摘要
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 <span style="font-family:Verdana;">proposed. It is based on the principle of minimum potential energy with</span><span style="font-family:Verdana;"> equality of internal and external forces. The equations for strain internal energy have been derived, including compressed and tensile concrete and reinforce</span><span style="font-family:Verdana;">ment. The energy equations of the external forces with axial flexural dis</span><span style="font-family:Verdana;">placement 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</span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">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)</span></span></span><span><span><span style="font-family:;" "=""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">results with the excellent agreement and one calculation result with a great disagreement, by obtaining results of virtual principle method.</span></span></span><span><span><span style="font-family:;" "=""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">With this method is avoiding the adoption of an unsure (EJ), as in the case of underestimating or overestimate initial flexural rigidity.</span></span></span>
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 <span style="font-family:Verdana;">proposed. It is based on the principle of minimum potential energy with</span><span style="font-family:Verdana;"> equality of internal and external forces. The equations for strain internal energy have been derived, including compressed and tensile concrete and reinforce</span><span style="font-family:Verdana;">ment. The energy equations of the external forces with axial flexural dis</span><span style="font-family:Verdana;">placement 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</span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">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)</span></span></span><span><span><span style="font-family:;" "=""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">results with the excellent agreement and one calculation result with a great disagreement, by obtaining results of virtual principle method.</span></span></span><span><span><span style="font-family:;" "=""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">With this method is avoiding the adoption of an unsure (EJ), as in the case of underestimating or overestimate initial flexural rigidity.</span></span></span>
作者
Mirko Balabušić
Mirko Balabušić(Independent Designer of Structure, Hercg Novi, Montenegro)