Structural strength of work boats and high speed crafts with floating frames

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1 Structural strength of work boats and high speed crafts with floating frames JON E N G L U N D j o n e n g 9 k t h. s e M a s t e r T h e s i s, K T H C e n t r e f o r N a v a l A r c h i t e c t u r e S t o c k h o l m D e c e m b e r

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3 ABSTRACT This thesis investigates the usage of floating frames in boats. A floating frame is a transverse frame fitted to the longitudinal stiffener flanges without contact with the shell plating, as opposed to the traditional fixed frame which is welded to the shell plating with the stiffeners most commonly fitted through cut outs in the frame. To study the floating frame structure in a bigger perspective a finite element analysis is performed on a mid ship compartment of an existing 60 m high speed catamaran ferry. The analysis is performed on a model with scantlings as the original craft but with introduced floating frames. Stresses are analysed with respect to maximum allowable stress as given in the DNV-rules for HAZ. High stresses are found in the bottom of the frames due to the reduced bending stiffness without effective flange from the shell plating. A large deformation in the shell plating relative the transverse frames is found, creating high stresses in the stiffener webs. This deformation is induced by a large vertical deformation of the frames. It is concluded that the transverse frames requires an increased stiffness to achieve acceptable stress levels. Possible solutions to increase stiffness are discussed, further studies are required to achieve an acceptable structure. A design criterion for stiffeners in floating frame constructions is evaluated. The criterion considers the interaction between a concentrated contact force and a bending moment with the purpose of simplifying the design process of stiffeners. The criterion is a combination of design methods from DNV HSLC and Eurocode 9. The design criterion is found to give conservative results, although not unreasonably conservative. The criterion is suitable for the design of smaller work boats where the scantlings traditionally are not very optimized. 3

4 CONTENTS Abstract... 3 Contents... 4 Introduction... 5 Background... 5 Objectives Finite element analysis of the 60m Jumbo Cat Geometry Element mesh Loads Boundary Conditions Verification Results Analysis of floating frames Maximum allowable stress levels Comparison between fixed and floating frames Decreased stiffener spacing Increased frame thickness Combined increased frame thickness and decreased stiffener spacing Stiffener analysis Suggestions Conclusions Stiffener design Interaction between bending moment and concentrated contact force Finite Element Analysis Eurocode rules combined with DNV HSLC Panel Tests Conclusions...35 Thanks...35 References...35 Appendix 1 Material properties...36 Appendix 2 Profile drawing...38 Appendix 3 Model Flaw...39 Appendix 4 Aluminium alloy 6082 T

5 INTRODUCTION The purpose of this thesis is to study the effects of a floating frame structure in combination with extruded aluminium panels. Finite element compartment models of a 60 meter catamaran ferry are created to examine the feasibility of using the floating frame structure on a large high speed ship, and an evaluation of a proposed design rule for stiffeners in such structure is performed. BACKGROUND Aluminium is a commonly used material in construction of small work boats, high speed passenger ferries and catamaran ferries. The construction of ship hulls is traditionally a time-consuming task, with the fitting and welding of panels, stiffeners, and bulkheads. With the relief project utvikling av kostnadseffektive båter i aluminiumspaneler sanctioned by The Research Council of Norway the goal is to find methods to reduce the production cost of aluminium hulls for small workboats. By the use of prefabricated aluminium panels, with extruded and friction welded profiles, see Figure 1, the construction time and cost is significantly reduced. These panels are used for the ships sides, bottom and deck. The ability to create complex structures is somewhat limited with pre-fabricated panels, as the bending process is quite difficult, where double curvature of the panels is particularly difficult to achieve. Figure 1. Cross-section of extruded profiles with T-shaped stiffeners. The extruded profiles are welded together by friction stir welding (FSW), this automated process reduces the welding time, creates a more even surface and reduces the internal stresses. As opposed to other welding techniques no weld metal is required, which improves the work environment with the absence of toxic fumes. Traditionally bulkheads and frames are welded directly on to the shell plating, and the stiffeners welded to the plating are fitted through cut outs in the frames and bulkheads. The construction time can be significantly reduced by welding the transverse frames to the flanges of the longitudinal stiffeners, a so called floating frame, see Figure 2. This method reduces the time spent on both welding and fitting. Calculation methods for this type of construction, however, are not described in the common rules for small boats (DNV High Speed, Light Craft and Naval Surface (HSLC) [1], Nordic Boat Standard (NBS) [2]). In addition it is today not an accepted construction method in either set of rules. Figure 2. Bottom section of hull with floating frames and prefabricated aluminium panels. 5

6 Floating frames is not a new concept, Spencer mentions floating frames in a paper from 1975 [3] and boats using these frames have proven to withstand heavy loads over many years [4]. Floating frames are not a common design for larger ships however, Herrington and Latorre performed an analysis on a 33- knot aluminium catamaran ferry in 1998 [5], with alternating floating and fixed frames, which was constructed in compliance with the ABS High Speed Craft rules. OBJECTIVES This thesis is split into two chapters. The first chapter is an analysis of a floating frame construction on a larger ship. The analysis is performed with finite element models. The purpose of this analysis is to identify possible issues with this construction method, with the long term goal of providing the groundwork for a possible future DNV approval. As the stiffeners in ships constructed with floating frames are subjected to load cases not described in the common design rules for ships, a design method for stiffeners is evaluated in chapter 2. Finite element analysis is a costly process and the purpose of this design method is to create a simple and cheap method for the design of ships with floating frames. 6

