Patent Publication Number: US-9845112-B2

Title: Twelve-cornered strengthening member, assemblies including a twelve-cornered strengthening member, and methods of manufacturing and joining the same

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 14/559,671, filed Dec. 3, 2014, which is a continuation-in-part of U.S. patent application Ser. No. 14/010,115, filed Aug. 26, 2013, now U.S. Pat. No. 9,174,678, which is a continuation of U.S. patent application Ser. No. 12/233,808, filed Sep. 19, 2008, now U.S. Pat. No. 8,539,737, the entire content of each of which is incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     The present teachings relate generally to a strengthening assembly for a vehicle body or other structures. The present teachings relate more specifically to a strengthening member, motor vehicle assemblies including a strengthening member, connected to another automotive component, and methods of making and joining the strengthening member and assemblies. 
     BACKGROUND 
     It is desirable, for vehicle strengthening members, to maximize impact energy absorption and bending resistance while minimizing mass per unit length of the strengthening member. Impact energy absorption may be maximized, for example, by assuring that the strengthening member compacts substantially along a longitudinal axis of the strengthening member upon experiencing an impact along this axis. Such longitudinal compaction may be referred to as a stable axial crush of the strengthening member. 
     When a compressive force is exerted on a strengthening member, for example a force due to a front impact load on a vehicle&#39;s front rail or other strengthening member in the engine compartment, the strengthening member can crush in a longitudinal direction to absorb the energy of the collision. In addition, when a bending force is exerted on a strengthening member, for example a force due to a side impact load on a vehicle&#39;s front side sill, B-pillar or other strengthening member, the strengthening member can bend to absorb the energy of the collision. 
     Conventional strengthening members rely on increasing the thickness and hardness of corner portions to improve crush strength. However, such increased thickness and hardness increases weight and decreases manufacturing feasibility. It may be desirable to provide a strengthening assembly configured to achieve the same or similar strength increase as provided by the thickened corners, while minimizing mass per unit length of the member, and maintaining a high manufacturing feasibility. 
     It also may be desirable to provide a strengthening member that can achieve increased energy absorption and a more stable axial collapse when forces such as front and side impact forces are exerted on the strengthening member. Additionally, it may be desirable to provide a strengthening member that possesses improved noise-vibration-harshness performance due to work hardening on its corners. 
     It also may be desirable to provide structures to connect the strengthening member to another automotive component to promote a stable axial crush. When the other automotive component has a different shape than the strengthening member, it may be difficult to apply welding techniques to connect the strengthening member and the other component due to the variation in shape. This difficulty may result in a connection that is not secure and which causes an unstable axial crush. 
     SUMMARY 
     In accordance with the various exemplary embodiments, the present disclosure provides a motor vehicle assembly that includes a strengthening member having a twelve-cornered cross section along at least a portion of the strengthening member, and an automotive component having a four-cornered cross section along at least a portion of the automotive component. The cross section of one of the strengthening member and the automotive component transitions between twelve corners and four corners to facilitate a connection between the strengthening member and the automotive component. 
     In accordance with the various exemplary embodiments, the present disclosure further provides a strengthening member for an automotive vehicle. The strengthening member has a first end having a twelve-cornered cross section including sides and corners creating internal angles and external angles, a second end configured to connect to a four-cornered cross section of another automotive component, and at least one protrusion on each of first and second opposite sides of the strengthening member. The protrusions of the strengthening member are configured to facilitate a stable axial collapse of the strengthening member. 
     In accordance with the various exemplary embodiments, the present disclosure further provides a strengthening member for an automotive vehicle. The strengthening member has a first portion having a twelve-cornered cross section including sides and corners creating internal angles and external angles, a second portion having a four-cornered cross section configured to connect to a four-cornered cross section of another automotive component, and a tapered portion configured to direct an axial crush of the strengthening member away from the second portion. 
     Additional objects and advantages will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the present teachings. The objects and advantages of the teachings will be realized and attained by means of the elements and combinations particularly pointed out in the appended claims. 
     It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention, as claimed. The accompanying drawings, which are incorporated in and constitute part of this specification, illustrate exemplary embodiments of the invention and together with the description, serve to explain principles of the disclosure. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       At least some features and advantages of the present teachings will be apparent from the following detailed description of exemplary embodiments consistent therewith, which description should be considered with reference to the accompanying drawings, wherein: 
         FIG. 1  illustrates an exemplary embodiment of a twelve-cornered cross section for a strengthening member in accordance with the present teachings; 
         FIG. 2  illustrates strengthening members of varying cross sections having a substantially constant thickness and perimeter; 
         FIG. 3  illustrates an exemplary axial collapse of the strengthening members shown in  FIG. 2 ; 
         FIG. 4  is a graph of mean crush force and associated axial crush distance for exemplary strengthening members having the cross sections shown in  FIG. 2 ; 
         FIGS. 5A-5D  illustrate a vehicle front rail without convolutions, having varying cross sections including twelve-cornered cross sections in accordance with the present teachings; 
         FIGS. 6A-6D  illustrate a vehicle front rail with convolutions, having varying cross sections including twelve-cornered cross sections in accordance with the present teachings; 
         FIG. 7  illustrates geometries of twelve-cornered cross sections of varying shapes and a square cross section having the same thickness and perimeter; and 
         FIG. 8  shows a comparison of crash energy absorbed (for a given force) by strengthening members having the exemplary cross sections illustrated in  FIG. 7 . 
         FIG. 9A  is a perspective view of a strengthening member having a twelve-cornered cross section directly connected to an automotive component having a four-cornered cross section. 
         FIG. 9B  depicts an unstable axial crush resulting when an axial impact is applied along the longitudinal axis of the structure of  FIG. 9A . 
         FIG. 9C  is a view along the twelve-cornered cross section taken along the line C-C of  FIG. 9A . 
         FIG. 9D  is a view along the overlap between the twelve-cornered cross section and the four-cornered cross section taken along the line D-D of  FIG. 9A . 
         FIG. 9E  is a view along the four-cornered cross section taken along the line E-E of  FIG. 9A . 
         FIG. 10A  is a perspective view of a strengthening member that transitions from a twelve-cornered cross section at a first end to a four-cornered cross section having a second end to facilitate connection to an automotive component in accordance with the present teachings. 
         FIG. 10B  depicts a stable axial crush resulting when an axial impact is applied along the longitudinal axis of  FIG. 10A . 
         FIG. 10C  is a view along the twelve-cornered cross section of the strengthening member taken along the line C-C of  FIG. 10A . 
         FIG. 10D  is a view along the overlap between the four-cornered cross section of the strengthening member after the transition and a four-cornered cross section of the automotive component taken along line D-D of  FIG. 10A . 
         FIG. 10E  is a view along the four-cornered cross section of the automotive component taken along the line E-E of  FIG. 10A . 
         FIG. 11A  is a perspective view of an embodiment of a connection between a strengthening member having a twelve-cornered cross section and an automotive component having a four-cornered cross section in accordance with the present teachings. 
         FIG. 11B  depicts a stable axial crush resulting when an axial impact is applied along the longitudinal axis of the strengthening member of  FIG. 11A . 
         FIG. 12A  is a perspective view of a second embodiment of a connection between a strengthening member having a twelve-cornered cross section and an automotive component having a four-cornered cross section in accordance with the present teachings. 
         FIG. 12B  depicts a stable axial crush resulting when an axial impact is applied along the longitudinal axis of the strengthening member of  FIG. 12A . 
