# Section 3107F Structural Analysis and Design of Components

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.

This section addresses MOTs constructed using the following structural components:

- Reinforced concrete decks supported by batter and/or vertical concrete piles
- Reinforced concrete decks supported by batter and/or vertical steel piles, including pipe piles filled with concrete
- Reinforced concrete decks supported by batter and/or vertical timber piles
- Timber decks supported by batter or vertical timber, concrete or steel pipe piles
- Retaining structures constructed of steel, concrete sheet piles or reinforced concrete

The following parameters shall be established in order to compute the component strength:

- Specified concrete compressive strengths
- Concrete and steel modulus of elasticity
- Yield and tensile strength of mild reinforcing and prestressed steel and corresponding strains
- Confinement steel strength and corresponding strains
- Embedment length
- Concrete cover
- Yield and tensile strength of structural steel
- Ductility

- Environmental effects, such as reinforcing steel corrosion, concrete spalling, cracking and chemical attack
- Fire damage
- Past and current loading effects, including overload, fatigue or fracture
- Earthquake damage
- Discontinuous components
- Construction deficiencies

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

f_{y} = Specified yield strength of reinforcement or specified minimum yield stress steel

f_{p} = 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).

Knowledge factor, k, shall be applied on a component basis.

The following information is required, at a minimum, for a component strength assessment:

- Original construction records, including drawings and specifications.
- A set of "as-built" drawings and/or sketches, documenting both gravity and lateral systems (Section 3102F.1.5) and any postconstruction modification data.
- A visual condition survey, for structural components including identification of the size, location and connections of these components.
- 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).
- Assessment of component conditions, from an in-situ evaluation, including any observable deterioration.
- 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]).

TIME FRAME | PILING | BEAMS | SLABS |

1900-1919 | 2,500-3,000 | 2,000-3,000 | 1,500-3,000 |

1920-1949 | 3,000-4,000 | 2,000-3,000 | 2,000-3,000 |

1950-1965 | 4,000-5,000 | 3,000-4,000 | 3,000-4,000 |

1966-present | 5,000-6,000 | 3,000-5,000 | 3,000-5,000 |

ASTM | STEEL TYPE | YEAR RANGE^{3} | GRADE | STRUCTURAL^{1} | INTERMEDIATE^{1} | HARD^{1} | |||

33 | 40 | 50 | 60 | 70 | 75 | ||||

Minimum Yield^{2} (psi) | 33,000 | 40,000 | 50,000 | 60,000 | 70,000 | 75,000 | |||

Minimum Tensile^{2} (psi) | 55,000 | 70,000 | 80,000 | 90,000 | 95,000 | 100,000 | |||

A15 | Billet | 1911-1966 | X | X | X | ||||

A16 | Rail^{4} | 1913-1966 | X | ||||||

A61 | Rail^{4} | 1963-1966 | X | ||||||

A160 | Axle | 1936-1964 | X | X | X | ||||

A160 | Axle | 1965-1966 | X | X | X | X | |||

A408 | Billet | 1957-1966 | X | X | X | ||||

A431 | Billet | 1959-1966 | X | ||||||

A432 | Billet | 1959-1966 | X | ||||||

A615 | Billet | 1968-1972 | X | X | X | ||||

A615 | Billet | 1974-1986 | X | X | |||||

A615 | Billet | 1987-1997 | X | X | X | ||||

A616 | Rail^{4} | 1968-1997 | X | ||||||

A617 | Axle | 1968-1997 | X | X | |||||

A706 | Low-Alloy^{5} | 1974-1997 | X | ||||||

A955 | Stainless | 1996-1997 | X | X | X |

- The terms structural, intermediate and hard became obsolete in 1968.
- Actual yield and tensile strengths may exceed minimum values.
- 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.
- Rail bars should be marked with the letter "R. "
- ASTM steel is marked with the letter "W."

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, EI_{e}, for lateral analyses (see Section 3107F.5 for definition of symbols).

CONCRETE COMPONENT | EI_{e}/EI_{g} |

Reinforced Pile | 0.3 + N/(f'_{c}A_{g}) |

Pile/Deck Dowel Connection^{1} | 0.3 + N/(f'_{c}A_{g}) |

Prestressed Pile^{1} | 0.6 < EI_{e}/EI_{g} < 0.75 |

Steel Pile | 1.0 |

Concrete w/Steel Casing | |

Deck | 0.5 |

- The pile/deck connection and prestressed pile may also be approximated as one member with an average stiffness of 0.42 EI
_{e}/EI_{g}(Ferritto et al, 1999 [7.2])

N = is the axial load level.

E_{s}= Young's modulus for steel

I_{s}= Moment of inertia for steel section

E_{c}= Young's modulus for concrete

I_{c}= Moment of inertia for uncracked concrete section

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.

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.

Alternative stress-strain models are acceptable if adequately documented and supported by test results, subject to Division approval.

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}