Design for bending for rectangular sections (concrete beam: EC2)
| Calculate the value of K from; | ||
| K |
|
MEd/(fck*bw*d2) |
| Then calculate the limiting value of K, known as K' from; | ||
| K' |
|
(2*η*αcc /γC)*(1 - λ*(δ - k1)/(2*k2))*( λ*(δ - k1)/(2*k2)) for fck ≤ 50 N/mm2 |
| K' |
|
(2*η*αcc /γC)*(1 - λ*(δ - k3)/(2*k4))*( λ*(δ - k3)/(2*k4)) for fck > 50 N/mm2 |
|
where |
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| ki |
|
moment redistribution factors |
| δ |
|
moment redistribution ratio ( = 1.0 in the current release) |
| γC |
|
the NDP partial safety factor for concrete |
| αcc |
|
coefficient to take account of long term effects on compressive strength of concrete |
| λ |
|
0.8 for fck ≤ 50 N/mm2 |
|
0.8 - (fck-50)/400 for 50 < fck ≤ 90 N/mm2 | |
| η |
|
1.0 for fck ≤ 50 N/mm |
|
1.0 - (fck-50)/200 for 50 < fck ≤ 90 N/mm2 | |
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| For design in accordance with UK NA, Irish NA, Malaysian NA, Singapore NA, Finnish NA and Norwegian NA; | ||
| γC |
|
1.5 |
| αcc |
|
0.85 |
|
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| For design in accordance with EC2 Recommendations and Swedish NA; | ||
| γC |
|
1.5 |
| αcc |
|
1.0 |
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IF K ≤ K' THEN compression reinforcement is not required. Calculate the lever arm, z from; |
||
| z |
|
MIN(0.5*d*[1 + (1 - 2*K/(η*αcc/γC))0.5], 0.95*d) |
| The area of tension reinforcement required is then given by; | ||
| Ast,reqd |
|
MEd/(fyd*z) |
| where | ||
| fyd |
|
fyk/γS |
| γS |
|
the NDP partial safety factor for reinforcement |
| The depth to the neutral axis, xu is given by; | ||
| xu |
|
2*(d-z)/λ |
|
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| For design in accordance with UK NA, EC2 Recommendations, Irish NA, Malaysian NA, Singapore NA, Finnish NA, Norwegian NA and Swedish NA; | ||
| γS |
|
1.15 |
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IF K > K' THEN compression reinforcement is required. Calculate the depth to the neutral axis from; |
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| xu |
|
d*(δ-k1)/k2 for fck ≤ 50 N/mm2 |
| xu |
|
d*(δ-k3)/k4 for fck > 50 N/mm2 |
| Calculate the stress in the reinforcement from; | ||
| fsc |
|
MIN(Es*εcu3*(1-(d2/xu), fyd) |
| where | ||
| d2 |
|
the distance from the extreme fibre in compression to the c of g of the compression reinforcement |
| Calculate the limiting bending strength, M' from; | ||
| M' |
|
K'*fck*bw*d2 |
| Calculate the lever arm from; | ||
| z |
|
0.5*d*[1 + (1 - 2*K'/(η*αcc/γC))0.5] |
| The area of compression reinforcement required, As2,reqd is given by; | ||
| As2,reqd |
|
(MEd-M')/(fsc*(d-d2)) |
| The area of tension reinforcement required, Ast,reqd is given by; | ||
| Ast,reqd |
|
M'/(fyd*z) + As2,reqd*fsc/fyd |