         FIG. 13A  is a perspective view of a third embodiment of a connection between a strengthening member having a twelve-cornered cross section and an automotive component having a four-cornered cross section in accordance with the present teachings. 
         FIG. 13B  depicts a stable axial crush resulting when an axial impact is applied along the longitudinal axis of the strengthening member of  FIG. 13A . 
         FIG. 14A  is a perspective view of a fourth embodiment of a connection between a strengthening member having a twelve-cornered cross section and an automotive component having a four-cornered cross section in accordance with the present teachings. 
         FIG. 14B  depicts a stable axial crush resulting when an axial impact is applied along the longitudinal axis of the strengthening member of  FIG. 14A . 
         FIG. 15A  is a perspective view of a fifth embodiment of a connection between a strengthening member having a twelve-cornered cross section and an automotive component having a four-cornered cross section in accordance with the present teachings. 
         FIG. 15B  depicts a stable axial crush resulting when an axial impact is applied along the longitudinal axis of the strengthening member of  FIG. 15A . 
         FIG. 16A  is a perspective view of an embodiment of a connection between a strengthening member having a twelve-cornered cross section and an automotive component having a twelve-cornered cross section in accordance with the present teachings. 
         FIG. 16B  depicts a stable axial crush resulting when an axial impact is applied along the longitudinal axes of the strengthening member and automotive component of  FIG. 16A . 
         FIG. 16C  is a cross-sectional view of the automotive component of  FIG. 16A  taken along line C-C in  FIG. 16A . 
         FIG. 16D  is a cross-sectional view of the automotive component of  FIG. 16A  taken along line D-D in  FIG. 16A . 
         FIG. 16E  is a cross-sectional view of the strengthening member of  FIG. 16A  taken along line E-E in  FIG. 16A . 
         FIG. 17A  is a perspective view of a connection between a strengthening member having a twelve-cornered cross section and an automotive component having a four-cornered cross section where a portion of the automotive component is received by the strengthening member in accordance with the present teachings. 
         FIG. 17B  depicts a stable axial crush resulting when an axial impact is applied along the longitudinal axes of the strengthening member and automotive component of  FIG. 17A . 
         FIG. 17C  is a cross-sectional view of the automotive component of  FIG. 17A  taken along line C-C in  FIG. 17A . 
         FIG. 17D  is a cross-sectional view of the automotive component of  FIG. 17A  taken along line D-D in  FIG. 17A . 
         FIG. 17E  is a cross-sectional view of the strengthening member of  FIG. 17A  taken along line E-E in  FIG. 17A . 
         FIG. 17F  is a cross-sectional view of the automotive component of  FIG. 17A  taken along line F-F in  FIG. 17A . 
         FIG. 17G  is a cross-sectional view of the automotive component of  FIG. 17A  taken along line G-G in  FIG. 17A . 
         FIG. 18  is a perspective view of a connection between a strengthening member having a twelve-cornered cross section and an automotive component having a four-cornered cross section via a bridge connection member. 
         FIG. 19  depicts test results for energy absorption for strengthening members undergoing a stable axial collapse and an unstable axial collapse, according to an exemplary embodiment. 
     
    
    
     Although the following detailed description makes reference to illustrative embodiments, many alternatives, modifications, and variations thereof will be apparent to those skilled in the art. Accordingly, it is intended that the claimed subject matter be viewed broadly. 
     DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     Reference will now be made in detail to various embodiments, examples of which are illustrated in the accompanying drawings. The various exemplary embodiments are not intended to limit the disclosure. To the contrary, the disclosure is intended to cover alternatives, modifications, and equivalents. 
     The present teachings contemplate providing a strengthening member with a twelve-cornered cross section having a substantially increased stiffness throughout the sides and corners without increasing thickness within the corners. The strengthening member can achieve increased energy absorption and a more stable axial collapse when forces such as front and side impact forces are exerted on the strengthening member. The strengthening member can also possess improved durability and noise-vibration-harshness (NVH) performance due to work hardening on the twelve corners. The degrees of the internal and external angles of the present teachings can achieve the same strength increase as thickened corners, while minimizing mass per unit length of the member and maintaining a high manufacturing feasibility because the member can be formed by bending, rolling, stamping, pressing, hydro-forming, molding, extrusion, cutting, casting, and forging. 
     An exemplary embodiment of a twelve-cornered cross section for a strengthening member in accordance with the present teachings is illustrated in  FIG. 1 . As illustrated, the cross section comprises twelve sides having lengths S 1 -S 12  and thicknesses T 1 -T 12 , eight internal corners with angles θ i1 -θ i8  and four external corners with angles θ e1 -θ e4 . The internal and external angular degrees can be varied to achieve improved strength and other performance features (e.g., stability of folding pattern) compared to existing 90°-angled cross sections. This improved strength obviates the need for increased corner thickness, which is an unexpected and unpredicted benefit of fine-tuning the internal and external angular degrees of a strengthening member having a twelve-sided cross section. In accordance with various embodiments of the present teachings, each internal angle can range from about 100° to about 110°, and each external angle can range from about 105° to about 130°. The lengths S 1 -S 12  and thicknesses T 1 -T 12  of the sides can be varied to a certain degree, as would be understood by one skilled in the art, for example in accordance with available packaging space within a vehicle. Each internal angle and each external angle of the strengthening member may have an angular degree selected to promote the stable axial crush in accordance with the disclosed range of degrees, while accommodating package constraints of an environment in which the assembly is to be used. 
     In certain embodiments of the present teachings a thickness of the sides and corners can range from about 0.7 mm to about 6.0 mm. In certain embodiments, the thickness of the sides is substantially the same as the thickness of the corners. 
     Conventional strengthening members having square or rectangular cross sections are widely used due to their high manufacturing feasibility. Because a strengthening member with a twelve-cornered cross section in accordance with the present teachings has substantially increased strength and stiffness without requiring thicker corner portions, it has a higher manufacturing feasibility than previously-contemplated twelve-cornered members that have thickened 90° corners. While still providing a desired strength, a strengthening member in accordance with the present teachings can be formed in one or multiple sections by, for example, bending, rolling, stamping, pressing, drawing, hydro-forming, molding, extrusion, cutting, casting, and forging. Thus-formed sections can be joined via welding, adhesive, fastening, or other known joining technologies. 
     In accordance with certain exemplary embodiments of the present teachings, the thickness of the strengthening member may vary, for example, within one side or from side to side to optimize the overall axial crush and bending performance. Examples of such varied thickness embodiments are illustrated in  FIGS. 5D and 6D , which are described in detail below. 
     In comparing crash energy absorption of strengthening members of varying shapes having the same thickness and perimeter, as illustrated in  FIG. 2 , for example for an impact with a rigid wall at 35 mph, a twelve-cornered cross section in accordance with the present teachings demonstrated the shortest crush distance and smallest folding length. The twelve-cornered cross section in accordance with the present teachings also demonstrated the most stable axial collapse and the highest crash energy absorption. In fact, a twelve-cornered cross section in accordance with the present teachings can achieve about a 100% increase in crash energy absorption over a square cross section and a 20-30% increase in crash energy absorption over hexagonal and octagonal cross sections.  FIG. 3  illustrates an exemplary axial collapse of the strengthening members shown in  FIG. 2 . As can be seen, the strengthening member having a twelve-cornered cross section in accordance with the present teachings exhibits the shortest crush distance and most stable folding pattern. 
