Abstract:

ESDU 91001 gives background information and guidance on the values for various quantities needed in calculating the response of flexible structures. Axes systems used are defined and the equation of motion for a single mode in translational or rotational vibration is stated. Likely inaccuracies to be met in estimated or full-scale measured values of natural frequency, structural damping and generalised mass are suggested. Natural frequencies are given for the first four modes of vibration of single- and multi-span beams and the simple equations for the frequency of the fundamental mode of vibration of a tall building is given, with an indication of the likely error. A similar equation is also provided for stacks, towers and columns. Treatment of additional masses and non-uniform mass is considered. Mode shape functions are provided for cantilever and single- and two-span structures in various translational modes, for single-support structures in rotation about the support, and for a cantilever in the first torsional mode. Typical values of structural damping are tabulated for stacks, towers and tubes. Equations of mode-generalised mass and inertia are stated, and generalised masses in bending are listed for buildings and single-span beams. Typical ranges of structural density are shown graphically for stacks, and stated for buildings, and a table gives area and moment of area for a wide range of section shapes.