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Research Papers

Pressure-Impulse Diagrams for Blast Loaded Continuous Beams Based on Dimensional Analysis

[+] Author and Article Information
A. S. Fallah

e-mail: arash.soleiman-fallah@imperial.ac.uk

E. Nwankwo

e-mail: ebuka.nwankwo08@imperial.ac.uk

L. A. Louca

e-mail: l.a.louca@imperial.ac.uk
Department of Civil and Environmental Engineering,
Skempton Building,
South Kensington Campus,
Imperial College London,
London SW7 2AZ, UK

1Corresponding author.

Manuscript received September 8, 2012; final manuscript received January 5, 2013; accepted manuscript posted February 12, 2013; published online July 12, 2013. Assoc. Editor: Weinong Chen.

J. Appl. Mech 80(5), 051011 (Jul 12, 2013) (11 pages) Paper No: JAM-12-1440; doi: 10.1115/1.4023639 History: Received September 08, 2012; Revised January 05, 2013; Accepted February 12, 2013

Pressure-impulse diagrams are commonly used in preliminary blast resistant design to assess the maxima of damage related parameter(s) in different types of structures as a function of pulse loading parameters. It is well established that plastic dynamic response of elastic-plastic structures is profoundly influenced by the temporal shape of applied pulse loading (Youngdahl, 1970, “Correlation Parameters for Eliminating the Effect of Pulse Shape on Dynamic Plastic Deformation,” ASME, J. Appl. Mech., 37, pp. 744–752; Jones, Structural Impact (Cambridge University Press, Cambridge, England, 1989); Li, and Meng, 2002, “Pulse Loading Shape Effects on Pressure–Impulse Diagram of an Elastic–Plastic, Single-Degree-of-Freedom Structural Model,” Int. J. Mech. Sci., 44(9), pp. 1985–1998). This paper studies pulse loading shape effects on the dynamic response of continuous beams. The beam is modeled as a single span with symmetrical semirigid support conditions. The rotational spring can assume different stiffness values ranging from 0 (simply supported) to ∞ (fully clamped). An analytical solution for evaluating displacement time histories of the semirigidly supported (continuous) beam subjected to pulse loads, which can be extendable to very high frequency pulses, is presented in this paper. With the maximum structural deflection, being generally the controlling criterion for damage, pressure-impulse diagrams for the continuous system are developed. This work presents a straightforward preliminary assessment tool for structures such as blast walls utilized on offshore platforms. For this type of structures with semirigid supports, simplifying the whole system as a single-degree-of-freedom (SDOF) discrete-parameter model and applying the procedure presented by Li and Meng (Li and Meng, 2002, “Pulse Loading Shape Effects on Pressure–Impulse Diagram of an Elastic–Plastic, Single-Degree-of-Freedom Structural Model,” Int. J. Mech. Sci., 44(9), pp. 1985–1998; Li and Meng, 2002, “Pressure-Impulse Diagram for Blast Loads Based on Dimensional Analysis and Single-Degree-of-Freedom Model,” J. Eng. Mech., 128(1), pp. 87–92) to eliminate pulse loading shape effects on pressure-impulse diagrams would be very conservative and cumbersome considering the support conditions. It is well known that an SDOF model is a very conservative simplification of a continuous system. Dimensionless parameters are introduced to develop a unique pulse-shape-independent pressure-impulse diagram for elastic and elastic-plastic responses of continuous beams.

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Figures

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Fig. 1

A generic P-I diagram in the space of nondimensional pressure and impulse

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Fig. 2

Idealized continuous beam system with semirigid supports (varying from simply supported, to fixed support)

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Fig. 3

Fourier series transformation of a rectangular pulse: (a) pulse time history; (b) amplitude against frequency for (i) duration td = 1 second, (ii) duration td = 0.1 second

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Fig. 4

Four typical normalized pulse-loading shapes: rectangular, concave, exponential and triangular

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Fig. 5

Moment span and support moment versus nondimensional value α

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Fig. 6

Moment-rotation and stress-strain diagrams: (a) moment rotation characteristics of support spring; (b) stress-strain diagram for the beam

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Fig. 7

Equivalent system as soon as plastic hinge forms at the mid span

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Fig. 8

Equivalent system as soon as plastic hinges form at the supports

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Fig. 9

Equivalent profile when plastic hinges form at supports and mid span

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Fig. 10

Elastic P-I diagrams for α = 1.0 for four typical descending loads

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Fig. 11

Pulse shape independent elastic P-I diagrams for four typical descending loads

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Fig. 12

Unique elastic-plastic pulse shape independent P-I diagrams for α = 1, χ = 0.087

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Fig. 13

Unique elastic-plastic pulse shape independent P-I diagrams for α = 6, χ = 0.087

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Fig. 14

Unique elastic-plastic pulse shape independent P-I diagrams for α = 10, χ = 0.087

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