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Short Paper Proc. of Int. Conf. on Advances in Robotic, Mechanical Engineering and Design 2011

Dynamic Lateral Loading of Cylindrical tubes_ A FE Analysis Reza emami1*, Epkoorapati Eshwara Prasad2, Elahe Sadat Alavi Moghadam3 1

departmant of mechanical engineering, JNTU, Hyderabad, India Email: Reza.Mtech@gmail.com 2 departmant of mechanical engineering, JNTU, Hyderabad, India Email: epkoorapati@gmail.com 3 Faculty of engineering, Bu Ali Sina, Hamedan, Iran Email: killdeer_rain@yahoo.com quasi static. The behavior of tubes with lateral and axial loads together is neglected in most researches. In this research the effects of the axial load on the lateral dent and also the effects of the lateral dents on the reduction of the axial load carrying capacity is investigated.

Abstract_ Here the effects of lateral dynamic and static loads on steel tubes are investigated with finite elements analysis using LS DYNA, which is an implicit, explicit finite element package. The effects of some parameters such as thickness, boundary conditions and axial pre loads on the residual strength are studied. The residual strength is predicted and the results are compared with results of previous methods. The finite element results are validated by comparing the results with previously published experimental results.

II. FINITE ELEMENT MODELING The finite element analysis is done using the finite elements package LS DYNA. Here a cylindrical tube is modeled with 20, 500 and 3500 mm, thickness, diameter and length respectively. These values are convenient for the sea structures, since tubes that are used have the ratio of diameter to thickness less than 300 and the ratio of length to diameter that is 7 to 15. Shell elements with Belytschko Tsay formulation are used and for more accurate analysis the mesh size is smaller at the places that the load is applied. The material model for this analysis is linear elastic with linear hardening with the material specifications shown in Table I. The concentrated lateral load for the nonlinear analysis is applied to the model in several stages in the mid span of the tube. The load displacement diagram is plotted and the results are compared with experimental results from the literature [4] in Fig. 2. Table II shows the load and dimensions for the FE and experimental analysis

Index terms_ steel tubes, axial pre loads, residual strength

I. INTRODUCTION Tubular metallic structures are widely used in industry because of their load carrying capacity. The application of these structures varies from energy absorbers in automotive and locomotive industry to off shore structures as load carrying devices. In off shore structures since they are sometimes subjected to lateral static and dynamic impact loads and also they can be simultaneous with axial loads they should be analyzed to predict the collapse of these structures. Reference [1] represents a solution to estimate the axial strength regarding the geometry of the dents using the equilibrium equations. Reference [2] represents another method for estimating the lateral ultimate load for simple or constrained supports. Reference [3] suggests replacing an ideal condition that contains a model with the dent to do the estimations with minimum data that is the depth of dent. Rickles, Hamport and Gillum [4] represented a model to estimate the residual strength of the tubes with dents that were subjected to bending moment and axial loads that relied on the experimental results. They tried to find the relation between the moment, axial load and rotation for steel tubes with dent that were used as beams. Zeinoddini, Harding and Parke [5] studied the behavior of tubes with axial preloading under lateral dynamic loads. In most of the conducted researchers the loads are considered as quasi static and in a few ones the dynamic effects of loads are considered. Also in most of the researches the local behavior of the structure is investigated but the effects of this distortion is not investigated for its effect on the reduction in the load carrying capacity. References [6, 7] represent some researches about the final deflection of the tubes that contain helpful information but these researches rely on the nonlinear behavior of tubes under lateral loading that is considered as ÂŠ 2011 AMAE DOI: 02.ARMED.2011.01.514

TABLE I. MATERIAL SPECIFICATIONS USED FOR FE MODELING

TABLE II. MODEL DETAILS OF THE TUBES

As it is seen in Fig. 1 the FE results and experimental results have the same trends and the difference can be because of the difference between the material properties and geometry. It should be noted that these values are for the conditions with constrained ends. 33

Short Paper Proc. of Int. Conf. on Advances in Robotic, Mechanical Engineering and Design 2011 III. INVESTIGATING THE BEHAVIOR OF STEEL TUBES WITH DIFFERENT CONDITIONS

C. Effects of End Supports In some previous researches to estimate the maximum load that an structure can bear, the structure is at first investigate with two constrained ends under lateral loads and finally to increase the axial load and estimating the maximum value the two ends are free and are consumed as two joints while the present research shows that the boundary conditions can be very effective in damaging the structures and it must be considered for estimating the behavior of the structure for real conditions. To investigate this effect two models are made by varying the boundary conditions for the models type1_type3. Type 1: both ends are free to tome or rotate Type2: two ends can have only axial displacement Type 3: both ends are fully constrained Fig. 4 compares the load displacement behavior for different support types. Here it can be seen that these conditions can be very effective for the deformation depth. These curves are derived in the conditions that the axial load is 30 percent of the maximum load. The research shows that the results for the type 1 and type 2 conditions are closer

