ABSTRACT
The engineer must solve the beam-column equation, presented in Chapter 2, by nondimensional methods or by a computer program. The response of the soil is characterized by equations shown in Chapter 3 or by similar methods. The diameter of a cylindrical pile as a function of depth, or the equivalent diameter of a pile with a non-circular cross section, must be known to solve the soil-response equations. An approach for computing the equivalent diameter of a pile with a non-circular cross section is presented in this chapter. The solution of the beam-column equation requires values of the bending stiffness
EpIp. If the engineer is interested in small deflections, a constant value for EpIp may be employed along the pile. However, in many instances, the engineer is required to find a loading that produces failure, which may be defined as excessive deflection or the formation of a plastic hinge. In the latter case, the value of the ultimate bending moment Mult must be found, and in both instances, the value of EpIp at each cross section must be found as a function of the applied loading. As noted earlier, and as emphasized in this chapter, the nonlinear behavior of soil
requires that the load that causes a pile to fail must be found in order to find the safe load that can be applied. In nearly all cases of practical design, the value of Mult is required. The value of EpIp in the nonlinear range of the materials of which a pile is constructed is a function of the axial load and the bending moment. Methods for the computation of nonlinear values of EpIp are presented in this chap-
ter. A linear value of EpIp may be used for piles made of structural steel. Iteration on pile stiffness is usually not required; rather, failure by formulation of a plastic hinge is assumed to occur when increasing the loading causes the maximum stress to reach a value equal to the proportional limit of the steel. A failure of the steel pile in deflection, if not achieved at a lower level of loading, is assumed to occur at the loading required to cause the plastic hinge. For a pile of reinforced concrete, the value of EpIp is nonlinear beginning with a
low level of stress. Therefore, as the loading on the pile is increased, the diagram for the nonlinear EpIp must be implemented, requiring a second level of iteration in the solution of the differential equation for response of the pile. The use of nonlinear values of EpIp is discussed in some detail in Chapters 5 and 6.