       FIG. 4  illustrates a graph of mean crush force for an impact with a rigid wall at 35 mph, in kN, exerted axially on exemplary strengthening members having the cross sections shown in  FIG. 2 . As can be seen, a strengthening member having a twelve-cornered cross section in accordance with the present teachings can sustain a much higher crushing force for a given resulting crushing distance. This allows improved impact energy management while minimizing mass per unit length. 
     A twelve-cornered cross section in accordance with the present teachings is contemplated for use with a number of structural members such as a front rail, a side rail, a cross member, roof structures, and other components that can benefit from increased crash energy absorption. In addition, the present teachings can be applied to both body-on-frame and unitized vehicles or other type of structures. 
       FIGS. 5A-5D  illustrate exemplary embodiments of a vehicle front rail having a cross section in accordance with the present teachings. The front rail is of a type without convolutions.  FIG. 5A  illustrates a front rail having a known, substantially rectangular cross section with four corners  510 ,  512 ,  514 ,  516  of about ninety degrees, and four sides  520 ,  522 ,  524 ,  526 .  FIGS. 5B through 5D  illustrate front rails having twelve-cornered cross sections in accordance with the present teachings, the corner indentations I 1  in  FIG. 5C  being greater than the indentations I 2  in  FIG. 5B . In these illustrated exemplary embodiments, the rails have a two-part construction comprising pieces A and B. The present teachings contemplate rails of other construction such as one-piece or even 3-or-more piece construction, the number of pieces in  FIGS. 5A through 5D  being exemplary only. 
     The embodiments of  FIGS. 5B and 5C  include top and bottom sides S B  and S T  having substantially the same length as each other, and left and right sides S L  and S R  also having substantially the same length as each other. Piece A includes side S R  and part of sides S B  and S T . Piece B includes side S L  and part of sides S B  and S T . To simplify  FIGS. 5B-5D , all of the sides S 1  through S 12 , as illustrated in  FIG. 1 , are not labeled but are of course present. Similarly, the eight internal corners (angles: θ i1 -θ i8 ) and four external corners (angles: θ e1 -θ e4 ), as illustrated in  FIG. 1 , are not labeled but are present. 
       FIG. 5D  illustrates a front rail having a twelve-cornered cross section, the rail being formed with different depths of indentations, for example to accommodate packaging constraints of a vehicle&#39;s engine compartment. In accordance with such an embodiment needing to have a varied shape to accommodate engine compartment constraints, to achieve optimized axial crush performance, the thicknesses of the sides, angles of the corners, and indentation depths can all be adjusted to provide optimal strength, size and shape. In the example of  FIG. 5D , corner indentations I 3  and I 4  have the different depths, corner indentation I 4  being shallower than corner indentation I 3 . Corner indentations I 5  and I 6  have substantially the same depth as each other, that depth differing from the depths of corner indentations I 3  and I 4 . The top and bottom sides S B  and S T  have different lengths, with S T  being longer than S B , and the left and right sides S L  and S R  have differing lengths, with S R  being longer than S L . The internal and external angles θ may also differ as a result of the differing side lengths and corner indentation depths. The present teachings also contemplate a twelve-cornered cross section where each of the corner indentations has a different depth and a different angle, and each of the sides has a different length, or where some of the sides have the same length and some of the corner indentations have the same depth and perhaps the same internal and external angles θ. 
     For a front rail comprising SAE1010 material, a front rail as illustrated in  FIG. 5B  (with shallower indentations) can save, for example, about 17% weight compared to a square or rectangular cross section, and a front rail as illustrated in  FIG. 5C  (with deeper indentations) can save, for example, about 35% weight. For a front rail comprising DP600 material, a front rail as illustrated in  FIG. 5B  (with shallower indentations) can save, for example, about 23% weight and a front rail as illustrated in  FIG. 5C  (with deeper indentations) can save, for example, about 47% weight. Such weight savings are realized because the increased strength of the twelve-cornered cross section allows the use of a thinner gauge material to provide the same strength. 
       FIGS. 6A-6D  illustrate exemplary embodiments of a vehicle front rail having a cross section in accordance with the present teachings. The front rail is of a type with convolutions.  FIG. 6A  illustrates a convoluted front rail having a known, substantially rectangular cross section with four corners  610 ,  612 ,  614 ,  616  of about ninety degrees, and four sides  620 ,  622 ,  624 , and  626 .  FIGS. 6B through 6D  illustrate convoluted front rails having twelve-cornered cross sections in accordance with the present teachings, the corner indentations I 8  in  FIG. 6C  being greater than the indentations I 7  in  FIG. 6B . In these illustrated exemplary embodiments, the rails have a two-part construction with pieces C and D. As stated above, the two-piece constructions shown in  FIGS. 6B through 6D  are exemplary only and the present teachings contemplate rails of other construction such as one-piece or even 3-or-more piece construction. 
     The embodiments of  FIGS. 6B and 6C  include top and bottom sides S B  and S T  having substantially the same length as each other, and left and right sides S L  and S R  also having substantially the same length as each other. Piece C includes side S R  and part of sides S B  and S T . Piece D includes side S L  and part of sides S B  and S T . To simplify  FIGS. 6B-6D , all of the sides S 1  through S 12 , as illustrated in  FIG. 1 , are not labeled but are present. Similarly, the eight internal corners (angles: θ i1 -θ i8 ) and four external corners (angles: θ e1 -θ e4 ), as illustrated in  FIG. 1 , are not labeled but are present. 
       FIG. 6D  illustrates a convoluted front rail having twelve-cornered cross section, the rail being formed with different depths of indentations, for example to accommodate packaging constraints of a vehicle&#39;s engine compartment. In accordance with such an embodiment needing to have a varied shape to accommodate engine compartment constraints, to achieve optimized axial crush performance, the thicknesses of the sides, angles of the corners, and indentation depths can all be adjusted to provide optimal strength, size and shape. In the example of  FIG. 6D , corner indentations I 9  and I 10  have the different depths, with corner indentation I 10  being shallower than corner indentation I 9 . Corner indentations I 11  and I 12  have substantially the same depth as each other, that depth differing from the depths of corner indentations I 9  and I 10 . The top and bottom sides S B  and S T  have different lengths, with S T  being longer than S B , and the left and right sides S L  and S R  have differing lengths, with S R  being longer than S L . The internal and external angles θ may also differ as a result of the differing side lengths and corner indentation depths. The present teachings also contemplate a twelve-cornered cross section where each of the corner indentations has a different depth and a different angle, and each of the sides has a different length, or where some of the sides have the same length and some of the corner indentations have the same depth and perhaps the same internal and external angles θ. 
     For a convoluted front rail comprising SAE1010 material, a front rail as illustrated in  FIG. 6B  (with shallower indentations) can save, for example, about 20% weight compared to a square or rectangular cross section, and a front rail as illustrated in  FIG. 6C  (with deeper indentations) can save, for example, about 32% weight. For a convoluted front rail comprising DP600 material, a front rail as illustrated in  FIG. 6B  (with shallower indentations) can save, for example, about 30% weight and a front rail as illustrated in  FIG. 6C  (with deeper indentations) can save, for example, about 41% weight. 
