Twenty-eight-cornered strengthening member for vehicles

Abstract

A strengthening member and a vehicle including a strengthening member are provided. The strengthening member can have a cross section including twenty-eight corners and twenty-eight sides creating twenty internal angles and eight external angles, and at least one recessed area extending along a length of the strengthening member.

Claims

1. A strengthening member, comprising: a cross section consisting essentially of twenty-eight corners and twenty-eight sides creating twenty internal angles and eight external angles; and at least one recessed area extending along a length of the strengthening member.

2. The strengthening member of claim 1, wherein each internal angle ranges between about 30 degrees and about 175 degrees.

3. The strengthening member of claim 1, wherein each external angle ranges between about 45 degrees and about 175 degrees.

4. The strengthening member of claim 1, wherein each of the twenty internal angles have substantially the same measurement.

5. The strengthening member of claim 1, wherein each of the eight external angles have substantially the same measurement.

6. The strengthening member of claim 1, wherein: each of the twenty internal angles has a first measurement; each of the eight external angles has a second measurement; and the first measurement and the second measurement are different from one another.

7. The strengthening member of claim 1, wherein: each of eight of the twenty internal angles has a first internal angle measurement; each of another eight of the twenty internal angles has a second internal angle measurement; each another four of the twenty internal angles has a third internal angle measurement; and the first internal angle measurement, the second internal angle measurement, and the third internal angle measurement are different from one another.

8. The strengthening member of claim 1, wherein: each of four of the eight external angles has a first external angle measurement; each of another four of the eight external angles has a second external angle measurement; and the first external angle measurement and the second external angle measurement are different from one another.

9. The strengthening member of claim 1, wherein the strengthening member further comprises four recessed areas, each recessed area extending along the length of the strengthening member.

10. The strengthening member of claim 1, wherein four of the twenty internal angles and two of the eight external angles of the cross section of the strengthening member define the at least one recessed area.

11. The strengthening member of claim 10, wherein at least two of the four internal angles defining the recessed area are equal to one another.

12. The strengthening member of claim 10, wherein the two external angles defining the recessed area are equal to one another.

13. The strengthening member of claim 10, wherein the two external angles defining the recessed area differ from one another.

14. The strengthening member of claim 10, wherein each of the four internal angles defining the recessed area is obtuse and each of the two external angles defining the recessed area is obtuse.

15. The strengthening member of claim 1, wherein the at least one recessed area is defined by five sides of the strengthening member.

16. The strengthening member of claim 15, wherein four of the five sides that define the at least one recessed area have the same cross-sectional length.

17. The strengthening member of claim 15, wherein four sides of the five sides that define the at least one recessed area have the same cross-sectional length and the other of the five sides that define the at least one recessed area has a different cross-sectional length.

18. The strengthening member of claim 1, wherein the corners of the cross section have substantially the same thickness as the sides of the cross section.

19. A strengthening member for a motor vehicle, comprising a cross section including twenty-eight corners and having twenty-eight sides arranged to create internal angles and external angles, wherein the angles alternate in a pattern comprising five consecutive internal angles and two consecutive external angles.

20. The strengthening member of claim 19, further comprising a longitudinal axis, wherein the strengthening member tapers along the longitudinal axis.

21. The strengthening member of claim 19, wherein the cross section has more than two bisecting planes of symmetry.

22. The strengthening member of claim 19, wherein the cross section has four bisecting planes of symmetry.

23. The strengthening member of claim 19, wherein at least one internal angle of the cross section varies along at least a portion of a longitudinal length of the strengthening member.

24. The strengthening member of claim 19, wherein a thickness of at least one side of the strengthening member varies along at least a portion of a longitudinal length of the strengthening member.

25. A vehicle comprising: a strengthening member comprising a cross section consisting essentially of twenty-eight corners and twenty-eight sides creating twenty internal angles and eight external angles; and at least one recessed portion extending along a length of the strengthening member.

26. The vehicle of claim 25, wherein the strengthening member is or forms a part of at least one vehicle structural member selected from the group consisting of: a crush can, a front horn, a front rail, a front side rail, a rear side rail, a rear rail, a frame cross member, a shotgun, a hinge-pillar, an A-pillar, a B-pillar, a C-pillar, a door beam, a cross car beam, a front header, a rear header, a cow top, a roof rail, a lateral roof bow, longitudinal roof bow, a body cross member, a back panel cross member, a rocker, an underbody cross member, and an engine compartment cross member.

27. The vehicle of claim 25, wherein a brake line, pipe, electric wire, cable, and/or seatbelt is disposed within the recessed portion.

28. A strengthening member, comprising: twenty-eight sides; and twenty-eight corners, wherein a cross section of the strengthening member includes four lobe portions extending from a central portion defined by four of the twenty-eight sides.

29. The strengthening member of claim 28, wherein a side of the central portion and a side of each of two of the lobe portions adjacent to each other define a recess that extends along a length of the strengthening member.

30. The strengthening member of claim 28, wherein the strengthening member includes four recesses extending along a length of the strengthening member, each recess defined by a side of the central portion and a side of each of two of the lobe portions adjacent to each other.

31. The strengthening member of claim 28, wherein the twenty-eight corners comprise twenty internal angles and eight external angles.

32. The strengthening member of claim 28, wherein each lobe portion is defined by six sides of the twenty-eight sides.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) 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:

(2) FIG. 1A is a cross-sectional view of a strengthening member having a twenty-eight-cornered cross section including twenty internal angles and eight external angles in accordance with the present teachings;

(3) FIG. 1B is another cross-sectional view of the strengthening member of FIG. 1A, and with various lengths, thicknesses, and angles identified;

(4) FIGS. 2A-2B are top and perspective views, respectively, of a first exemplary embodiment of a strengthening member having a twenty-eight-cornered cross section with twenty internal angles and eight external angles, as shown in FIG. 1A;

(5) FIGS. 3A-3B are top and perspective views, respectively, of a second exemplary embodiment of a strengthening member having a twenty-eight-cornered cross section with twenty internal angles and eight external angles in accordance with the present teachings;

(6) FIGS. 4A-4B are top and perspective views, respectively, of a third exemplary embodiment of a strengthening member having a twenty-eight-cornered cross section with twenty internal angles and eight external angles in accordance with the present teachings;

(7) FIGS. 5A-5B are top and perspective views, respectively, of a fourth exemplary embodiment of a strengthening member having a twenty-eight-cornered cross section with twenty internal angles and eight external angles in accordance with the present teachings;

(8) FIGS. 6A-6B are top and perspective views, respectively, of a fifth exemplary embodiment of a strengthening member having a twenty-eight-cornered cross section with twenty internal angles and eight external angles in accordance with the present teachings;

(9) FIGS. 7A-7B are top and perspective views, respectively, of a sixth exemplary embodiment of a strengthening member having a twenty-eight-cornered cross section with twenty internal angles and eight external angles in accordance with the present teachings;

(10) FIGS. 8A-8B are top and perspective views, respectively, of a seventh exemplary embodiment of a strengthening member having a twenty-eight-cornered cross section with twenty internal angles and eight external angles in accordance with the present teachings;

(11) FIG. 9 illustrates strengthening members of various cross-sections having substantially the same thickness, substantially the longitudinal length, and cross-sectional dimensions along perpendicularly oriented transverse axes with substantially the same lengths;

(12) FIG. 10 illustrates an exemplary quasi-static axial collapse of the strengthening members shown in FIG. 9;

(13) FIG. 11 illustrates an exemplary dynamic crush of the strengthening members shown in FIG. 9;

(14) FIG. 12 is a graph of the dynamic crush force and associated crush distance for the exemplary strengthening members shown in FIG. 9;

(15) FIG. 13 is a graph of the dynamic axial crush energy and associated axial crush distance for the exemplary strengthening members shown in FIG. 9;

(16) FIG. 14 is a perspective view of an exemplary embodiment of a vehicle frame having several components for which a strengthening member having a twenty-eight-cornered cross section with twenty internal angles and eight external angles can be used; and

(17) FIG. 15 is a perspective view of an exemplary embodiment of a vehicle upper body having several components for which a strengthening member having a twenty-eight-cornered cross section with twenty internal angles and eight external angles can be used.

