Design for bending for rectangular sections (beams and slabs: EC2)

Tekla Structural Designer
2021
Tekla Structural Designer

Design for bending for rectangular sections (beams and slabs: 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*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

k i
  =  
moment redistribution factors
δ
  =  
moment redistribution ratio ( = 1.0 in the current release)
γ C
  =  
the NDP partial safety factor for concrete
α cc
  =  
coefficient to take account of long term effects on compressive strength of concrete
λ
  =  
  1. 8 for fck ≤ 50 N/mm2
  =  
  1. 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 and Singapore NA;

γC
  =  
1.5
αcc
  =  
0.85
For design in accordance with EC2 Recommendations;
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 and Singapore 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
  =  
MIN(Escu3*(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*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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