     Strengthening members having a variety of cross sections are illustrated in  FIG. 7 . As can be seen, CAE 006  has a twelve-cornered cross section with external angles of 90°. CAE 007  has a twelve-cornered cross section with external angles of 108° in accordance with the present teachings. CAE 008  has a twelve-cornered cross section with external angles of 124° in accordance with the present teachings. CAE 009  has a twelve-cornered cross section with external angles of 140°. CAE 010  has a twelve-cornered cross section with external angles of 154°. Finally, CAE 011  has a square cross section. A comparison of the axial crush strength of the illustrated square and twelve-cornered cross sections having differing external angles is illustrated in  FIG. 8 . As can be seen, the overall axial crush strength of the strengthening member having a twelve-cornered cross section is far greater than that of the strengthening member having a square cross section. 
     As can further be seen, the exemplary strengthening members with twelve-cornered cross sections having external angles of 108° and 124° show an overall increase in axial crush strength over twelve-cornered cross sections having external angles of 90°. In fact, deviation of the angles from 90° such that each internal angle is about the same as other internal angles and ranges from about 100° to about 110°, and each external angle is about the same as other external angles and ranges from about 105° to about 130°, increases strength without negatively affecting the stability of a crush mode of the strengthening member. Such an increase in strength obviates the need for reinforcing (e.g., thickening) the concave portions at the four corners of the strengthening member, decreasing weight and cost and increasing manufacturing feasibility. 
     Strengthening members in accordance with the present teachings can comprise, for example, steel, aluminum, magnesium, fiberglass, nylon, plastic, a composite or any other suitable materials. 
     In addition to the structure of the strengthening member, the manner of connection of the strengthening member also plays a role in the ability of the strengthening member to provide a stable axial collapse and high energy absorption under crash conditions. Further, the various exemplary embodiments described herein contemplate strengthening members having a shape to facilitate a stable axial collapse. A strengthening member connected in accordance with the present teachings may provide approximately a 20% increase in amount of energy absorbed versus a direct connection between a twelve-cornered strengthening member and a four-cornered automotive component. 
     In accordance with certain embodiments, the present teachings contemplate joints between a strengthening member having a twelve-cornered cross section in at least a portion of the strengthening member and an automotive component having a four-cornered cross section in at least a portion of the automotive component. For example, a bridge connection member can be used to join a strengthening member and automotive component to promote a stable axial crush by ensuring a secure connection between the different shapes of the strengthening member and the other automotive component. 
     In one embodiment, the connection member comprises a transition on one end of the strengthening member from twelve corners to four corners to allow this end to be securely welded to the automotive component. In another embodiment, the bridge connection member comprises a backing plate interposed between the strengthening member and the automotive component. In another embodiment, the bridge connection member comprises at least one bracket connecting the strengthening member and the automotive component. 
     In further embodiments, slot welds or fish-mouth welds connect the strengthening member and the automotive component. In yet another embodiment, an automotive component transitions at one of its ends from four corners to twelve corners to allow the end to be securely welded to the strengthening member. It is also within the scope of the present teachings to combine any of the embodiments set forth above. 
     Strengthening members of the various exemplary embodiments described herein may be used a structural member in various locations of a vehicle. For example, the strengthening members may be used as a front rail of a vehicle frame, a side rail of a vehicle frame, a rear rail of a vehicle frame, a cross member of a vehicle frame, a cross member of a vehicle frame outside of the vehicle engine compartment, a door beam, roof structures, or any other structural component of a vehicle that uses a beam structure or strengthening member. 
       FIG. 9A  illustrates a strengthening member  900  having a twelve-cornered cross section, in accordance with the present disclosure, connected to an automotive component  950  having a four-cornered cross section. Automotive component  950  may be, for example, a portion of a vehicle frame to which strengthening member  900  is joined. Connections between automotive parts generally include welding each of the corners of the parts to be connected. However, when a strengthening member  900  in accordance with the present disclosure is connected with an automotive component  950  in this manner, it is not possible to apply welds at all corners of the strengthening member, which decreases the stability of the connection. Because the connection is not stable, there is a tendency for the connection itself to be distorted upon application of an impact load. This distortion rotates the strengthening member  900  and prevents the strengthening member  900  from compacting along a longitudinal direction, which results in an unstable axial crush, as shown in  FIG. 9B . 
     Strengthening member  900  may be shaped to facilitate a stable axial crush. According to an exemplary embodiment, strengthening member  900  may include a tapered section  910  that facilitates a stable collapse of strengthening member  900  along an axial direction (e.g., along a longitudinal axis  920 ) of strengthening member  900 . Tapered section  910  may taper so that a cross-sectional area of strengthening member changes along the axial direction (e.g., along longitudinal axis  920 ) of the strengthening member  900 . For example, tapered section  910  may taper so that the cross-sectional area increases in a direction along longitudinal axis  920  from the front to the rear of strengthening member  900 , such as when strengthening member  900  is joined to automotive component  950  in the configuration shown in  FIG. 9A . According to an exemplary embodiment, tapered section  910  may taper so that the cross-sectional area of tapered section changes in a range of, for example, about 30% to about 70% along the length of tapered section  910  (e.g., along longitudinal axis  920 ). 
     According to an exemplary embodiment, a cross-section of a strengthening member is a twelve-cornered cross-section throughout the length of the tapered section. 
     As depicted in  FIG. 9A , tapered section  910  may be shaped so that a top surface  916  of strengthening member  900  is sloped while bottom surface  918  is substantially straight. Further, lateral surfaces  914  of strengthening member may be sloped to form tapered section  910 . Other configurations of surfaces  914 ,  916 ,  918  are envisioned by the exemplary embodiments described herein in order to provide tapered section  910 . For example, top surface  916  may be substantially straight while bottom surface  918  tapers, both top surface  916  and bottom surface  918  may taper, and other configurations may be utilized to form tapered section  910 . As shown in  FIG. 9A , the portions of surfaces  914 ,  916 ,  918  rearward of tapered section  910  may be substantially straight to facilitate joining of strengthening member  900  to automotive component  950   
     As depicted in the exemplary embodiment of  FIG. 9A , tapered section  910  may be located at a front portion  912  of strengthening member  900 , with respect to a front-rear direction of a motor vehicle in which strengthening member  900  is installed, such as when automotive component  950  is a front portion of a frame of the motor vehicle. Other configurations of strengthening member  900  relative to automotive component  950  are envisioned by the various exemplary embodiments described herein. For example, strengthening member  900  may be reversed with respect to the front-rear direction of a motor vehicle and located behind automotive component  950  so that tapered section  910  faces the rear of a motor vehicle, such as when automotive component  950  is a rear portion of the frame of the motor vehicle. 
       FIGS. 9C, 9D, and 9E  are exemplary embodiments of cross-sectional shapes that may be used for the twelve-cornered cross section of the strengthening member  900  and the four-cornered cross section of the automotive component  950 . As depicted in  FIG. 9C , strengthening member  900  may have a two-part construction comprising pieces  902  and  904 . The present teachings contemplate strengthening members of other constructions, such as one-piece constructions or even 3-or-more piece constructions, the number of pieces in  FIGS. 9C through 9E  being exemplary only.  FIG. 9C  resembles the structures illustrated in at least  FIGS. 1 and 7  and may have internal angles and external angles according to the various exemplary embodiments described herein. For example, the internal angles of the strengthening member may range from about 100° to about 110°, and the external angles may range from about 105° to about 130°. In this example, the internal angles of corner indentations of the strengthening member  900  are generally depicted as being similar, but it is possible to have different internal angles at each of the corner indentations, as shown in  FIGS. 5D and 6D . 
