## Bemessung von Stahlbetonstützen unter Zwangsverformungen

### Thürlimann, Christoph Bruno ; Favre, Renaud (Dir.)

### Thèse Ecole polytechnique fédérale de Lausanne EPFL : 1984 ; no 524.

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- Buildings are very often horizontally stabilized by means of a core or by shear walls. Bridge girders are also often laterally restrained by a horizontal fixed support at the abutment. It follows that the columns of such systems are restrained against any lateral movement. The actual design actions for such reinforced concrete columns are difficult to estimate. For the design of such a column using a normal force and moment, it is usual to isolate the column from the rest of the structure. Consequently, the nonlinear interaction of the column with the structure is neglected. Actually if the maximum flexural resistance due to external loads will be attained in a section of the column a plastic hinge will simply be formed which allows further large deformations to occur. The normal force starts to centre itself at the rotated column end after the maximum flexural resistance has been reached. The column fails when the deflection within the plastic hinge produces a moment which becomes equal to the remaining resistance. The imposed end deformation and the applied normal force are important for the design of a column and not the maximum flexural resistance. A new design method is proposed in this work, which takes into account the fact that these are problems of imposed deformations. The design of a column is carried-out by considering the normal force and the imposed end rotations due to the interaction of the column with the slabs (or the girder). The imposed end rotations are then compared with the possible limit end rotations of the column for the given normal force. Results from tests on reinforced concrete columns under imposed deformations and theoretical considerations make it possible to define reasonable limits for the possible strains and curvatures in columns for the ultimate and serviceability limit states. A reinforced concrete column can reach a compression strain of 2×10-3 at time to and 7×10-3, after creep, at time t∞ without any concrete spalling. Average strains of about 1.1×10-3 in tension reinforcement bars lead to small, permissible cracks. The admissible limit curvature in a column depends on the level of the applied normal force and is limited by the two above mentioned strain limits. A strain of 20×10-3 and more can be reached in the compression reinforcement bars and in the core of reinforced concrete columns with closely spaced (50 to 100 mm) stirrups (8 to 12 mm) without buckling of the reinforcement bars nor any significant loss in the resistance of the core concrete. The maximum limit curvature can be fixed to 0.02/h · ψ, which is sufficiently large to allow large plastic rotations. ψ is equal to the ratio of the distance between the longitudinal reinforcement of opposite faces and the column width, h. The definition of the possible limit curvatures in a column allows the estimation of the admissible and maximum limit angle for the given deformation case. N.B. IAPSE has published in 1984 a small summary of this thesis: "Design of R.C. Columns Subjected to Imposed End Deformations"