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As was mentioned above, there exists general concept of “strut-and-tie” model for the prediction of torsion effects in concrete. In this model, the top compression and bottom tensile members represent the compressive concrete and tensile reinforcement, respectively. The procedure for design can be represented by diagram below:
The formulas which are used for the calculation of each component of this model are the following.
Torsional cracking moment is calculated according to equation 6.26 in EN 1992-1-1, provided that the stress caused by torsional moment is equal to design axial tensile strength of concrete (value fctd). It follows
TRdc = 2 ∙ fctd ∙ tef ∙ Ak
Maximum of torsional resistance moment (TRd,max) is determined according to formula 6.30 in EN 1992-1-1.
TRd,max = 2 ∙ ν ∙ αcw ∙ fcd ∙ Ak ∙tef ∙cos θ ∙ sin θ
Statically required cross-sectional area of the shear reinforcement per meter is calculated according to formula below
Aswm,req = Aswt,req / sl,req = |TEd| / (2 ∙ Ak ∙ fywd ∙ cot θ)
Design torsional resistance moment of torsional reinforcement (TRd,st) is calculated according to formula below
TRdst = 2 ∙ Ak ∙ (Aswt / st) ∙fywd ∙ cot θ
Final design value of torsional moment (TRd) carried by member is calculated based on the following formulas
TRd = TRd,c ≤ TRd,max
TRd = TRd,s ≤ TRd,max
where
| TEd |
torsional moment |
| TRd,c | the design value of torsional cracking moment |
| tef | effective wall thickness, see "Calculation of basic characteristics" |
| Ak |
the area enclosed by the centre-lines of the thin-walled closed cross-section, including inner hollow areas, see "Calculation of basic characteristics" |
| fctd | design axial tensile strength of concrete |
| TRd,max | Maximum of torsional resistance moment |
| αcw | coefficient taking into account state of the stress in the compression chord, see note 3 in clause 6.2.3(3) in EN 1992-1-1. The value 1 is always taken into account for non-prestressed structures |
| ν | strength reduction factor for concrete cracked in shear loaded from Manager for National annexes, see equation 6.6N in EN 1992-1-1 |
| fcd | design value of concrete compressive strength |
| θ | Angle between concrete compression strut and beam axis perpendicular to the shear force, see "Angle between concrete compression strut and beam axis" |
| TRd,st | design torsional resistance moment of torsional reinforcement |
| Aswm.req | Statically required cross-sectional area of the shear reinforcement per meter |
| Aswt | the cross-sectional area of the shear reinforcement calculated from inputted parameters in design default, see "Design Defaults"
Asw = 0,25 ∙ π ∙ dss2 |
| dss | diameter of stirrups loaded from Concrete setting or Concrete data, see "Design Defaults" |
| sl.req |
the spacing of the stirrups in longitudinal direction sl,req = Aswt / Aswm,req |
| fywd |
the design yield strength of the shear reinforcement. |