An investigation into the vibrational response of structural components : with particular reference to reinforced concrete

Two very important structural engineering areas, the design and analysis of reinforced concrete and vibration analysis, have been linked in this thesis. The thesis presents an understanding of the mechanism of the response for reinforced concrete to vibration forces. The formulation of the equations of motion for structural elements have been presented together with some of the methods of solution for these equations. A technique of vibration functions for the solution of resonant frequency and mode shape has been developed for structures and structural elements. Together with these functions, a linearisation technique to aid in the solution is given. The use of these functions is illustrated by comprehensive examples worked in full and comparisons of results for steel frames under test. The responses to vibration of five reinforced concrete beams and two reinforced concrete portal frames have been studied. The adjustable magnitude of vibration and continuously variable excitation frequency enabled the response of the structures to be studied under variable control parameters. The variation of resonant frequency with amplitude for the structures tested is presented and comparisons are made throughout with suitable analysis and design methods. The computational problems associated with non-linear vibrations of reinforced concrete are discussed. The study of the crack propagation,during the vibration of reinforced concrete beams, indicates that the criteria governing crack height and spacing is substantially the same as for the beam subjected to statically loaded conditions. The vibration conditions imposed on the two reinforced concrete portal frames indicate in some cases severe cracking and problems associated with the spalling of concrete. In particular the corner details of frames subject to vibration require careful detailing and close supervision in construction to minimise the occurence of cracking and spalling. Measured values of damping for the reinforced concrete beams vary from less than 1% to approximately 5%, of critical viscous damping, with the majority of values lying between 1% and 3%. Magnitudes of damping were marginally higher for the portal frames, varying between approximately 2% and 8% of critical viscous damping for the two mode shapes investigated. Damping was shown to be dependent on the variation of the magnitude of resonant frequency and consequently depend-ent on the extent of crack formation. The greater the crack formation, the higher the value of damping