(18) Although the following detailed description makes reference to exemplary 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

(19) Reference will now be made in detail to various exemplary 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 of the exemplary embodiments. In the drawings and the description, similar elements are provided with similar reference numerals. It is to be noted that the features explained individually in the description can be mutually combined in any technically expedient manner and disclose additional embodiments of the present disclosure.

(20) The present teachings contemplate strengthening members with twenty-eight-cornered cross sections. The cross-sectional configuration of these strengthening members provides increased stiffness throughout the sides and corners of the strengthening members when compared to conventional strengthening members. Such conventional strengthening members must rely on increasing thickness within the corners to achieve increases in strength, which result in increases in the weight of the conventional strengthening members. The strengthening members of the present disclosure are designed based in part on, for example, a variety of tunable parameters configured to achieve strength increases (i.e., load carrying and energy absorption) over basic polygonal designs (e.g., polygonal strengthening member cross sections having less or the same number of sides), while also allowing design flexibility to meet a range of vehicle applications.

(21) In accordance with the present teachings, the shape of the strengthening members disclosed herein provides the strengthening member with stabilized folding, reduced crush distance, and increased energy absorption in response to an axially applied crash force when compared to conventional strengthening members. In at least some embodiments, the shape also improves moisture shedding abilities of the strengthening member and permits a more customized fit with other vehicle components.

(22) The strengthening members in accordance with the present teachings 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. Furthermore, the side lengths and configurations, and/or degrees of the internal and external angles, of the strengthening members in accordance with the present teachings can achieve a similar, if not greater, 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 stamping, bending, press forming, hydro-forming, molding, casting, extrusion, uniform or non-uniform roll forming, machining, forging, 3-D printing, and/or other known suitable manufacturing processes. Thus-formed sections can be joined via welding, brazing, soldering, adhesive bonding, fastening, press fitting or other known joining technologies.

(23) Strengthening members in accordance with the present teachings may be made, for example, of steel alloys, titanium alloys, aluminum alloys, magnesium alloys, nylons, plastics, polymers, composites, fiber-reinforced composites, silicone, semiconductor, papers, hybrid materials (i.e., multiple dissimilar materials), shape-memory materials, foams, gels or any other suitable materials. Those of ordinary skill in the art would understand, for example, that the material used for a strengthening member may be chosen based at least in part on intended application, strength/weight considerations, cost, packaging space, and/or other design factors.

(24) Turning to the drawings, an exemplary embodiment of a cross section of a strengthening member 100 having twenty-eight corners in accordance with the present teachings is illustrated in FIG. 1A. The strengthening member 100 has twenty-eight sides S.sub.1-S.sub.28. The sides S.sub.1-S.sub.28 of the strengthening member may define a cross-section of the strengthening member having four lobe portions 141-144 and a central portion 151, in accordance with the present teachings. Each lobe portion may be defined by six sides, for example, sides S.sub.1-S.sub.6 define a first lobe portion 141, sides S.sub.8-S.sub.13 define a second lobe portion 142, sides S.sub.15-S.sub.20 define a third lobe portion 143, and sides S.sub.22-S.sub.27 define a fourth lobe portion 144 of the cross-section of strengthening member 100. Central portion 151 may be defined by four sides, for example, sides S.sub.7, S.sub.14, S.sub.21, and S.sub.28 define a central portion 151 of the cross-section of strengthening member 100.

(25) As labeled in FIG. 1B, the illustrated cross-section of strengthening member 100 comprises twenty-eight sides S.sub.1-S.sub.28 having cross-sectional lengths L.sub.1-L.sub.28 and cross-sectional thicknesses T.sub.1-T.sub.28. Sides S.sub.1-S.sub.28 define twenty internal corners with angles .sub.i1-.sub.i20, and eight external corners with angles .sub.e1-.sub.e8.

(26) The perimeter of the twenty-eight-sided cross section generally forms a polygon comprising a plurality of internal and external corners. As embodied herein and shown in FIGS. 1A-1B, the polygon may be formed of alternating internal and external angles, and in particular, the cross-section may be formed by alternating the angles in a pattern, for example, a repeating pattern comprising five consecutive internal corners/angles followed by two external corners/angles. This repeating pattern (i.e., an alternating five-in-two-out configuration), results in a cross-section with up to four bisecting planes of symmetry. Under an axial and symmetric loading condition, strengthening members with symmetrical, polygonal cross-sections, including the various embodiments of the present teachings, may have better load carrying capabilities and energy absorbing capabilities than those with asymmetrical, polygonal cross sections with an equivalent number of corners and sides. Furthermore, strengthening members with symmetrical, polygonal cross-sections with more than two bisecting planes of symmetry (e.g., three bisecting planes of symmetry, four bisecting planes of symmetry, or five or more bisecting planes of symmetry), including the various embodiments of the present teachings, may have better load carrying capabilities and energy absorbing capabilities than those with symmetrical, polygonal cross sections with two or fewer bisecting planes of symmetry and an equivalent number of corners and sides. For example, the exemplary cross section shown in FIGS. 1A and 1B has four bisecting planes of symmetry. However, as those of ordinary skill in the art will understand, use of asymmetrical cross sections may offer other benefits that provide advantages that cannot be realized using a symmetrical cross-section. The present disclosure contemplates that a twenty-eight-sided, twenty-eight-cornered cross section, in accordance with the present teachings, may be either symmetrical or asymmetrical.

(27) Depending upon the particular application and/or the desired features of the strengthening member, the cross-sectional lengths of the sides of the strengthening member and the cross-sectional thicknesses of the sides of the twenty-eight-sided, twenty-eight-cornered strengthening member as well as the internal and external corner angles of the strengthening member can be varied (i.e., can be tuned) to achieve improved strength and other performance features (e.g., stability of folding pattern) of the strengthening member when compared to conventional strengthening members. Varying these features of the twenty-eight-sided, twenty-eight-cornered strengthening member may obviate the need for increased side and/or corner thickness. In accordance with various exemplary embodiments of the present teachings, the cross-sectional lengths L.sub.1-L.sub.28 of sides S.sub.1-S.sub.28, the cross-sectional thicknesses T.sub.1-T.sub.28 of the sides as well as the cross-sectional internal angles .sub.i1-.sub.i20 of the internal corners and external angles .sub.e1-.sub.e8 of the external corners 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.

