1.4 Behaviour of Reinforced Concrete Sections
1.4.1 Mechanical Characteristics of Reinforcement
In normal reinforced concrete, steel products inbarsor in wiresare used as rein- forcement; the former are provided in bundles of straight rods, usually of 12 m length and possibly bent in half to facilitate transportation; the latter are usually supplied wrapped in coils for considerable length.
Hot-rolled bars and wires can be left without further processing; theirnatural hardnesssteel is characterized byr–ediagrams similar to the one represented in Fig.1.24a. These diagrams, deduced from tensile tests on pieces of bars or wires, exhibit
• linear elastic behaviour up to the yield limitfy;
• elastic modulusEsequal to, for all types of steel, 205,000 MPa;
• subsequent perfectly plastic behaviour with horizontal trend;
• restart, after a relevant elongation, of the increase of stresses due to the hard- ening of the material;
• attainment of the maximum resistance capacity ft for considerable values of ultimate strain (uniform under maximum load)eu;
• decrease of the curve after the maximum loading due to necking of the specimen;
• considerably ductile rupture at a strain eteven greater;
• ductility parameterseu,etgenerally smaller for steel higher strengths.
The behaviour in compression results substantially symmetric, apart from the stages near rupture.
The classification made with reference to themechanical characteristicsof steel is based on the following parameters:
ft tensile strength fy yield stress ft/fy hardening ratio
eu ultimate strain (under maximum loading).
Bars and wires for RC can also be produced by cold drawing. In this case the relative curves r–edo not show the horizontal plastic phase any more. Even the ultimate strain is reduced significantly. As a clear yield limit is not measurable experimentally, the value off0.2is assumed as reference stress for strength calcu- lations, equal to the stress corresponding to the residual elongation of 0.2% after unloading (see Fig.1.24b).
With reference to the ultimate strain of the material, threeductility classesare distinguished:
• low ductility‘A’
witheuk2:5%ðft=fyÞk1:05
• normal ductility‘B’
witheuk5:0%ðft=fyÞk1:08
• high ductility‘C’
witheuk7:5%ðft=fyÞk1:15: Fig. 1.24 Stress–strain
curves of reinforcing steel
For the calculations offatigue strengththe characteristic value of the limit range Dris to be provided, which leads to brittle rupture after 2106loading cycles. Such limit is measured experimentally applying to the specimen a tension force varying cyclically from a maximum ofrmax= 0.6fvkto a minimumrmin¼rmaxDr.
Technological characteristicsof reinforcement basically consist of the degree of bond allowed by the surfacefinish of the product, of its bendability and weldability of the material itself.
Aboutbondthree types offinishes are distinguished:
• smooth‘E’with low bond
• indented‘I’with small teeth
• ribbed‘R’with improved bond.
In practice, apart from particular uses, onlyribbed barsare used in reinforced concrete structures.
Bendabilityis assessed with a bending test to guarantee the possibility of shaping the bar without evident damage.
Welding can be used to connect the bars, without the risk of embrittlement of the material or decay of its mechanical characteristics, only for steel of proven weldability.
In reinforced pre-stressed concrete, high-strength hardened steel is used, such as cold-deformed bars(e.g. twisted) andcold-drawn wires. Thermally treated products are also used such astempered wires, obtained with rapid cooling. The relativer–e diagrams are shown in Fig.1.25. The classification done with respect to the mechanical characteristics of steel is based on the following parameters:
Fig. 1.25 Stress–strain curves of pre-stressing steel
fpt tensile strength
f0.1 stress at 0.1% residual elongation at unloading for wires f0.1/fpt hardening (inverse) ratio
eptepu ultimate rupture strain,
where sometimes in catalogues for strands f0.1 is substituted by fp1 at 1% of elongation under loading. For that category of products, which is quite homoge- neous, the two values are not much different.
High-strength hardened steel has always low ductility, witheuk 3.5%, (f0.1/ fpt)k 0.8 and it is not weldable. Among the technological properties of these products for prestressed concreterelaxation and susceptibility to stress corrosion are also mentioned. Further discussion will be presented in Chap.10.
