Slope deflection analysis of trussed rigid frames

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Virginia Polytechnic Institute

A procedure for analyzing a two and three dimensional truss-rigid-frame with elope deflection method is investigated in this thesis.

In the first few chapters of this thesis the elope deflection equations for solving the trussed-rigid-frame problem were derived. The point of great importance in deriving slope deflection equations is that the imaginary plates or bars are added at separated domains or parts. Because of the existence of imaginary plates or bars the whole trussed-rigid-frame can be regarded as the rigid beam frame. The equations for determining the coefficients for the equivalent slope deflection equations of the separate domains can be formulated by applying the Castigliano’s theorems. The reactions and the stresses in every member of the trusses can be calculated after the reactions at the “joints” have been determined.

In the last few chapters an illustrative example is given. Its solutions are checked with the solutions obtained by applying Castigliano's theorem to the whole frame. This proves that it is possible to analyze the trussed-rigid-frame by using the procedure mentioned in this thesis.

The advantage in using this method is that the whole structure may be separated into domains when the number of members increases to such an extent that the capacity of a computer is exceeded.