(28) In addition, in a strengthening member in accordance with the present teachings, each internal corner angle .sub.i1-.sub.i20 of a cross-section of the strengthening member can range from about 30 to about 175, and each external corner angle .sub.e1-.sub.e8 of a cross section of the strengthening member can range from about 45 to about 175. In accordance with the present teachings, the internal angles .sub.i1-.sub.i20 of a cross section of the strengthening member may all be substantially the same, and/or, the external angles .sub.e1-.sub.e8 of a cross-section of the strengthening member may all be substantially the same. Additionally or alternatively, the present disclosure contemplates embodiments in which at least some of the internal angles .sub.i1-.sub.i20 of a cross section of the strengthening member differ from one another, and/or similarly, at least some of the external angles of .sub.e1-.sub.e8 a cross-section of the strengthening member differ from one another.

(29) In various exemplary embodiments according to the present disclosure, the internal angles .sub.i1-.sub.i5, .sub.i6-.sub.i10, .sub.i11-.sub.i15, and .sub.i16-.sub.i20 that at least partially define each lobe portion 141-144 may or may not all be substantially the same, and/or, the internal angles .sub.e1-.sub.e8 that at least partially define the central portion may or may not all be substantially the same, and/or the external angles .sub.e1-.sub.e8 may all be substantially the same. For example, FIG. 1B illustrates an exemplary cross section in which internal angles .sub.i1-.sub.i5, .sub.i6-.sub.i10, .sub.i11-.sub.i15, and .sub.i16-.sub.i20 that at least partially define each lobe portion 141-144 are not all substantially the same and internal angles .sub.e1-.sub.e8 that at least partially the central portion are substantially the same. In various exemplary embodiments, eight internal angles .sub.i1, .sub.i5, .sub.i6, .sub.i10, .sub.i11, .sub.i15, .sub.i16, and .sub.i20 may each range from about 110 to about 140 or from about 122 to about 126; another eight internal angles .sub.i2, .sub.i4, .sub.i7, .sub.i9, .sub.i12, .sub.i14, .sub.i17, and .sub.i19 may each range from about 120 to about 150 or from about 135 to about 139; another four internal angles .sub.i3, .sub.i8, .sub.i13, and .sub.i8 may each range from about 110 to about 140 or from about 122 to about 126; and each external corner angle .sub.e1-.sub.e8 may range from about 85 to about 115 or from about 100 to about 104. For example, in the exemplary embodiment of FIGS. 1A-1B, eight of the internal angles .sub.i1, .sub.i5, .sub.i6, .sub.i10, .sub.i11, .sub.i15, .sub.i16, and .sub.i20 are each about 124; another eight of the internal angles .sub.i2, .sub.i4, .sub.i7, .sub.i9, .sub.i12, .sub.i14, .sub.i17, and .sub.i19 are each about 137; the remaining four internal angles .sub.i3, .sub.i8, .sub.i13, and .sub.i8 are each about 124; and external angles .sub.e1-.sub.e8 that at least partially the central portion are about 102. For the purposes of this disclosure, an individual angle measurement (internal or external) is measurement of the angular size of the arc extending between the middle of the respective thicknesses of the two sides that form the angle.

(30) In certain exemplary embodiments of the present disclosure, such as in an automotive application, for example, a cross-sectional length L.sub.1-L.sub.28 of each side S.sub.1-S.sub.28 of a cross section of the strengthening member can range from about 10 mm to about 250 mm. In other exemplary embodiments, such as in an aircraft, spacecraft, watercraft, or building application, for example, a cross-sectional length L.sub.1-L.sub.28 of each side S.sub.1-S.sub.28 of the cross section of the strengthening member may be longer. FIG. 1B illustrates an exemplary cross section in which cross-sectional lengths L.sub.1-L.sub.6, L.sub.8-L.sub.13, L.sub.15-L.sub.20, and L.sub.22-L.sub.27 of respective sides S.sub.1-S.sub.6, S.sub.8-S.sub.13, S.sub.15-S.sub.20, and S.sub.22-S.sub.27 are each a first length, e.g., 24 mm; and cross-sectional lengths L.sub.7, L.sub.14, L.sub.21, and L.sub.28 of respective sides S.sub.7, S.sub.14, S.sub.21, and S.sub.28 are each a second length, e.g., 28 mm. While the first and second lengths are different in this example, it is contemplated that the first and second lengths may be substantially the same. It is also contemplated that more than two lengths may be used.

(31) In certain exemplary embodiments of the present disclosure, such as in an automotive application, for example, a thickness T.sub.1-T.sub.28 of the sides of the cross section of the strengthening member can range from about 0.6 mm to about 6.0 mm. In other exemplary embodiments of the strengthening member, such as in an aircraft, spacecraft, watercraft, or building application, for example, a thickness T.sub.1-T.sub.28 of the sides of a cross section of the strengthening member may be greater. In one exemplary embodiment, a cross-sectional thickness T.sub.1-T.sub.28 of each of the sides of the strengthening member may be about 3.3 mm. In another exemplary embodiment, a cross-sectional thickness T.sub.1-T.sub.28 of each of the sides may be about 2.3 mm. In another exemplary embodiment, a cross-sectional thickness T.sub.1-T.sub.28 of each of the sides may be about 2.0 mm. In some exemplary embodiments, the cross-sectional thickness T.sub.1-T.sub.28 of the sides is substantially the same as the thickness of the corners for each side. In some exemplary embodiments the cross-sectional thickness T.sub.1-T.sub.28 of each side wall, (e.g., side walls S.sub.201-S.sub.228, respectively (see FIG. 2A)), can vary with respect to each other side wall. Alternatively or concurrently, the cross-sectional thickness T.sub.1-T.sub.28 can vary along the respective cross-sectional lengths L.sub.1-L.sub.28 of the sides S.sub.1-S.sub.28.

(32) Top and perspective views of a first exemplary embodiment of a strengthening member 200 having a twenty-eight-cornered cross section, with twenty internal angles and eight external angles are illustrated in FIGS. 2A-2B, respectively. Strengthening member 200 has twenty-eight corners C.sub.i201-C.sub.i220 and C.sub.e201-C.sub.e208 and twenty-eight side walls S.sub.201-S.sub.228. Twenty of the corners are internal angle corners C.sub.i201-C.sub.i220 and eight of the corners are external angle corners C.sub.e201-C.sub.e208. The strengthening member 200 includes four lobe portions 241-244 and a central portion. Each lobe portion is defined by four sides, for example, sides S.sub.201 S.sub.206 define a first lobe portion 241, sides S.sub.208-S.sub.213 define a second lobe portion 244, sides S.sub.215-S.sub.220 define a third lobe portion 243, and sides S.sub.222-S.sub.227 define a fourth lobe portion 244 of strengthening member 200. The central portion 251 (REF #) also is at least partially defined by four sides, for example, sides S.sub.207, S.sub.214, S.sub.221, and S.sub.228 define the central portion 251 of strengthening member 200.

(33) Also, as shown in FIGS. 2A-2B, strengthening member 200 includes four recessed areas 231, 232, 233, and 234. Each recessed area 231, 232, 233, and 234 extends along the length of the strengthening member 200 from first end 260 to second end 270. A side of the central portion and a side of each of two adjacent lobe portions define each recess along a length of the strengthening member 200.

