Integrated impact failure analysis of concrete slab structures with consideration of impact load characteristics

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Nuclear Engineering and Design 150 (1994) 295- 301

Nuclear Engineed.ng and Design

Integrated impact failure analysis of concrete slab structures with consideration of impact load characteristics M i c h a e l W. K i n g a, A y a h o M i y a m o t o b aSun-Mix Concrete Sdn. Bhd., 11500 Penang, Malaysia bDepartment of Civil Engineering, Kobe University, Rokkodai, Nada, Kobe 657, Japan

Abstract

This paper describes a method of integrating a multi-mass model, which is applied to simulate the impact load characteristics for an impact collision, to a dynamic finite element analysis for concrete slab structures through an interactive procedure. Examples of the applicability and merit of the proposed linked procedure are then discussed.

1. Introduction An integrated analytical procedure for analysis of reinforced concrete structures under soft impact collisions is proposed. The impacting body is modeled using a lumped-mass model, which is capable of predicting the resultant impact load characteristics for an arbitrary collision (Miyamoto, 1992). However, a non-linear dynamic layered finite element procedure is employed for predicting the ultimate behaviors and also impact failure modes of concrete slab structures (Miyamoto, 1991). Both the analyses are then linked up through a dynamic interactive procedure. The interactive procedure is capable of simulating accurately the effects of the effective mass and effective stiffness of the concrete structure, and the results can be upgraded at each time step. Furthermore, the energy transmission process during impact collision also can be predicted. Finally, the ultimate behaviors and failure modes for reinforced concrete handrails under

impact collision are studied as a case-study. The kinetic energy transmitted by an impacting body, as well as the energy absorbed by concrete slab structures are found to be affected by the final failure modes in the structure.

2. Integrated analysis

2.1. Linking procedure Linking (coupling) the multi-mass model to a dynamic response analysis of concrete structures, through an interactive process, is necessary for a complete analysis of an entire impact collision (King, 1991a,b, 1992). It has been reported that uncoupling of both analyses would produce adequate results for the total behaviour of concrete structures subjected to soft impact (Eibl, 1987). Uncoupling the analyses would result in imaginary (unrealistic in some cases) impact load characteristics being speculated, as shown in Fig. 1.

0029-5493/94/$07.00 © 1994 Elsevier Science S.A. All rights reserved SSDI 0029-5493 (94) 0 0 7 4 3 - I

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M.W. King, A. Mivamoto / Nuclear Engineering and Design 150 (1994) 295 301

Impact force

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The impact load that occurs during an impact collision is a function of the spring constant k t and coefficient of viscous damping ct applied in the multi-mass model. In other words, the impact force during the impact collision depends on the degree of resistance from the concrete target. A high degree of resistance (stiff structures) would result in a larger maximum impact force, while a lower degree of resistance would produce a smaller maximum impact force. When cracking or failure occurs in the concrete structure, the spring constant k t would automatically reduce to a smaller value, which would indirectly cause the impact force to decrease. When the analyses are uncoupled, the multi-mass model would result in an increasing impact force, which would not be realistic. The authors consider that it is feasible to uncouple the analyses when determining the impact load characteristics and also the design impact load. However, when a detailed study of the dynamic behavior of the concrete structure is necessary, coupling of both analyses is important. An

outline of the procedure employed for coupling of both analyses is shown in Fig. 2. Another main problem when considering the dynamic behavior of concrete structures is the evaluation of the effective mass as well as the effective stiffness of the structure that is directly involved in the impact collision. By applying an interactive method, as shown in Fig. 2, the total mass of the structure as well as the effective stiffness from the dynamic behavior analysis can be directly input into the multi-mass model. This results in a proper and updated evaluation of the effective mass as well as the effective stiffness of the concrete structure. The linked analysis can be performed until structural failure occurs or until the end of the impact collision. By checking the data from both analyses, the dynamic behavior of both the concrete target and the impacting body can be effectively evaluated. The amount of kinetic energy that is transmitted into the concrete structure can be evaluated, thus being major assistance when considering the design of concrete structures subjected to impact collisions.