       FIG. 9D  is an exemplary embodiment of an overlapping portion where the strengthening member  900  is inserted into the automotive component  950 . As depicted in  FIG. 9D , automotive component  950  may have a two-part construction comprising pieces  952  and  954 . As shown in the exemplary embodiment of  FIG. 9D , the twelve-cornered cross-sectional profile of the strengthening member  900  does not align with the corners of the four-cornered cross-sectional profile of the automotive component  950 . While planar edges of the distinct cross sections formed by pieces  902 ,  904  and  952 ,  954  are in proximity, the lack of corner alignment prevents welding of the connection between the cross sections at all corners, and thereby leads to instability during crash conditions, as illustrated in  FIG. 9B . 
       FIG. 9E  is an exemplary embodiment of a four-cornered automotive component  950 , comprising pieces  952  and  954 , along the longitudinal axis  920  in  FIG. 9A  and rearward of the overlapping portion depicted in  FIG. 9D . While the corners are shown as having a rounded shape, this particular shape is not intended to limit the claimed subject matter in any way. 
     In accordance with the present disclosure, a stable connection between a twelve cornered strengthening member and an automotive component having less than twelve corners may be facilitated by a bridge or transitional part or portion of a part such that corners and/or edges of strengthening member and automotive component parts to be connected are aligned in a manner that permits sufficient connection by welding or other means, such as mechanical fasteners like brackets, bolts, and/or nuts. It should be understood that a desired connection can be formed by, for example, modifying one end of the strengthening member to correspond with one end of the automotive component, modifying one end of the automotive component to correspond with one end of the strengthening member, or an intermediate piece such as a bridge plate or bracket may be provided. 
     In accordance with one aspect of the present disclosure and as illustrated in  FIG. 10A , an exemplary embodiment of a connection between a twelve-cornered strengthening member  1000  and a four-cornered automotive component  1050  has a transition  1020  at one end of the strengthening member  1000  from twelve corners to four corners. This configuration allows the strengthening member  1000  to be connected directly to the automotive component by an overlapping portion  1030  and welding  1040  at aligned corners or other means of attachment between complementary shapes. 
     Strengthening member  1000  may include a tapered section  1010  to facilitate a stable axial collapse, as described above with regard to the exemplary embodiment of  FIG. 9A . Strengthening member  1000  may include other shapes or structure in addition to, or alternative to, tapered section  1010  to facilitate a stable axial collapse of strengthening member  1000 . According to an exemplary embodiment, strengthening member  1000  may include protrusions  1012  to facilitate a stable axial collapse, as will be described below. A strengthening member  1000  may include various numbers of protrusions  1012 , such as, for example, one, two, three, four, five, six, seven, eight, or more protrusions  1012 . The protrusions  1012  may be located on a lateral surface  1014  of strengthening member and on a surface (not shown) that is an opposite side of strengthening member  1000  to lateral surface  1014 . Top  1016  and bottom  1018  surface of strengthening member  1000  may lack protrusions  1012 , as depicted in the exemplary embodiment of  FIG. 10A , or may include protrusions  1012  to facilitate a stable axial collapse of strengthening member  1000 . The protrusions  1012  may be located and spaced relative to one another to promote an axial crush beginning at a portion of the strengthening member  1000  located away from the connection between the twelve-cornered strengthening member  1000  and the four-cornered automotive component  1050 , such within tapered section  1010 . 
     Protrusions may be configured to have a predetermined shape that facilitates a stable axial collapse of strengthening member. For example, protrusions  1012  may be provided with an undulating or wave-like shape that is more likely to compress along an axial direction, such as in a manner similar to the compression of an accordion. Disposing protrusions  1012  and tapered section  1010  at locations away from the connection between the strengthening member  1000  and automotive component  1050  enables a single strengthening member  1000  to be used in various motor vehicles of differing weights. By way of example, if a strengthening member  1000  provides too much resistance to compression, a vehicle having a lower weight may not be able to axially crush the strengthening member  1000  in a stable manner, and so impact energy may be more likely to be transmitted into the automotive component  1050 , and thereby into the rest of the vehicle. 
     Protrusions  1012  may have various configurations to facilitate a stable axial collapse of a strengthening member. According to an exemplary embodiment, a protrusion  1012  may extend along only a portion of a surface of a strengthening member  1010 , such as along the front-rear and top-bottom directions depicted in  FIG. 10A . For example, protrusions  1012  may extend along a portion of lateral surface  1014  along the top-bottom direction in  FIG. 10A  so that flat portions  1060  of lateral surface  1014  are present between protrusions  1012  and corners  1062  forming top and bottom edges of lateral surface  1014 . According to an exemplary embodiment, protrusions  1012  may extend along a top-bottom direction of a surface over an extent of, for example, about 30% to about 60% of the length of the surface along the top-bottom direction. Further, a protrusion  1012  may extend from lateral surface  1014  to increase the width of strengthening member  1000  (in a direction transverse to the front-rear direction) by an amount of, for example, about 5% to about 10%, such as at a center of a protrusion  1012 . 
     Protrusions of the various exemplary embodiments described herein may have an increased strength in comparison to other portions of a strengthening member (e.g., portions of a strengthening member where a protrusion is not present). The increased strength of a protrusion may be due to the material strength and/or the structural geometry of the protrusion. For example, the material of a protrusion may be work hardened during the manufacturing operation that forms the protrusion in a strengthening member, resulting in the protrusion having a higher strength than other portions of the strengthening member. As a result, the protrusion a stable axial collapse of a strengthening member. 
     The protrusions  1012  and the tapered section  1010  may help ensure that an axial crush begins away from the connection between the strengthening member  1000  and the automotive component  1050  and the crush continues as the cross section, and corresponding impact energy absorption, of the strengthening member  1000  increases, such as towards a rear portion of the strengthening member  1000 . Because vehicles may vary in configurations and differ in weight, it may be desirable to provide a strengthening member  1000  that is configured to promote a stable axial crush along the strengthening member  1000  from an area having smaller resistance (e.g., a front portion of tapered section  1010 ) to compression to an area having a larger resistance to compression (e.g., a rear portion of strengthening member  1000 , such as where strengthening member  1000  connects to automotive component  1050 ). 
     By configuring a strengthening member according to the various exemplary embodiments described herein, a strengthening member is provided that absorbs energy during a crash and can be efficiently used in various motor vehicles. According to an exemplary embodiment, the strengthening members may be designed to accommodate varying amounts of crush force, such as less crush force for smaller vehicles and greater crush force for larger vehicles. For example, the strengthening members of the embodiments described with respect to  FIGS. 9A-19  have a mean crush force, exerted axially, for an impact with a rigid wall at 35 mph of about 100 kN to about 300 kN at a crush distance of about 400 mm. In another example, a strengthening member has a mean crush force, exerted axially, for an impact with a rigid wall at 35 mph of about 100 kN to about 200 kN at a crush distance of about 150 mm. In another example, a strengthening member has a mean crush force for an impact with a rigid wall at 35 mph, exerted axially, of about 200 kN to about 300 kN at a crush distance of about 400 mm. 
