# EC2: Minimum and maximum longitudinal reinforcement

**7.3.2 Minimum reinforcenlent areas**

(1)P If crack control is required, a minimum amount of bonded reinforcement is required to control cracking in areas where tension is expected. The amount may be estimated from equilibrium between the tensile force in concrete just before cracking and the tensile force in reinforcement at yielding or at a lower stress if necessary to limit the crack width.

(2) Unless a more rigorous calculation shows lesser areas to be adequate, the required minimum areas of reinforcement may be calculated as follows. In profiled cross sections like Tbeams and box girders, minimum reinforcement should be determined for the individual parts of the section (webs, flanges).

_{s,mín}·σ

_{s}= k

_{c}· k · f

_{ct,eff}· A

_{ct}

where:

- A
_{s,min}is the minimum area of reinforcing steel within the tensile zone - A
_{ct}is the area of concrete within tensile zone. The tensile zone is that part of the section which is calculated to be in tension just before formation of the first crack - σ
_{s}is the absolute value of the maximum stress permitted in the reinforcement immediately after formation of the crack. This may be taken as the yield strength of the reinforcement, f_{yk}. A lower value may, however, be needed to satisfy the crack width limits according to the maximum bar size or spacing (see 7.3.3 (2)) - f
_{ct,eff}is the mean value of the tensile strength of the concrete effective at the time when the cracks may first be expected to occur:

f_{ct,eff}= f_{ctm}or lower, (f_{ctm(}t)), if cracking is expected earlier than 28 days - k is the coefficient which allows for the effect of non-uniform self-equilibrating stresses, which lead to a reduction of restraint forces

= 1,0 for webs with h ≤ 300 mm or flanges with widths less than 300 mm

= 0,65 for webs with h ≥ 800 mm or flanges with widths greater than 800 mm

intermediate values may be interpolated - k
_{c}is a coefficient which takes account of the stress distribution within the section immediately prior to cracking and of the change of the lever arm:

For pure tension k_{c}= 1,0

For bending or bending combined with axial forces:

- For rectangular sections and webs of box sections and T -sections:

(7.2)

- For flanges of box sections and T -sections:

(7.3)

where- σ
_{c}is the mean stress of the concrete acting on the part of the section under consideration:

σ_{c}= N_{Ed}/ (bh)(7.4) - N
_{Ed}is the axial force at the serviceability limit state acting on the part of the cross-section under consideration (compressive force positive). N_{Ed}should be determined considering the characteristic values of prestress and axial forces under the relevant combination of actions - h* = h for h < 1,0 m

h* = 1,0 m for h ≥ 1,0 m - k
_{1}is a coefficient considering the effects of axial forces on the stress distribution:

k_{1}= 1,5 if N_{Ed}is a compressive force

k_{1}= 2h*/(3h) if N_{Ed}is a tensile force - F
_{cr}is the absolute value of the tensile force within the flange immediately prior to cracking due to the cracking moment calculated with f_{ct,eff}

- σ

**9.2 Beams**

**9.2.1 Longitudinal reinforcement**

**9.2.1.1 Minimum and maximum reinforcement areas**

(1) The area of longitudinal tension reinforcement should not be taken as less than A_{s,min}.

Note 1: See also 7.3 for area of longitudinal tension reinforcement to control cracking.

Note 2: The value of A_{s,min} for beams for use in a Country may be found in its National Annex. The recommended value is given in the following:

_{s,min}= 0.26·f

_{ctm}/f

_{yk}·b

_{t}·d, but not less than 0.0013·b

_{t}·d

where:

- b
_{t}denotes the mean width of the tension zone; for a T-beam with the flange in compression, only the width of the web is taken into account in calculating the value of b_{t} - f
_{ctm}should be determined with respect to the relevant strength class according to Table 3.1:

f_{ctm}= 0,30 × f_{ck}^{(2/3)}, f_{ck}≤ 50

f_{ctm}= 2.12·Ln(1+(f_{cm}/10)), f_{ck}> 50/60

with f_{cm}= f_{ck}+8 (MPa)

(2) Sections containing less reinforcement than A_{s,min} should be considered as unreinforced.

(3) The cross-sectional area of tension or compression reinforcement should not exceed A_{s,max} outside lap locations.

