0,08 |
| fck | Characteristic cylinder concrete strength in [MPa] |
| fywk | Characteristic yield strength of shear reinforcement in [MPa] |
Final minimal area is calculated by
Asw,ρ,min = ρw,min ∙ bw ∙ sin α
where
| ρw,min | Minimal shear reinforcement ratio according to clause 9.2.2(5) |
| bw | Minimum width of cross-section in tensile area |
| α | Angle of stirrup links - 90 ° for vertical stirrups |
Minimal area of shear reinforcement for torsion 9.2.3(3)
Based on statement from clause 9.2.3(3) from EN 1992-1-1. It can be transformed to formula
ssl,tor,max = min(u / 8; sl,max; bmin)
where
| u | Outer perimeter of equivalent thin-walled cross-section |
| sl,max | Maximum longitudinal spacing of shear links according to clause 9.2.2(6) |
| bmin | Lesser dimension of the beam cross-section |
Final minimal area is calculated by
Asw,tor,min = 1 / ssl,tor,max ∙ π ∙ ϕ2 / 4 ∙ ns,tor
where
| ssl,tor,max | Maximum longitudinal spacing of shear links for torsion according to clause 9.2.3(3) |
| ϕ | Diameter of shear reinforcement |
| ns,tor | Number of cuts effective on torsion (for normal stirrups (type of stirrup = Single) ns,tor = 1) |
Minimal area of shear reinforcement for torsion is calculated only when torsion force is presented in the section.
The values of coefficients or calculation procedures used in all detailing provisions can be modified by National annexes, for details see "National annexes theoretical background".