(34) Strengthening member 200 also has a first transverse axis 230, a second transverse axis 240, and a longitudinal axis 250. Although shown with its longitudinal axis 250 positioned substantially vertically (in FIG. 2B), when strengthening member 200 (as well as all of the other various embodiments in accordance with the present teachings) is installed within a vehicle, the longitudinal axis 250 of the strengthening member may be oriented substantially horizontally.

(35) The strengthening member 200 of FIGS. 2A-2B also has a uniform cross section along a length of the strengthening member 200, from first end 260 to second end 270 of the strengthening member 200. Additionally, the longitudinal length LL.sub.200 of each cross-sectional side S.sub.201-S.sub.228 is approximately the same, as shown in FIG. 2B. As also illustrated, for all cross sections of strengthening member 200, the twenty internal angles are not all substantially the same, and all eight of the external angles are substantially the same. In various exemplary embodiments, eight internal angles .sub.i201, .sub.i205, .sub.i206, .sub.i210, .sub.i211, .sub.i215, .sub.i216, and .sub.i220 may each range from about 110 to about 140 or from about 122 to about 126; another eight internal angles .sub.i202, .sub.i204, .sub.i207, .sub.i209, .sub.i212, .sub.i214, .sub.i217, and .sub.i219 may each range from about 120 to about 150 or from about 135 to about 139; another four internal angles .sub.i203, .sub.i208, .sub.i213, and .sub.i218 may each range from about 110 to about 140 or from about 122 to about 126; and each external corner angle .sub.e201-.sub.e208 may range from about 85 to about 115 or from about 100 to about 104. For example, in the exemplary embodiment of FIGS. 2A-2B, eight of the internal angles .sub.i201, .sub.i205, .sub.i206, .sub.i210, .sub.i211, .sub.i215, .sub.i216, and .sub.i220 are each about 124; another eight of the internal angles .sub.i202, .sub.i204, .sub.i207, .sub.i209, .sub.i212, .sub.i214, .sub.i217, and .sub.i219 are each about 137; the remaining four internal angles .sub.i203, .sub.i208, .sub.i213, and .sub.i218 are each about 124; and all eight of the external angles .sub.e201-.sub.e208 that at least partially define the central portion are about 102. The thicknesses of each sidewall S.sub.201-S.sub.228 are also substantially the same.

(36) Top and perspective views of an alternative exemplary embodiment of a strengthening member 300 having a twenty-eight-cornered cross section, with twenty internal angles and eight external angles, are illustrated in FIGS. 3A-3B, respectively. The cross section of the strengthening member 300 includes a four lobe portions and a central portion. Each lobe portion is defined by six sides, for example, sides S.sub.301-S.sub.306 define a first lobe portion 341, sides S.sub.308-S.sub.313 define a second lobe portion 342, sides S.sub.315-S.sub.320 define a third lobe portion 343, and sides S.sub.322-S.sub.327 define a fourth lobe portion 344 of the cross section of strengthening member 300. The central portion 351 is at least partially defined by four sides, for example, sides S.sub.307, S.sub.314, S.sub.321, and S.sub.328 define the central portion 351 of strengthening member 300.

(37) Strengthening member 300 may differ from strengthening member 200 in several aspects. For example, as shown in FIGS. 3A and 3B, one or more of the side walls of the strengthening member may be angled with respect to the longitudinal axis 350 of the strengthening member 300 to provide a taper to at least a portion of the shape of the strengthening member 300. As shown in FIGS. 3A-3B, strengthening member 300 is tapered along its length from first end 360 of the strengthening member 300 to second end 370 of the strengthening member. The strengthening member 300 tapers along its length at an angle , which may range from about 1 to about 65. The degree of taper of each side wall may be substantially the same, or different side walls may exhibit differing degrees of taper. Tapering may be required due to component packaging constraints and/or to effectively couple, attach or otherwise bond other components to a strengthening member.

(38) In the exemplary embodiment of FIGS. 3A-3B, the twenty internal angles that at least partially define each lobe portion 341-344 are not all the same and each of the eight external angles are substantially the same. In particular, like the exemplary embodiment of FIGS. 2A-2B, eight of the internal angles .sub.i301, .sub.i305, .sub.i306, .sub.i310, .sub.i311, .sub.i315, .sub.i316, and .sub.i320 are each about 124; another eight of the internal angles .sub.i302, .sub.i304, .sub.i307, .sub.i309, .sub.i312, .sub.i314, .sub.i317, and .sub.i319 are each about 137; the remaining four internal angles .sub.i303, .sub.i308, .sub.i313, and .sub.i318 are each about 124; and all eight of the external angles .sub.i301-.sub.i308 at least partially define the central portion are about 102. Also, as shown in FIGS. 3A-3B, strengthening member 300 includes four recessed areas 331, 332, 333, and 334. Each recessed area 331, 332, 333, and 334 extends along the length of the strengthening member 300 from first end 360 to second end 370. A side of the central portion 351 and a side of each of two adjacent lobe portions define each recess along a length of the strengthening member 300.

(39) In the disclosed exemplary embodiment of FIGS. 3A-3B, the cross-sectional lengths of each of the twenty-eight sides are each approximately the same as the cross-sectional lengths of other sides when taken at any cross section along the longitudinal length of the strengthening member 300. However, the cross-sectional length of each side gradually/incrementally increases along the longitudinal axis 350 of the strengthening member 300 from first end 360 to second end 370 to provide the tapered shape. As noted above, the embodiment of FIGS. 3A-3B is exemplary, and therefore all of the contemplated embodiments with variations to the cross-sectional lengths and thicknesses of the sides, and to the angles of the internal and external corner angles of the twenty-eight-cornered cross sections, with twenty internal angles and eight external angles, of the strengthening members in accordance with the present teachings are not shown in the figures, but based on the teachings herein, will be apparent to those of skill in the art.

(40) Top and perspective views of an alternative exemplary embodiment of a strengthening member 400 having the twenty-eight-cornered cross section, with twenty internal angles and eight external angles, are illustrated in FIGS. 4A-4B, respectively. The cross section of the strengthening member 400 includes four lobe portions 441-444 and a central portion 451. Each lobe portion is defined by six sides, for example, sides S.sub.401-S.sub.406 define a first lobe portion 441, sides S.sub.408-S.sub.413 define a second lobe portion 442, sides S.sub.415-S.sub.420 define a third lobe portion 443, and sides S.sub.422-S.sub.427 define a fourth lobe portion 444 of the cross section of strengthening member 400. Central portion 451 is at least partially defined by four sides, for example, sides S.sub.407, S.sub.414, S.sub.421, and S.sub.428 define the central portion 451 of strengthening member 400.

(41) Similar to the strengthening member 200, strengthening member 400 has a uniform cross section along a length LL.sub.1400 of the strengthening member 400, from a first end 460 to a second end 470 of the strengthening member 400. However, as shown in FIGS. 4A-4B, strengthening member 400 may differ from strengthening members 200 and 300 in that the dimension-to-dimension ratio of the cross section of the strengthening member, taken along transverse axes 430, 440 is not 1:1; rather, the aspect ratio is about 7:10. FIGS. 4A-4B illustrate a strengthening member cross section that has a first length 480 along a first (minor) transverse axis 430 and a second length 490 along a second (major) transverse axis 440, where the second transverse axis 440 is perpendicular to the first transverse axis 430. The aspect ratio of a strengthening member may be defined as [length along minor axis]:[length along major axis] or [first length 480]:[second length 490].