7 1. FINITE ELEMENT ANALYSIS OF THE 60M JUMBO CAT Several models were created based on Fjellstrand s 60 meter Jumbo Cat, a car and passenger high speed catamaran ferry, with main characteristics in Table 1. The models are based on frame #27 for the transverse frames and frame #26 for the bulkheads. No drawings are included in this thesis, due to confidentiality reasons. Table 1. Main characteristics of Jumbo Cat 60 Main characteristics Vessel forward speed, V Length between perpendiculars, L pp Breadth, B Fully loaded draught, T Displacement, Δ Breadth of one hull at water line amidships, B hull Value 35 knots 54 m 16.2 m 2.2 m 580 tonnes 3.7 m A finite element analysis has previously been performed on this ferry by O. D. Ökland [8]. This analysis studied the effects of an increased frame spacing of 20 % with a compartment model with extent and load conditions similar to the floating frame models. Due to the many similarities, data from this analysis will be used to verify the created models. The primary purpose of the analyses is to study the structural response of floating transverse frames and to recommend possible modifications of the structure to meet the maximum allowable stress levels of DNV HSLC. Two finite element (FE) models were created for this purpose; one fixed and one floating with the same scantlings used for both models. The fixed model was created to serve as a comparison for the floating model. The models are prismatic longitudinally, meaning a constant longitudinal cross section. The modelled compartment was the mid ship section, extending between two bulkheads with eight frames in between. Since the ferry is symmetrical along its longitudinal axis, only half the cross section was modelled. The focus of this analysis is local loads and local structural responses, and as the superstructure primarily adds to the global strength of the vessel it was not modelled. Figure 3 shows the extent of the compartment model. Figure 3. Extent of compartment model. 1.1 GEOMETRY To enable the possibility of varied stiffener dimensions as web height and stiffener spacing, a script was created in Matlab. This script enables the user to quickly generate a hull section with varied dimensions. This script generates a macro to be used with the pre-processor MSC Patran 2008 r1 to generate the ship geometry, which then can be meshed. The script is able to generate three basic hull sections, with a frame or bulkhead in the middle with a longitudinal extent of half the frame spacing at each side. The three basic 7

8 hull sections are bulkhead, floating and fixed frame, see Figure 4. Multiple frames are then generated to form a compartment. Figure 4. Three different cross sections, from left to right: bulkhead, fixed frame and floating frame. Due to the complex shape of the hull, this script has a number of limitations; to enable an efficient mesh of multiple joined surfaces in MSC Patran, the simplest solution is to ensure all neighbouring surface edges are of the same length and sharing two corners. Otherwise the meshed surfaces are likely to have overlapping nodes at the edges, making them two disconnected surfaces, as illustrated in Figure 5. This makes creating surfaces extending over multiple surfaces difficult, which is the case for the brackets at the centre of the hull; these are added manually and given an approximate shape. Surfaces with two shared corners Surfaces with overlapping corners MESH One homogenous surface, 15 nodes Two unconnected surfaces, 18 nodes Figure 5. Meshing of two adjoined surfaces. The transverse bulkhead above the tunnel is stiffened on the original ship, but to simplify the modelling the shell thickness is simply doubled to account for the stiffeners, cut outs in the bulkhead are also not modelled. Since the studied load case is bottom slamming, which primarily affects the bottom structure, this simplification does not have a large impact. However, if another load case was to be studied, for example asymmetric slamming which generates large transverse bending of the hull, the bulkhead could be modelled with layered elements to account for the stiffeners. The shell is grouped in to six different plate fields, see Figure 6, where each field can be assigned different dimensions. 8

9 Field 6 Field 4 Field 5 Field 2 Field 3 Field 1 Figure 6. Six plate fields. Due to the stricter design specifications of the bottom section, the stiffeners in Field 1 have a larger web height than the neighbouring fields 2 and 3. The intersection between these fields is a difficult section to generate automatically with a script, with both varied stiffener spacing and height. To achieve an accurate geometry the geometry is simplified in those areas, which creates sharp corners not ideal for finite element analysis, as seen in Figure 7. Figure 7. Modelled floating transverse frame at turn of bilge. 1.2 ELEMENT MESH The entire compartment has been modelled with 3 and 4 node shell elements, using the Abaqus S4R element for stiffener flanges and S4R5 for the rest of the model, discussed in greater detail in Chapter 2.1. The stiffeners were modelled with two elements over the height of the web and one over the breadth of the flange. Due to the larger mesh size of the surrounding elements this creates elements with high aspect ratio at the stiffener flanges, in addition the web frame elements at the stiffener intersection shares the breadth, see Figure 8. Six elements have been used over the height of the web frames, as opposed to the by DNV Classification Notes 30.8 [9] recommended three, this gives the elements at the stiffener intersection on the frame an aspect ratio of 2.5, where the highest recommended ratio is 3. 9

10 Figure 8. Element mesh on stiffeners and web frame, fixed and floating model. The element mesh on the shell plating is three elements between each stiffener and ten over the length of one frame spacing, DNV recommends an element size of one stiffener spacing, but to avoid a too high aspect ratio at the stiffener flanges a finer element mesh was chosen. 1.3 LOADS For this thesis only load condition 2 in DNV HSLC C200 is studied, see Figure 9. This is symmetrical bottom slamming and is commonly the design load condition for the bottom structure. As stated in DNV HSLC it is applied on the bottom panels of the centre frame of the compartment and sea pressure is applied on the bottom panels of the other frames. In addition a deck load is added on the modelled car deck. The static sea pressure was calculated by Ökland [8] to a linear variation from 50.0 kn/m 2 at the keel to 32.6 kn/m 2 at the waterline, although the static pressure only extends to the upper turn of bilge for this load case. The deck load is to be taken as the worst of an evenly distributed pressure and a number of point loads representing wheel loads on the deck, Ökland found both load cases to give almost identical results. Since an even pressure is easier to model, this was the chosen load case with a constant pressure at 4.0 kn/m 2. LC2 Figure 9. Load condition 2; symmetric bottom slamming, with vertical extent from keel to upper turn of bilge. The design bottom slamming pressure is given by sl 1.3 l 0 cg p k T a na (1) 10

