Keywords: beams, columns, semi-rigid connections, stiffness, stability, frames.

In the analysis and design of steel and precast concrete skeletal structures the members forming the planar frames are general1y assumed to be rigidly or pin connected. In fact, both of the foregoing assumptions are unrealistic when one is considering steel frames and precast reinforced concrete structures. In such structures beams and columns behave as if they are semi-rigidly, or flexibly, connected, as far as rotations of the ends are concerned [1,2,3]. Hence, experimentally determined effective rotational spring constants for those connections should be used in the analyses of such structures. In the present study a computer program was prepared that treats the aforementioned type of structures elegantly, taking into consideration the behaviour of the flexible connections along with the effect of geometric nonlinearity due to the axial forces in the members and the effect of shear deformations. The nonlinear, or second order, analysis is not relevant only for its own sake, although it does contribute considerably to the precision of the solution, but also for the stability analysis of the same kind of structure [4]. As is well known, the upper limit of the load in any structure is the critical value of the load, the buckling load, which is found by taking geometric nonlinearity into consideration.

The well-known stiffness method was used in the present study. First, the stiffness matrix of a bar elastically supported against rotation at both ends is obtained using the second order analysis. Then, the fixed end forces are found for a bar elastically supported at the two ends by rotational springs for a uniformly distributed load, a concentrated load, a linearly distributed load, a symmetrical trapezoidal distributed load and a nonsymmetrical triangular distributed load. For the latter analysis, the second order theory was employed once again, along with the use of differential equations which yielded trigonometric functions for the case of compressive axial force and hyperbolic functions for the case of tensile axial force.

A computer program was prepared to solve static problems of planar frames composed of members that are flexibly connected at the nodes by taking into consideration the effect of shear deformations. The validity of the implemented computer program was proved by solving some example problems in different ways and showing the match between the results. Using the implemented computer program and solving some examples, the variations of some elastostatic quantities with spring constants were examined and presented graphically.

The conclusion of the present study is that the displacements and critical extremum values of bending moment for the same structure become larger when the spring constants of flexible connections become less. The variation is between the values pertaining to pin and rigid connections. Hence, the result of the present study will constitute the foundation of a stability analysis for the same type of structures.

1

O. Aksogan, F. Akkaya, "A Computer Program for the Analysis of Flexibly Connected Frames", Ç.Ü J.Fac.EngArch., Vol.6, No.2, 25-41, 1991.

2

O. Aksogan, R. Dinçer, "Nonlinear Analysis of Planar Frames with Linear Prismatic Members Having Rigid End Sections Taking Shear Deformation info Consideration", Ç.Ü J.Fac.EngArch., Vol.6, No.1, 125-137, June, 1991.

3

O. Aksogan, H. Görgün, "The Nonlinear Analysis of Planar Frames Composed of Flexibly Connected Members", Ç.Ü J.Fac.EngArch., Vol.8, No.2, 117-129, 1993.

4

O. Aksogan, S.S. Akavci, H. Görgün, "Analysis of Frames with Flexible Connections", Ç.Ü J.Fac.EngArch., Vol.20, No.1, 1-11, 2005.

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