A. The deflection of cross section under single lateral load Investigating the deflection of the cross section shows that at the same time that a deflection happens at the load point there is some deflection at the opposite point on the tube but the deflection is less and slower. Fig. 2 shows the time absolute deflection diagram for three points on the boundary of the tube. As it can be seen, point P2 on the cross section of the tube is moving at a higher velocity compared to point P3. If the deflection continues, the tube loses its lateral stability and the inward deflection that is seen in the back of the tube is reverses. B. Effects of Thickness One of important factors for mechanical behavior of such tubular structures is thickness. The behavior of some tubes with thickness such as 2.5, 3, 4, 4.5 cm is investigated. Here, 30 percent of the ultimate axial load is applied in the axial direction. The results are shown in Fig. 3. As an example, if a tube is loaded with 20000N in the lateral direction when the thickness is 25mm, only 50 percent of this load is enough to have a deflection as 35mm. On the other hand if the thickness is 45mm almost 85 percent of that load will be required to have the same deflection. As it is clear from Fig. 3 by increasing the thickness the lateral deflection is decreased.

Figure 4: deformation time for the tubular structure with different boundary conditions.

D. Effects of Axial Preloading Usually at the times of possible impact of ships with tubular structures, offshore structures these structures are under lateral and axial loading that can damage the structures. If the time deformation diagram is plotted for different point loads it can be understood well that. The procedure for most of the researches is in a way that they assumed a primary imperfection because of a lateral load on the tube [3]. The researches show that the deflection of the tube due to the lateral load are similar for the loads less than 20 percent of the ultimate load but for the loads more than this amount show a dramatic difference for the value of the deformation. In many previous researches it has been neglected at the time that they investigated the maximum load. In these researches at first the load has been applied to a tube without any primeval load and the tube has gone through a local deflection due to this load and after that the axial load is applied to the extent that the structure cannot bear any more loads. The difference between this load and the load that the tube without local deflection can bear is known as the reduction in the loading capacity but in this research the load has been applied to a tube with pre axial loading because this is the real condition of the situation. In this condition the deflection depth is more than the other case and also in reality the tubular structures

Lateral deflection/D Figure1 comparison of FE and experimental results

Figure 2 Time deflection for three points on the tube

Figure 3. load lateral deflection for different thicknesses and 30 percent of ultimate axial load.

ÂŠ 2011 AMAE DOI: 02.ARMED.2011.01.514

Short Paper Proc. of Int. Conf. on Advances in Robotic, Mechanical Engineering and Design 2011 at the time of impact being used by the application loads and it is clear that any tube with more local deflection depth will have less axial deflection ultimate load. By plotting these diagrams it is possible to estimate the load carrying capacity for the structures with axial loading. As an example the load deflection diagram is shown in Fig. 5 for three different cases. For a load equal to 37 percent of lateral load in the case of pre axial loading of 10 percent of the ultimate load the deflection is 21.6 mm that it has been shown in figure.

Figure7. Comparison of two methods for estimating the strength

L1 is for a case that the lateral load is applied at the same time that the structure is under axial load. L2 shows a condition that the local deflection is applied in the structure and after that the structure is increased till the structure collapses. As it can be seen in the figure in this condition more deflection is required to reach the ultimate load of the tube. It shows that in the researches that the imperfection is introduced to the structure and after that the axial load is increased to the point that the structure collapses [8, 9, 10] the value for the load is overestimated and L1 is more realistic. Usually the loads are mostly dynamic loads and the dynamic effects of loads must be considered. Here the model is subjected to dynamic loads to the value of 800 N and the results are compared for the cases that there is no axial loading and the cases that the axial loading is about 30 percent of the ultimate load that are shown in Fig. 8 and Fig. 9. The dynamic load is applied with a step function in the first time step. And the behavior of three points on the tube is considered for three points at the location that the load is applied. To make the behavior more realistic damping has been considered as 10 percent.

Figure 5. Load deflection for three different pre axial loading conditions

If a tube without pre axial loading has the same deflection a load equal to 4 percent of the lateral load is required. And now the load defection is investigated for a tube with 30 percent of the ultimate axial load. In this case a force equal to 37 percent of the lateral load can have 26 mm deflection while if a tube has the same deflection without pre axial loads the load has to be 44 percent of the ultimate load. So applying a lateral load as 30 percent of the ultimate force and 37 percent of the lateral ultimate load can have the same effects. Here the ultimate load carrying capacity for the conditions with 37 percent of the ultimate lateral loads for two cases with 10 percent and 30 percent of ultimate load are investigated using the mentioned method. For the first case at the time that 67 percent of the load is applied the tube collapses. In the second case the tube is not under lateral loads with 44 percent of the ultimate lateral load and the deflection in that is equal to a case that the tube is under 30 percent of the ultimate axial load and 37 percent lateral load is allied. In this case the new conditions are analyzed and the supports conditions for the same node is plotted and compared. As it is clear from Fig. 6 at the time that 56 percent of the load is applied the tube collapses. It can be seen that as the axial load increases form 10 to 30 percent the residual strength of the structure is reduced about 11 percent for an impact. Fig. 7 shows different ultimate load results for the model.