11 with the assumption of a constant dead rise between the ships centre of gravity and the studied frames. Ökland calculated this pressure to 77.5 kn/m 2 for the same craft with a 20 % increased frame spacing. Only the design load area, A in Equation (1), is dependent of the increased frame spacing, where this area is the frame spacing times the length of the frame between the upper turn of bilge. The slamming pressure is calculated for the model as = 81.9 kn/m 2. Additional loads as load from superstructure or engine is not modelled. 1.4 BOUNDARY CONDITIONS As the ship and all loads are symmetric about the vertical plane through the centre line, symmetry boundary conditions have been used at this plane. DNV Classification Notes 30.8 states a local model should preferably extend from the middle of one compartment to the middle of the next compartment, with a bulkhead in the middle of the model and symmetry boundary conditions at the ends. The objective of this analysis is to investigate the floating frames and for this reason the model extends between two bulkheads, covering one compartment, the modelled frames are shown in Figure 10. Analogous to the symmetry boundary conditions for a model extending between the middle of two compartments are bulkheads fixed in deflection for a model extending between two bulkheads, as demonstrated in Figure 11. Figure 10. A modelled section containing eight web frames and two bulkheads. 11

12 Bulkhead Maximum deflection Maximum bending moment No rotation Symmetry Web frame No deflection Figure 11. Principal (local) deflection pattern of a longitudinal compartment. By using these boundary conditions the inclusion of bulkheads in the compartment model is essentially pointless. 1.5 VERIFICATION As results from a similar finite element analysis are available in [8], a comparison between the fixed model and the Ökland model will be performed. Although there is no reason to believe the Ökland analysis is more correct, if the results from the analyses are similar it is a good indication that the models give a correct representation of the real structure. The Ökland model has a 20 % larger frame spacing and it must be considered in the evaluation Results A transverse line load q is acting on the web frames, where q = p l, p is the bottom pressure and l is the distance between web frames. The static sea pressure is, as opposed to the slamming pressure, not dependent of the frame spacing, which means the line load acting on the Ökland model is 1.2 times the load acting on the fixed model. Assuming the stresses in the web frames are proportional to q and as all other geometry is the same in the two models, we have the following relation between the stresses: σ Ökland = 1.2 σ fixed. The results available from the Ökland analysis are printed contour plots and only rough estimates can be made from these results. Several differences between the Ökland model and the fix model can be found; the Ökland model consisted of a bulkhead in the middle and three frames at each side of the bulkhead, where the slamming load was applied at the frame with a bulkhead. Symmetry boundary conditions were applied at each end of the model and the longitudinal stiffeners were modelled with beam elements. To receive a better comparison between the two models, a frame in between the ends and the slamming load was studied; Frame F in the Ökland model and the equivalent Frame H in the fixed model, see Figure

13 Ökland model A B C D E F G Slamming pressure Fixed model A B C D E F G H I J Slamming pressure Figure 12. Studied frame in each model. Contour plots from each analysis can be found in Figure 13 and Figure 14. Although the mesh is finer in the fixed model, some similarities can be seen in the stresses for both plots; both models have stress concentrations at the top side of the frame at the turn of bilge, the stress magnitudes are slightly higher at the inside frame (right side in plots) than the outside for both models. Figure 13. Von Mises stresses [Pa] in Frame F, Ökland model. 13

14 Figure 14. Von Mises stresses [MPa] in Frame H, fixed model. Similar stress patterns can also be seen when studying bending stress in the frame, see Figure 15. The neutral axis of the frame in the bottom of the hull coincides at around one third of the web height for both models. Stress concentrations occur at the bottom corner of both frames, although much more defined in the fixed model most likely due to the sharp corner of the frame. Figure 15. Contour plots of transverse bending stress, left fixed model and right Ökland model. A more detailed study of the stress levels was made for six areas of the frame, see Figure 16. Stresses in the fixed model were taken as the highest element stress in the studied areas. Since the only source for the stresses in the Ökland model was the above contour plot, the data is a very rough estimate. Table 2 displays a comparison of the stress levels. Locations with low stresses have good similarity between the results, but locations 3 and 5 with high stresses deviate more. 14

15 Figure 16. Locations at the web frame. 2 Table 2. Comparison of von Mises stresses in both models. Location Ökland Fixed Fixed*1.2 [MPa] [MPa] [MPa] Since the element sizes of the two models differ a lot and the available data from the Ökland model is limited, it is difficult to make any definite conclusions. The geometry is less smooth in the Ökland model and stress concentrations are expected in the corners. In light of this the results are not too dissimilar; similar stress patterns can be recognized in both models and the stresses are around the same levels in large parts of the frames. 1.6 ANALYSIS OF FLOATING FRAMES In this chapter several models with floating frames are studied. Comparisons are made between them and suggestions of possible improvements of the structure are made Maximum allowable stress levels Two aluminium alloys are used for this compartment; NV-5083, used for cold rolled structural components as web frames and brackets, and NV-6082 for extruded parts as stiffeners and shell plating. DNV HSLC defines strength with the factor f 1, see Table 3. See Appendix 4 for a description of the alloy Table 3. Factor f1 as defined in DNV HSLC. Alloy Yield strength [MPa] f 1 f 1 (HAZ) NV NV This factor is used to determine maximum allowable stress for different structural components, see Table 4. The most critical regions in the floating frame structure are in HAZ, as the intersection between transverse frame and stiffener or the frame flange. Due to this the maximum allowable stresses used will be for HAZ. 15

