# 3107F.2.5 Concrete Piles

The capacity of concrete piles is based on permissible concrete and steel strains corresponding to the desired performance criteria.

Different values may apply for plastic hinges forming at in-ground and pile-top locations. These procedures are applicable to circular, octagonal, rectangular and square pile cross sections.

Stability considerations are important to pier-type structures. The moment-axial load interaction shall consider effects of high slenderness ratios (kl/r). An additional bending moment due to axial load eccentricity shall be incorporated unless:

(7-4)

**where:**

e = eccentricity of axial load

h = width of pile in considered direction

The plastic hinge length is required to convert the moment-curvature relationship into a moment-plastic rotation relationship for the nonlinear pushover analysis.

The pile's plastic hinge length, L_{p} (above ground) for reinforced concrete piles, when the plastic hinge forms against a supporting member is:

(7-5)

L = distance from the critical section of the plastic hinge to the point of contraflexure

d_{b}= diameter of the longitudinal reinforcement or dowel, whichever is used to develop the connection

f_{ye} = design yield strength of longitudinal reinforcement or dowel, whichever is used to develop the connection (ksi)

If a large reduction in moment capacity occurs due to spalling, then the plastic hinge length shall be:

(7-6)

The plastic hinge length, L_{p} (above ground), for pre-stressed concrete piles may also be computed from Table 31F-7-4 for permitted pile-to-deck connections as described in ASCE/COPRI 61 [7.5].

When the plastic hinge forms in-ground, the plastic hinge length may be determined using Equation (7-7) [7.5]:

(7-7)

**where:**

D = pile diameter or least cross-sectional dimension

CONNECTION TYPE | L_{p} AT DECK (in.) |

Pile Buildup | 0.15f_{ye}d_{b} ≤ L_{p} ≤ 0.30f_{ye}d_{b} |

Extended Strand | 0.20f_{pye}d_{st} |

Embedded Pile | 0.5D |

Dowelled | 0.25f_{ye}d_{b} |

Hollow Dowelled | 0.20f_{ye}d_{b} |

External Confinement | 0.30f_{ye}d_{b} |

Isolated Interface | 0.25f_{ye}d_{b} |

d_{b} = diameter of the prestressing strand or dowel, whichever is used to develop the connection (in.)

f_{ye} = design yield strength of prestressing strand or dowel, as appropriate (ksi)

D = pile diameter or least cross-sectional dimension

d_{st} = diameter of the prestressing strand (in.)

f_{pye} = design yield strength of prestressing strand (ksi)

The plastic rotation is:

(7-8)

**where:**

L_{p} = plastic hinge length

Φ_{p} = plastic curvature

Φ_{m} = maximum curvature

Φ_{y} = yield curvature

The maximum curvature, Φ_{m} shall be determined by the concrete or steel strain limit state at the prescribed performance level, whichever comes first.

Alternatively, the maximum curvature, Φ_{m} may be calculated as:

(7-9)

**where:**

ε_{cm}= maximum limiting compression strain for the prescribed performance level (Table 31F-7-5)

c_{u} = neutral-axis depth, at ultimate strength of section

COMPONENT STRAIN | LEVEL 1 | LEVEL 2 |

MCCS Pile/deck hinge | ε_{c} ≤ 0.004 | ε_{c} ≤ 0.025 |

MCCS In-ground hinge | ε_{c} ≤ 0.004 | ε_{c} ≤ 0.008 |

MRSTS Pile/deck hinge | ε_{s} ≤ 0.01 | ε_{s} ≤ 0.05 |

MRSTS In-ground hinge | ε_{s} ≤ 0.01 | ε_{s} ≤ 0.025 |

MPSTS In-ground hinge | εp ≤ 0.005 (incremental) | εp ≤ 0.025 (total strain) |

MCCS = Maximum Concrete Compression Strain, ε_{c}

MRSTS = Maximum Reinforcing Steel Tension Strain, ε_{s}

MPSTS = Maximum Prestressing Steel Tension Strain, ε_{p}

Either Method A or B may be used for idealization of the moment-curvature curve.

For Method A, the yield curvature, Φ_{y} is the curvature at the intersection of the secant stiffness, EI_{c}, through first yield and the nominal strength, (ε_{c} = 0.004).

