Influence Functions for Beams on Elastic Foundations

Equations for beams on elastic foundations are summarized and simplified. Dimensionless influence functions are developed. Analysis of beams is reduced to simple evaluation of one-term algebraic expression. Deflection, slope, moment, and shear functions due to unit load or moment are evaluated for beams of constant elastic properties and foundation modulus. The functions are tabulated for beams of finite length and graphed for beams of semi-infinite length. The basis for comparison of functions of beams of finite with semi-infinite and infinite length is established. The tabulated and plotted data can be directly used in design or in construction of influence lines. Evaluation of functions for beams of variable elastic properties and modulus of foundation is explained, and their use in the design of a compatible beam is demonstrated.