16 Table 4. Maximum allowable stress in dynamic loading for different alloys in HAZ. Alloy NV 6082 (HAZ) NV 5083 (HAZ) Stress [MPa] eqv. stress bending shear eqv. stress bending shear eqv. stress bending shear Plating 220 f f 1 90 f Stiffeners and girders 200 f f 1 90 f Comparison between fixed and floating frames The first FE-model with floating frames had the same scantlings as the fixed model, the purpose of this model was to investigate the structural response of the floating frame structure and to study the difference in stress levels compared to the fixed frame. This study concentrates on a frame in the middle of the compartment (Frame F in Figure 12.) Figure 17 shows contour plots with equivalent von Mises stress for both models, the stress range in the plots are chosen so dark red corresponds to the maximum allowable stress. The floating model exceeds the maximum allowable stress levels in several regions, most notably Region 2 and 3 where the peak stress reaches 200 MPa in the frame flange, however the fixed model has a peak stress of 160 MPa in the same area at the frame flange. This can largely be explained by model flaws, with the corner in that region which is even sharper for the floating model. See Appendix 3 for a more detailed study of the model flaw. Region 3 Region 2 Region 1 Figure 17. Von Mises Stress [MPa] for Frame F, fixed and floating model. For a floating frame structure the surrounding shell plating does not contribute to the bending stiffness and strength as opposed with a fixed frame. The neutral axis will therefore be located higher up on the web for a floating frame and as can be seen in Figure 17 the peak stress occurs at the bottom of the frame web for the floating frame, where the maximum stress occurs at the top for the fixed. As the original ferry was designed as a fixed construction, the floating frame will require an increased stiffness to satisfy the design criteria. This becomes even clearer when studying the shear and axial stresses in the frame, Figure 18, both of which exceeds the maximum allowable stress levels. 16

17 Figure 18. Transverse axial stress [MPa] left and shear stress [MPa] right, floating frame. The stresses in the shell plating of the floating construction are very low, with a maximum equivalent stress at 34 MPa, and it is the only structural component of the model where the fixed exceeds the floating model in maximum stress, both of which are well below maximum allowable stress levels, see Figure 19. It should however be noted that the studied load case is the design load case given by DNV HSLC for transverse frames, and is most commonly not the design load case for stiffeners or shell plating. Figure 19. Von Mises stresses [MPa] in the bottom shell plating for Frame E and F, floating left and fixed right. High stresses can be found in the stiffeners of the floating frame model, where two stiffeners exceed maximum allowable stress, Stiffener A and B as labelled in Figure 20. These stiffeners are smaller than the stiffeners below and connect with the frame at a highly loaded point. Stiffener A Stiffener B Figure 20. Stiffener A and B at turn of bilge. 17

18 Figure 21 shows shear and equivalent stress in Stiffener A. The predicted maximum equivalent stress reaches 103 MPa in the stiffener web, exceeding allowable stress by 7 MPa. The maximum shear stress was found at 56.7 MPa, also in the stiffener web, which is far above the maximum allowable shear stress at 43.2 MPa. Figure 21. Von Mises stress [MPa] left and shear stress [MPa] right. Stiffener A intersection with Frame E. However, it should be noted that these stresses are very approximate for an element mesh this rough. It is particularly an issue for the stiffener flange; the bottom slamming pressure is transferred by the web frame to the shell plating at the sides, it is transferred from the web frame through the stiffeners out to the shell by a force normal to the stiffener web, this is illustrated in Figure 22. This is not an optimal load case for a shell element; the shell element has five integration points over the thickness of the element and during an analysis the material response at each integration point is calculated, giving good estimations for bending around the x- or z axis as defined in Figure 23. For a force acting in the x-direction at the stiffener flange, deformations are only calculated at each node, making the stresses very approximate for the rectangular flange elements. A more detailed study of the stiffeners is performed in Chapter 2.7. Transverse force Normal force Sea pressure Figure 22. Principal deformation of a hull with floating frames. 18

19 Figure 23. Stiffener modelled with shell elements Decreased stiffener spacing A third model was created with 33 % reduced stiffener spacing. The theory behind was for an infinite number of stiffeners the frame will behave similar to a fixed frame, and thus an increased number of stiffeners will increase the resemblance of a fixed frame. This under the assumption a stiffener contributes a small degree of effective flange from the shell plating to the frame. The weight of the structure was kept constant for this model by reducing the stiffener area of 33 %. To determine the stiffener dimensions three conditions was made; the flange breadth would remain to avoid small elements at the frame intersection, the moment of inertia I xx was reduced by 33 % and the slenderness of the stiffener web would remain constant to avoid buckling. For a stiffener as shown in Figure 24 the slenderness factor λ was calculated as: h h h (2) t w1 w w tw w t 1 w where index 1 denotes the original dimensions. b f y t f h w x t w Figure 24. L-shaped stiffener. The stiffener area is calculated as 2 2 hw A A1 t f bf twhw t f bf (3) 3 where λ, A 1 and b f are known. The flange thickness is made dependent of the web height: 19

20 t f 2 2 hw A1 3 (4) b f The moment of inertia: hw h 2 w 2 hw hw I xx I xx y 1 cg A1 ycg (5) The web height is finally solved by minimizing I xx 2/3 I xx1. This method has some disadvantages however, as the flange breadth is constant the final flange ended up very thin and as a result moment of inertia around the web I yy is greatly reduced, reducing the capacity for transverse forces. Figure 25 shows the transverse cross section with decreased stiffener spacing. Figure 25. Hull bottom, with and without reduced stiffener spacing. The stresses in the web frame are increased with the reduced spacing, Figure 26 shows equivalent stress in two frames with different stiffener spacing. The peak stress in the bottom of the frame at the turn of bilge reaches 140 MPa, compared to 118 MPa with the regular spacing. This is most likely a result of the stiffeners reduced capacity for transverse loads. The stresses are also increased in the rest of the frame with the reduced spacing but only by a few percents. Figure 26. Von Mises stress [MPa] at web frame bottom for reduced stiffener spacing left and regular spacing right. The stress in the stiffeners is reduced, although the maximum shear stress is still above allowable levels. 20

