The behaviour of tubular steel beams subjected to transverse blast loads
Jama, Hussein Haji
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A series of blast experiments was performed on tubular beams with different cross-section slenderness, lengths and boundary conditions. As a result of a transverse blast load, cold-formed hollow beams undergo global and local permanent deformations. Global deformation refers to the overall beam bending deformation and local deformation refers to the local cross section failure of the beams. The local deformations were complex and the measurement of the local deformation was taken to be the distance traversed by the top flange. It was observed that as the impulse on the beams was increased, the deformed cross section changed from a molar to a tear-drop shape. It was found that the impulse recorded using a ballistic pendulum is directly proportional to the mass of the explosive detonated. Further, as a result of the experimental work undertaken, it was found that a ballistic pendulum can be used to achieve replicable results. The global deformation of tubular beams subjected to blast loads is significantly affected by the boundary condition at the supports. As in the quasi-static testing regime, beams with fixed-ended supports deform less than beams with partially-fixed supports. In the range tested, it was found that local deformations of SHS beams are not affected by axial restraint. This can be understood if the beam is idealised as consisting of four plates of equal size. Initially the impulse is imparted only onto the top flange which has only ¼ of the mass of the beam. Therefore, severe local deformations occur at the top flange before the rest of the beam responds. The local deformations of all the beams tested progressed in a similar manner from molar to tear-drop shape as the magnitude of the impulse was increased. Nevertheless, the local deformations of the 300mm and 600mm beams are similar, the local deformation/beam depth being observed in the range of 1~1.4. The global deformations of the Series III beams, when compared to the Series IV beams, appear to indicate prima facie that global deformation is inversely proportional to the length of these beams. This apparent contradiction of beam theory is explained by the fact that the 1000mm beam is heavier than the 600mm span. In addition, the local deformation of the 1000mm beam occurs over a longer length and absorbs more energy. The interaction between local deformation and global beam bending deformation was investigated by examining the energy distribution. In this analysis shear effects were shown to be negligible and were therefore excluded. A proposal by Wegener and Martin  was utilised to simplify the analysis. Wegener and Martin  hypothesised that local and global deformations are uncoupled, with the local deformations preceding the global deformations. The energy consumed in the local deformation was estimated from the final deformed cross-section using hingeline mechanics. Stationary and rolling hinge approaches were utilised and found to yield similar energy levels. Thereafter, the principle of the conservation of energy was invoked and the distribution of the energy consumed in local and global deformation of the beams was shown. The energy consumed in the local deformation of the fixed 600mm span beams was found to be 63%, 66% and 49% of the input energy for the 35mm, 40mm and 50mm beams respectively. In the 600 mm span beams with partially-fixed boundary condition, a similar distribution of the energy was found. In the 1000mm beams, there was significantly more energy consumed in local deformation as shown by the fact that 73%, 69% and 83% of the input energy was consumed in local deformation for the 35mm, 40mm and 50mm beams respectively. SHS steel beams subjected to blast loads were found to undergo local cross-sectional deformations that consumed more than 50% of the input energy, which can be estimated using rigid-plastic analysis and the experimental results. Once the energy consumed in the local deformation is accounted for, the flexural beam bending deformation can be found using the bound of Jones equations and the remaining energy. Using these results, a semi-empirical general design guideline which yields a lower bound solution has been outlined and a design guideline has been proposed. Finite element simulations of some of the experiments were performed in order to determine the influence of strain-rate hardening and thermal softening on the results. Two boundary conditions, fully-fixed and partially-fixed beams with 600 mm span lengths were simulated. Linear Piecewise Plasticity (LPP), Linear Piecewise Plasticity with strain-rate (LPP+ ) and Linear Piecewise Plasticity with strain-rate and thermal softening (LPP+ +T) material models were used.