     The shape of the portion of the strengthening member that connects to an automotive component may be designed to facilitate connection between the strengthening member and the automotive component, such as when the strengthening member and automotive component differ in cross-sectional shapes. For example, the shape at the end of transition  1020 , which transitions the cross-section of strengthening member  1000  from twelve corners to four corners, may be substantially complementary to the shape of the automotive component  1050 . In this manner, the strengthening member  1000  may be inserted into the automotive component  1050 , or vice versa, at overlapping portion  1030 , and all of the corners and sides of strengthening member  1000  and automotive component  1050  may align for welding (e.g., at weld locations  1040 ) in order to securely connect the strengthening member  1000  to the automotive component  1050 . This secure connection facilitates a stable axial collapse, as shown in  FIG. 10B . A stable axial collapse (e.g.,  FIG. 10B ) provides additional energy absorption in comparison to an unstable axial collapse (e.g.,  FIG. 9B ). For example, the exemplary embodiment of  FIG. 19  depicts energy absorption test results for a stable axial collapse and an unstable axial collapse, with the stable axial collapse exhibiting a 20% greater amount of energy absorption. Further, the connection between strengthening member  900  and automotive component  950  reduces the need for additional intermediate connection structures, thereby reducing the overall weight and cost of the system. In addition, the use of fewer parts may provide a stable connection and a resulting stable axial crush while optimizing manufacturing feasibility. 
       FIGS. 10C, 10D, and 10E  are exemplary embodiments of cross-sectional shapes that may be used for the twelve-cornered cross section of the strengthening member  1000 , the overlapping portion  1030 , and the four-cornered cross section of the automotive component  1050  in  FIG. 10A . In  FIG. 10C , the portion of the strengthening member  1000  before the transition  1020  (e.g., forward of transition  1020  along the front-rear direction shown in  FIG. 10A ) has a cross section similar to the cross section which is illustrated in  FIG. 9C . As depicted in  FIG. 10C , strengthening member  1000  and automotive component  1050  may have two-part constructions respectively comprising pieces  1002 ,  1004  and  1052 ,  1054 , or may have other constructions, as described above with regard to  FIG. 9C . Further,  FIG. 10C  resembles the structures illustrated in at least  FIGS. 1 and 7  and may have internal angles and external angles according to the various exemplary embodiments described herein. 
       FIG. 10D  is an exemplary embodiment of an overlapping portion where the strengthening member  1000  is inserted into the automotive component  1050 . As shown in the exemplary embodiment of  FIG. 10D , the shape of the strengthening member  1000  after the transition  1020  (e.g., rearward of transition  1020  along the front-rear direction in  FIG. 10A ) is substantially complementary to the four-cornered shape of the automotive component  1050 . In other words, the cross-sectional shape of strengthening member  1000  transitions from the shape shown in  FIG. 10C  to the shape depicted in  FIG. 10  in order to be complementary to the cross-sectional shape of automotive component  1050 . The particular shapes and angles are not intended to limit the scope of the disclosure, and merely represent an exemplary embodiment for transitional cross-sections between a twelve-cornered cross section and a four-cornered cross section. 
     An amount of overlap  1030  between the strengthening member  1000  and the automotive component  1050  may depend on various factors, such as, for example, dimensions of the strengthening member  1000  and automotive component  1050 , the type of weld used, or if the strengthening member  1000  is inserted within the automotive component  1050  or vice versa. For the exemplary embodiment of  FIG. 10A , there may be an overlap  1030  of, for example, approximately 15 mm to approximately 25 mm for flat weld joint. A transition  1020  of the strengthening member  1000  from twelve corners to four corners may be located forward of (e.g., adjacent to) the overlapping portion  1030  along the front-rear direction depicted in  FIG. 10A . 
       FIG. 10E  is an exemplary embodiment of a four-cornered automotive component  1050  rearward of the overlapping portion  1030 . While the corners are shown as having a rounded shape, this particular shape is not intended to limit the claimed subject matter in any way. 
       FIG. 11A  is a view of another exemplary embodiment of a connection between a twelve-cornered strengthening member  1100  and a four-cornered automotive component  1150 . As with  FIG. 10A , the strengthening member  1100  may include a tapered section  1110  and/or protrusions  1112 , as described above. Protrusions  1112  may be configured as described above with regard to  FIG. 10A  or may have different shapes. For example, protrusions  1112  may extend from a top to bottom of lateral side  1114  (e.g., from corner  115  to corner  1116  on lateral side  1114 ), as depicted in the exemplary embodiment of  FIG. 11A . 
     In  FIG. 11A , the connection between the strengthening member  1100  and the automotive component  1150  comprises a backing plate  1130  interposed between the strengthening member  1100  and the automotive component  1150 . Backing plate  1130  may therefore serve as a transition or bridge between strengthening member  1100  and automotive component  1150 . This configuration facilitates connection of the strengthening member  1100  to the automotive component  1150  via the backing plate  1130 . For example, backing plate  1130  may be respectively connected to strengthening member  1100  and automotive component  1150 , such as via welds  1140  at the respective ends of the strengthening member  1100  and automotive component  1150 , such as along the corners and sides of each connected element. In another example, the backing plate  1130  is bolted to the automotive component  1150  (e.g., bolted to a flange (not shown) of the automotive component  1150 ) or attached by any other known means, such as via other fastening means. This secure connection between the strengthening member  1100 , backing plate  1130 , and automotive component  1150  facilitates a stable axial crush, as shown in  FIG. 11B . The backing plate  1130  can be formed as one plate or two plates respectively joined to strengthening member  1100  and automotive component  1150  and connected to one another. In an exemplary embodiment where the backing plate  1130  is formed as one plate, both strengthening member  1100  and automotive component  1150  may be welded to the same backing plate  1130 . In an exemplary embodiment where the backing plate  1130  is formed as two plates, strengthening member  1100  and automotive component  1150  may be welded to separate plates, and the separate plates may be bolted together or joined via other means known in the art. 
     As depicted in the exemplary embodiment of  FIG. 11A , strengthening member  1100  may have a twelve-cornered cross-section from the front to the rear of the strengthening member  1100 . Therefore, backing plate  1130  may facilitate joining strengthening member  1100  to automotive component  1150 , such as when automotive component  1150  has a four-cornered cross-section. Other configurations may be utilized for strengthening member  1100 , such as a cross-section that transitions from a twelve-cornered cross-section to a four-cornered cross-section, as described above in regard to  FIG. 10A . 
       FIG. 12A  is another exemplary embodiment of a connection between a twelve-cornered strengthening member  1200  and a four-cornered automotive component  1250 . Strengthening member  1200  may include a tapered section  1210 , as described above with regard to the exemplary embodiment of  FIG. 9A . The strengthening member  1200  may include protrusions  1212  as described above. For example, protrusions  1212  may extend along a portion of a surface, such as lateral surface  1214 , along a top-bottom direction in  FIG. 12A . For instance, flat portions  1260  may be provided between protrusions  1212  and top and bottom edges of surface  1214  that are formed by corners  1260  of strengthening member  1200 . Further, although protrusions  1212  may be formed by curved surfaces, as depicted in  FIGS. 9A and 10A , protrusions  1212  may be formed by various angled surfaces that form corners  1264 , as depicted in  FIG. 12A . 