21 1.6.4 Increased frame thickness As it is clear from previous results the web frames do not satisfy the design criteria, a third floating model was created with increased web thickness in the transverse frames. The thickness was increased by 15 % in fields 1 to 3 (see Figure 6), this corresponds with an increase of transverse moment of inertia by 10 %. This increase was not based on any calculations. Axial stresses in the transverse frames were reduced by around 10 % in the analysis as expected, but still with peak stresses exceeding acceptable levels. Equivalent and shear stress in the frame were also reduced by 8 14 % and the equivalent stress satisfied maximum acceptable levels in all areas of the frame except the frame flange at the turn of bilge Combined increased frame thickness and decreased stiffener spacing The final model was a combination of the second and third model; with reduced stiffener spacing and increased frame thickness. As the stress in the shell plating was well below acceptable stress levels for all previous models the shell thickness in field 1 was reduced by 20 %. The reduced shell thickness still satisfied the minimum thickness requirement according to DNV HSLC The combined weight of shell and frame in field 1 3 increases by 5 % compared to the first model. To get a better overview of the stress levels for the final model a summary of the results for all models are given in Table 5, were the models are defined as: Model 1, regular floating frame. Model 2, reduced stiffener spacing. Model 3, increased web frame thickness. Model 4, increased frame thickness and reduced stiffener spacing. Peak stresses in the frames are taken from the regions given in Figure 27. Table 5. Peak stresses in the different models. Data exceeding maximum allowable stress by more than 7 % marked with red, less than 7 % with green and data within allowable levels black (see Table 6). Model 1 Model 2 Stress [MPa] eqv. stress bending shear eqv. stress bending shear Web frame Region Stiffener Shell Model 3 Model 4 Web frame Region Stiffener Shell Table 6. Maximum allowable stress in HAZ [MPa]. eqv. stress bending shear Web frame Shell Stiffener

22 Region 2 Region 1 Region 3 Figure 27. Defined regions in the transverse frame. The lowest peak stresses in the transverse frame was found in Model 3, Model 4 has a slightly reduced equivalent stress in the stiffeners but stresses in the web frame are significantly higher than in Model 3. Shear and axial stresses are the critical stresses for the transverse frame. However a closer study shows the areas exceeding the maximum allowable stresses are small and concentrated. Figure 28 shows a contour plot of areas exceeding maximum allowable shear stress, these could be avoided by local reinforcements. Figure 28. Areas exceeding maximum allowable shear stress. Frame E model STIFFENER ANALYSIS As the predicted stresses in the stiffeners are very approximate, a locally refined mesh on Stiffener A (see Figure 20) was introduced in Model 1. The stiffener had six elements over the height of the web and three elements over the breadth of the flange and covered one half frame spacing in each direction with Frame E in the centre. Figure 29 shows a comparison of the frame with and without a refined mesh. The most obvious difference is the stress concentration at the stiffener intersection in the refined model, of which there are no signs of in the rough model. This is explained by the sharp corner, where the bending stress is concentrated. 22

23 Figure 29. Comparison between rough and refined mesh at frame in turn of bilge, von Mises stress [MPa]. Figure 30 shows the von Mises stresses in the stiffeners are greatly underestimated with a rough element mesh. Very high stresses at the stiffener web can be seen just below the flange at the frame intersection. Such high stresses are unwanted since the studied load condition is the design condition for web frames; the design load for the bottom stiffeners is a uniform pressure of 142 kpa compared to the studied load of 82 kpa. Figure 30. Comparison rough and refined mesh in stiffener, von Mises stress [MPa]. A study of the stiffener deformation shows the origin of the high stresses, see Figure 31. The stiffeners have a large rotation around the flanges as the deformed shell plating forces the webs outwards normal to the web, creating a large local deformation of the stiffener webs. In Figure 32 the axial stresses are plotted over the web thickness in one element in the stiffener with refined mesh. The longitudinal stress is not constant, which would be expected in a fixed construction, this indicates longitudinal bending is not the dominant stress. The design load for stiffeners mentioned earlier is only applied on a small area surrounding the stiffener and would not give large deformations to the transverse frame. The DNV design criteria for stiffeners with the addition of the Eurocode interaction criteria, as discussed in Chapter 2, would be sufficient for the design of stiffeners, as the large stresses in the stiffeners observed here primarily must be avoided by increased stiffness of the transverse frames. 23

24 Stress [MPa] Figure 31. Deformations of transverse section, scale factor Vertical bending stress Longitudinal bending stress Von Mises stress Thickness [-] Figure 32. Stresses plotted over the thickness of an element of a stiffener. 1.8 SUGGESTIONS The critical component of the floating frame construction is the transverse frame, the large deformations must be reduced to reduce the stiffener stresses. Table 7 shows a comparison of deformations between different models; although there is a slightly reduced deformation with increased frame thickness it is nowhere near the deformation of the fixed structure. Table 7. Deformations in the different models. Deformations [mm] Model 1 Model 3 Fixed Model Shell Frame

25 Increasing the frame stiffness has some drawbacks; the most effective solution would be a transverse frame with I-profile. This would increase the workload significantly with more fitting and welding time. By increasing the web or flange thickness of the frame, the welding and fitting time would not be increased, but the weight of the structure would rapidly increase. Connecting the shell plating to the frames with lugs at intervals could give a significant reduction of deformation, although it would require more fitting and welding, it is seen as the most feasible solution. A more daring approach is a reduction of stiffness of stiffeners and shell plating to increase the flexibility and reduce stresses. This would however require a very detailed analysis, shear stresses are in particular expected to increase. Increasing the stiffness of the longitudinal members (stiffeners and longitudinal girders) is not seen as an effective option, although stiffeners with closed profiles could prove to be effective as they have high torsion stiffness. 1.9 CONCLUSIONS Although high stresses were found in the frames of the models with floating frames, it is not the primary issue; the large local deformation of the stiffeners is what must be reduced to achieve an acceptable floating frame structure. These deformations must be reduced by increased stiffness of the frames. The design of a ship with a floating frame structure is quite problematic today, although a design criterion for stiffeners is evaluated in Chapter 2, to determine the required stiffness of the frames finite element calculations is necessary. A calculation method to determine the deformation and stresses in stiffeners is needed as finite element analysis is very expensive and the benefits of floating frames would most likely not compensate for this. It is also important to consider whether the weight increase associated with the required increased stiffness of the frames is beneficial in the long run, with respect to increased fuel consumption and of course the environmental effects. 25

