Design for bending for rectangular sections (concrete slab: EC2)
Calculate the value of K from; | ||
K | = | MEd/(fck*b*d2) |
Where | ||
b | = | 1000mm (the unit design width) |
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 NAand Norwegian NA; | ||
k1 | = | 0.40 |
k2 | = | 1.0*(0.6+0.0014/εcu2) |
k3 | = | 0.40 |
k4 | = | 1.0*(0.6+0.0014/εcu2) |
γC | = | 1.5 |
αcc | = | 0.85 |
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For design in accordance with EC2 Recommendations and Swedish NA; | ||
k1 | = | 0.44 |
k2 | = | 1.25*(0.6+0.0014/εcu2) |
k3 | = | 0.54 |
k4 | = | 1.25*(0.6+0.0014/εcu2) |
γC | = | 1.5 |
αcc | = | 1.0 |
IF K ≤ K' THEN compression reinforcement is not required. Calculate the lever arm, z from; |
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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 NAand Swedish NA; | ||
γS | = | 1.15 |
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 | = | MAX (MIN(Es*εcu3*(1-(d2/xu), fyd),1) |
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*b*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 |