Transactions on the Built Environment vol 22, 1996 WIT Press, ISSN

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1 Estimating structural components resistance to blasting loading using laboratory static tests M.Y. Rafiq School of Civil and Structural Engineering, University of Plymouth, UK Abstract This paper proposes simplified methods for determining the resistance relationships of structural components. The study will cover strain rate effects and ductility limits for certain materials. These relationships are suitable for the analysis of structural resistance to blast loading. A series of laboratory static tests have been carried out on different sizes of timber samples. The results of these laboratory tests and methods of extending these static test results to generate load resistance relationships suitable for non-linear blast loading analysis will be discussed. 1 Introduction Due to the high cost of structures to resist the effects of blast loading, design of structure against blast loading are traditionally limited to particular military structures or some particular purpose-built civilian buildings. For this reason the majority of the research data related to blast loading and techniques available for analysis of blast effects on the structures have been developed by military sources, particularly sources from the US Army. Historically, research in this area was mostly based on the study of the effects of high explosives and the data collected from World War II. During the cold war period, results from the study of the effects of nuclear weapons or large conventional weapons become available from the US army sources' \ Unfortunately, due to the unstable nature of the present world, explosions caused by terrorist activists and accidental explosions, such as chemical or gas explosions, which induce much smaller and localised loading on structures have become more common. Study of the effects of blasts on structures is not a design criteria, but mostly it is limited to checking the capacity of building subjected to the blast loading, or determining the extent of damage caused by the blast on the elements of the structure. 2. Blast load parameters Explosions by their nature release a large amount of energy, stored in an explosive device, in a relatively short time. When the blast occurs an instantaneous increase in

2 40 Structures Under Shock And Impact the atmospheric pressure will take place. This high intensity air pressure known as 'blast wave' propagates radially away from the 'burst source', known as 'Ground zero', as 'shock front'. At the same time the surrounding air is set in motion which causes an additional dynamic pressure. Figure 1.0 shows a typical pressure time history developed by a blast wave in free air. A Pressure Impulse = Area under the curve Ps = free field pressure Po = Ambient pressure Po time Figure 1.0 Pressure time history for blast in free air For analysis and design purposes usually the positive phase of the blast pressure is considered. When the 'shock front' strikes the face of a structure it reflects. The increase in pressure due to reflection, depends on the intensity of the pressure which can be many times the original 'shock front' pressure. When the wave front from an explosion reaches a structure, sudden large loads are induced, especially on those structures located in the vicinity of the explosion source. The blast pressure dissipates radially as it moves away for the burst source. Figure 2.0 shows the reflection of the blast pressure when the blast wave interacts with the front wall of the structure. Pressure Ps = freefieldpressure Pd = dynamic pressure Pr = reflected pressure Pso Clearing time Side-on pressure P(t) = Ps(s) + Cd Pd(t) tc Tp Time Figure 2.0 Typical load time history for front wall of structure (Positive phase only) As the blast wave strikes a structure it interacts with the structure and induces blast loads on the structure; a rapid variation in pressure, air density, temperature and particle velocity will take place. Imperical methods, mainly derived by the US Army source'^, are commonly used to estimate, with relative accuracy, the blast parameters such as shock front arrival time, velocity and load time history of the blast. The accuracy of the estimates depends on the accuracy of the information

3 Structures Under Shock And Impact 41 about the type and sources of explosion and the location of the source of the explosion from the structure under consideration as well as structure surrounding environment. Some important blast wave parameters are summarised as follows^: The velocity of the shock front depends only on the peak over-pressure, and is given by: Where Us is the velocity of sound Po is atmospheric pressure and Pso is peak over-pressure in free air. Maximum reflected pressure is given by: Pr =; Maximum dynamic pressure is given as: 2 IPo+Pso Relationship for positive phase pressure is given by* Relationship for dynamic pressure is given as: Relationship for side-on pressure on the structure is given by: where Cd is drag coefficient, b time constant, T is the duration of the positive phase of the blast wave. Integrating the positive phase pressure gives the impulse is as*: 3. Structure Response to Blast Loading Structure response to blast loading is an uncertain area which requires more research; although relatively more data are available on the responses of different materials to static loading. This information is presented in the form of stress strain or load deflection curves for specific materials. Except for steel and concrete, due to the uncertain nature of other construction materials, information in this area is not readily available from the Codes of Practice. Sudden application of large intensity loading, caused by blast, on the structure causes non-linear permanent deformation to the structural components. The analysis of blast loading is therefore a non-linear dynamic analysis. Hence, the study of the effects of blast loading on structures requires extra knowledge of the behaviour of the material (most of the time composite in nature) such as the strain rate effect caused by the sudden application of blast loads, degree of ductility and extent of the plastic and permanent deformation to be taken into account in the analysis or design. It is obvious that most common construction materials absorb more energy beyond their elastic limit region. The extent to which this region should be utilised totally depends on the ductility criteria of the material of which the structure is composed. These criteria can be established from laboratory tests on each material.

