Columns with Spiral and Circular Hoop Reinforcement

Confined Concrete

4.3 Mechanism of Concrete Confinement

4.3.2 Columns with Spiral and Circular Hoop Reinforcement

In the preceding section we observed that concrete could be effectively confined by using closely spaced spiral reinforcement. This section develops algebraic expressions for concrete confined by steel spiral or circular hoop reinforcement.

Confinement Stress

Figure 4.3 illustrates the column geometry. The concrete core dimension measured to the outside of the spiral or hoop reinforcement is D.¹ The core is confined by spiral or circular hoop reinforcement having cross-sectional area A_sp and pitch or spacing s. Spacing s is small relative to the column diameter D.² The cross section also contains longitudinal reinforcement of total cross-sectional area A_st.

FIGURE 4.3 Concrete column confined by circular hoop or spiral reinforcement: (a) elevation;

(b) section A-A; (c) free body diagram of a slice of the column core of thickness s.

Dilation under the action of axial compression results in spiral steel stress f_s and opposing confining stresses f₂ = f₃. Force equilibrium requires

The ratio of the volume of spiral reinforcement to the total volume of core confined by the spiral, ρ_s, is defined as

Solving Eq. (4.1) for f₂ and using Eq. (4.2) results in

The confining stresses f₂ = f₃ defined by Eq. (4.3) will be used to determine the compressive strength of spiral or circular hoop-confined concrete.

Before addressing compressive strength, however, two additional aspects

require consideration. These are the effects of wide spiral pitch (or circular hoop spacing) and the limits of the confinement reinforcement stress f_s. Spiral Spacing, Arching Action, and Confinement Effectiveness Most building codes require that spiral reinforcement be closely spaced, such that the confining pressure of the spiral can be considered essentially uniform. For completeness, however, we also consider the case of wider spacing of spiral or circular hoop reinforcement. Although spirals and circular hoops have different configuration, and this difference results in slightly different behavior, the effects are not sufficiently different to warrant a separate consideration here. The discussion here emphasizes the simpler geometry of circular hoops.

As illustrated in Figure 4.4, a circular hoop produces a concentrated ring of confinement stresses acting radially inward at the level of each hoop.

Away from the hoops, the circumference of the core is a free surface that is not confined by reinforcement. Within the core, the concentrated ring pressure spreads longitudinally and radially until the internal core pressure is essentially uniform. It is this internal uniform pressure that is defined by Eq. (4.3).

FIGURE 4.4 Confinement action in circular hoop-confined column: (a) cross section at level of hoop showing radial pressure from hoop; (b) elevation through diameter showing spread of internal stresses, arching action, and effectively confined core dimension.

The behavior described above can be viewed in an alternative way. As a column core is loaded axially, dilation of the core concrete presses outward against the confinement reinforcement. Concrete particles located near the hoop reinforcement are well supported by the hoops, whereas

particles located away from the hoops do not find a solid reaction and spall away. As this action continues a series of arches develops internally, spanning vertically from one ring to another. This behavior is known as arching action. The wider the longitudinal spacing s, the deeper the arch extends into the concrete core, and the lower is the confinement effectiveness. We sometimes refer to the effectively confined core area as the minimum cross-sectional area of the confined core as defined by the arching action.

For small values of the ratio s/D, as is usually the case, arching action in a spiral-confined column does not reduce the confinement effectiveness significantly. As s/D increases, however, an adjustment for confinement effectiveness should be made. Various approaches have been recommended in the literature (Iyengar et al., 1970; Ahmad and Shah, 1982; Martinez et al., 1984; Mander et al., 1988a). Iyengar et al. (1970) observed that hoops were practically ineffective when the spacing was equal to the core diameter, and proposed that confinement effectiveness varies linearly from a maximum value for zero spacing to zero for hoop spacing equal to the core diameter. Based on this recommendation, we can define a confinement effectiveness factor, k_e, defined by

Although arching action refers strictly to a reduction in the effective core area, a more convenient and widely used alternative is to consider the full core area to be effective and instead reduce the confinement stress using factor k_e, resulting in effective confinement stress f_2e defined by

We will use this effective confinement stress to define strength of the confined core.

