Beam Element Stiffness Matrix for X-Braced Truss

The techniques of discrete field analysis are utilized to investigate the response of X-braced trusses to various static loading conditions. Deflection formulas for arbitrary static loads are presented in finite Fourier series form. These formulas are used to derive stiffness coefficients which comprise the equivalent beam element stiffness matrix for a given X-braced truss. Fixed end moments for arbitrary static loads are also derived from the deflection formulas. All stiffness formulas are exact in the context of linear, elastic truss analysis and are valid for an arbitrary number of panels. These stiffness coefficients when compared to approximate estimates are found to vary by as much as 100% within a given range of span lengths. The formulas can be used to analyze a variety of structural systems which have X-braced trusses as the basic component. Examples include two-way truss systems, trussed frames, and planar trusses continuous over several supports. The analysis of such systems would be identical to that in which the individual components were beams except that here modified stiffness coefficients would be used.