(7-10)

For Method B, the elastic portion of the idealized moment-curvature curve is the same as in Method A (see Section 3107F.2.5.4.1). However, the idealized plastic moment capacity, M_{p}, and the yield curvature, Φ_{y}, is obtained by balancing the areas between the actual and the idealized moment-curvature curves beyond the first yield point (see Figure 31F-7-5). Method B applies to moment-curvature curves that do not experience reduction in section moment capacity.

Strain values computed in the nonlinear push-over analysis shall be compared to the following limits.

Ultimate concrete compressive strain [7.1]:

(7-12)

**where:**

ρ_{s} = effective volume ratio of confining steel

f_{yh} = yield stress of confining steel

ε_{sm} = strain at peak stress of confining reinforcement, 0.15 for grade 40, 0.10 for grade 60

f '_{cc} = confined strength of concrete approximated by 1.5 f '_{c}

The maximum allowable concrete strains may not exceed the ultimate values defined in Section 3107F.2.5.5. The following limiting values (Table 31F-7-5) apply for each performance level for both existing and new structures. The "Level 1 or 2" refer to the seismic performance criteria (see Section 3104F.2.1).

For all non-seismic loading combinations, concrete components shall be designed in accordance with the ACI 318 [7.7] requirements.

Note that for existing facilities, the pile/deck hinge may be controlled by the capacity of the dowel reinforcement in accordance with Section 3107F.2.7.

If expected lower bound of material strength Section 3107F.2.1.1 Equations (7-2a, 7-2b, 7-2c) are used in obtaining the nominal shear strength, a new nonlinear analysis utilizing the upper bound estimate of material strength Section 3107F.2.1.1 Equations (7-3a, 7-3b, 7-3c) shall be used to obtain the plastic hinge shear demand. An alternative conservative approach is to multiply the maximum shear demand, V_{max} from the original analysis by 1.4 (Section 8.16.4.4.2 of ATC-32 [7.8]):

(7-13)

If moment curvature analysis that takes into account strain-hardening, an uncertainty factor of 1.25 may be used:

(7-14)

Shear capacity shall be based on nominal material strengths, and reduction factors according to ACI 318 [7.7].

As an alternative, the method of Kowalski and Priestley [7.9] may be used. Their method is based on a three-parameter model with separate contributions to shear strength from concrete (V_{c}), transverse reinforcement (V_{s}), and axial load (V_{p}) to obtain nominal shear strength (V_{n}):

(7-15)

A shear strength reduction factor of 0.85 shall be applied to the nominal strength, V_{n}, to determine the design shear strength. Therefore:

(7-16)

The equations to determine V_{c}, V_{s} and V_{p} are:

(7-17)

**where:**

k = factor dependent on the curvature ductility , within the plastic hinge region, from Figure 31F-7-6. For regions greater than 2D_{p}(see Equation 7-18) from the plastic hinge location, the strength can be based on μ_{Φ} = 1.0 (see Ferritto et. al. [7.2]).

f'_{c} = concrete compressive strength

A_{e} = 0.8A_{g} is the effective shear area

Circular spirals or hoops [7.2]:

(7-18)

**where:**

A_{sp} = spiral or hoop cross section area

f_{yh} = yield strength of transverse or hoop reinforcement

D_{p} = pile diameter or gross depth (in case of a rectangular pile with spiral confinement)

c = depth from extreme compression fiber to neutral axis (N.A.) at flexural strength (see Figure 31F-7-7)

c_{0} = distance from concrete cover to center of hoop or spiral (see Figure 31F-7-7)

θ = angle of critical crack to the pile axis (see Figure 31F-7-7) taken as 30° for existing structures, and 35° for new design

s = spacing of hoops or spiral along the pile axis

Rectangular hoops or spirals [7.2]:

(7-19)

**where:**

A_{h} =total area of transverse reinforcement, parallel to direction of applied shear cut by an inclined shear crack

Shear strength from axial mechanism, V_{p} (see Figure 31F-7-8):

(7-20)

**where:**

N_{u} = external axial compression on pile including seismic load. Compression is taken as positive; tension as negative

F_{p} = prestress compressive force in pile

α = angle between line joining centers of flexural compression in the deck/pile and in-ground hinges, and the pile axis

Φ = 1.0 for existing structures, and 0.85 for new design

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