3107F.2.5 Concrete Piles
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:
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, Lp (above ground) for reinforced concrete piles, when the plastic hinge forms against a supporting member is:
L = distance from the critical section of the plastic hinge to the point of contraflexure
db= diameter of the longitudinal reinforcement or dowel, whichever is used to develop the connection
fye = 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:
When the plastic hinge forms in-ground, the plastic hinge length may be determined using Equation (7-7) [7.5]:
D = pile diameter or least cross-sectional dimension
|CONNECTION TYPE||Lp AT DECK (in.)|
|Pile Buildup||0.15fyedb ≤ Lp ≤ 0.30fyedb|
db = diameter of the prestressing strand or dowel, whichever is used to develop the connection (in.)
fye = design yield strength of prestressing strand or dowel, as appropriate (ksi)
D = pile diameter or least cross-sectional dimension
dst = diameter of the prestressing strand (in.)
fpye = design yield strength of prestressing strand (ksi)
The plastic rotation is:
Lp = plastic hinge length
Φp = plastic curvature
Φm = maximum curvature
Φy = yield curvature
Alternatively, the maximum curvature, Φm may be calculated as:
εcm= maximum limiting compression strain for the prescribed performance level (Table 31F-7-5)
cu = neutral-axis depth, at ultimate strength of section
|COMPONENT STRAIN||LEVEL 1||LEVEL 2|
|MCCS Pile/deck hinge||εc ≤ 0.004||εc ≤ 0.025|
|MCCS In-ground hinge||εc ≤ 0.004||εc ≤ 0.008|
|MRSTS Pile/deck hinge||εs ≤ 0.01||εs ≤ 0.05|
|MRSTS In-ground hinge||εs ≤ 0.01||εs ≤ 0.025|
|MPSTS In-ground hinge||εp ≤ 0.005 (incremental)||εp ≤ 0.025 (total strain)|
MCCS = Maximum Concrete Compression Strain, εc
MRSTS = Maximum Reinforcing Steel Tension Strain, εs
MPSTS = Maximum Prestressing Steel Tension Strain, εp
Either Method A or B may be used for idealization of the moment-curvature curve.
For Method A, the yield curvature, Φy is the curvature at the intersection of the secant stiffness, EIc, through first yield and the nominal strength, (εc = 0.004).
For Method B, the elastic portion of the idealized moment-curvature curve is the same as in Method A (see Section 3107F.184.108.40.206). However, the idealized plastic moment capacity, Mp, and the yield curvature, Φy, 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.
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.
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, Vmax from the original analysis by 1.4 (Section 220.127.116.11.2 of ATC-32 [7.8]):
If moment curvature analysis that takes into account strain-hardening, an uncertainty factor of 1.25 may be used:
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 (Vc), transverse reinforcement (Vs), and axial load (Vp) to obtain nominal shear strength (Vn):
The equations to determine Vc, Vs and Vp are:
k = factor dependent on the curvature ductility , within the plastic hinge region, from Figure 31F-7-6. For regions greater than 2Dp(see Equation 7-18) from the plastic hinge location, the strength can be based on μΦ = 1.0 (see Ferritto et. al. [7.2]).
Ae = 0.8Ag is the effective shear area
Circular spirals or hoops [7.2]:
Asp = spiral or hoop cross section area
fyh = yield strength of transverse or hoop reinforcement
Dp = pile diameter or gross depth (in case of a rectangular pile with spiral confinement)
s = spacing of hoops or spiral along the pile axis
Rectangular hoops or spirals [7.2]:
Ah =total area of transverse reinforcement, parallel to direction of applied shear cut by an inclined shear crack
Nu = external axial compression on pile including seismic load. Compression is taken as positive; tension as negative
Fp = 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