     According to an exemplary embodiment, at least one of the strengthening member and the automotive component may include one or more cutouts to facilitate welding the strengthening member and automotive component to one another. For example, in  FIG. 12A , the connection comprises slot welds in the sides of the automotive component  1250  within the overlapping portion  1230  between strengthening member  1200  and automotive component  1250 . Cutouts can be provided in at least one of the strengthening member  1200  and the automotive component  1250  to facilitate the welding, such as by providing one or more slots  1220  around a circumference of the automotive component  1250 . As a result, when the strengthening member  1200  is inserted into the automotive component  1250 , additional surface area of the strengthening member  1200  may be welded at location(s)  1240  at the slot(s)  1220  and portions of the strengthening member  1200  and automotive component  1250  to be joined may be more accessible during welding. This configuration may also be reversed such that the slots are formed in the strengthening member  1200  and the automotive component  1250  is inserted into the strengthening member  1200 . This secure connection facilitates a stable axial crush, as shown in  FIG. 12B . 
     According to an exemplary embodiment, slots  1220  and welds  1240  may be discrete and extend along portions of surfaces of strengthening member  1200  and automotive component  1250 . For example, slots  1220  and welds  1240  may extend along a portion of surfaces of strengthening member  1200  and automotive component  1250  between corners  1260  of strengthening member  1200  because corresponding surfaces of strengthening member  1200  and automotive component  1250  are in contact or close proximity to one another at those locations, in comparison to corners  1260  because of the difference in cross-sectional shapes of strengthening member  1200  and automotive component  1250 . As a result, slots  1220  and welds  1240  facilitate joining strengthening member  1200  and automotive component  1250  when they have differing cross-sections, such as when strengthening member  1200  has a twelve-cornered cross-section and automotive component  1250  has a four-cornered cross-section, as depicted in the exemplary embodiment of  FIG. 12A . Other configurations are envisioned for strengthening member  1200  and automotive component, such as a cross-section for strengthening member  1200  that transitions from a twelve-cornered cross-section to a four-cornered cross-section, as described above in regard to  FIG. 10A . 
       FIG. 13A  is a view of another exemplary embodiment of a connection between a twelve-cornered strengthening member  1300  and a four-cornered automotive component  1350 . Strengthening member  1300  may include a tapered section  1310  and/or protrusions  1312 , as discussed in the exemplary embodiments herein. In  FIG. 13A , the connection includes one or more fish-mouth weld joints, which may include removal of material at a connected end of the automotive component  1350  to form cutouts  1320  having a fish-mouth shape, insertion of the strengthening member  1300  into the fish-mouth shaped cutouts  1320  to create an overlapping portion  1330 , and welding at locations  1340  along the increased surface area of the strengthening member  1300  exposed by the fish-mouth shape. 
     According to an exemplary embodiment, fish-mouth shaped cutouts  1320  and welds  1340  may be discrete and extend along portions of strengthening member  1300  and automotive component  1350 . As a result, fish-mouth shaped cutouts  1320  and welds  1340  facilitate joining strengthening member  1300  and automotive component  1350  when they have differing cross-sections, as discussed above with regard to the exemplary embodiment of  FIG. 12A . Other configurations are envisioned for strengthening member  1300  and automotive component, such as a cross-section for strengthening member  1300  that transitions from a twelve-cornered cross-section to a four-cornered cross-section, as described above in regard to  FIG. 10A . 
     While  FIG. 13A  shows the strengthening member  1300  inserted into the automotive component  1350 , this configuration may also be reversed such that the material is removed from an end of the strengthening member and the automotive component is inserted into the strengthening member. This secure connection facilitates a stable axial crush, as shown in  FIG. 13B . In the exemplary embodiment of  FIG. 13A , it may be desirable to provide an overlapping portion  1330  with an approximately 10 mm inner overlap (e.g., a distance  1370  between a rear edge  1360  of strengthening member  1300 , depicted via a dashed line in  FIG. 13A , and a rear edge  1322  of fish-mouth shaped cutout  1320 ) and 10 mm outer overlap (e.g., a distance  1372  between a front edge  1324  of fish-mouth shaped cutout  1320  and the rear edge  1322  of the fish-mouth shaped cutout  1320 ) to secure the fish-mouth weld joint. Thus, a total overlap between strengthening member  1300  and automotive component  1350  may include both the inner overlap (e.g., distance  1370 ) and the outer overlap (e.g., distance  1372 ). 
       FIGS. 14A and 15A  are views of further exemplary embodiments of a connection between a twelve-cornered strengthening member  1400  or  1500  and a four-cornered automotive component  1450  or  1550 . Strengthening members  1400 ,  1500  may respectively include tapered sections  1410 ,  1510  and/or protrusions  1412 ,  1512 , as discussed in the exemplary embodiments herein. Further, the strengthening members may include bridge connection members. In the embodiments of  FIGS. 14A and 15A , one or more bridging brackets  1420  or  1520  extend between the strengthening member  1400  or  1500  and the automotive component  1450  or  1550  at overlapping portions  1430  or  1530 , respectively. For example,  FIG. 14A  depicts a strengthening member  1400  joined to an automotive component  1450  via a single bracket  1420  while  FIG. 15A  depicts a strengthening member  1500  joined to an automotive component  1550  via a plurality of brackets  1520 . The brackets  1420  or  1520  may be secured by welding, such as at locations  1440  or  1540 , or any other known means of attachment. This secure connection facilitates a stable axial crush, as shown in  FIGS. 14B and 15B . 
     Brackets  1420 ,  1520  facilitate joining strengthening members  1400 ,  1500  and automotive components  1450 ,  1450  when they have differing cross-sections, as discussed above with regard to the exemplary embodiment of  FIG. 12A . Other configurations are envisioned for the strengthening members and automotive components, such as a cross-section for strengthening members  1400 ,  1500  that transitions from a twelve-cornered cross-section to a four-cornered cross-section, as described above in regard to  FIG. 10A . 
       FIG. 16A  is a view of another exemplary embodiment of a connection between a twelve-cornered strengthening member  1600  and a four-cornered automotive component  1650 . Strengthening member  1600  may include a tapered section  1610  and/or protrusions  1612 , as discussed in the exemplary embodiments herein. In  FIG. 16A , the connection between strengthening member  1600  and automotive component  1650  comprises a transition  1620  at one end of the automotive component  1650  in which the cross-section of automotive component  1650  transitions from a twelve-cornered cross-section to a four-cornered cross section along at least a portion of automotive component  1650 , such as along a longitudinal axis  1614  of automotive component  1650 . As a result, the cross-section of the end of the automotive component  1650  at the connection may correspond to the cross-section of strengthening member  1600 , which may have a twelve-cornered cross-sectional shape, as depicted in the exemplary embodiment of  FIG. 16A . This configuration allows the strengthening member  1600  to be connected directly to the automotive component  1650  at overlapping portion  1630  by welding, such as at locations  1640 , or other known means of attachment. The shape at the end of the transition will be substantially complementary to the shape of the strengthening member, so all of the corners and/or sides may be welded together to securely connect the strengthening member to the automotive component. This secure connection facilitates a stable axial crush, as shown in  FIG. 16B . 
       FIGS. 16C-16E  illustrate a transition from a four-cornered cross section to a twelve-cornered cross section of automotive component  1650 . As depicted in  FIGS. 16C-16E , strengthening member  1600  and automotive component  1650  may have two-part constructions respectively comprising pieces  1602 ,  1604  and  1652 ,  1654 , or may have other constructions, as described above with regard to  FIG. 9C . Further,  FIG. 16C  resembles the structures illustrated in at least  FIGS. 1 and 7  and may have internal angles and external angles according to the various exemplary embodiments described herein. For example, the internal angles of the strengthening member may range from about 100° to about 110°, and the external angles may range from about 105° to about 130°. 
