Date of Award

Fall 2012

Degree Type


Degree Name

Doctor of Philosophy (PhD)


Civil Engineering


A. Ghani Razaqpur


Michael Tait



Committee Member

K.S. Sivakumaran


In this thesis the dynamic response of wide-flange steel beams and columns to blast loading was experimentally evaluated. A total of twenty six steel members were field tested using live explosives, where the charge size ranged from 50 to 250 kg of ANFO and the ground stand-off distance from 7.0 to 10.3 m. Blast wave characteristics, including incident and reflected pressures were recorded. In addition, time-dependant displacements, accelerations, and strains at different locations along the steel members were measured, and the post-blast damage and mode of failure of the test specimens were observed. This study also presented detailed analysis of the experimental data. The blast load characteristics were compared with those obtained using the Technical Manual UFC 3-340-02 model (UFCM). The spatial and temporal variations of strain rate were computed from the recorded strain time histories and analyzed. In addition, time-dependant deformations were analyzed to study the contributing modes of vibration in the dynamic response using Power Spectral Density (PSD) function. Moreover, the effect of the axial load on the maximum deformations, vibration periods, strain rates, and contributing modes in the dynamic response were study by comparing the beam results with the column results tested in the same blast shots.

The experimental results were compared with those obtained from an equivalent Single-Degree-of-Freedom (SDOF) model, which included material nonlinearity, strain rate effect, and P-δ effect. To account for strain rate effect on member stiffness and strength, its full moment-curvature response is determined by dividing its cross-section into a number of layers and a strain rate-dependent stress-strain relationship, based on the Cowper-Symonds strain rate model, was used to capture the nonlinear stress distribution over the section. The P-δ effect was modelled using the equivalent lateral load (ELL) method to simulate the secondary moment due to axial load. To determine the effects of higher modes of vibration and the variation of steel member mechanical properties along its length on its dynamic response, the test steel members were also analyzed using Multi-Degree-of-Freedom (MDOF) models, based on Finite Element Modelling (FEM). These dynamic models were also used to investigate the effect of axial-bending interaction and dynamic stability of columns. In addition, the results of the dynamic models were used to evaluate the results of the Moment Magnification Factor (MMF) commonly used in the interaction formulas to design steel beam columns under blast. Moreover, the effect of strain rate caused by the blast loading on the local stability of steel columns was also evaluated insofar as it might lead to a shift in the governing mode of failure.

Results showed the UFCM pressure predictions compared reasonably well with the measured pressure in the positive phase in terms of both the peak pressure and overall time variations. Results also showed that when proper accounting for secondary-moment due to axial load and strain rate effect on the member resistance function, the SDOF model adequately captured both the overall response, such as the time-dependant deformations and internal forces, and instability behaviour of steel columns under blast loading. It is also shown that using MMF method overestimates the column capacity for ductility ratios µ greater than one, irrespective of the axial load to Euler elastic buckling load ratio (P/Pe). Also for P/Pe > 0.5, even if µ >1.0, the UFC method still overestimates the actual column capacity. The results of the dynamic models were used to generate stability diagrams for the assessment of the critical load and Pressure-Impulse (PI) diagrams for checking the column performance against the allowable deflection limits, which can be implemented in design standard of steel structures under blast loading.

McMaster University Library

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