(42) In the exemplary embodiment of FIGS. 4A-4B, the internal corner angles internal angles .sub.i401-.sub.i420 are not all the same. In various exemplary embodiments, four internal angles .sub.i401, .sub.i410, .sub.i411, and .sub.i420 may each have a first measurement that ranges from about 105 to about 135 or from about 120 to about 124; another four internal angles .sub.i402, .sub.i409, .sub.i412, and .sub.i419 may each have a second measurement that ranges from about 135 to about 165 or from about 146 to about 150; another four internal angles .sub.i403, .sub.i408, .sub.i413, and .sub.i418 may each have a third measurement that ranges from about 120 to about 150 or from about 134 to about 138; another four internal angles .sub.i404, .sub.i407, .sub.i414, and .sub.i417 may each have a fourth measurement that ranges from about 105 to about 135 or from about 118 to about 122; and another four internal angles .sub.i405, .sub.i406, .sub.i416, and .sub.i416 may each have a fifth measurement that ranges from about 115 to about 145 or from about 127 to about 131. For example, in the exemplary embodiment of FIGS. 4A-4B, internal angles .sub.i401, .sub.i410, .sub.i411, and .sub.i420 have a first measurement, e.g., of about 122; internal angles .sub.i402, .sub.i409, .sub.i412, and .sub.i419 have a second measurement, e.g., of about 148; internal angles .sub.i403, .sub.i408, .sub.i413, and .sub.i418 have a third measurement, e.g., of about 136; internal angles .sub.i404, .sub.i407, .sub.i414, and .sub.i417 have a fourth measurement, e.g., of about 120; and internal angles .sub.i405, .sub.i406, .sub.i415, and .sub.i416 have a fifth measurement, e.g., of about 129.

(43) Additionally, in the exemplary embodiment of FIGS. 4A-4B, the external angles are not all same. In various exemplary embodiments, four external angles .sub.e401, .sub.e404, .sub.e405, and e408 may each have a first measurement that ranges from about 90 to about 130 or from about 105 to about 109; another four external angles .sub.e402, .sub.e403, .sub.e406, and .sub.e407 may each have a second measurement that ranges from about 80 to about 120 or from about 96 to about 100. For example, as shown in the exemplary embodiment of FIG. 4A, the external angles .sub.e401, .sub.e404, .sub.e405, and .sub.e408, have a first measurement, e.g., of about 107; and external angles .sub.e402, .sub.e403, .sub.e406, and .sub.e407 have a second measurement, e.g., of about 98.

(44) As also shown in FIGS. 4A-4B, sides S.sub.401 S.sub.428 of strengthening member 400 may have differing cross-sectional lengths. In addition, strengthening member 400 of the exemplary embodiment shown in FIGS. 4A-4B includes recessed areas 431-434 spaced around the perimeter of strengthening member 400 and extending along the length LL.sub.400 of the strengthening member 400, each recessed area 431-434 extending from first end 460 to second end 470 of strengthening member 400. Sides of neighboring lobe portions and a side of the central portion between the two neighboring lobe portions define each recess along a length of the strengthening member 400. As noted above, the embodiment of FIGS. 4A-4B is exemplary, and therefore all of the contemplated embodiments with variations to the cross-sectional lengths of the sides, thicknesses of the sides, the angles of the internal and external corner angles, and the aspect ratio of the twenty-eight-cornered cross sections, with twenty internal angles and eight external angles, of the strengthening members in accordance with the present teachings are not shown in the figures.

(45) Top and perspective views of an alternative exemplary embodiment of a strengthening member 500 having the twenty-eight-cornered cross section, with twenty internal angles and eight external angles, are illustrated in FIGS. 5A-5B, respectively. The cross section of strengthening member 500 includes four lobe portions and a central portion. Each lobe portion is defined by six sides, for example, sides S.sub.501-S.sub.506 define a first lobe portion 541, sides S.sub.508-S.sub.513 define a second lobe portion 542, sides S.sub.515-S.sub.520 define a third lobe portion 543, and sides S.sub.522-S.sub.527 define a fourth lobe portion 544 of the cross section of strengthening member 500. The central portion 551 is at least partially defined by four sides, for example, sides S.sub.507, S.sub.514, S.sub.521, and S.sub.528 define the central portion 551 of strengthening member 500. In addition, strengthening member 500 of the exemplary embodiment shown in FIGS. 5A-5B includes recessed areas 531-534 spaced around the perimeter of strengthening member 500 and extending along length LL.sub.500 of strengthening member 500, each recessed area 531-534 extending from first end 560 to second end 570 of strengthening member 500.

(46) Similar to the strengthening member 300, strengthening member 500 tapers along its longitudinal axis 550 from first end 560 of strengthening member to second end 570 of strengthening member 500. Strengthening member 500 tapers along its length at an angle , which may range from about 1 to about 65. In the exemplary embodiment of FIGS. 5A-5B, the twenty internal angles that at least partially define each lobe portion 541-544 are not the same and each of the eight external angles that at least partially define the central portion 551 are substantially the same. In various exemplary embodiments, eight internal .sub.501, .sub.505, .sub.506, .sub.510, .sub.i511, .sub.i515, .sub.i516, and .sub.i520 may each range from about 125 to about 155 or from about 138 to about 142; another eight internal angles .sub.i502, .sub.i504, .sub.i507, .sub.i509, .sub.i512, .sub.i514, .sub.i517, and .sub.i519 may each range from about 125 to about 155 or from about 135 to about 139; another four internal angles .sub.i503, .sub.i508, .sub.i513, and .sub.i518 may each range from about 120 to about 150 or from about 132 to about 136; and each external corner angle .sub.e501-.sub.e508 may range from about 105 to about 135 or from about 116 to about 120. For example, in the exemplary embodiment of FIGS. 5A-5B, eight of the internal angles .sub.i501, .sub.i505, .sub.i606, .sub.i510, .sub.i511, .sub.i515, .sub.i516, and .sub.i520 are each about 140; another eight of the internal angles .sub.i502, .sub.i504, .sub.i507, .sub.i509, .sub.i512, .sub.i514, .sub.i517, and .sub.i519 are each about 137; the remaining four internal angles .sub.i503, .sub.i508, .sub.i513, and .sub.i518 are each about 134; and all eight of the external angles .sub.i503, .sub.i508 that at least partially define the central portion 551 are about 118.