4 42 Structures Under Shock And Impact In order to utilise the full capacity of the structural material it would be necessary to consider both elastic and plastic regions of the load deflection curves. Blast loading is applied to the structures very rapidly. This would cause an enhancement in the resistance capacity of the material compared with the static loading. This effect is known as strain rate effect^. In the following sections static laboratory tests carried out on timber samples and methods of development of load deflection curves suitable for blast load analysis and estimating ductility limits will be discussed. This paper proposes simplified methods for determining the resistance relationships of structural components. These relationships are suitable for the analysis of structural resistance to blast loading. A series of laboratory static tests have been carried out on a number of timber samples. The results of these laboratory tests and methods of extending these static test results to generate load resistance relationships suitable for non-linear blast loading analysis will be discussed. 4. Static Laboratory Tests On Timber Samples In the present study 21 timber samples (75mmx75mm section and 1.2 m long, 1.0 m span) were tested. Samples were simply supported at each end and a single central point load was applied. All samples were tested to destruction. Figure 3.0 shows the experimental arrangements and test set-up. Figure 3.0 Timber test set-up Load was gradually applied at a rate of deformation of 0.1 mm per second. Loads and deflections were continuously recorded. Figure 4.0 shows a typical load deflection curve recorded during the laboratory test. 4.1 Simplified Load deflection curves The load deflection curves measured in the laboratory, such as the example shown in Figure 4.0, can be simplified to a number of straight lines (tri-linear curve).for blast load analysis these curves can be further simplified to bi-linear curves. The

5 Structures Under Shock And Impact 43 process of simplification for test sample No. 10 is shown in Figure Figure 4 Typical load deflection curve obtained from laboratory test To convert a tri-linear curve to a bi-linear curve it was ensured that the area under the two curves - from origin to A to C was equal to the area under the curve from the origin to B to C. Test No. 10 Converting tri-linear load deflection curve to bi-linear curve Figure 5.0 Simplified load deflection curve for test sample No Point load to UDL conversion Simple static tests carried out in the laboratory were for simply supported beams with a single central point load. Blast loads induce a uniform pressure on the structure. To convert the load deflection obtained form the laboratory tests the following two points must be taken into consideration: Convert the load deflection curve to uniform blast pressure. I PkN Beam with central Point load Central plastic hinge Beam with UDL Central ptastk hinge

6 44 Structures Under Shock Ami Impact (a) (b) Transactions on the Built Environment vol 22, 1996 WIT Press, ISSN Include the enhancement caused by rapid application of the blast loading (strain rate effect).conversion from point load to UDL Central point load Strain energy absorbed by the system Wi = Mp*20 External work done by point load We = P*y = P*6*L/2 Wi = We = = > Mp = P*L / 4 Uniform load Strain energy absorbed by the system Wi = Mp*20 External work done by point load We = 2(wL/2*y/2)= wl/2*0*l/2 Wi = We = = > Mp = w*u / 8 Bending capacity of the timber Mp is the same for both systems: P*L / 4 = w*u / 8 = = > wl = 2P (kn) The stiffness of the point load system k^ = pu / 48 El The stiffness of the UDL system k^, = (384/5)wL* / El * Kpoint = Strain rate effect Load in the laboratory is applied very slowly on the samples, while the blast load applied on the structure is very rapid. Rapidly applied loads causes enhancement in the capacity of the material. This enhancement is known as strain rate effect. Tests carried out on steel and concrete* have shown that the strain rate for the range of pressure which the structure can survive is about Test results on timber, carried out by the author, have shown that the strain rate enhancement of 1.25 is reasonable for timber as well. In the derivation of load deflection curves for timber the enhancement factor of 1.25 has been included. Results of tests on timber for a single central point load are summarised in columns 2 and 3 of the Table 1.0. The results are expressed for one metre width. Using the relationships derived in 4.2 and 4.3 the information given in Table 1.0 can be processed for uniformly distributed loads, suitable for blast load analysis. Summary of the the results for the UDL is given in Table 1.0 columns 4-6. The last column in Table 1.0 shows the ductility ratio for the timber. This is an important property which can only be determined from the laboratory test results. Variation in ductility ratio, given in Table 1.0, is due to the nature of the material, in this case timber. For timber with knots the ductility ratio is small while for timber without knots this ratio is reasonably high. Designing the structure in accordance with Codes of Practice, partial safety factors for material are applied (1.5 for concrete, 1.15 for steel etc.)*. Also, in the normal distribution of test results, the characteristic strength of 95% of the samples should be above the required limit. For blast loading all partial safety factors are normally removed. Test results have shown that a mean value of the characteristic strength (50% pass rate) would be sufficient for blast load analysis. 5. Structural response to blast loading The most simple and common system consists of representing a structure as a mass on a spring model. This is known as a Single-Degree-of-Freedom (SDOF) system. The equation of motion (Newton's Second Law), for this system is: m^ + c

