Design values of shear resistance and torsional resistance moment (concrete beam: EC2)
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The design value of the shear resistance of a concrete section with vertical shear reinforcement, VRd,max is given by; |
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| VRd,max |
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0.9*αcw*bw*d*ν1*fcwd/(cotθ + tanθ) |
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where |
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| θ |
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MIN{θmax, MAX[0.5*sin-1[2*VEd,max/( αcw*bw*0.9*d*ν1*fcwd)], θmin]} |
| where | ||
| νEd |
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VEd,max /(bw*d) |
| τEd |
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TEd,max/(2*Ak*tef) |
| Ak |
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(h-tef)*(bw-tef) |
| tef |
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MAX(A/u, 2*(h-do)) |
| A |
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h*bw |
| u |
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the outer circumference of the cross-section |
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2*(h+bw) |
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| do |
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the effective depth of the outer layer of longitudinal reinforcement |
| VEd,max |
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max. absolute value from all the shear regions |
| TEd,max |
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max. torsion on the member |
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| The maximum design value of the torsional resistance moment, ΤRd,max is given by | ||
| ΤRd,max |
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2*ν1*αccw*fcwd*Ak*t ef*sinθ*cosθ |
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| For design in accordance with UK NA, Irish NA, Malaysian NA and Singapore NA; | ||
| fcwd1 |
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αccw*min (fck,50)/γC |
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For design in accordance with EC2 Recommendations, Finnish NA, Norwegian NA and Swedish NA; |
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| fcwd |
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αccw*fck/γC |
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For design in accordance with EC2 Recommendations, UK NA, Irish NA, Malaysian NA, Singapore NA, Finnish NA, Norwegian NA and Swedish NA; |
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| αcw |
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1.0 |
| γC |
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1.5 |
| γ1 |
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0.6*(1 – fck/250) |
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| For design in accordance with EC2 Recommendations, UK NA, Irish NA, Malaysian NA, Singapore NA and Swedish NA; | ||
| αccw |
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1.0 |
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| For design in accordance with Finnish NA and Norwegian NA; | ||
| αccw |
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0.85 |
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The design value of the torsional resistance moment of a concrete section with no shear reinforcement, ΤRd,c is given by2; |
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| ΤRd,c |
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2*Ak*tef*fctd |
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where |
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| fctd |
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the design tensile strength of the concrete |
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αct*fctk,0.05/γC | |
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| For design in accordance with EC2 Recommendations, UK NA, Irish NA, Malaysian NA, Singapore NA, Finnish NA and Swedish NA; | ||
| αct |
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1.0 |
| γC |
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1.5 |
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| For design in accordance with Norwegian NA; | ||
| αct |
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0.85 |
| γC |
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1.5 |
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If the maximum torsional moment acting on the beam, TEd,max is less than the ignorable torque limit then no further calculations are necessary. |
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Otherwise: |
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If (ΤEd,max,i/ΤRd,max) + (VEd,max,i/VRd,max) ≤ 1.0 |
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then the torsion design process can proceed. |
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ELSE the torsion design FAILS since the section size is inadequate for torsion. |
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Footnotes
1 Eqn (3.15) EN 1992-1-1:2004 Section 3.1.6(1)P
2 EN 1992-1-1:2004
Eqn (6.26) with τt,i = fctd