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M.W. King, A. Miyamoto / Nuclear Engineering and Design 150 (1994) 295-301

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2.2. Case-study Two different analyses are carried out to study the merit of employing the linked analysis for impact collision (King 1992a,b). First, the collision of a single solid mass of 2.5 tonf weight into a reinforced concrete handrail (Fig. 3(a), Model I) and the collision of a system of three interconnected lumped masses, with total weights of 1.2 and 1.6 tonf, into a similar handrail (Fig. 3(b), Models II and III) are considered. A practical example of the application of the analytical procedure is the analysis of impacting bodies colliding into concrete handrails attached

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to expressways. Three different types of impacting body, i.e. Models I, II and III in Fig. 3, are considered. The analysis with Model I is meant to simulate the results of full-scale tests performed in the past on a similar type of reinforced concrete handrail (Bull, 1991). Full-scale tests are performed on actual reinforced concrete handrails, where a single solid metal mass of 2.5 tonf weight is impacted from a height of 105.2 cm (potential energy, 2.63tonfm) in a motion similar to a pendulum. In contrast, Models II and III are meant to simulate vehicles crashing into a concrete handrail (King, 1992a). The impacting body in Model II is presumed to be that of a front-

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Fig. 4. Layered finite element meshes for reinforced concrete (RC) handrail (1/2 portion). impact collision energy. Therefore, it is necessary to design concrete handrails to fail under bending, because energy absorption is better during ductile type o f failure. The collision speed and total weights for Models II and I I I are based on the design specifications o f an expressway in J a p a n ( H E P C , 1972), while the spring constant is based on the average stiffness o f a normal automobile obtained f r o m static failure (crush) tests (Kamal, 1982). Details o f the analytical results on the three different models are given in Table 1. Failure is defined in the analysis as the point where concrete crushing occurs. Local deformation is a main problem when dealing with impact loads, espe-

engine automobile, while Model I I I represents a small truck. The finite element mesh for the m o d eled handrail is illustrated in Fig. 4. A n ideal design procedure o f concrete handrails for expressways is quite difficult. A n ideal handrail should be able to withstand the impact f r o m a colliding vehicle. F o r comparatively slow collisions, the handrail should act more as a rigid barrier and allow the colliding vehicle to absorb most o f the energy at impact. However, for collisions at high speeds (large a m o u n t o f m o m e n tum), the handrail should not act as a solid barrier to stop the collision but more as a flexible wall that is capable o f absorbing most o f the Table 1 Results of analysis on reinforced concrete handrails Model

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699 13745 13947

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aMaximum deflection at loaded point. bAt section C-C of Fig. 4. CAmount of kinetic energy lost in impacting body. aObtained by integration of impact load midspan deflection curve. eB, bending; PS, punching shear.

M. IF. King, A. Miyamoto / Nuclear Engineering and Design 150 (1994) 295-301

cially during impact loading with high loading rates. The curvature at failure (l/R) is introduced here to study quantitatively the effects of local deformation. Since the curvature is affected by the size of the maximum deflections at the loaded point, it is impossible to compare directly the curvature for different loading cases. Therefore, the index of local deformation given by {curvature at failure (I/R) / deflection at failure (6u)} is applied here. From Table 1, the results for Models II and III are approximately similar, while Model I indicates a totally different type of behavior. The loading rate for Model I is comparatively large, but the amounts of impulse and kinetic energy transmitted remain small. This is due to the large impact force being applied in a very short time duration, causing local failure to occur immediately. As in Models II and III, the impact forces at failure are relatively small but, because of the small loading rate, the amounts of impulse and kinetic energy lost in the impacting body increase tremendously. Only a small amount of kinetic energy is dispersed during local punching shear failure, while the bending failure mode indicates the capability to disperse a larger amount of kinetic energy. Also, the index of local deformation corresponds well to the failure modes, with a high index of local deformation during punching shear failure. The impact failure mode for an impact collision can be determined based on the deformation characteristics in the handrail. Fig. 5 shows the results of the impact force-deflection relationship for analysis of the three models. The distributions of the deflections in the cross-sections at failure are shown in Fig. 6. Fig. 5 shows that the impact force-deflection relationships for both Models II and III are similar, while the results of Model I are totally different. The loading rate in Model I is larger, because the impacting body is rigid, resulting in a higher initial stiffness as well as loading rate. This phenomenon also can be attributed to the effects of inertia in the structure. A larger amount of inertia can be expected under higher loading rates. In the case of both vehicles, deformation of the vehicles occurs during the collision, resulting in a slow loading rate. Although the maximum impact force is larger for