Stress in the Confinement Reinforcement

Thus far we have expressed the confinement stress in terms of the stress f_s in the transverse reinforcement. The amount of transverse straining that occurs when a confined core is compressed is typically sufficient to produce yielding of the confinement reinforcement (Figure 4.2). In some cases, however, yielding of the confinement reinforcement is not observed

(Sheikh and Uzumeri, 1980; Ahmad and Shah, 1982; Martinez et al., 1984;

Bing et al., 2001; Paultre and Légeron, 2008). This is especially a consideration where high-strength confinement reinforcement is used.

Razvi and Saatcioglu (1999) concluded that the stress developed in the transverse reinforcement depends on the concrete strength and on the volumetric ratio and configuration of the confining reinforcement. For confinement reinforcement having f_yt up to 200,000 psi (1400 MPa) (the maximum value in the tests considered), they proposed

Except where high-strength reinforcement is used, the stress f_s given by Eq.

(4.6) will be equal to the yield stress f_yt. Strength of the Confined Core

From Section 3.6.3, we can recall the relation between strength of confined concrete and confining pressure, that is

Equation (4.7) introduces the term C to account for differences between in-place concrete strength and standard cylinder compressive strength . For large-scale columns common in building construction, Richart and Brown (1934) recommended C = 0.85. This value is widely adopted in building codes, including ACI 318 (2014). CSA (2004) adjusts the value as a function of concrete compressive strength, specifying

in which λ_c = 0.00001 (psi) or 0.0015 (MPa).

Combining Eqs. (4.5) and (4.7) results in

Richart et al. demonstrated the applicability of Eq. (4.8) to spirally

confined cylinders (Richart et al., 1929) and large-scale columns (Richart et al., 1934) for different stresses f_s that developed as loading progressed.

Figure 4.5 compares results at the ultimate load for the smaller cylinder tests, for which the coefficient C has been taken equal to 1.0.

FIGURE 4.5 Comparison of test data with Eq. (4.8). Data points represent averages of multiple tests at the ultimate loading point. (After Richart et al., 1929, courtesy of the University of Illinois at Urbana–Champaign.)

Several researchers have noted that the coefficient 4.1 in Eq. (4.7) underestimates the confined concrete strength for lower values of the confinement stress (Richart et al., 1928; Ahmad and Shah, 1982; Sheikh and Uzumeri, 1982; Mander et al., 1988a). Figure 4.6 presents one model that recognizes this effect (after Mander et al., 1988a). In this figure, f_2e and f_3e are the effective confining stresses in the 2 and 3 directions, with f_2e ≥ f_3e, C is a constant to account for differences between in-place concrete strength

and standard cylinder compressive strength (commonly taken as 0.85 for columns, 1.0 otherwise), and is the confined concrete strength. The failure surface for biaxial loading (f_3e = 0) is the leftmost curve. The curves moving toward the right are for increasing f_3e, with the rightmost curve corresponding to f_2e = f_3e. As an example, for the dash-dot lines intersect at As another example, for

and the dashed lines intersect at

Use of this chart to determine confined concrete compressive strength is acceptable as an alternative to Eq. (4.8).

FIGURE 4.6 Confined concrete strength as function of effective confinement stresses. (After Mander et al., 1988a.)

Example 4.1. A cylindrical column has diameter of 24 in (610 mm), 8 No. 9 (29) longitudinal bars, and No. 3 (10) spiral reinforcement at pitch of 1.75 in (44 mm). Strength of concrete measured in companion cylinders is 5000 psi (34 MPa) and reinforcement is A706 Grade 60 (420). Determine the strength of the confined core.

Solution

Assuming concrete cover of 1.5 in (38 mm) over the spiral, the core diameter is 21 in (533 mm), resulting in spiral reinforcement ratio ρ_s = (4) (0.11 in²)/(21 in)(1.75 in) = 0.012. Confinement effectiveness factor is k_e = (1 – 1.75 in/21 in) = 0.92. Expected yield strength of A706 Grade 60 reinforcement is 1.15 × 60 ksi = 69 ksi (476 MPa). Using Eq. (4.8),

confined concrete strength is

Alternatively, we can use Figure 4.6. By this approach, from Eq. (4.5) we have f_2e = (0.92) (0.012)(69,000 ksi)/2 = 380 psi (2.6 MPa). Thus, From Figure 4.6, we can read Therefore, by this method,