       FIG. 16C  illustrates the strengthening member  1600 , which is provided with a twelve-cornered cross section as previously discussed. In this exemplary embodiment, strengthening member  1600  does not include a transition to any other cross-sectional shape. Instead, the transitional structure is included in the automotive component  1650 . 
       FIG. 16D  is an exemplary embodiment of an overlapping portion in which the strengthening member  1600  is inserted into the automotive component  1650 . As shown in the exemplary embodiment of  FIG. 16D , the shape of the automotive component  1650  after the transition  1620  is substantially complementary to the twelve-cornered shape of the strengthening member  1600 . The particular shapes and angles are not intended to limit the scope of the disclosure, and merely represent an exemplary embodiment for transitional cross-sections between a twelve-cornered cross section and a four-cornered cross section. 
     An amount of overlap  1630  between the strengthening member  1600  and the automotive component  1650  may depend on other dimensions, type of weld used, or which element is overlapping. For the exemplary embodiment of  FIG. 16A , there may be an overlap  1630  of approximately 15 mm for flat weld joint. A transition  1620  of the automotive component  1650  from four corners to twelve corners may be located just after the overlapping portion  1630 . 
       FIG. 16E  is an exemplary embodiment of a four-cornered automotive component  1650  after the overlapping portion  1630 . While the corners are shown as having a rounded shape, this particular shape is not intended to limit the claimed subject matter in any way. 
       FIG. 17A  is a view of another exemplary embodiment of a connection between a twelve-cornered strengthening member  1700  and a four-cornered automotive component  1750 . Strengthening member  1700  may include a tapered section  1710  and/or protrusions  1712 , as discussed in the exemplary embodiments herein. In  FIG. 17A , the connection comprises a transition  1720  along at least a portion of the length of the strengthening member  1700  (e.g., along longitudinal axis  1760 ) from twelve corners to four corners, as well as a fish-mouth shaped cutouts  1725 , and a mating component  1735 . Mating component  1735  may be, for example, a bracket connected to outer or inner surfaces of the strengthening member  1700  and the automotive component  1750 . The connection also comprises a fish-mouth weld joint as described above and illustrated by the fish-mouth shaped cutouts  1725  of the strengthening member  1700  at the overlapping portion  1730 , along with welds, such as at locations  1740 , or other known connections formed by other means of attachment as previously discussed. This secure connection facilitates a stable axial crush, as shown in  FIG. 17B . 
       FIGS. 17C-17G  illustrate cross sections of the exemplary embodiment of  FIG. 17A , in which the connection comprises the mating component  1735  and the fish-mouth weld joint including fish-mouth shaped cutouts  1725  and welds.  FIG. 17C  illustrates the strengthening member  1700 , which is provided with a twelve-cornered cross section as previously discussed. In this exemplary embodiment, strengthening member  1700  includes a transition  1720  as discussed above. As depicted in  FIGS. 17C-17G , strengthening member  1700  and automotive component  1750  may have two-part constructions respectively comprising pieces  1702 ,  1704  and  1752 ,  1754 , or may have other constructions, as described above with regard to  FIG. 9C . Further,  FIG. 17C  resembles the structures illustrated in at least  FIGS. 1 and 7  and may have internal angles and external angles according to the various exemplary embodiments described herein. For example, the internal angles of the strengthening member may range from about 100° to about 110°, and the external angles may range from about 105° to about 130°. 
       FIG. 17D  shows the strengthening member  1700  after the transition  1720  to four corners, with the mating component  1735  connected to an outer surface of the strengthening member  1700 . It is also possible to connect the mating component  1735  to an inner surface of the strengthening member  1700 . 
       FIG. 17E  shows an exemplary embodiment of an overlapping portion  1730  where the automotive component  1750  is inserted into the strengthening member  1700 , with the mating component  1735  still connected. As shown in the cross sections of the exemplary embodiment illustrated in  FIGS. 17D-17E , the shape of the strengthening member  1700  may include the transition  1720  from a twelve-cornered cross section to a four-cornered cross section, as discussed in detail with respect to other embodiments. 
       FIG. 17F  shows an exemplary embodiment of a four-cornered automotive component  1750  connected to the mating component  1735 .  FIG. 17G  shows an exemplary embodiment of a four-cornered automotive component  1750  at a portion where the mating component  1735  is no longer connected. While the corners of the automotive component  1750  are shown as having a rounded shape, this particular shape is not intended to limit the claimed subject matter in any way. 
     As previously noted, it is also within the scope of the present invention to combine any of the embodiments disclosed above. For example, a connection may comprise a transition from twelve corners to four corners, or vice versa, a fish-mouth weld, and one or more mating components, as shown in  FIGS. 9A-17B , or any other combination of the exemplary embodiments according to the present disclosure. 
     As discussed in the exemplary embodiments above, a bridge connecting member may be used to connect a strengthening member and an automotive component. The present disclosure contemplates bridge connecting members that include a transition from a twelve-cornered cross section to a four-cornered cross section to facilitate a connection between the strengthening member and the automotive component. Turning to  FIG. 18 , exemplary embodiments of a strengthening member  1800 , automotive component  1850 , and bridge connecting member  1810  to connect strengthening member  1800  and automotive component  1850  are shown. Strengthening member  1800  and automotive component  1850  may be configured according to the various exemplary embodiments described herein. For example, strengthening member  1800  may have a twelve-cornered cross-section (e.g., along an entire length of strengthening member  1800 ) and automotive component  1850  may have a four-cornered cross-section, as depicted in  FIG. 18 . To facilitate a connection between member  1800  and component  1850 , bridge connecting member  1810  may transition from a twelve-cornered cross section, such as at a first end  1812  that connects to strengthening member  1800 , to a four-cornered cross section, such as at a second end  1814  that connects to automotive component  1850 . As a result, a strong connection between strengthening member  1800  and automotive component  1850  is facilitated, as a well as a stable axial collapse of strengthening member  1800 . 
     While the present teachings have been disclosed in terms of exemplary embodiments in order to facilitate a better understanding, it should be appreciated that the present teachings can be embodied in various ways without departing from the scope thereof. Therefore, the invention should be understood to include all possible embodiments which can be embodied without departing from the scope of the invention set out in the appended claims. 
     For the purposes of this specification and appended claims, unless otherwise indicated, all numbers expressing quantities, percentages or proportions, and other numerical values used in the specification and claims, are to be understood as being modified in all instances by the term “about.” Accordingly, unless indicated to the contrary, the numerical parameters set forth in the written description and claims are approximations that may vary depending upon the desired properties sought to be obtained by the present invention. At the very least, and not as an attempt to limit the application of the doctrine of equivalents to the scope of the claims, each numerical parameter should at least be construed in light of the number of reported significant digits and by applying ordinary rounding techniques. 
     It is noted that, as used in this specification and the appended claims, the singular forms “a,” “an,” and “the,” include plural referents unless expressly and unequivocally limited to one referent. As used herein, the term “include” and its grammatical variants are intended to be non-limiting, such that recitation of items in a list is not to the exclusion of other like items that can be substituted or added to the listed items. 
     It will be apparent to those skilled in the art that various modifications and variations can be made to the devices and methods of the present disclosure without departing from the scope of its teachings. Other embodiments of the disclosure will be apparent to those skilled in the art from consideration of the specification and practice of the teachings disclosed herein. It is intended that the specification and embodiment described herein be considered as exemplary only.