Static analysis of an infinite beam resting on a tensionless Pasternak foundation

This paper addresses the static response of an infinite beam supported on a unilateral (tensionless) two-parameter Pasternak foundation and subjected to complex transverse loads, including self weight. The transfer displacement function method (TDFM) is employed to determine the initially unknown lengths that remain in contact. In contrast to a Winkler Foundation System (WFS), the lift-off points in a PFS (Pasternak Foundation System) are not necessarily at zero displacement but may be determined sequentially through considering the compatibility conditions at the junctions of contact and non-contact segments. After the response of the whole system including the beam and foundation is expressed through the displacement constants of the initial segment, the contact problem is reduced to two nonlinear algebraic equations with two unknowns. The foundation reactions and the internal actions of the beam may also be determined from the displacement response of the system. Two simple cases are solved to illustrate the influence of the foundation stiffness factors and finally, a third example of a beam with several contact segments is presented to demonstrate the application of the TDFM.