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As an extension of previously reported work on effects of internal resonance on non-linear vibration of beams, it has been shown that for blade-like beams excited parametrically by support motion in the plane of maximum stiffness, complex combination instabilities are observed. In addition to the well-known sum-type combination instability existing between the fundamental out-of-plane bending and the torsional modes of the beam, investigation has revealed the occurrence of higher order instabilities producing detectable bending and torsional vibrations which are not synchronous with external excitations. These effects are subsequently shown to exist in a related way in coupled beam configurations shown to exist in a related way in coupled beam configurations under forced vibration when specific internal resonance conditions exist between the natural frequencies of the various modes, and to produce visible patterns of non-linear energy flow between modes. This study considers one such effect both experimentally and theoretically, consisting predominantly of a coupling between the fundamental and second nonplanar bending modes, and torsion mode. This combination resonance was modelled by taking the perturbation analysis to second order and including other contributory terms in the system governing equations. An expression for the transition curve for this resonance has been derived which shows the regions of stable and unstable solutions in a two parameter plane. Very close agreement is obtained between theoretical and experimental results for different beam lengths. It is also shown that if the geometry of the system is such that theses two combination resonances can be excited simultaneously, very small alternations to the internal tuning of the system can generate noticeable intermodal energy exchange effects. This system is then examined in the context of non-linear forced vibration and to this end an arrangement of coupled beams is studied. The vertical blade-like beam is coupled to the free end of a horizontal cantilever beam which is externally excited at a frequency in the region of its second bending mode frequency. This allows for the possibility of four mode interaction between the three nonplanar modes described above and also the second planar bending mode. A four-degree-of-freedom model was formulated and perturbation analysis revealed that complex multimodal responses could occur for a single-frequency excitation. Steady-state solutions were derived by means of numerical integration techniques. A reasonable degree of agreement was observed between theoretical and experimental results.

Some concern has been expressed that the load capacity of corner columns might be reduced in fire due to the expansion of unprotected fire-exposed connected beams, even through the columns themselves are protected from fire. A structural analysis program VULCAN has been used to perform a series of parametric studies on corner sub-frames. In order to obtain the best possible representation of the column cross- section, the formulation of beam-column elements was developed to allow the cross- section to be divided into large numbers of segments. The analyses indicate that the existing fire design codes, such as BS5950: Part 8, give an un-conservative result. The finite element method is shown to be capable of modelling this type of sub- frame, but is too complex to be used routinely. As an alternative, a generalised simplified approach to enable a rapid assessment of the sub-frame by hand or spreadsheet calculation has been developed. The results, in comparison with the finite element analyses, give some confidence in the use of this approach. The beam-column elements of the program VULCAN were further developed to model the three-dimensional behaviour of asymmetric steel beams for fire conditions. The general approach, including the principles and details of the modifications to the formulation for asymmetric cross-sections, together with the refinement of the cross- section, are presented. The modified program has been validated by comparison with classical analytical results and test results at ambient and high temperatures. A new generalised beam model has been developed, which can model not only reinforced concrete sections but also steel sections of different shapes including hollow sections, for three-dimensional composite structures at ambient and high temperatures. The method currently includes both geometrical and material non linearities and considers the cracking and crushing of concrete. Several material models have been included, especially for concrete in tension which shows significant effects on the results. The thermal expansion and degradation of both steel and concrete materials with elevated temperatures are also included. The cross- section is divided into an appropriate number of segments so that non-uniform temperature profiles, and variations of strain and stress across the section, can be represented with more accuracy. The formulation is used to further develop the program VULCAN, and is then validated by comparison with theoretical and experimental results.

The development of synthetic adhesives based on epoxy resins has opened new possibilities for bonding structural materials together. The present work was concerned with the use of epoxy resins to strengthen reinforced concrete beams by externally bonded steel plates. It was found in the first part that the assessment of the properties of the epoxy adhesive is of paramount importance as they varied considerably with the thickness of the test specimen and the rate of loading. The adhesive proved to offer a bond stronger than concrete in shear and resulted in a composite action between the beams and steel plates. Preloading the beams prior to strengthening them did not have any adverse effect on their behaviour. The added strength from the plates was fully exploited even in beams which were held under a preload of 70% of their ultimate strength while being strengthened. Stopping the plate in the shear span, short of the support, created a critical section where premature bond failure occurred beyond a certain plate thickness. Failure was caused by the combination of high peeling and bond stresses present in the region where the plate was stopped. These stresses were due to the transfer of tensile forces from the plate to the bars in that region and were higher with thicker plates. Bonding steel plates on the tension face of the beams increased their shear capacity by 9 to 15%. This may have been due to dowelling action from the plates which had a greater contact area with concrete than an equivalent amount of internal steel bars. The use of externally bonded steel as shear reinforcement was effective but requires further investigation. The external web strips failed prematurely as compared to equivalent stirrups. The long term deformations in plated beams were highly affected by the conditions of their environment but despite 47 month exposure no visual deterioration of the concrete-epoxy-steel joint was observed.

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