Note: The value of A_{s,max} for beams for use in a Country may be found in its National Annex. The recommended value is 0.04·A_{c}.

**9.3 Solid slabs**

(1) This section applies to one-way and two-way solid slabs for which b and l_{eff} are not less than 5h (member for which the minimum panel dimension is not less than 5 times the overall slab thickness).

**9.3.1 Flexural reinforcement**

**9.3.1.1 General**

(1) For the minimum and the maximum steel percentages in the main direction 9.2,1,1 (1) and (3) apply.

(2) Secondary transverse reinforcement of not less than 20% of the principal reinforcement should be provided in one way slabs. In areas near supports transverse reinforcement to principal top bars is not necessary where there is no transverse bending moment.

(3) The spacing of bars should not exceed s_{max,slabs}.

Note; The value of s_{max,slabs} for use in a Country may be found in its National Annex. The recommended value is:

- for the principal reinforcement, 3·h ≤ 400 mm, where h is the total depth of the slab;

- for the secondary reinforcement, 3.5·h ≤ 450 mm

In areas with concentrated loads or areas of maximum moment those provisions become respectively:

- for the principal reinforcement, 2·h ≤ 250 mm

- for the secondary reinforcement, 3·h ≤ 400 mm.

**9.5 Columns**

(1) This clause deals with columns for which the larger dimension h is not greater than 4 times the smaller dimension b.

**9.5.1 General**

**9.5.2 Longitudinal reinforcement**

(1) Longitudinal bars should have a diameter of not less than Φ_{min}.

Note: The value of ¢min for use in a Country may be found in its National Annex. The recommended value is 8 mm.

(2) The total amount of longitudinal reinforcement should not be less than A_{s,min}

Note: The value of A_{s,min} for use in a Country may be found in its National Annex. The recommended value is given by Expression (9.12N)

_{s,min}= max (0.1·N

_{Ed}/f

_{yd}; 0.002·A

_{c})

where:

- f
_{yd}is the design yield strength of the reinforcement - N
_{Ed}is the design axial compression force

(3) The area of longitudinal reinforcement should not exceed A_{s,max}

Note: The value of A_{s,max} for use in a Country may be found in its National Annex. The recommended value is 0.04·A_{c} outside lap locations unless it can be shown that the integrity of concrete is not affected, and that the full strength is achieved at ULS. This limit should be increased to 0.08·A_{c} at laps.

(4) For columns having a polygonal cross-section, at least one bar should be placed at each corner. The number of longitudinal bars in a circular column should not be less than four.

**9.6 Walls**

**9.6.1 General**

(1) This clause refers to reinforced concrete walls with a length to thickness ratio of 4 or more and in which the reinforcement is taken into account in the strength analysis

**9.6.2 Vertical reinforcement**

(1) The area of the vertical reinforcement should lie between A_{s,vmin} and A_{s,vmax}.

Note 1: The value of A_{s,vmin} for use in a Country may be found in its National Annex. The recommended value is 0.002·A_{c}.

Note 2: The value of A_{s,vmax} for use in a Country may be found in its National Annex. The recommended value is 0.04·Ac outside lap locations unless it can be shown that the concrete integrity is not affected and that the full strength is achieved at ULS. This limit may be doubled at laps.

(2) Where the minimum area of reinforcement, A_{s,vmin}, controls in design, half of this area should be located at each face.

(3) The distance between two adjacent vertical bars shall not exceed 3 times the wall thickness or 400 mm whichever is the lesser.

**9.6.3 Horizontal reinforcement**

(1) Horizontal reinforcement running parallel to the faces of the wall (and to the free edges) should be provided at each surface. It should not be less than A_{s,hmin}.

Note: The value of A_{s,hmin} for use in a Country may be found in its National Annex. The recommended value is either 25% of the vertical reinforcement or 0.001·A_{c}, whichever is greater.

(2) The spacing between two adjacent horizontal bars should not be greater than 400 mm.

**9.8 Foundations**

**9.8.1 Column and wall footings**

(1) A minimum bar diameter Φ_{min} should be provided

Note: The value of Φ_{min} for use in a Country may be found in its National Annex. The recommended value is 8 mm.