(coating of the tendons (and wk = |02|
NOTE for definition of decompression, see (7) above.
126.96.36.199 Minimum reinforcement areas
P(1) In assessing the minimum area of reinforcement required to ensure controlled cracking in a member or part of a member which may be subject to tensile stress due to the restraint of imposed deformations, it is necessary to distinguish between two possible mechanisms by which such stress may arise. The two mechanisms are:
i) restraint of intrinsic imposed deformations — where stresses are generated in a member due to dimensional changes of the member considered being restrained (for example stress induced in a member due to restraint to shrinkage of the member), ii) restraint of extrinsic imposed deformations — where the stresses are generated in the member considered by its resistance to externally applied deformations (for example where a member is stressed due to settlement of a support).
P(2) It is also necessary to distinguish between two basic types of stress distribution within the member at the onset of cracking. These are:
a) bending — where the tensile stress distribution within the section is triangular (i.e. some part of the section remains in compression).
b) tension — where the whole of the section is subject to tensile stress.
(3) Unless more rigorous calculation shows a lesser area to be adequate, the required minimum areas of reinforcement may be calculated from the relation given below:
Ag = area of reinforcement within tensile zone
Act = 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.
Os = the maximum stress permitted in the reinforcement immediately after formation of the crack. This may be taken as | 100 % | of the yield strength of the reinforcement, fyk. A lower value may, however be needed to satisfy the crack width limits (see Table 4.11)
fcteff = the tensile strength of the concrete effective at the time when the cracks may first be expected to occur. In many cases, such as where the dominant imposed deformation arises from dissipation of the heat of hydration, this may be within 3—5 days from casting depending on the environmental conditions, the shape of the member and the nature of the formwork. Values of fct ef may be obtained from Table 3.1 by taking as the class the strength at the time cracking is expected to occur. When the time of cracking cannot be established with confidence as being less than 28 days, it is suggested that a minimum tensile strength of|3| N/mm2 be adopted.
kc = a coefficient which takes account of the nature of the stress distribution within the section immediately prior to cracking. The relevant stress distribution is that resulting from the combination of effects of loading and restrained imposed deformations.
= 1.0 for pure tension
= 0.4 for bending without normal compressive force For sections subject to normal force or prestress, see (7) below. k = a coefficient which allows for the effect of non-uniform self-equilibrating stresses.
Values of k for various situations are given below:
— tensile stresses due to restraint of intrinsic deformations generally k = 0.8
— tensile stresses due to restraint of extrinsic deformations k = l.0
Parts of sections distant from the main tension reinforcement, such as outstanding parts of a section or the webs of deep sections, may be considered to be subjected to imposed deformations by the tension chord of the member. For such cases, a value in the range 0.5 < k < l.0 will be appropriate. (4) The minimum reinforcement may be reduced or even be dispensed with altogether if the imposed deformation is sufficiently small that it is unlikely to cause cracking. In such cases minimum reinforcement need only be provided to resist the tensions due to the restraint.
P(5) In prestressed members and reinforced concrete members subject to compressive normal force the minimum reinforcement area may be reduced below that necessary for ordinary reinforced concrete due to the influence of:
— the increased flexural stiffness of the compression zone.
— the contribution of the prestressing tendons.
(6) In prestressed members, the minimum reinforcement for crack control is not necessary in areas where, under the rare combination of actions and the relevant estimated characteristic value of prestress or normal force, the concrete remains in compression
(7) If the conditions in (6) are not fulfilled, the required minimum area should be calculated according to (3) above with the following values for kc.
For box sections, kc = 0.4 for the webs
= 0.8 for the tension chord
For rectangular sections, the value of kc may be interpolated between 0.4 for pure bending without normal force and zero when either:
a) the conditions just satisfy (6) above or b) where, under the action of the relevant estimated value of prestress, the depth of the tension zone, calculated on the basis of a cracked section under the loading conditions leading to formation of the first crack, does not exceed the lesser of h/2 or 0.5 m.
(8) Prestressing tendons may be taken into account as minimum reinforcement within a 300 mm square surrounding the tendon, provided that the different bond behaviour of the tendons and reinforcement are taken into account. In the absence of better information, this may be done by assuming prestressing tendons to be 50 % effective.
188.8.131.52 Control of cracking without direct calculation
(l) For reinforced or prestressed slabs in buildings subjected to bending without significant axial tension, measures specifically to control cracking are not necessary where the overall depth does not exceed 200 mm and the provisions of 5.4.3 have been applied.
(2) Where at least the minimum reinforcement given by 184.108.40.206, is provided, the limitation of crack widths to acceptable values and the avoidance of uncontrolled cracking between widely spaced bars may generally be achieved by limiting bar spacings and/or bar diameters. Table 4.11 and Table 4.12 below are designed to ensure that crack widths will not generally exceed 0.3 mm for reinforced concrete and 0.2 mm for prestressed concrete. It should be noted, however, that larger cracks could occasionally occur but that this should not be considered to be serious.
Crack widths will not generally be excessive provided that:
— for cracking caused dominantly by restraint, the bar sizes given in Table 4.11 are not exceeded where the steel stress is the value obtained immediately after cracking [i.e. Bs in Equation (4.78) in 220.127.116.11(3)] and
— for cracks caused dominantly by loading, either the provisions of Table 4.11 or the provisions of Table 4.12 are complied with.
For prestressed concrete sections, the stresses in the reinforcement should be calculated regarding the prestress as an external force without allowing for the stress increase in the tendons due to loading.
Maximum bar size
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