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Partially restrained frames can be adopted as secondary lateral load resisting systems in areas of high seismic risk such as California, and as primary systems in areas of low to moderate seismic risk, such as Virginia which experienced an M5.8 earthquake in August of 2011.Taking advantage of partially restrained connections in frame design leads to about 4% to 11% in reduction in weight of the material (Gerstle and Ackroyd 1990).This dissertation proposes a finite element formulation and its implementation for the investigation of stability analysis and design of elastic, geometrically non-linear frames with large displacements, small to moderate strains and partially restrained connections.The goal of the research is to enhance the stability analysis and design of structural frames with partially restrained connections by developing a finite element formulation to determine internal forces in such frames. Currently there are no code provisions for specific guidance on how to analyze frames with partially restrained connections to determine appropriate internal forces for design. The finite element formulation proposed here is derived from rigorous principles of continuum mechanics and extends the previous work by (Yang and Kuo, 1994), to include partially restrained connections.The uniqueness of the proposed formulation is that it passes the rigid body test compared with other similar formulations which uses geometric stiffness matrices that are either not tested or do not pass the rigid body test.A computer program was developed by extending the work of Smith and Griffiths (1997) to implement the proposed formulation. To demonstrate the versatility of the new program, six cases of two different multistory frames with fully and partially restrained connections were analyzed as practical examples using the developed computer program. The first structure consists of two-bay, two-story steel frames and the second consists of two bay eleven story steel frames. The buckling load for each frame type was determined separately using the newly developed program for this research and code provisions from the 14th Edition of the American Institute of Steel Construction (AISC) manual. The buckling loads were used to determine the nominal compressive strength, Pn, per Chapter E of the AISC manual. The results show that, the nominal compressive strength calculated from buckling loads using the new program exceed those using the AISC provisions (Story Buckling Approach) for the two story and eleven story buildings by 5.9% and 11.2 %, respectively for partially restrained frames, and 6% and 8.1%, respectively for fully restrained frames.The program may be used for any number of stories. However, the height of the frame is limited to eleven stories for stability analysis and design for side sway unhindered moment frames with partially restrained connections. This is due to the accumulation of connection deformation and rotation in addition to frame deformation accounting for difficulty in achieving drift limitations. This is also confirmed by the Council on Tall Buildings and Urban Habitat (1992) and Steel Design Guide 8 (1996).

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