Design for bending for rectangular sections (concrete slab: EC2)

Tekla Structural Designer
Modified: 2 Jun 2023
2024
Tekla Structural Designer

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*αccC)*(1 - λ*(δ - k1)/(2*k2))*( λ*(δ - k1)/(2*k2)) for fck ≤ 50 N/mm2
K' = (2*η*αccC)*(1 - λ*(δ - k3)/(2*k4))*( λ*(δ - k3)/(2*k4)) for fck > 50 N/mm2

where

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
   
   
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
   
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;

z = MIN(0.5*d*[1 + (1 - 2*K/(η*αccC))0.5], 0.95*d)
The area of tension reinforcement required is then given by;
Ast,reqd = MEd/(fyd*z)
where
fyd = fykS
γS = the NDP partial safety factor for reinforcement
The depth to the neutral axis, xu is given by;
xu = 2*(d-z)/λ
   
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;

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(Escu3*(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*αccC))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

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