Figure8. Displacement of the load applied point, opposite point and the side point without dynamic load.

As it is seen in Fig. 7 and 8 the deflection behind the tube is opposite to the top point and at any time that the top point comes inside the tube the opposite point also comes inside and vice verse but the deflection value is less than the above point. It shows that the tube has not gone through a global deformation and the effects of the lateral load can be studied locally. By increasing the pre axial loading the natural frequency of the structure does not have a considerable change but the deflection curve becomes sharper that shows

Figure6. Variation of reaction force at the tube support

ÂŠ 2011 AMAE DOI: 02.ARMED.2011.01.514

Short Paper Proc. of Int. Conf. on Advances in Robotic, Mechanical Engineering and Design 2011 the structure has become more susceptible to the lateral impact.

Besides the effects of pre axial loading in the progress of damage due to impact is investigated. It is shown that due to an increase in the axial load from 10 to 30percent of ultimate load, there will be 11 percent reduction in the ultimate strength of the member. Here it was proved that considering the pre axial and lateral loads in dynamic form makes the investigation more realistic for studying the impact of ships and other impact cases. The behavior of different points of the tube is shown in the form of load displacement diagrams for both static and dynamic loads. The methods for estimating the residual strength are compared for two case that in one of them the lateral loading and axial loading are considered and the other case that the deflection is introduced and afterwards the ultimate load is estimated. The results of this comparison are shown in a diagram. A suitable method is introduced to estimatethe residual capacity. Finally the dynamic effects of the loads and quasi static effects and also the effects of pre axial loading at the time of applying the lateral dynamic loads are investigated that are shown in the forms of time deflection diagram.

Figure 9. Displacement of the load applied point, opposite point and the side point under the load.

Owning to the fact that the lateral force has been the same for both the models the deflection curve for the second case (with pre axial loading) shows more values for the deflection that means the deflection for the first case is 31 mm and for the second case 34 mm. as it can be seen that the more the imperfection of the structure the more the maximum left load of the structure is reduced. Accordingly by increasing the pre applied loads the left capacity is reduced. More investigation has been done for this case. And the results can be seen in Fig. 9. A comparison between the static and dynamic analysis has been done using 800 N load within 0.35 seconds. As it can be seen the maximum deflection in this case is 25 and 29 mm for static and dynamic loads respectively.

REFERENCES [1] C.P Ellinas, “Ultimate strength of damaged tubular bracing members”. ASCE, j of structural eng., Vol.110, No.2, PP 245–259, 1983. [2] C.P Ellinas, S Valsagrad, “collision and damage of offshore structure”. ASME, Vol.112, No.2 pp 475–495, 1985. [3] L.A. Pacheco, S. Durkin, “Denting and collapse of tubular members– A numerical and experimental study,” International journal of mechanical sciences, Vol. 30, pp 317 –331, 1988. [4] Rickles, J.M, Hamport, T.E Gillum, “Residual Strength of damaged offshore steel tubular bracing,” 24 th Annual offshore technology conference, May 1992. [5] M. Zeinodini, J.E. G.A.R. Parke,” Dynamic behavior of axially pre loaded tubular steel members of offshore structures subjected to impact damage,” Ocean engineering, Vol 26, pp. 963–978, October 1999. [6] J.D Allan, J. Marshall, “the effects of ship impact on the load carrying capacity of steel tubes,” Health safety exclusive, OTH90 317, 1992. [7] P.A. Frieze, S.R Cho, “Impact Damage and assessment of offshore tubular,” 25 th offshore technology conf. pp. 193–200, 1992. [8] J. Harding, T. Onoufriou, “Behavior of ring stiffened cylindrical members damaged by local denting.” Journal of constructional steel research, Vol.33, pp.237-257, 1995. [9] J.F Rambech, T. Dahl, “Capacity of stiffened tubular cross section subjected to concentrated load impact from ship collision,” 13 th international conference on offshore mechanics, 1994. [10] J.M Ricles, W.B lampore W.B, T.E Gillium,” Residual strength of damaged offshore steel bracing,” 24th international conference, OCT 6938, pp 585-595,1992.

Figure 10Load_lateral Deflection curves under lateral dynamic loads

CONCLUSIONS In this paper the behavior of tubular steel members is investigated both under static and dynamic loads. The effects of parameters such as thickness change and also boundary conditions are studied.