(47) As illustrated in FIG. 5A, the cross-sectional length of side walls S.sub.501, S.sub.504, S.sub.508, S.sub.511, S.sub.515, S.sub.518, S.sub.522, and S.sub.525 are short relative to the cross-sectional lengths of the remaining side walls. This difference in the lengths of the sides provides recessed areas 531, 532, 533, and 534, each of which extends along the length LL.sub.500 of strengthening member 500 from first end 560 to second end 570 of strengthening member 500. A side of the central portion 551 and a side of each of two adjacent lobe portions define each recess along length LL.sub.500 of strengthening member 500. These recessed areas 531-534 each have a depth .sub.533-.sub.537, which is reduced (and may be considered relatively shallow) in comparison to the recessed areas shown in the strengthening members illustrated in FIGS. 2A-4B. These types of parameter tuning, i.e., changing the cross-sectional lengths of the sides and changing the external angles, reduce the depth of the recessed areas 531-534 and can increase the internal volume of the strengthening member 500, thereby providing more internal space for other vehicle components. In particular, the combination of the decreased depth and the modified external angles of the recessed area work together to increase the total volume of the strengthening member, thereby increasing the space inside the strengthening member in which other vehicle components may be permanently, temporarily or periodically fitted, located, or otherwise disposed. Such vehicle components may include, for example, brake line(s), pipe(s), electric wire(s), cable(s), and/or seatbelt(s). Disposition of the vehicle components within the completely enclosed side walls of the strengthening member function as a shelter to protect the other vehicle components from being damaged, for example, during vehicle impact events.

(48) Top and perspective views of an alternative exemplary embodiment of a strengthening member 600 having the twenty-eight-cornered cross section, with twenty internal angles and eight external angles, are illustrated in FIGS. 6A-6B, respectively. The cross section of strengthening member 600 includes four lobe portions and a central portion. Each lobe portion is defined by six sides, for example, sides S.sub.601-S.sub.606 define a first lobe portion 641, sides S.sub.608-S.sub.613 define a second lobe portion 642, sides S.sub.615-S.sub.620 define a third lobe portion 643, and sides S.sub.622-S.sub.627 define a fourth lobe portion 644 of the cross section of strengthening member 600. The central portion is at least partially defined by four sides, for example, sides S.sub.607, S.sub.614, S.sub.621, and S.sub.628 define central portion 651 of strengthening member 600.

(49) Similar to strengthening members 300 and 500, strengthening member 600 tapers along its longitudinal axis 650 from first end 660 of strengthening member 600 to second end 670 of strengthening member 600. Strengthening member 600 tapers along its length LL.sub.600 at an angle , which may range from about 1 to about 65. In the exemplary embodiment of FIGS. 6A-6B, twenty of the internal angles that at least partially define each lobe portion 641-644 do not have the same measurements while each of the eight external angles are substantially the same. In various exemplary embodiments, eight internal .sub.i601, .sub.i605, .sub.i606, .sub.i610, .sub.i611, .sub.i615, .sub.i616, and .sub.i620 may each range from about 105 to about 135 or from about 116 to about 120; another eight internal angles .sub.i602, .sub.i604, .sub.i607, .sub.i609, .sub.i612, .sub.i614, .sub.i617, and .sub.i619 may each range from about 120 to about 150 or from about 134 to about 138; another four internal angles .sub.i603, .sub.i608, .sub.i613, and .sub.i618 may each range from about 120 to about 150 or from about 133 to about 137; and each external corner angle .sub.e601-.sub.e608 may range from about 80 to about 110 or from about 94 to about 98. For example, in the exemplary embodiment of FIGS. 6A-6B, eight of the internal angles .sub.i601, .sub.i605, .sub.i606, .sub.i610, .sub.i611, .sub.i615, .sub.i616, and .sub.i620 are each about 118; another eight of the internal angles .sub.i602, .sub.i604, .sub.i607, .sub.i609, .sub.i612, .sub.i614, .sub.i617, and .sub.i619 are each about 136; the remaining four internal angles .sub.i603, .sub.i608, .sub.i613, and .sub.i618 are each about 135; and all eight of the external angles .sub.e601-.sub.e608 that at least partially define the central portion are about 96.

(50) In addition, strengthening member 600 of the exemplary embodiment shown in FIGS. 6A-6B includes recessed areas 631-634 spaced around the perimeter of strengthening member 600 and extending along the length LL.sub.600 of strengthening member 600, each recessed area 631-634 extending from first end 660 to second end 670 of strengthening member 600. A side of central portion 651 and a side of each of two of adjacent or neighboring lobe portions define each recessed area 631-634 along length LL.sub.600 of strengthening member 600. These recessed areas 631-634 each have a depth .sub.634-.sub.637, respectively, which is larger (and may be considered relatively deep) in comparison to the recessed areas shown in the strengthening members illustrated in FIGS. 2A-5B. These types of parameter tuning, i.e., changing the cross-sectional lengths of the sides of the strengthening member and changing the external angles, increase the depth of the recessed areas 634-637 and can reduce the internal volume of strengthening member 600, thereby reducing the footprint of the strengthening member cross section and providing more external space for other vehicle components around the strengthening member. In particular, the combination of the increased depth and the modified external angles of the recessed area work together to decrease the total volume of the strengthening member, thereby increasing the space outside the strengthening member in which other vehicle components may be permanently, temporarily or periodically fitted, located, or otherwise disposed. Such vehicle components may include, for example, brake line(s), pipe(s), electric wire(s), cable(s), and/or seatbelt(s). The side walls defining the recessed area can function as a shelter to protect the other vehicle components from being damaged, for example, during vehicle impact events; however, the components remain accessible by virtue of their disposition outside the strengthening member, thereby improving the feasibility of repair and/or replacement of the components.

(51) Top and perspective views of an alternative exemplary embodiment of a strengthening member 700 having a twenty-eight-cornered cross-section, with twenty internal angles and eight external angles, are illustrated in FIGS. 7A-7B, respectively. Strengthening member 700 has twenty-eight corners C.sub.i701-C.sub.i720 and C.sub.e701-C.sub.e708, and twenty-eight side walls S.sub.701-S.sub.728. Twenty of the corners are internal angle corners C.sub.i701-C.sub.i720 and eight of the corners are external angle corners C.sub.e701-C.sub.e708. Strengthening member 700 also has a first transverse axis 730, a second transverse axis 740, and a longitudinal axis 750. Although shown with its longitudinal axis 750 positioned substantially vertically in FIG. 7B, when strengthening member 700 (as well as all of the other various embodiments in accordance with the present teachings) is installed within a vehicle, longitudinal axis 750 of strengthening member 700 may be oriented substantially horizontally. In this position, first transverse axis 730 may be oriented substantially horizontally and second transverse axis 740 may be oriented substantially vertically, as shown in FIG. 7A. When installed in such a position, the shape of strengthening member 700 may reduce or prevent moisture collection or pooling along portions of the walls S.sub.701-S.sub.728 of strengthening member 700. For example, certain conventional strengthening members whose walls form adjacent external angles of 90 degrees or form rectangular, square, or U-shaped recesses or depressions may collect moisture or permit moisture to pool in the recesses, increasing the possibility of weakening of the strengthening member via rusting, stripping, cracking, etc. (i.e., any form of oxidation or other chemical or physical distortion which the material of manufacture of the strengthening member may be more susceptible to due to the presence of moisture).

