STRUCTURAL DESIGN CONSIDERATIONS - GENERAL

143 Where I Load factor a multiplier applied to force effects.
φ = Resistance factor a multiplier applied to nominal resistance, as specified in AASHTO. i Load modifier a factor relating to ductility, redundancy, and operational classification.
Q
i
= Force effect. Rn Nominal resistance.
R
r
= Factored resistance Rn. Foundation elements subject to lateral loads are designed to take into account the simultaneous occurrence of shear, moment and axial load effects. The interaction between these load effects results in the foundation element being designed as a compression member with bending, i.e., as a beam-column. The typical interaction of load effects occurs in the following combinations (i) axial load combined with moment, and (ii) axial load combined with shear. Designing for shear without considering the interaction with the simultaneously occurring axial load will result in a conservative design. The interaction between axial load and moment must always be considered.
Design is an iterative process wherein the applied factored load effects are compared to the structural resistance of the pile. If the computed factored maximum load effects exceed the nominal structural capacity of the foundation elements, then the design of the foundation element must be modified. This may include adding additional reinforcement in the case of concrete elements, using a heavier steel section in the case of steel piles and/or generally increasing the size (diameter, thicknesses or exterior dimensions) of the foundation element. If the size of the foundation element is increased, the
Geotechnical Strength Limit State should be reviewed and reanalyzed to determine if the length can be reduced based on the increased size and/or stiffness of the foundation element. This iterative process requires coordination and communication between the geotechnical and structural design activities. As stated above, a pile/shaft subject to lateral loads acts essentially as a beam-column. For some design purposes, the bending behavior of this beam-column can be represented by a constant, linear bending stiffness value E
p
I
p
. In this case, the nonlinear effects due to concrete cracking (concrete pile/shafts) or plastic hinge formation (steel piles) are avoided. A linear assumption for the bending stiffness maybe sufficient if the purpose of the analysis is to estimate the preliminary magnitude and distribution of moment and shear load effects along the pile/shaft and thereby obtain a preliminary value of the required area and distribution of longitudinal and transverse reinforcement in the case of concrete or the size of the steel section. Also, if the objective is to study the response of the pile/shaft under small deflections, a constant value for E
p
I
p maybe adopted. Where
E
p
= Modulus of elasticity of the pile.
I
p
= Moment of inertia of pile. However, in many instances, the pile/shaft bending stiffness cannot be appropriately represented by a linear, constant value. When the loading scenario is such that the structural response causes nonlinear effects in bending, the formation of yield moments (i.e., related to plastic hinge formation along the pile/shaft) must be considered. Therefore, the bending stiffness (E
p
I
p
) at each cross section must be determined as a function of the applied loading, and the yield or ultimate bending moment M
ult must be determined. Procedures for accomplishing a nonlinear bending analysis using commercially available general purpose structural analysis software can be found in the literature on this subject.

144 When nonlinear bending is considered, the assumption normally made in concrete piles is that cracks will form where the net tensile stress exceeds the tensile strength of concrete anywhere along the pile/shaft. Nonlinear stress-strain curves are used for both steel and concrete. Per the common practice of reinforced concrete, it is assumed that failure of the concrete in compression occurs when the strain c in concrete reaches approximately up to approximately 0.0038. For steel, yield is achieved when the strain in either tension or compression reaches a value defined as the ratio of the steel yield strength and the steel elastic modulus. Refer to FHWA Report Number FHWA NHI-16-009: Geotechnical Engineering Circular Number 12 – Volumes 1 & 2 Design and Construction of Driven Pile Foundations for the evaluation of driving stresses in piles.

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