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// CODE SNIPPET

3107F.2.5 Concrete Piles

Los Angeles Building Code > 31F [SLC] Marine Oil Terminals > 3107F Structural Analysis and Design of Components > 3107F.2 Concrete Deck With Concrete or Steel Piles > 3107F.2.5 Concrete Piles
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3107F.2.5.1 General

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.

3107F.2.5.2 Stability

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

3107F.2.5.3 Plastic Hinge Length

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:

(7-5)

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:

(7-6)

The plastic hinge length, Lp (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

TABLE 31F-7-4
PLASTIC HINGE LENGTH FOR PRESTRESSED CONCRETE PILES [7.5]
CONNECTION TYPELp AT DECK (in.)
Pile Buildup0.15fyedb ≤ Lp ≤ 0.30fyedb
Extended Strand0.20fpyedst
Embedded Pile0.5D
Dowelled0.25fyedb
Hollow Dowelled0.20fyedb
External Confinement0.30fyedb
Isolated Interface0.25fyedb

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)

3107F.2.5.4 Plastic Rotation

The plastic rotation is:

(7-8)

where:

Lp = plastic hinge length

Φp = plastic curvature

Φm = maximum curvature

Φy = yield curvature

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

Alternatively, the maximum curvature, Φm may be calculated as:

(7-9)

where:

εcm= maximum limiting compression strain for the prescribed performance level (Table 31F-7-5)

cu = neutral-axis depth, at ultimate strength of section

TABLE 31F-7-5
LIMITS OF STRAIN
COMPONENT STRAINLEVEL 1LEVEL 2
MCCS Pile/deck hingeεc ≤ 0.004εc ≤ 0.025
MCCS In-ground hingeεc ≤ 0.004εc ≤ 0.008
MRSTS Pile/deck hingeεs ≤ 0.01εs ≤ 0.05
MRSTS In-ground hingeεs ≤ 0.01εs ≤ 0.025
MPSTS In-ground hingeεp ≤ 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.

3107F.2.5.4.1 Method A

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).

(7-10)

FIGURE 31F-7-4
METHOD A - MOMENT CURVATURE ANALYSIS

3107F.2.5.4.2 Method B

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, 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.

FIGURE 31F-7-5
METHOD B — MOMENT CURVATURE ANALYSIS [7.6]

3107F.2.5.5 Ultimate Concrete and Steel Flexural Strains

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

3107F.2.5.5.1 Unconfined Concrete Piles:

An unconfined concrete pile is defined as a pile having no confinement steel or one in which the spacing of the confinement steel exceeds 12 inches.

Ultimate concrete compressive strain:

(7-11)

3107F.2.5.5.2 Confined Concrete Piles:

Ultimate concrete compressive strain [7.1]:

(7-12)

where:

ρs = effective volume ratio of confining steel

fyh = yield stress of confining steel

εsm = 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

3107F.2.5.6 Component Acceptance/Damage Criteria

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.

3107F.2.5.7 Shear Design

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 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 (Vc), transverse reinforcement (Vs), and axial load (Vp) to obtain nominal shear strength (Vn):

(7-15)

A shear strength reduction factor of 0.85 shall be applied to the nominal strength, Vn, to determine the design shear strength. Therefore:

(7-16)

The equations to determine Vc, Vs and Vp 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 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]).

f'c = concrete compressive strength

Ae = 0.8Ag is the effective shear area

Circular spirals or hoops [7.2]:

(7-18)

where:

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)

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

c0 = 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

FIGURE 31F-7-6
CONCRETE SHEAR MECHANISM (from Fig. 3-30 of [7.2])
FIGURE 31F-7-7
TRANSVERSE SHEAR MECHANISM

Rectangular hoops or spirals [7.2]:

(7-19)

where:

Ah =total area of transverse reinforcement, parallel to direction of applied shear cut by an inclined shear crack

Shear strength from axial mechanism, Vp (see Figure 31F-7-8):

(7-20)

where:

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

FIGURE 31F-7-8
AXIAL FORCE SHEAR MECHANISM

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