(52) In contrast, strengthening member 700 does not include a recessed portion in which liquids or moisture can remain for a long period of time. In particular, each of internal angles .sub.i701-.sub.i720 and external angles .sub.e701-.sub.e708 have been selected such that walls S.sub.701-S.sub.728 of strengthening member 700 are angled relative to one another to promote shedding of any moisture or fluid that falls within any recessed portion of strengthening member 700. For example, as shown in FIGS. 7A and 7B, strengthening member 700 includes a first recessed portion 731 defined by side walls S.sub.705-S.sub.709. Internal angles .sub.i704, .sub.i705, .sub.i706, and .sub.i707 are obtuse, and external angles .sub.e702 and .sub.e703 are obtuse. As a result, side walls S.sub.704-S.sub.710 are sloped/angled such that fluid impinging or collecting on side walls S.sub.704-S.sub.710 will run off and toward an end of side wall S.sub.709 due in part or in whole to gravitational forces. Similarly, for example, as shown in FIGS. 7A and 7B, strengthening member 700 includes second recessed portion 734 defined by side walls S.sub.726-S.sub.728, S.sub.701, and S.sub.702. Internal angles .sub.i719, .sub.i720, .sub.i701, and .sub.i702 are obtuse, and external angles .sub.e708 and .sub.e701 are obtuse. As a result, side walls S.sub.712-S.sub.716 are sloped/angled such that fluid impinging or collecting on side walls S.sub.712-S.sub.716 will run off and toward an end of side wall S.sub.726 due in part or in whole to gravitational forces. Also included are a third recessed portion 732 defined by side walls S.sub.712-S.sub.716; and a fourth recessed portion 733 defined by side walls S.sub.719-S.sub.723.

(53) In the exemplary embodiment of FIGS. 7A-7B, the twenty of the internal angles that at least partially define each lobe portion 741-744 are not the same and each of the eight external angles are not the same. In various exemplary embodiments, four internal angles .sub.i701, .sub.i706, .sub.i711, and .sub.i716 may each have a first measurement that ranges from about 150 to about 180 or from about 161 to about 165; another four internal angles .sub.i705, .sub.i710, .sub.i715, and .sub.i720 may each have a second measurement that ranges from about 150 to about 180 or from about 156 to about 160; another four internal angles .sub.i702, .sub.i707, .sub.i712, and .sub.i717 may each have a third measurement that ranges from about 115 to about 145 or from about 130 to about 134; another four internal angles .sub.i704, .sub.i709, .sub.i714, and .sub.i719 may each have a fourth measurement that ranges from about 130 to about 160 or from about 146 to about 142; another four internal angles .sub.i703, .sub.i708, .sub.i713, and .sub.i718 may each have a fifth measurement that ranges from about 120 to about 150 or from about 131 to about 135; four of the external angles .sub.e701, .sub.e702, .sub.e705, and .sub.e706 may each have a sixth measurement that ranges from about 140 to about 170 or from about 153 to about 157; and the other four external angles .sub.e703, .sub.e704, .sub.e707, and .sub.e708 may each have a seventh measurement that ranges from about 105 to about 135 or from about 116 to about 118. For example, in the exemplary embodiment of FIGS. 7A-7B, four of the internal angles .sub.i701, .sub.i706, .sub.i711, and .sub.i716 are each about 163; another four of the internal angles .sub.i705, .sub.i710, .sub.i715, and .sub.i720 are each about 158; yet another four of the internal angles .sub.i702, .sub.i707, .sub.i712, and .sub.i717 are each about 132; yet another four of the internal angles .sub.i704, .sub.i709, .sub.i714, and .sub.i719 are each about 144; the remaining four internal angles .sub.i703, .sub.i708, .sub.i713, and .sub.i718 are each about 133; four of the external angles .sub.e701, .sub.e702, .sub.e705, and .sub.e706 are about 155; and the other four external angles .sub.e703, .sub.e704, .sub.e707, and .sub.e708 are about 118.

(54) Recessed portions 731-734 are relatively shallow compared to the depth the recessed areas 831-834 shown in strengthening member 800, illustrated in FIGS. 8A-8B. Recessed areas having reduced depths, such as those of strengthening member 700, can be advantageous when vehicle components, such as electric cables/wires, fuel lines/pipes, brake lines/wires, and seatbelts, need to be run through or installed inside the internal space of a strengthening member.

(55) Top and perspective views of an alternative exemplary embodiment of a strengthening member 800 having the twenty-eight-cornered cross-section, with twenty internal angles and eight external angles, are illustrated in FIGS. 8A-8B, respectively. Similar to strengthening member 700, each of internal angles .sub.i801-.sub.i820 and each of external angles .sub.e801-.sub.e808 of strengthening member 800 are obtuse such that moisture and fluid run off from recessed areas 831-834 is facilitated.

(56) In the exemplary embodiment of FIGS. 8A-8B, twenty of the internal angles at least partially define lobe portions 841-844 and do not all have the same measurement. Additionally, the eight external angles do not all have the same measurement. In various exemplary embodiments, eight internal .sub.i801, .sub.i805, .sub.i806, .sub.i810, .sub.i811, .sub.i815, .sub.i816, and .sub.i820 may each range from about 160 to about 180 or from about 168 to about 172; another eight internal angles .sub.i802, .sub.i804, .sub.i807, .sub.i809, .sub.i812, .sub.i814, .sub.i817, and .sub.i819 may each range from about 110 to about 140 or from about 121 to about 125; another four internal angles .sub.i803, .sub.i808, .sub.i813, and .sub.i818 may each range from about 120 to about 150 or from about 131 to about 135; four of the external angles .sub.e801, .sub.i802, .sub.i805, and .sub.e806 may each range from about 130 to about 160 or from about 145 to about 151; and another four of the external angles .sub.e803, .sub.e804, .sub.e807, and .sub.e808 may each range from about 110 to about 140 or from about 122 to about 126. For example, in the exemplary embodiment of FIGS. 8A-8B, eight of the internal angles .sub.i801, .sub.i805, .sub.i806, .sub.i810, .sub.i811, .sub.i815, .sub.i816, and .sub.i820 are each about 170; another eight of the internal angles .sub.i802, .sub.i804, .sub.i807, .sub.i809, .sub.i812, .sub.i814, .sub.i817, and .sub.i819 are each about 123; the remaining four internal angles .sub.i803, .sub.i808, .sub.i813, and .sub.i818 are each about 133; four of the external angles .sub.e801, .sub.e802, .sub.e805, and .sub.e806 are about 147; and the other four external angles .sub.e803, .sub.e804, .sub.e807, and .sub.e808 are about 124.

(57) The cross-sectional lengths L.sub.801-L.sub.828 of the sides S.sub.801-S.sub.828, respectively, have each been selected such that recessed areas 831-834 have a depth .sub.831-.sub.834, respectively. This depth is relatively greater than the depth the recessed areas 731-734 shown in strengthening member 700, illustrated in FIGS. 7A-7B. Thus, strengthening member 800 provides an exemplary embodiment of a strengthening member in accordance with the present disclosure that can promote moisture shedding and also provide more space around the exterior of the strengthening member in which other vehicle components may be permanently, temporarily or periodically fitted, located, or otherwise disposed.

(58) More generally, the various exemplary embodiments of the present teachings contemplate, for example, strengthening members with corners having different bend radii, with non-uniform cross sections, having non-symmetrical shapes, with sides having variable thicknesses, and/or having variable tapered sides. Various additional exemplary embodiments contemplate strengthening members that are bent and/or curved. Moreover, to further adjust a member's folding pattern and/or peak load capacity, various additional exemplary embodiments also contemplate strengthening members having trigger holes, flanges, and/or convolutions as would be understood by those of ordinary skill in the art. Combinations of one or more of the above described variations are also contemplated.

