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3107F.1 General
3107F.1.1 Purpose
This section establishes the minimum performance standards for structural components. Evaluation procedures for seismic performance, strength and deformation characteristics of concrete, steel and timber components are prescribed herein. Analytical procedures for structural systems are presented in Section 3104F.
3107F.1.2 Applicability
This section addresses MOTs constructed using the following structural components:
  1. Reinforced concrete decks supported by batter and/or vertical concrete piles
  2. Reinforced concrete decks supported by batter and/or vertical steel piles, including pipe piles filled with concrete
  3. Reinforced concrete decks supported by batter and/or vertical timber piles
  4. Timber decks supported by batter or vertical timber, concrete or steel pipe piles
  5. Retaining structures constructed of steel, concrete sheet piles or reinforced concrete
3107F.2 Concrete Deck With Concrete or Steel Piles
3107F.2.1 Component Strength
The following parameters shall be established in order to compute the component strength:
  1. Specified concrete compressive strengths
  2. Concrete and steel modulus of elasticity
  3. Yield and tensile strength of mild reinforcing and prestressed steel and corresponding strains
  4. Confinement steel strength and corresponding strains
  5. Embedment length
  6. Concrete cover
  7. Yield and tensile strength of structural steel
  8. Ductility
In addition, for "existing" components, the following conditions shall be considered:
  1. Environmental effects, such as reinforcing steel corrosion, concrete spalling, cracking and chemical attack
  2. Fire damage
  3. Past and current loading effects, including overload, fatigue or fracture
  4. Earthquake damage
  5. Discontinuous components
  6. Construction deficiencies
3107F.2.1.1 Material Properties
Material properties of existing components, not determined from testing procedures, and of new components, shall be established using the following methodology.
The strength of structural components shall be evaluated based on the following values (Section 5.3 of [7.1] and pp. 3-73 and 3-74 of [7.2]):
Specified material strength shall be used for non ductile components (shear controlled), all mechanical, electrical and mooring equipment (attachments to the deck) and for all non seismic load combinations:
(7-1a)
(7-1b)
(7-1c)
In addition, these values (7-1a, 7-1b and 7-1c) may be used conservatively as alternatives to determine the nominal strength of ductile components (N).
Expected lower bound estimates of material strength shall be used for determination of moment-curvature relations and nominal strength of all ductile components:
(7-2a)
(7-2b)
(7-2c)
Upper bound estimates of material strength shall be used for the determination of moment-curvature relations, to obtain the feasible maximum demand on capacity protected members:
(7-3a)
(7-3b)
(7-3c)
where:
f'c = Specified compressive strength of concrete
fy = Specified yield strength of reinforcement or specified minimum yield stress steel
fp = Specified yield strength of prestress strands
"Capacity Design" (Section 5.3 of [7.1]) ensures that the strength at protected components (such as pile caps and decks), joints and actions (such as shear), is greater than the maximum feasible demand (over strength), based on realistic upper bound estimates of plastic hinge flexural strength. An additional series of nonlinear analyses using moment curvature characteristics of pile hinges may be required.
Alternatively, if a moment-curvature analysis is performed that takes into account the strain hardening of the steel, the demands used to evaluate the capacity protected components may be estimated by multiplying the moment-curvature values by 1.25.
Based on a historical review of the building materials used in the twentieth century, guidelines for tensile and yield properties of concrete reinforcing bars and the compressive strength of structural concrete have been established (see Tables 6-1 to 6-3 of FEMA 356 [7.3]. The values shown in these tables can be used as default properties, only if as-built information is not available and testing is not performed. The values in Tables 31F-7-1 and 31F-7-2, are adjusted according to equations (7-1) through (7-3).
3107F.2.1.2 Knowledge Factor (K)
Knowledge factor, k, shall be applied on a component basis.
The following information is required, at a minimum, for a component strength assessment:
  1. Original construction records, including drawings and specifications.
  2. A set of "as-built" drawings and/or sketches, documenting both gravity and lateral systems (Section 3102F.1.5) and any postconstruction modification data.
  3. A visual condition survey, for structural components including identification of the size, location and connections of these components.
  4. In the absence of material properties, values from limited in-situ testing or conservative estimates of material properties (Tables 31F-7-1 and 31F-7-2).
  5. Assessment of component conditions, from an in-situ evaluation, including any observable deterioration.
  6. Detailed geotechnical information, based on recent test data, including risk of liquefaction, lateral spreading and slope stability.
The knowledge factor, k, is 1.0 when comprehensive knowledge as specified above is utilized. Otherwise, the knowledge factor shall be 0.75 (see Table 2-1 of FEMA 356 [7.3]).