7 Structures Under Shock And Impact 45 Table 1 Summary of the results of timber tests converted to UDL (strain rate effects included in UDL results only) Point Load (per m w) Converted to UDL (per ni width) Stiffness Stiffness Resistance Ductility Test No. (kn/m/m-w) Resist (kn) (kn/m/m-w) (kn/mwidth) Ratio 1 11, , , , , , , , , , ,144 15,904 7,906 10, ,230 25,446 12,650 17, , , , , , , , , , , , , , , , , , , , , , , , Average 13, , Solution to the equation motion can be obtained by trial and error and presenting the solution graphically in terms of dimensionless parameters wt and x^,, / (p/k) as shown in Figure 6.0 The solution presented in Figure 6.0 is approximated by two straight line asymptotes, which are Quasi- static and Impulsive asymptotes. For very large values of /t T (greater than 40) the Quasi-static solution will give reasonable answers. Also for very small values of / T (less than 0.4) the impulsive solution can be used with reasonable accuracy. In the region represented by analytical solution in the graph, (where value of 0.4 < /, T<40) deformation depends upon the entire load history; no approximate solution will give reasonable answers'. In this region dynamic analysis should be carried out to determined the response of the structure.

8 46 Structures Under Shock And Impact Xmax/(P/k) Quasi-static asymptote Impulsive asymptote Figure 6.0 Quasi-static, Impulsive and Dynamic response[2] When the dynamic response of a structure to an explosion caused by a small charge on a large structure is required, generally the response of individual elements of the structure are analysed. In general individual elements of the structure can be analysed using Single Degree Of Freedom SDOF systems, if the natural period of elements are sufficiently different. As a general rule-of-thumb, it may be said that two such elements may be treated separately if the periods differ by a factor of 2 or more \ In the University of Plymouth a computer program has been developed which uses the SDOF model to analyse the response of structural elements to blast loading. The system is composed of the following functions: Generates load time histories for a give weight of TNT and a given stand-off distance from the structure. Generates the load deflection curves for the structure elements. Analyses the resistance of the structure to a given loading. Carries out a recursive analysis until a failure pressure / stand off distance is found. Figure 7.0 shows an example of load time history generated by the system A Example of Pressure Time History * d» Reflected pressure» Side-on * Face-on * Reflected pressure clearing time Figure 7.0 Time (millisecond) Typical load time history generated by the system for positive duration of loading only

9 Structures Under Shock And Impact 47 Transactions on the Built Environment vol 22, 1996 WIT Press, ISSN Results of the computer analysis From the static test results summarised in Table 1.0 the resistance properties of the structure in terms of load deflection curves can be obtained. The computer program is then used to evaluate the response of the structure to the blast loading. Result of the analysis for timber results are summarised in Figure 8.0. Load deflection curve (75 mm thick timber) Structure response to blast loading Deflection (mm) Time - (msec) Figure 8.0 Load deflection curve and the resistance capacity of the 75mm timber to blast loading (simply supported beam 1.0 m span one metre width) Result of the computer analysis is summarised as follows: The structure fails at the pressure of 816 kpa (Free field pressure). This pressure was generated from 500 kg of TNT at a distance of 8.4 m from the explosion sourse, by the computer program. Quasi-static analysis predict a failure pressure of 321 kpa. This prediction is poor because the ratio of period of loading to period of structure about 10.0<40.0 not suitable for quasi static analysis. 6.0 Discussion and Conclusions From the result of the simple single point load test on timber samples the following conclusions can be made: It is possible to determine the load deflection properties of the material/structural components with reasonable accuracy, suitable for the blast loading analysis. Ductility ratio is an important property of the material. This information is not easily available in the Codes of Practice. This can be easily established from simpe static tests on material/structural components. For timbre an average ductility ratio of 1.7 was determined from the tests. The simple static described in this paper can be extended to various material for analytical modelling purposes. More research is needed to establish a realistic value for strain rate effects for various material. SDOF analysis gives reasonable results for the majority of practical cases. Quasi-static analysis, generally used in practice, is not always reliable for the prediction of the dynamic behaviour of the structure.

10 48 Structures Under Shock And Impact Due to the uncertain nature of the elastic modulus of the material, accurate calculation of the stiffness of the structural element at elastic range is difficult. Most of the structural components are made of composite which makes this task even more difficult. By using simple tests, as described in this paper, it is possible to calculate the stiffness of the structural elements with reasonable accuracy. Acknowledgements The author thanks Mr M. Penrose for helping with the laboratory timber tests in connection with his research project. References 1. The Effects of Nuclear Weapons, (ENW), US Department of Defence and Atomic Energy Commission, Baker, W. E., Cox, P. A, Westine, P. S., Kulesz, J. J and Strehlow, R. A., "Explosion Hazard and Evaluation", Elsevier Biggs, J., introduction to Structural Dynamics, McGraw Hill, ASCE Design of Structures to Resist Neuclear Weapons Effects. ASCE Manuals and Reports on Engineering Practice. No TM Structures to resist the effects of the accidental explosions. US Dept. of the Army, Picatinny Arsenal, New Jersey, , Technical manual. 6. BS8110 Structural use of concrete: Part 1, London, British Standards Institutions, 1985