Analytical Model for Fictitious Crack Propagation in Concrete Beams
Publication: Journal of Engineering Mechanics
Volume 121, Issue 1
Abstract
An analytical model for load-displacement curves of concrete beams is presented. The load-displacement curve is obtained by combining two simple models. The fracture is modeled by a fictitious crack in an elastic layer around the midsection of the beam. Outside the elastic layer the deformations are modeled by beam theory. The state of stress in the elastic layer is assumed to depend bilinearly on local elongation corresponding to a linear softening relation for the fictitious crack. Results from the analytical model are compared with results from a more detailed model based on numerical methods for different beam sizes. The analytical model is shown to be in agreement with the numerical results if the thickness of the elastic layer is taken as half the beam depth. It is shown that the point on the load-displacement curve where the fictitious crack starts to develop and the point where the real crack starts to grow correspond to the same bending moment. Closed-form solutions for the maximum size of the fracture zone and the minimum slope on the load-displacement curve are given.
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Published In
Journal of Engineering Mechanics
Volume 121 • Issue 1 • January 1995
Pages: 7 - 15
Copyright
Copyright © 1995 American Society of Civil Engineers.
History
Published online: Jan 1, 1995
Published in print: Jan 1995
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