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Title: Degree of freedom condensation method for the nonlinear analysis of plane reinforced concrete frames. Summary of the method and examples

Author(s): Rodriguez Santiago, J.; Azcón González de Aguilar, A.; Torroja Cavanillas, J.A.

Publication: ACHE

Volume: 40

Issue: 171

Appears on pages(s): 83 - 94



Date: 1/3/1989

A nonlinear method has been developed for analysing plane reinforced concrete frames with an iteration procedure by which final equilibrium is obtained, defined by a deformation which is the sum of the partial deformations obtained in each iteration. Linear analysis of deformation in eac hiteration is performed in two steps, in accordance with an original procedure. The first step analyses horizontal members subjected to vertical loads and moments at joints; the second step analyses vertical memebers subjected to horizontal loads. At each step the effect of bars at right angles to those considered is substituted by independent rotational constraints. Subsequentyl, a correction is made to take axual column deformation into acount. This procedure reduces the number of degrees of freedom handled simultaneously, providing a solution with minor differences compared to using the complete stiffness matrix. This difference is corrected in subsequent iterations. The deformation obtained is used to analyse the bending moments corresponding to this deformation in accordance with nonlinear material behaviour; these moments are adopted instead of those calculated previously. A system of forces is introduced to reestablish equilibrium, deduced from the difference between the bending moments obtained, adding in forces due to second order effects. Two original procedures have been introduced to improve iteration convergence, which consist of applying a deformation multiplier to each iteration (minimising the loads to be applied in the next iteration) and applying concentrated rotations in sections where plastic hinges occur. This paper describes the method, compares the results obtained with this method and with methods published by other authors and, finally, includes examples illustrating some of the applications.

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