Steel Reinforcement
2.3 Steel Reinforcement under Monotonic Loading
intended for applications where controlled tensile properties,
restrictions on chemical composition to enhance weldability, or both, are required. The specification requires that the bars be marked with the letter W for type of steel. Note that A706 Grade 80 (550)
reinforcement is permitted to resist flexural or axial forces in special moment frames or special structural walls only if tests and analytical studies are presented in support of its use.
• For the design of transverse reinforcement providing concrete
confinement or lateral support of longitudinal bars, the maximum value of fy permitted in design calculations is 100,000 psi (690 MPa). For the design of transverse reinforcement providing shear strength,
however, the maximum value of fyt permitted in design calculations is either 60,000 psi (420 MPa) or 80,000 psi (550 MPa), depending on the reinforcement type.
• Welded wire reinforcement is permitted as transverse reinforcement in special seismic systems where the welded wire wraps around the member. It is not permitted to rely on the weld to support longitudinal bars or confine concrete. This is because the specification for welds does not require that the weld be capable of developing the strength of the welded wire, with the result that brittle failures can occur.
Welding of reinforcing bars should be done only in accordance with approved procedures, and generally is not preferred. In U.S. practice, welding of reinforcing bars is to conform to AWS D1.4-11 (2011). Type and location of welded splices and other required welding of reinforcing bars are to be indicated in the construction documents. Except for A706 bars, bar specifications should be supplemented to require a report of material properties necessary to conform to the requirements in AWS D1.4. A706 bars have chemical content specially suited for welding. Cross-welding of bars, or welding of attachments to structural bars, can result in embrittlement and should be avoided.
2.3 Steel Reinforcement under Monotonic
The stress–strain relation of steel reinforcement is measured in a standardized tension test of a full-size bar. The stress–strain relation is in terms of engineering stress and engineering strain, where engineering stress is the force divided by the original cross-sectional area and engineering strain is the change in length divided by the original length of a gauge length of the test specimen.
Figure 2.4 shows a typical stress–strain relation for nonprestressed steel and defines several parameters and behavior ranges. The steel responds linearly at first, yields at an upper yield point, then responds at a lower yield stress along a yield plateau. In some steels there is no yield plateau.
Yielding is followed by a strain-hardening region. Strain-hardening is an important characteristic to induce yielding to spread along the length of the bar and produce ductile response. At the peak of the stress–strain relation, necking occurs, causing localized reduction in the cross-sectional area and leading to failure in the necked region. A gauge length including the necked region will show continued straining as the bar is elongated to failure, whereas a gauge length outside the necked region will show unloading with reduced strain.
FIGURE 2.4 Monotonic stress–strain relation for mild steel in tension.
Elongation after rupture generally is measured along an 8-in (200-mm) gauge length including the fracture zone. Thus, elongation includes the plastic strain including the strain in the necked region minus the recovered elastic strain after unloading. The strain εsu corresponding to the peak stress fsu is sometimes referred to as the uniform elongation or uniform strain limit, as this is the largest deformation in the test bar for which the tensile strains are uniform throughout the length. It marks the onset of necking in a bar. It is a useful property for design of earthquake-resistant buildings because it is the maximum strain that should be relied on in a location of yielding. This property, however, is not generally reported.
2.3.2 Tensile Properties of Steel Reinforcement
Figure 2.5 plots characteristic stress–strain relations for A615 Grades 40, 60, and 75 (280, 420, and 520), A706 Grade 60 (420), and A1035 Grade 100 (690) reinforcement. The salient properties are as follows:
• The initial modulus Es is approximately 29,000 ksi (200,000 MPa).
• The grade number refers to the minimum yield strength in ksi (MPa).
ASTM also specifies minimum tensile strengths. See Table 2.3. For A706 bars, the actual yield strength must not exceed the minimum value by more than 18 ksi (124 MPa), and the actual tensile strength must be at least 1.25 times the actual yield strength.
• Producers generally aim for an actual yield strength higher than the minimum value so that, given variations in properties, there is only a small chance of the actual yield strength falling below the minimum value. Bournonville et al. (2004) report data on actual bar properties from mill tests (Table 2.6).
• The length of the yield plateau is not specified in the ASTM specifications and is variable. The general trend is that bars with lower strength have longer yield plateaus, and bars with higher strengths may or may not have yield plateaus. A706 Grade 60 (420) bars tend to have longer yield plateaus than A615 Grade 60 (420) bars.