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Model I, the deflection at failure is small when compared with those in the other two models. This phenomenon can be attributed to the short duration of loading in Model I. The final amount of deflection in the handrail of Model I can be expected to be larger, i.e. appearing only after failure (concrete crushing) occurred. From Fig. 6, it is clear that the deflection is concentrated only at the middle of the slab for Model I, while the deflections are distributed all over the structure for Models II and III. Fig. 7 shows the expected crack patterns in the front and rear faces from the analysis for Models I and II. The crack patterns for both models are considerably different. The results from Figs. 5 and 6 indicate that, in the analysis of Model I, the effets of inertia and higher modes of vibration are evident, and this causes local failure to occur. This is the main cause of the crack patterns in Fig. 7(a). In Fig. 7(b), total structural failure can be expected, so the crack patterns are uniformly distributed. Comparing Fig. 7(a) and the crack patterns obtained from the actual full-scale tests for Model I shows that the actual crack patterns are roughly simulated. Fig. 8 shows the deformation mode at failure in the handrails, as found from analysis. It is clear that the deformation mode for Model I indicates punching shear failure at the middle of the handrail, while bending or total structural failure can be expected for Model II.

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M.W. King, A. Miyamoto / Nuclear Engineering and Design 150 (1994) 295 301

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3. Conclusions A multi-mass model is applied to simulate the impact load characteristics of deformable impacting bodies during impact collision. The model is then linked to a dynamic response analysis of concrete slab structures, through an interactive process, to enable complete analysis of the interaction between the impacting body and concrete

target during soft impacts. The linked analysis is considered to be a powerful tool for application to the dynamic design of concrete structures that are subjected to soft impact collisions. The main conclusions from the present study can be summarized as follows. (1) Linking the multi-mass model to a dynamic response analysis of concrete structures, through an interactive process, would enable complete

M. IV. King, A. Miyamoto / Nuclear Engineering and Design 150 (1994) 295-301

while a deformable body (vehicle) would more likely cause flexural failure to occur. (3) The kinetic energy transmitted by an impacting body, as well as the energy absorbed by the conrete slab structure are affected by the final failure modes in the structure. Energy absorption is better during bending failure, while punching shear failure results in a lower amount of energy being absorbed.

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global analysis of soft impact collisions to be performed. The effective stiffness and effective mass of the concrete target can be simulated accurately and upgraded at each time step, using such a procedure. Furthermore, the amount of kinetic energy that is transmitted into the concrete structure can be evaluated, thus being a major assistance when considering the design of concrete structures during impact collisions. (2) The impact failure modes in reinforced concrete handrails are affected by the rigidity of the impacting body. The punching shear failure mode is dominant during the collision of a rigid body,

J.W. Bull (ed.), Precast Concrete Raft Units, Blackie, London, 1991, pp. 101 131. J. Eibl, Design of concrete structures to resist accidental impact, Struct. Eng. A 65(1) (1987) 27-32. HEPC, Manual for Setting of Preventive Structures, Hanshin Expressway Public Corp., Osaka, 1972 (in Japanese). M.M. Kamal and K.H. Lin, Collision simulation, in M.M. Kamal and J.A. Wolf, Jr. (eds.), Modern Automotive Structural Analysis, Van Nostrand Reinhold, New York, 1982, pp. 316-355. M.W. King, A. Miyamoto and T. Ishibashi, Modeling of impact load characteristics and its application to analysis of RC slab structures, Proc. Jpn. Conc. Inst. 13(2) (1991a) 1039-1044. M.W. King, A. Miyamoto and M. Fujii, Analytical prediction of impact failure modes in concrete slab structures due to accidential collisions, Proc. Int. Symp. on Natural Disaster Reduction and Civil Engineering, Japan Society of Civil Engineers Kansai Chapter, September, 1991b, pp. 147 158. M.W. King and A. Miyamoto, Interfacing of impact load characteristic analysis with dynamic response analysis of concrete slab structures, Mem. Grad. School Sci. Technol. Kobe Univ. 10A (1992a) 41 71. M.W. King, A. Miyamoto and M. Fujii, Application of layered finite element method for analysis of impact failure in concrete structures, Proc. Int. Symp. on Impact Engineering, Vol. I, 1992b, pp. 235-240. A. Miyamoto, M.W. King and M. Fujii, Nonlinear dynamic analysis of reinforced concrete slabs under impulsive loads, J. Am. Conc. Inst. 88(4) (1991) 411-419. A. Miyamoto, M.W. King and T. Ishibashi, Simulation of impact load characteristics and investigation of design impact load, J. Struct. Eng. Jpn. Soc. Civil Eng. A 38(3) (1992) 1515-1528 (in Japanese).