TABLE 31F-7-1
COMPRESSIVE STRENGTH OF STRUCTURAL CONCRETE (psi)1
TIME FRAMEPILINGBEAMSSLABS
1900-19192,500-3,0002,000-3,0001,500-3,000
1920-19493,000-4,0002,000-3,0002,000-3,000
1950-19654,000-5,0003,000-4,0003,000-4,000
1966-present5,000-6,0003,000-5,0003,000-5,000
  1. Concrete strengths are likely to be highly variable for an older structure.
TABLE 31F-7-2
TENSILE AND YIELD PROPERTIES OF REINFORCING BARS FOR VARIOUS ASTM SPECIFICATIONS AND PERIODS (after Table 6-2 of [7.3])
ASTMSTEEL TYPEYEAR RANGE3GRADESTRUCTURAL1INTERMEDIATE1HARD1
334050607075
Minimum Yield2 (psi)33,00040,00050,00060,00070,00075,000
Minimum Tensile2 (psi)55,00070,00080,00090,00095,000100,000
A15Billet1911-1966XXX
A16Rail41913-1966X
A61Rail41963-1966X
A160Axle1936-1964XXX
A160Axle1965-1966XXXX
A408Billet1957-1966XXX
A431Billet1959-1966X
A432Billet1959-1966X
A615Billet1968-1972XXX
A615Billet1974-1986XX
A615Billet1987-1997XXX
A616Rail41968-1997X
A617Axle1968-1997XX
A706Low-Alloy51974-1997X
A955Stainless1996-1997XXX
General Note: An entry "X" indicates that grade was available in those years.
  1. The terms structural, intermediate and hard became obsolete in 1968.
  2. Actual yield and tensile strengths may exceed minimum values.
  3. Untilabout 1920, a variety of proprietary reinforcing steels were used. Yield strengths are likely to be in the range from 33,000 psi to 55,000 psi, but higher values are possible. Plain and twisted square bars were sometimes used between 1900 and 1949.
  4. Rail bars should be marked with the letter "R. "
  5. ASTM steel is marked with the letter "W."
3107F.2.2 Component Stiffness
Stiffness that takes into account the stress and deformation levels experienced by the component shall be used. Nonlinear load-deformation relations shall be used to represent the component load-deformation response. However, in lieu of using nonlinear methods to establish the stiffness and moment curvature relation of structural components, the equations of Table 31F-7-3 may be used to approximate the effective elastic stiffness, EIe, for lateral analyses (see Section 3107F.5 for definition of symbols).

TABLE 31F-7-3
EFFECTIVE ELASTIC STIFFNESS
CONCRETE COMPONENTEIe/EIg
Reinforced Pile0.3 + N/(f'cAg)
Pile/Deck Dowel Connection10.3 + N/(f'cAg)
Prestressed Pile10.6 < EIe/EIg < 0.75
Steel Pile1.0
Concrete w/Steel Casing
Deck0.5
  1. The pile/deck connection and prestressed pile may also be approximated as one member with an average stiffness of 0.42 EIe/EIg (Ferritto et al, 1999 [7.2])
    N = is the axial load level.
    Es = Young's modulus for steel
    Is = Moment of inertia for steel section
    Ec = Young's modulus for concrete
    Ic = Moment of inertia for uncracked concrete section
3107F.2.3 Deformation Capacity of Flexural Members
Stress-strain models for confined and unconfined concrete, mild and prestressed steel presented in Section 3107F.2.4 shall be used to perform the moment-curvature analysis.
The stress-strain characteristics of steel piles shall be based on the actual steel properties. If as-built information is not available, the stress-strain relationship may be obtained per Section 3107F.2.4.2.
For concrete in-filled steel piles, the stress-strain model for confined concrete shall be in accordance with Section 3107F.2.4.1.
Each structural component expected to undergo inelastic deformation shall be defined by its moment-curvature relation. The displacement demand and capacity shall be calculated per Sections 3104F.2 and 3104F.3, as appropriate.
The moment-rotation relationship for concrete components shall be derived from the moment-curvature analysis per Section 3107F.2.5.4 and shall be used to determine lateral displacement limitations of the design. Connection details shall be examined per Section 3107F.2.7.
3107F.2.4 Stress-Strain Models
3107F.2.4.1 Concrete
The stress-strain model and terms for confined and unconfined concrete are shown in Figure 31F-7-1.


FIGURE 31F-7-1
STRESS-STRAIN CURVES FOR CONFINED
3107F.2.4.2 Reinforcement Steel and Structural Steel
The stress-strain model and terms for reinforcing and structural steel are shown in Figure 31F-7-2.


FIGURE 31F-7-2
STRESS-STRAIN CURVE FOR MILD REINFORCING STEEL OR STRUCTURAL STEEL [7.1]
3107F.2.4.3 Prestressed Steel
The stress-strain model of Blakeley and Park [7.4] may be used for prestressed steel. The model and terms are illustrated in Figure 31F-7-3.


FIGURE 31F-7-3
STRESS-STRAIN CURVE FOR PRESTRESSED STEEL [7.4]
3107F.2.4.4 Alternative Stress-Strain Models
Alternative stress-strain models are acceptable if adequately documented and supported by test results, subject to Division approval.
3107F.2.5 Concrete Piles
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]
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