A lumped-mass model for the dynamic analysis of the spatial beam-like lattice girders

A method is presented to replace the distributed mass of each bay of a spatial beam-like lattice girder by 24 lumped masses, half of the latter being located at the upper plane and the other half at the lower one of the bay respectively, where the correct magnitude and location of each lumped mass are determined according to the actual arrangement of all the members constituting the bay. Based on the locations of the 24 lumped masses, the coefficients associated with the "masses" translating in the x̄, ȳ and z̄ directions and those associated with the "mass moment of inertias" rotating about the x̄-, ȳ-, and z̄-axis for the effective mass matrix of a bay-equivalent (continuum) beam are calculated. Numerical results show that the presented lumped-mass model together with the effective stiffness matrix of the bay-equivalent beam derived on the assumption that the cross-sections at both ends of each bay remain plane after deformation will give more accurate natural frequencies for the multi-bay spatial X-braced, Pratt or Warren beam-like lattice girders. Besides, the presented lumped-mass model is available for various transverse side-length ratios R_ab and longitudinal side-length ratios R_aL.