It is recalled that steel density is equal to 7850 kg/m3; its coefficient of thermal expansion is 1.010−5°C−1, close to one of the concretes. Thanks to the fact that these coefficients are very similar for steel and concrete, no self-induced stresses developed in the composite material.
Products for reinforced concrete reinforcement are as follows:
• bars
• wires
• welded mesh
• lattice girders.
The last two are obtained from the wire, by electric welding carried out in factory and delivered in plane panels thewelded meshand in straight truss beams thelattice girders. No further information is given about lattice girders, which use the same reinforcement as the welded mesh: for them one can refer to the cata- logues for commercial shapes and sizes.
Among the many different products for RC available in the different countries, one can refer to those made of the following three types of steel named B450A, B450B and B450C, respectively, with low, medium and high ductility. They are produced in diameters from 6 to 40 mm. The nominal characteristic value of yield strength, expressed in MPa, is indicated after the symbolB. All these types of steel (see Fig.1.26) are weldable and bendable.
Tendons for P.C. consist of
• bars
• wires
• strands.
In particular, stands can be obtained by combining 2 or 3 wires of small diameter (2.43.5 mm) twisted around themselves, or 7 wires of even bigger diameter (6 mm), with a straight central wire and six peripheral wires wrapped around it in spiral. The equivalent elastic modulus, deduced from tensile tests on pieces of strands, is a little lower than one of the single wires (Ep195,000 MPa) because of the geometrical effect of their straightening under loading.
Among the great variety of available products for pre-stressing reinforcement only the most commonly used types are listed below (see Fig.1.26):
• bars Fe1030 and Fe1230 in diameters from 20 to 50 mm;
• wire Fe1570, Fe1670, Fe1770, Fe1860 in diameters from 4 to 10 mm;
• strands 3W Fe1860, Fe1960, Fe2060 in diameters from 5.2 to 7.5 mm;
• strands 7W Fe1770, Fe1820, Fe1860 in diameters from 7.0 to 18.0 mm.
The type of steel is named with the symbol Fe followed by the characteristic tensile strength expressed in MPa. The class 1, 2 or 3 of relaxation of the product also has to be specified, according to what presented in Chap.10. Acompactedtype of 7-wire strands exists and it is indicated with the letter‘C’, made with trapezoidal wires instead of round, which do not leave voids inside the strand. The different strands are distinguished with the symbols 3W and 7W that indicate the number of elementary wires.
The European classification contemplates the following:
• Smooth‘E’or ribbed‘R’bars steel type Fe 1030 and Fe 1230 with diameters between 20 and 50 mm
• Smooth‘E’or indented ‘I’wires
steel type Fe 1570, Fe 1670, Fe 1770 and Fe 1860 with diameters between 4 and 10 mm
• Strands‘3W’(3-wires)
ε σ
0,1 N/mm2
0,2 5 10 15%
Fe1860
Fe1670
Fe1230
Fe1030
B500
FeB44k (B450) 500 1000 1500 Fig. 1.26 Synoptic
representation of different stress–strain curves
steel type Fe 1860, Fe 1960 and Fe 2060 with nominal diameters between 5.2 and 7.5 mm
• Strands‘7W’(7-wires)
steel type Fe 1770, Fe 1860 and Fe 2060
with nominal diameters between 7.0 and 18.0 mm
• Strands‘7WC’(7-wires compacted) steel type Fe 1770, Fe 1820 and Fe 1860
with nominal diameters between 12.7 and 18.0 mm.
The data relative to the type of products for R.C. and P.C. mentioned above are reported in Tables1.7,1.8,1.9,1.10,1.11,1.12,1.13,1.14,1.15,1.16,1.17,1.18, 1.19,1.20,1.21.
It is to be noted that the quality of steel of the current industrial production is with good approximation constant and reliable, with a relative dispersion of rep- resentative values much smaller than what can be expected for concrete.