26 2. STIFFENER DESIGN As finite element analysis is expensive and many smaller ship yards do not have the resources for this, a design criterion for the stiffeners in a floating frame construction will be evaluated in this chapter. This design criterion is a combination of criteria for stiffener design in both DNV HSLC [1] and Eurocode 9 [6]. With floating frames a load case arises where the stiffeners and transverse frames are subjected to concentrated loads in the intersection between stiffener and frame, as shown in Figure 33. Transverse frame Contact force Deck load or sea pressure Figure 33. Intersection between floating frame and stiffener. All outer loads from deck loads and sea pressure must be supported by the web frames, these loads can only be transferred through the contact point between stiffener and frame. At this contact point a concentrated force emerges, which may cause large compressive stress in the stiffener web. In addition the largest bending moment occurs at this point along the stiffener with compressive stress at the flange and tensile at the shell. With a traditional fixed frame this issue is avoided when a large portion of the outer loads are directly transferred through the shell to the frames. The stiffener in a floating construction is thus more exposed to loads than the fixed. The design criterion to be studied considers the interaction between a concentrated contact force and bending moment for stiffener and frame design, the results are validated by nonlinear finite element analysis and panel tests. The material properties used in the nonlinear finite element analyses and the extraction of true strain from engineering strain are detailed in Appendix INTERACTION BETWEEN BENDING MOMENT AND CONCENTRATED CONTACT FORCE Calculation methods to determine the resistance of a stiffener web to a transverse force F Rd are detailed in Eurocode 9. This design resistance considers both yielding and elastic buckling. In addition an interaction criterion for a structure subjected to both a concentrated force and a bending moment is defined as: F F Ed Rd MEd (6) M Rd where F Ed is the design load and M Ed the design bending moment. M Rd is the bending moment resistance. F Ed/F Rd or M Ed/M Rd exceeding 1.0 means the stiffener does not satisfy the design criteria. From this an interaction diagram may be created, see Figure

27 1 0.8 F / F rd Permitted zone M / M rd Figure 34. Interaction between bending moment and transverse force as described in Eurocode 9. From this figure it can be seen no reduction of the bending capacity is needed with F/F Rd < 0.6 as well as no reduction of the load capacity with M/M Rd < 0.5. Equation (6) is easily applicable to the design rules in DNV HSLC or NBS. The design bending moment resistance M Rd is determined from beam theory as: MRd Z (7) 02 where Z is the section modulus and σ 02 the yield stress of the material. A. Aalberg [7] has developed a rule modification to NBS which can be applied to DNV HSLC 3.3.5: k 1, F 0.6F Rd 2 ml sp Z 4 min k, k, F 0.6FRd F F Rd (8) where for a continuous longitudinal stiffener spanning over several frames, F = p s l and m = 1/12. It is important to separate the yield stresses in the different equations; σ 02 for 6082-T6 HAZ in (8) is 86.4 MPa according to DNV and 125 MPa in (7) according to Eurocode. In this chapter σ 02 = 260 MPa has been used if nothing else is specified. This rule modification requires multiple iterations to achieve an optimal design. A basic stiffener design that satisfies DNV design rules is first required, as all stiffener dimensions are used as input in the Eurocode formulas for the transverse force resistance F Rd. If this stiffener does not satisfy Equation (8) a new iteration is required. As both flange and web thickness are used as input to the Eurocode calculations an increase of, for example flange thickness, will both increase the stiffener section modulus and reduce the design section modulus Z min. Multiple iterations might therefore be required to achieve an optimal design Finite Element Analysis To evaluate the design criterion several finite element analyses were performed. Three finite element models were created using MSC Patran 2008 r1 as pre- and post-processor in combination with Abaqus 6.7 as the solver, the analyses were non-linear with respect to both geometry and material properties. The objective of the finite element analyses were to verify the reliability of the rule modification as well as the suitability of the element types, as the same elements were used for the compartment model analysed in Chapter 1. 27

28 Models A stiffened panel with a T-shaped stiffener was modelled, with varied dimensions to examine different moment and load capacities, see Table 8. These stiffeners were not based on existing profiles and the dimensions were only chosen to achieve different capacities. The model extends half the frame spacing in each direction with a frame in the middle. The Abaqus S4R5 element was used to model the shell and the stiffener web; this is a thin four node shell element with three translative and two in-plane rotational degrees of freedom. It is generally a more cost-effective element suitable for large models with thin elements and small strains. For the thicker stiffener flange the S4R shell element was used. With six degrees of freedom it is not as cost-effective as the S4R5 element, but is more suitable for thicker geometry as S4R5 does not consider transverse shear through the shell thickness. Table 8. Dimensions of stiffener profiles. Model #1 #2 #3 Span, l [mm] Spacing, s [mm] Web height, h w [mm] Web thickness, t w [mm] Flange breadth, b f [mm] Flange thickness, t f [mm] Shell thickness, t [mm] Moment capacity, M max /M Rd [-] Load capacity, F max /F Rd [-] As the T-stiffeners are symmetrical around the web, imperfections were introduced to the models. A buckling analysis was performed with each model and one mode was selected to be introduced as an imperfection in each model with a maximum magnitude of 0.2 mm. A multiple point constraint (MPC) was applied at the ends of the model. All end nodes but one were grouped as the slave nodes, the MPC gives the slave nodes the same longitudinal deflection as the single master node. This gives zero transverse rotation and ensures maximum bending moment at the ends, where the longitudinal direction is along the z-axis and transverse along the x-axis in Figure 37. This constraint assumes a stiffener spanning over several transverse frames, giving the stiffener a symmetrical deflection pattern around the frames, as shown in Figure 35. Figure 36 shows the actual deflection of a FE-model with applied MPCs. With the same reasoning the sides of the shell were locked in longitudinal rotation. maximum deflection no rotation frame extent of model Figure 35. Principal longitudinal deflection pattern of a longitudinal stiffener spanning over three transverse frames. Figure 36. Longitudinal bending of a stiffened plate. 28

