Keywords: semi-rigid, connections, analysis, frames, plane structures, bolts.

The cold-formed sections in structural design have been used in many constructions in civil engineering, therefore a more careful to analysis these structures is necessary. In the design and detail of these structures, many situations are considered by the constructor and designer. One of them is to consider the members of structures with several finites elements. The connection of the elements may be pinned or restrained. Although this consideration is simple to design it is not totally true. The connections of the elements have a semi-rigid behavior, and these connections strength can depend the actions on the structures. The considerations a semi-rigid behavior will present a more realistic structural analysis.

The engineering works using steel profiles are being used in the most varied types of works related to the building construction; therefore, the need of a larger concern in the analysis of such structures. In the design and detail of the this structures, several hypotheses and theorems are considered elaborated along the first builders' existence. One of the hypotheses is in discritized the structure in finite elements size, where, usually, the connections among the members are considered pinned or restrained.

In spite of these considerations they are not totally true, they are adopted by the application simplicity. The connections among the bars have a semi-rigid behaviour, because depending on the connection type, they can resist more or less to the efforts requested by the actions loads in the structure. In the present work, the analysis of the semi-rigid behaviour will bring an answer of more exact design of the structure, turning the closest results of the reality.

The numeric analysis of the model will be developed from the modification of the plane structure stiffness matrix, with three degrees of freedom, being two degrees with relationship to the displacements, and one degree with relationship to the rotation. The modification of the axial and rotational stiffness in the ends of the structural element will be made through the introduction of coefficients, obtained from the mathematical modification of the spring stiffness SR and SA. The obtaining the element stiffness matrix with both semi-rigid ends, it will be presented to proceed. It will be considered SRi and SAi, as the rotational and axial stiffness of the end of the connection, respectively. In the same way, considering SRj and SAj, the rotational and axial stiffness of the end of the connection, respectively.

To analysis the behaviour of the semi-rigid connection, it was considered a beam with both ends restraints and applied a concentrated load in the middle span. The connections in the truss plane structural element joints can be made with gusset plates and they could be welded or bolted. In paper, it was considered for the structure details a typical connection using two bolts. This detail is the minimum constructive connection to use in code NBR 8800:1986.

In the truss analysis, the first analysis was made to know the semi-rigid connection behaviour. After, in the second analysis tried to obtain the load value when the ends moment search the bolt connection moment strength. Later, in the third analysis the superior load value was considering to the previous ones so that there were the moment redistribution. The loads values for these three situations described previously were of kN, kN and kN, respectively.

1

Abdalla, K.M., Chen, W.F. Expanded Database of Semi-Rigid Steel Connections. Computers & Structures, v. 56, n. 4, p. 553-64, 1995. doi:10.1016/0045-7949(94)00558-K

2

Brazilian Association of Technical Norms. Project and execution of structures of steel in buildings: NBR 8800. Rio de Janeiro, 1996.

3

Carvalho, L.C.V., Andarde, S.A.L., Vellasco, P.C.G.S. Experimental analysis of bolted semi-rigid steel connections. Journal of Constructional Steel Research, v. 46, n.1/3, p. 238-40, 1998. doi:10.1016/S0143-974X(98)00092-3

4

Grupta, R., Gebremedhin, K.G., Cooke, J. R. Analysis of metal plate connected wood trusses with semi-rigid joints. American Society of Agricultural Engineers, v. 35, n. 3, p. 1011-8, 1992.

5

Riley, G., Gebremedhin, K.G., Cooke, J.R. Semi-rigid analysis of metal plate-connection wood trusses using fictious members. Transactions of the ASAE, V. 36, N. 3, P. 887-94. 1993.

6

Weaver, W.W., Gere, J.M. Matrix Analysis of Framed Structures. New York: Van Nostrand Reinhold Companu, 1986. 492 p.

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