Keywords: eight-bolt endplate connection, finite element, moment-rotation, frame analysis, three-parameter power model, fully versus partially restrained connections.

Connections considered in this research are limited to eight-bolt stiffened endplate connections. Frames analyzed in this research are all regular frames. The objective of this research is to promote consideration of properties of partially restrained (PR) or semi-rigid connections in frame analysis. It is well-known that a large portion of connections behave neither as ideally pinned nor as fully restrained as assumed in conventional frame analysis. In other words, many connections fall into the category of PR connections. PR connections have been researched extensively by many since connection behaviour often significantly influences the performance of steel frames in one way or another. However, knowledge about PR connections has not been easily implemented into code-based design practice and the current specifications (1999) of the American Institute of Steel Construction (AISC) for steel buildings do not provide specific guidance on semi-rigid frame design probably due to the lack of a comprehensive model to represent the behaviour of a PR connection. In order to incorporate the effects of PR connections in frame analysis, properties of those connections must be available beforehand. One way to find the moment-rotation properties of a connection is to conduct physical test or computer analysis; however, this is a very costly approach especially because results obtained this way have no generality. A better way to address this issue is to develop a mathematical model to describe the moment-rotation behaviour of connections as presented in this paper.

This research consists of three phases. In the first phase, a three-dimensional finite element model is developed to simulate the behaviour of eight-bolt stiffened beam-to-column endplate connections. The model may be set to include only the beam-side or both the beam- and column-side of a connection. The model also provides the option to choose between monotonic or cyclic loading analysis. Material nonlinearity is considered in this model, and the actual uniaxial stress-strain curve is idealized as a trilinear curve for all materials involved. Incremental plasticity theory, von Mises yield criterion, and Mroz's kinematic hardening model are used to model material nonlinear behaviour. A Newton-Raphson iterative procedure is used to solve simultaneous equations. If the effective stress in an element exceeds the ultimate strength then that element is considered to have failed, and the strain energy in it is redistributed to the surrounding elements. Different approaches are used to simulate the bolt-pretension process depending on whether the model includes just the beam-side or both sides of the connection. A contact algorithm is incorporated in this model to simulate the interaction between the beam-side and its support.

A computer program associated with the finite element model is developed to generate the moment-rotation curves of the connections analyzed. A pre-processor is developed to generate the finite element mesh for the computer program. In total, eleven specimens were analyzed which fall into three categories: four specimens including only beam-side and subjected to monotonic loading; three specimens with beam-side only but subjected to cyclic loading; and four specimens including both column- and beam-side and subjected to monotonic loading. The results from these analyses are compared with corresponding experimental results and the comparison shows that the computer program can adequately predict the moment-rotation response of the connections and therefore has the potential to simulate a test.

The second phase of this research involves parametric studies. In order to implement connection properties in the frame analysis, moment-rotation curves are fitted to three mathematical models (power model, Richard-Abbott model, and Ramberg-Osgood model) to find the values of parameters characterizing these models. Based on the curve-fitting results, the three-parameter power model is chosen to represent the moment-rotation behaviour of the connections. Relations between the three parameters and geometric variables of the connections are established through regressions. Thus, once the variables defining a connection are chosen, the values of the parameters in the power model can be calculated through the equations developed. To assess the validity of these equations, moment-rotation curves generated by the power model are compared with those obtained from tests and analyses. The comparison shows good agreement between them.

In the final phase, connections represented by the power model are incorporated in a frame analysis program published in reference [1]. A total of eight regular frames are analyzed. The results of frame analysis clearly demonstrate that frame response can be adjusted by modifying only the properties of its connections, and endplate connections can behave as rigid connections only if their properties satisfy certain stiffness requirement. A relationship between this requirement and the column to beam stiffness ratio is proposed to classify endplate connections into fully or partially restrained connections. More information of this research can be found in reference [2].

1

Chen, W.F., Kim, S.E., "LRFD steel design using advanced analysis", CRC Press, Boca Raton, 1997.

2

Zhou, F.F., "Model-based simulation of steel frames with endplate connections", Ph.D. Dissertation. University of Cincinnati, Cincinnati, 2005.

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