TABLE 2.6 Mean and Coefficient of Variation (CoV) of Reinforcement Mechanical Properties (after Bournonville et al., 2004)
• Initial strain-hardening modulus tends to be around 1000 ksi (7000 MPa), although the value is not specified in the ASTM specifications and is variable.
• ASTM specifies minimum required percentage elongations in an 8-in (200-mm) gauge length including the fractured section. Table 2.3
summarizes required elongations, and Table 2.6 summarizes measured elongation statistics from mill tests.
FIGURE 2.5 Characteristic engineering stress versus engineering strain relations for A615, A706, and A1035 deformed bars in tension. Strengths and elongations shown for A615 and A706 based on mean values from Bournonville et al. (2004). Stress–strain relation for A1035 is for MMFX-2 steel, with data from MMFX (2009) except elongation is modified based on observed values.
The monotonic stress–strain behavior of A615 and A706 bars in the strain-hardening range can be approximated by (Mander et al., 1984)
in which
2.3.3 Compressive Properties of Steel Reinforcing Bars
When reinforcing bars are loaded in tension, the cross section decreases because of the Poisson effect. In contrast, the cross section increases under compressive loading. As a result, the relations between engineering stress
and strain are different in tension and compression. Additionally, bars in compression may buckle, causing further deviations in behavior. This section will address the differences in tensile and compressive behavior associated with the Poisson effect. The problem of reinforcing bar buckling is considered in detail in Chapter 5.
The Poisson effect can be evaluated by assuming that the volume of a reinforcing bar is constant as it is strained beyond the yield point.
Conservation of volume for small strains requires a Poisson’s ratio of ν = 0.5. For this value of Poisson’s ratio, the cross-sectional area varies as where the longitudinal strain ε1 is taken positive in tension.
Thus, the ratio of cross-sectional areas for compressive loading and tensile loading is At strain εl = 0.05, this area ratio has value 1.10, suggesting 10% higher engineering stress in compression than in tension.
To demonstrate this effect, consider the stress–strain data in Figure 2.6.
The engineering stress versus engineering strain relations were measured in tension and compression tests on nominally identical reinforcing bar specimens (Dodd and Restrepo-Posada, 1995). As expected, the engineering stress–strain relations diverge with increasing strain.2 We can convert from engineering stress to true stress by dividing the engineering stress by the quantity.(1–0.5εl)2. The converted relations are nearly identical up to relatively large strain values (Figure 2.6). At very large strains, instability reduces the apparent resistance of the bar loaded in compression.
FIGURE 2.6 Stress–strain relations of reinforcing bars in tension and compression. (After Dodd and Restrepo-Posada, 1995.)
Although the Poisson effect is generally known, it is not taken into consideration in routine engineering calculations. Instead, it is more common to assume the tensile stress–strain relation represents behavior in both tension and compression. Effects of reinforcement buckling in compression, however, should be taken into consideration. See Chapter 5 for additional discussion.
2.3.4 Strain Rate Effect
Strain rate increases both the yield and ultimate strengths of reinforcing bars (Figure 2.7a). Malvar (1998) presents dynamic increase factors (ratios of apparent strength for dynamic loading to strength for near-static loading) (Figure 2.7b). As shown, the strain-rate effect is higher for yield strength than for ultimate strength, and higher for lower-strength reinforcement than for higher-strength reinforcement. The dynamic effect is greater for the upper yield point than for the lower yield point.
FIGURE 2.7 Strain-rate effect on tensile properties of reinforcing bars: (a) stress–strain relations (After Manjoine, 1944, with permission of ASME); (b) dynamic increase factors for upper yield and ultimate strengths for various reinforcement grades (After Malvar, 1998, with permission of
ASCE).
ASTM A370 describes test requirements for reinforcement. It permits strain rate as high as 0.001/s through the yield point, though it is more common for mill tests to follow the alternative procedure in which the rate is around 0.00006/s. The Concrete Reinforcing Steel Institute, Materials Properties Committee3 recommends a rate around 0.00003/s. Based on the data in Figure 2.7b, at these latter rates the measured strength can be assumed to be equal to the static strength appropriate for dead loads and most live loads. A slightly higher apparent strength might result from earthquake loading rates. For example, considering a structure with vibration period of 1 s and Grade 60 bars reaching maximum strain 3εy. the strain rate would be approximately 3 × 0.002/0.25 s = 0.024/s. According to Figure 2.7b, the dynamic increase factors for this strain rate are 1.17 and 1.05 for yield and ultimate strengths, respectively. Though appreciable, the dynamic rate effect is not routinely considered for earthquake analysis or design.