29 The frame was represented in the model by a zero vertical deflection of the flange nodes at the frame intersection, this is a slightly conservative approach as a floating frame is not rigid in vertical motion. Two nodes at the shell were locked in longitudinal deflection and two nodes in the web in transverse deflection to achieve balance in translation and rotation. Figure 37 shows an overview of the boundary conditions. The outer load was added as uniform pressure at the shell plating. Uy=0 Ux=0 Uz=0 Rz=0 Figure 37. Boundary conditions for the model, where R denotes rotation and U displacement. Results The vertical deflection curves of the stiffeners from the three FE-analyses can be seen in Figure 38. The capacity was assumed to be exceeded at the point the force-displacement curve levels out, as are marked with circles in the plots. As the first analysis is only affected by bending and the elastic bending capacity is used in Eurocode, the capacity is assumed to be exceeded when it reaches the plastic area. The third analysis stopped prematurely, but by changing all elements in the model to S4R elements the analysis continued further into the plastic area. This indicates the S4R5 elements are not suitable to describe this problem. The transverse web frame analysis performed in Chapter 1 is a linear elastic analysis however and is not affected by this issue, as it is clear in the analyses the two models are in agreement in the elastic area. 29

30 Pressure [kpa] Pressure [kpa] Pressure [kpa] 150 Model #1 200 Model # Deflection [mm] 500 Model # Deflection [mm] S4R5 S4R Deflection [mm] Figure 38. Load - deflection curves for the three FE-analyses. Exceeded capacity marked with circles. In Figure 39 the calculations based on the Eurocode design rules are displayed. The corresponding capacities determined in the FE-analyses are marked with an x in the plots and the pressures at which the capacities exceed 1.0 are denoted as p max. All analyses gave results corresponding well with the Eurocode criteria, a slight over prediction is desired to ensure a robust construction. Eurocode also specifies a safety factor of 1.1, which has not been used in these calculations, but which would result in even more conservative values. 30

31 F / F Rd Pressure [kpa] Model #1 p max = 75 kpa M / M Rd Pressure [kpa] F / F Rd Pressure [kpa] Model #2 p max = 167 kpa M / M Rd Model #3 p max = 402 kpa F / F Rd M / M Rd Figure 39. Calculations for three stiffeners based on the Eurocode criteria. F.E. results marked with x Eurocode rules combined with DNV HSLC As a reference from a real ship a check of the stiffeners in the bottom panels of the JumboCat 60 with floating frames was performed. According to Table 9, Appendix 4; the entire flange and a large portion of the web of the stiffener is in the HAZ at the frame intersection. The yield stress defined by Eurocode for the 6082 HAZ is σ 02 = 125 MPa. Using this yield gives a maximum pressure of 184 kpa, as shown in Figure 40, compared to the pure bending capacity which corresponds to a pressure of 210 kpa. Figure 40 also shows the design pressure calculated according to DNV HSLC 3.1.2, which is 142 kpa. At this pressure F Ed/F Rd = 0.49, where the interaction criteria is only applicable for F Ed/F Rd >

32 Pressure [kpa] p max = 184 kpa 0.8 F / F Rd M / M Rd Figure 40. Interaction diagram for stiffeners used in JumboCat 60. Design pressure defined by DNV marked with x. The primary reason for the large difference between the pressures is the fact that the yield stress used in DNV HSLC is 86.4 MPa compared to 125 MPa in Eurocode. The yield stress in DNV HSLC contains various safety factors, which amongst other things consider fatigue, where the Eurocode yield contains no safety factors. This means the interaction criteria is primarily an issue for stiffeners with very slender webs. The Eurocode rules are primarily used for static structures on land, which experiences the largest loads during assembly and is not subjected to large dynamic loads during its life time. This means fatigue is not a big concern during the design, as opposed to ship construction where dynamic loads are the primary design factor for a large part of the structure. For this reason it might be important to study the effects of cyclic loads of stiffeners subjected to transverse loads, as the safety factor of 1.1 in Eurocode might be non-conservative in this respect. 2.2 PANEL TESTS Three tests were performed to verify the Eurocode model with varying frame web thickness, as well as examining the effect of HAZ. In addition a FE-model of one test was created for a further verification of the FE-models. The tests were performed on extruded aluminium 6082-T6 panels with two longitudinal L-shaped stiffeners, see Appendix 2. The panels were simply supported on a circular support at each end, allowing the ends to rotate. A stiff T-beam was placed on the stiffener flanges in the middle of the panel, see Figure 41. The beam was descended at a rate of 10 mm/sec. 32

33 Load [kn] F stiffener Figure 41. Test setup. Two of the tests had varied frame web thickness, one with 10 mm and one with 6 mm, with the frame simply supported on the stiffener flanges in both cases. The third test had a 6 mm frame web welded to the stiffener flange. The same frame with 10 mm web thickness was used for all tests, but for the tests with 6 mm thickness a small area was machined on the frame web to only reduce the thickness at the intersection between frame and stiffener, and avoid any reduction of the frame stiffness. The reaction force acting on the frame and the extension of the frame for the tests can be seen in Figure 42. The web thickness of the intersecting frame has a big impact on the force capacity and is a parameter used in the Eurocode calculations, however all of the panels in these tests had a high force capacity and the bending moment was critical for each test. From the figure it is clear the web thickness has a large impact for the bending capacity as well, most likely because the bending moment in the intersection is concentrated over a larger area with increased frame web thickness mm frame 6 mm frame 6 mm frame, welded Extension [mm] Figure 42. Load-deflection curves for the three tests. The maximum force acting on the welded panel was 75 % of the force acting on the non-welded panel. As a rule of thumb the welded material is said to give a reduced strength between %. A finite element model was created for the 10 mm frame test. The frame was modelled as a rigid plate with a 10 mm width, the plate was descended at the stiffener and the reaction force was calculated in the analysis. A contact interaction was defined between the stiffener flange and the frame web assuming no slip, meaning no relative motion between the two surfaces in contact. The FE-model gave results in good agreement with the test, see Figure 43, the model also had a similar buckle in the web at the end of the analysis, see Figure 44. A 9 % difference was found at the maximum deflection, this is considered an acceptable difference. There are many possible sources of error; the measurements of the plate dimensions were not exact, an L-shaped stiffener modelled with shell elements also has a lower bending stiffness due to the loss of area at the top corner of the flange, see Figure 45. The bending capacity 33

