# Bending of steel fibers on partly supported elastic foundation

Hu, XiaoDong, Day, Robert and Dux, Peter (2001) Bending of steel fibers on partly supported elastic foundation. Structural Engineering and Mechanics, 12 6: 657-688.

Author Hu, XiaoDongDay, RobertDux, Peter Bending of steel fibers on partly supported elastic foundation Structural Engineering and Mechanics   Check publisher's open access policy 1225-4568 2001-12 Article (original research) 12 6 657 688 12 Chang-Koon Choi William Schnobrich eng 0905 Civil Engineering Fiber reinforced cementitious composites are nowadays widely applied in civil engineering. The postcracking performance of this material depends on the interaction between a steel fiber, which is obliquely across a crack, and its surrounding matrix. While the partly debonded steel fiber is subjected to pulling out from the matrix and simultaneously subjected to transverse force, it may be modelled as a Bernoulli-Euler beam partly supported on an elastic foundation with non-linearly varying modulus. The fiber bridging the crack may be cut into two parts to simplify the problem (Leung and Li 1992). To obtain the transverse displacement at the cut end of the fiber (Fig. 1), it is convenient to directly solve the corresponding differential equation. At the first glance, it is a classical beam on foundation problem. However, the differential equation is not analytically solvable due to the non-linear distribution of the foundation stiffness. Moreover, since the second order deformation effect is included, the boundary conditions become complex and hence conventional numerical tools such as the spline or difference methods may not be sufficient. In this study, moment equilibrium is the basis for formulation of the fundamental differential equation for the beam (Timoshenko 1956). For the cantilever part of the beam, direct integration is performed, For the non-linearly supported part, a transformation is carried out to reduce the higher order differential equation into one order simultaneous equations, The Runge-Kutta technique is employed for the solution within the boundary domain. Finally, multi-dimensional optimization approaches are carefully tested and applied to find the boundary values that are of interest. The numerical solution procedure is demonstrated to be stable and convergent. Engineering, CivilEngineering, MechanicalBeam On Elastic FoundationNon-linear ModulusBoundary ConditionsCantileverHigher Order Differential EquationRunge-kutta TechniqueOptimization ApproachDownhill Simplex MethodGenetic AlgorithmsBrittle-matrix CompositesFinite-elementBeamsModel C1 Provisional Code Unknown

 Document type: Journal Article Article (original research) School of Civil Engineering Publications

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