Theoretical approach with analytical and numerical procedure for
determination initial displacement of a reinforced and prestressed concrete
members, simple and cantilever beams, loaded by axial forces and bending
moments is proposed. It is based on the
principle of minimum potential energy with equality of internal and
external forces. The equations for strain internal energy have been derived,
including compressed and tensile concrete and reinforcement. The energy equations of the external forces with axial flexural
displacement effects have been derived from the assumed sinusoidal
curve. The trapezoid rule is applied to integrate the segment strain energy.
The proposed method uses a non-linear stress-strain curve for the concrete and bilinear elastic-plastic
relationship for reinforcement; equilibrium conditions at a sectional level to
generate the strain energies along the beam. At the end of this article are
shown three specific numerical examples with comparative, experimental (two
tests)results with the excellent agreement and one calculation result with a
great disagreement, by obtaining results of virtual principle method.With
this method is avoiding the adoption of an unsure (EJ), as in the case of
underestimating or overestimate initial flexural rigidity.
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