Shear between flanges and web of flanged beams (concrete beam: EC2)
The shear strength of the interface between the flanges and the web of a flanged beam is checked and, if necessary, transverse reinforcement is provided as shown in the diagram below.1
| The calculations for the transverse reinforcement are as follows: | ||
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The lever arm at the point of maximum sagging moment is given by; |
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| z | = | 0.5*d*[1 + (1 – 2*K/(η*αcc/γC))0.5] |
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where |
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K |
= | MEd,+max/(fck*beff*d2) |
| MEd,+max | = |
the maximum sagging (+ve) design moment on the beam |
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The depth of the compression block, dc is then given by; |
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| dc | = |
2*(d-z) |
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The following calculations are then carried out on each side, i of the beam. |
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IF dc ≤ hfi,min THEN the stress block is completely within the flange. |
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| where | ||
| hfi,min | = |
the minimum depth of the flange on each side of the beam |
| = |
MIN(hf1, hf2) |
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The force in the flange on side i of the beam, Fi is then given by; |
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| Fi | = |
η*fcd*dc*beff,i |
| where | ||
| beff,i | = |
the width of the flange on side i of the beam |
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IF dc > hfi,min THEN the force in the flange on side i of the beam, Fi is then given by; |
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| Fi | = | η*fcd*hfi*beff,i |
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where |
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| hfi | = |
the depth of the flange on side i of the beam |
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The maximum rate of change of the bending moment for all load combinations in the sagging region of the beam, (dMEd/dx)max (the moment gradient) is then determined. |
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The moment gradient is then given by; |
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| dMEd/dx | = | ABS(MEd,end-0)/interval length |
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The length over which the flange force is transferred to the web, LT is given by; |
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| LT | = |
MEd,+max/(dMEd/dx)max |
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The design shear stress on side i of the web is then given by; |
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| vEdi | = |
Fi/(hfi*LT) |
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The limiting value of the shear stress, vEd,lim is given by; |
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| vEd,lim | = |
k*fctd |
| where | ||
| k | = |
an NDP factor |
| For design in accordance with EC2 Recommendations, UK NA, Irish NA, Malaysian NA, Singapore NA, Finnish NA, Norwegian NA and Swedish NA; | |||
| IF vEdi ≤ vEd,lim THEN no additional transverse reinforcement is required | |||
| ELSE | |||
| Asfi,reqd | = | ((vEdi*hfi/fyd)/cotθfi)*1000 | mm2 per metre length of beam |
| The result for the beam is then given by; | |||
| Asfi,reqd | = | MAX(Asf1,reqd, Asf2,reqd) | |
| where | |||
| θfi | = |
MIN{θfmax, MAX(0.5*sin-1(2*vEdi/(ν*fcd)), θfmin)} |
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| ν | = |
an NDP value |
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| θfmax | = |
an NDP value |
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| θfmin | = |
an NDP value |
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| For design in accordance with EC2 Recommendations, UK NA, Irish NA, Malaysian NA, Singapore NA, Finnish NA and Swedish NA; | |||
| ν | = | 0.6*(1-(fck/250)) | |
| θfmax | = | tan-1(1) | |
| θfmin | = | tan-1(0.5) | |
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| For design in accordance with Norwegian NA; | |||
| ν | = | 0.6*(1-(fck/250)) | |
| θfmax | = | tan-1(1) | |
| θfmin | = | tan-1(0.4) | |
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Footnotes
1 EN 1992-1-1:2001
Section 6.2.4