Symbolic Equations for the Stiffness and Strength of Straight Longeron Trusses
AIR FORCE RESEARCH LAB KIRTLAND AFB NM SPACE VEHICLES DIRECTORATE
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Symbolic equations for the effective continuum stiffness and strength properties of several periodic beam-like trusses have been previously derived and are well documented in the literature. These equations are useful because they allow for rapid design and assessment of structures that would otherwise require a more time-consuming analysis. Previous investigations have considered changes in truss construction, such as the number of longerons and diagonal lacing as discrete cases unique sets of equations were derived for each unique construction. These equations did not restrict the relative sizes of longerons, diagonals and battens. In the present work, a generic set of equations is derived that is applicable to trusses with an arbitrary numbers of longerons and diagonal lacings, however, the diagonals must be soft relative to the longerons and battens. The resulting equations are useful in preliminary truss sizing and optimization routines because they allow the number of longerons and diagonals to be changed by simply changing the value of a constant in the equations. In this paper, equations are derived for effective continuum beam bending, torsion, shear and axial loading. Within the assumption of relatively soft diagonals, the equations are shown to be equivalent to the three, four and six longeron results previously published by Renton and are numerically verified through comparison to finite element analysis solutions.