The beam-to-column CONNECTIONs in steel frames are assumed to be either pinned or rigid. Using pinned or rigid CONNECTIONs simplify the analysis, but they can not present the real behavior of the structure. Because, the experiments have shown that the CONNECTIONs under the loads will have some flexibility. Therefore, it is recommended that the flexibility of the CONNECTION should be included in the frame analysis. In this paper, the elastic secant stiffness matrix of a beam-column element with semi rigid CONNECTIONs under axial force, end moments and transverse distributed loads are derived. Second-order elastic and stability analysis of two-dimensional steel frames are carried out, afterward. The proposed stiffness matrix is very general and can be applied to a frame member with any type of CONNECTION. Furthermore, it is more accurate and efficient than the corresponding matrices obtained by other authors. In addition, this method uses only one element for each member and presents a single formulation for both tensile and compressive members in the analysis. Load-deflection curve and numerical values obtained by the suggested technique are compared with those found by other investigators. The effect of the CONNECTION flexibility on the equilibrium path and the stability load are also discussed.

The influence of CONNECTION strength and rigidity on the seismic performance of steel moment resisting frames is investigated. The seismic response of frames with three, eight and fifteen story is evaluated. These frames with rigid and semirigid CONNECTIONs were subjected to five em1hquake records. In ultimate limit state, the response of rigid and semirigid frames is compared in terms of the base shear story drift ratio, failure mechanism and behavior factor. These studies indicate that, the semirigidity of steel frames does not necessarily result in larger drift or in more damage than in rigid frames. It was also observed that, a well-proportioned semirigid CONNECTION could participate in the nonlinear behavior of the structure and enhances the dynamic performance of steel frames.      

This paper presents analytical and numerical models for semirigid timber frame with Lagscrewbolt (LSB) CONNECTIONs. A series of static and reverse cyclic experimental tests were carried out for different beam sizes (400, 500, and 600 mm depth) and column–base CONNECTIONs with different numbers of LSBs (4, 5, 8). For the beam-column CONNECTIONs, with increase in beam depth, moment resistance and stiffness values increased, and ductility factor reduced. For the column–base CONNECTION, with increase in the number of LSBs, the strength, stiffness, and ductility values increased. A material model available in OpenSees, Pinching4 hysteretic model, was calibrated for all CONNECTION test results. Finally, analytical model of the portal frame was developed and compared with the experimental test results. Overall, there was good agreement with the experimental test results, and the Pinching4 hysteretic model can readily be used for full-scale structural model.

By using Berwald CONNECTION, we show that there are linear CONNECTIONs Ñ which are projectively equivalent and belong to the same projective structure on TM. We found a condition for the geodesics of the Berwald CONNECTION under which Ñ is complete.

Fixity of column base CONNECTION plays a major role in overall behavior of steel structures. Several parameters influence the real behavior of the column base CONNECTIONs, among them base plate thickness, anchor bolts and stiffeners details can be mentioned. A nonlinear three dimensional finite element method has been utilized for numerical studying of the behavior of the column base CONNECTION. Thickness of the base plate and stiffeners and also sizes and numbers of the anchor bolts were changed in a number of models to determine their effects on the nonlinear behavior of the regular column base CONNECTION. It was observed that column base CONNECTION characteristics such as its moment-rotation behavior, yielding pattern of base plate and anchor bolts and local stress concentration of the CONNECTION elements can be significantly affected by changing any detail of the connecting elements. The effects of each parameter on the behavior of column base CONNECTION were categorized and presented in this paper.