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Fig.6.6. Tsection. Approximate design method The reinforcement is given by the formula
Fig.6.6. Tsection. Approximate design method The reinforcement is given by the formula
+ Nc and it must be verified that the average compressive stress in the flange is not greater than fcd:
6.1.5 Bending with axial force in rectangular section with symmetric reinforcement bars
The ultimate limit state behaviour of a rectangular section with reinforcement bars As = A's placed symmetrically at the section edges and subjected to simple bending moment with an eccentric axial force NEd is studied. The analysis is carried out through the determination of the moment resistance MRd about the centroidal axis for given values of NEd and geometric and mechanical properties of the section.
The study starts from Fig. 6.1 which is reproduced as far as it's needed in Fig. 6.7. Four deformed configurations (1234) are taken into account. The first three, obtained by rotation around point B of the straight line that represents the plane section, are characterized by particular depths of the neutral axis x; line 4, that configures uniform strain £c2, is vertical in the representation and passes by point C.
Fig.6.7. Possible strain distributions at the ultimate limit state
Relations that are recalled in the treatment:. Strain of upper reinforcement A's (see point 6.1.2.1):
Strain of lower reinforcement As (see point 6.1.2.1):
Definition of line 1
Passing by B, the straight line assumes configuration 1 characterized, at the level of the upper reinforcement layer, by strain £s yk v E
(design limit of elasticity for B450 steel with tyk = 450 N/mm2 and Es = 200 kN/mm2). The depth of the neutral axis, calculated by (6.1) results:
y cu2 syd y
The k1 values for different concrete classes (as £cu2 is function of fck), are given in Table 6.6 (£cu2 in absolute value).
For x < x1 the upper reinforcement layer is in elastic field; for x > x1 it works at stress fyd. The lower reinforcement layer, for x < x1 , works at stress fyd .
Table 6.6 values of ki and k2
For x < x1 the upper reinforcement layer is in elastic field; for x > x1 it works at stress fyd. The lower reinforcement layer, for x < x1 , works at stress fyd .
Table 6.6 values of ki and k2
(N/mm2) 
£cu2 
ki 
k2 
< 50 
0,0035 
2,27 
0,64 

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