34 Load [kn] calculated in Figure 43 under predicts the capacity greatly. As seen from the previous tests the frame thickness has a large impact on the capacity, where the calculated bending capacity assumes a point load. A more detailed calculation of the bending moment with consideration of the frame intersection is required for a better result. This would most likely require extensive finite element analysis and tests to create generalized calculation methods. As of now an awareness of the conservative bending capacity is sufficient. As both the bending capacity and the DNV HSLC yield stress have been found to be conservative, it is likely the concentrated force have a larger impact on the capacity of a stiffener than these calculations have shown Test FE-analysis Load [kn] F max = 12.6 kn F / F rd Extension [mm] M / M rd Figure 43. Comparison FE-analysis and test, and bending capacity from beam theory. 10 mm non welded frame. Figure 44. Deformation comparison, FE-analysis and test. no area shell element node doubled area Figure 45. L-shaped stiffener modelled with shell elements. 34

35 2.3 CONCLUSIONS Comparisons between the finite element analyses and Eurocode 9 interaction formulas showed a good agreement, although the Eurocode results gave more conservative results compared to the FEM results. In addition the capacity of a real stiffener was found to be higher during the panel tests compared to the FEM results. The Aalberg modification is a helpful tool for the design of stiffeners for crafts with floating frames, but it is important to keep in mind no optimized structure is to be expected. The interaction formulas was found to have a reduced influence on the results when combined with the DNV design rules, due to different yield stresses and safety factors in the two set of rules. It is possible the Eurocode formulas requires a modification to consider fatigue, as structures designed according to the Eurocode rules are not commonly subjected to large cyclic loads. THANKS I would like to thank my three supervisors who all contributed with time and guidance during the project; Arne Aalberg and Jørgen Amdahl at NTNU, and Anders Rosén at KTH. I would also like to express my thanks to all members of the Alubåt project for valuable input from a more practical point of view. Finally I would like to thank Frank Klæbo at Marintek for his very helpful Patran guidance. REFERENCES 1. Det Norske Veritas. Rules for Classification of High Speed and Light Craft. DNV, Norway, July Nordisk Båt Standard. Yrkesbåter under 15 meter. Nordisk Teknisk Arbeidsgruppe, Spencer, J. S. Structural Design of Aluminum Crewboats. Marine Technology, Vol. 12, No. 3, pp , Aalberg, A. Redningsselskapets skøyte Knut Johan konstruert med stivere liggende utenpå spantprofiler. NTNU, Trondheim, Herrington, P. D., and Latorre, R. G. Development of An Aluminum Hull Panel for High-Speed Craft. Marine Structures, Vol. 11, No. 1-2, pp , European Committee for Standardisation. ENV /Eurocode 9: Design of aluminium structures - General structural rules. Brussels, May Aalberg, A. NOTAT Stiver lagt direkte på spant, ökt krav til motstandsmoment W for stiveren som fölge av konsentrert kraft på oppleggspunktet. NTNU, Trondheim, Ökland, O.D. Analysis of Transverse section of the 60m Jumbo Cat. Marintek, Trondheim, Det Norske Veritas. Classification Notes No Strength Analysis of Hull Structures in High Speed and Light Craft. DNV, Norway, August

36 APPENDIX 1 MATERIAL PROPERTIES The stress-strain curves for aluminium 6082-T6 are based on material tests performed previously at the Department for Structural Engineering at NTNU. These curves show the engineering, or nominal, strain and stresses, and eng eng, which are based on the average strain, as shown in Figure 46 and Equation (9). L 0 δ 1 L 1 δ 2 L 2 Figure 46. Tension in two steps.,, tot (9) L0 L1 L0 This is not an exact measure of strain; the logarithmic strain and true stress are therefore used. The logarithmic strain is defined as: while the engineering strain is defined as eng L dl L ln ln (10) L L L0 L L L L L L (11) This gives the logarithmic strain: ln ln 1 eng (12) and the true stress: 1 (13) true eng eng The true and engineering stress-strain curves are displayed in Figure

37 Stress [MPa] Engineering True Strain [%] Figure 47. Stress-strain curves for aluminium 6082-T6. 37

38 APPENDIX 2 PROFILE DRAWING 38

39 APPENDIX 3 MODEL FLAW To study the model flaw in greater detail, region 3 in Frame F was given a smooth transition in one model, Figure 48 shows a comparison between Frame E and F, as defined in Figure 12. The stress at the frame web top is greatly reduced and below acceptable stress levels with the smooth transition, the peak stress in the frame flange reaches 150 MPa for the smooth model which means the stress still exceed acceptable levels, but is reduced by 25 % from the previous 200 MPa. The bottom of the frame is not affected to the same degree, however a new stress concentration occurs in the lower part of the frame, although it is below the maximum acceptable stress. It is clear the sharp corner have a negative effect on the results, the stress at the frame web top can largely be assumed to originate from this flaw and the stress in the frame flange increases greatly with the flaw but cannot be overlooked. Figure 48. Frame at bilge turn with and without smooth transition (Von Mises). 39

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