(59) As discussed and embodied herein, the cross-sectional lengths L.sub.1-L.sub.28 and thicknesses T.sub.1-T.sub.28 of the sides of a strengthening member are tunable parameters of the strengthening member. The cross-sectional lengths L.sub.1-L.sub.28 and thicknesses T.sub.1-T.sub.28 of the sides may be tuned to provide desired characteristics in the strengthening member. For example, in the embodiment of FIGS. 3A-3B, these parameters are tuned to provide strengthening member 300 with side walls and corners that are tapered along the longitudinal length of strengthening member 300.

(60) As discussed and embodied herein, the aspect ratio of a cross section of a strengthening member is a tunable parameter of the strengthening member in accordance with the present teachings. The aspect ratio of a cross section of a strengthening member may be tuned to provide desired characteristics in the strengthening member. For example, in the embodiment of FIGS. 4A-4B, these parameters are tuned to provide strengthening member 400 with two cross-sectional dimensions along perpendicularly oriented transverse axes that are different in length.

(61) As discussed and embodied herein, the cross sectional lengths L.sub.1-L.sub.28 of the sides S.sub.1-S.sub.28 of the cross section of a strengthening member is a tunable parameter in accordance with the present teachings. The lengths L.sub.1-L.sub.28 of the sides S.sub.1-S.sub.28 of a strengthening member may be tuned to provide desired characteristics in the strengthening member. For example, in the embodiment of FIGS. 5A-5B this parameter is tuned to provide strengthening member 500 with recessed areas 531-534 having depths .sub.531-.sub.534 that extend along the longitudinal length of the strengthening member 500.

(62) As discussed and embodied herein, the twenty internal angles .sub.i1-.sub.i20 and eight external angles .sub.e1-.sub.e8 are tunable parameters of the strengthening member. The internal angles .sub.i1-.sub.i20 and external angles .sub.e1-.sub.e8 may be tuned to provide desired characteristics in the strengthening member. For example, in the embodiment of FIGS. 6A-6B, these parameters are tuned to provide strengthening member 600 with recessed areas 634-637 having depths .sub.634-.sub.637 that extend along the longitudinal length LL.sub.600 of strengthening member 600. Additionally, internal angles .sub.i1-.sub.i16 and external angles .sub.e1-.sub.e12 may be tuned to promote moisture shedding, as demonstrated in the embodiments of FIGS. 7A-7B and 8A-8B.

(63) As discussed and embodied herein, multiple tunable parametersincluding but not limited to the cross-sectional lengths L.sub.1-L.sub.28 and thicknesses T.sub.1-T.sub.28 of the sides of a strengthening member, the aspect ratio of a cross section of the strengthening member, the internal angles .sub.i1-.sub.i20 and external angles .sub.e1-.sub.e8 of the corners, the size of the recessed areas, and the size of the lobe portionsmay all be tuned within the same strengthening member to provide desired characteristics in the strengthening member.

(64) In the various illustrated exemplary embodiments of FIGS. 2A-8B, the strengthening members may have a one-piece construction. As stated above, the one-piece constructions shown in FIGS. 2A through 8B are exemplary only and the present teachings contemplate strengthening members of other constructions such as two-piece construction or having three or more pieces.

(65) To demonstrate the improved strength and performance features of a twenty-eight-cornered cross section having twenty internal angles and eight external angles in accordance with the present teachings, the inventors compared various existing and conventional strengthening member cross section designs to cross sections based on the designs disclosed herein. Exemplary strengthening members were modeled and crash simulation runs were conducted, as shown and described below with reference to FIGS. 9-13.

(66) Strengthening members having varying cross-sectional shapes and having the same mass, thickness, and longitudinal length were modeled as illustrated in FIG. 9. Crash simulations were then run for each member to simulate an impact with the same rigid mass (e.g., an impactor), impact speed, and initial kinetic energy.

(67) FIG. 10 shows strengthening members which have undergone a simulated quasi-static crush. During each quasi-static crush the impact speed is slow (e.g., 1 in/min). An impactor compresses the strengthening members with a controlled displacement. Therefore, all strengthening members reach the same crush distance with the same crush time. Thus, subjecting multiple strengthening members to a quasi-static crush provides a comparison of the folding length and the crush stability of the strengthening members. As shown in FIG. 10, the twenty-eight-cornered cross section in accordance with the present teachings demonstrated stable and progressive axial collapse, as well as the smallest folding length.

(68) FIG. 11 shows strengthening members which have undergone a simulated dynamic crush. During each dynamic crush, the impactor is propelled by a gas gun with a designated mass and initial impact velocity which creates a designated initial kinetic energy. The initial kinetic energy crushes the strengthening members. Performance of each strengthening member can be compared by measuring the crush distance and specific energy absorption of each strengthening member. As shown in FIG. 11, the twenty-eight-cornered cross section in accordance with the present teachings also demonstrated the shortest crush distance.

(69) FIG. 12 illustrates the dynamic crush force (in kN) and associated axial crush distance (in mm) for the simulated dynamic crush, exerted axially on the exemplary strengthening members shown in FIG. 9. As shown in FIG. 12, the strengthening member having a twenty-eight-cornered cross section could sustain a much higher crushing force for a given resulting crushing distance as compared with the square, hexagonal, circular, octagonal, and twelve-cornered cross sections. Specifically, the twenty-eight-cornered cross section in accordance with the present teachings achieved about a 135% increase in averaged crush force and/or crash energy absorption as compared with the octagon cross section.

(70) FIG. 13 illustrates the dynamic axial crush energy (in kN-mm) and associated axial crush distance (in mm) for a simulated dynamic crush exerted on the exemplary strengthening members shown in FIG. 9. As shown in FIG. 13, the strengthening member having a twenty-eight-cornered cross section could absorb the same total kinetic energy of the impact over a much shorter distance as compared with the square, hexagonal, circular, octagonal, and twelve-cornered cross sections. In particular, a twenty-eight-cornered cross section in accordance with the present teachings absorbed the full axial crush energy in about 42.5% of the axial crush distance as the basic octagonal cross section.

(71) Twenty-eight-cornered cross sections in accordance with the present teachings may, therefore, allow improved impact energy management over, for example, basic polygonal strengthening member cross sections, by minimizing mass per unit length, thereby providing mass saving solutions that reduce vehicle weight and meet new corporate average fuel economy (CAFE) and emission standards.

(72) Beyond the increased load carrying and energy absorption efficiency, strengthening members in accordance with the present teachings may provide additional advantages or benefits such as improved moisture shedding abilities (as noted above), increased bending energy absorption capacity, improved manufacturing feasibility, and better fitting of the shape amongst the other components of the complete device (e.g., vehicle, as noted above).

(73) In addition, a twenty-eight-cornered strengthening member in accordance with the present teachings also may be tuned to accommodate unique packaging requirements for use in various vehicles. By virtue of the particular shape of the cross section of at least some of the twenty-eight-cornered strengthening members, it may be easier to couple, bond, attach, or otherwise affix other device components to the strengthening member. Other device components can include, but are not limited to, engine mounts or transmission mounts.

(74) Twenty-eight-cornered strengthening members in accordance with the present teachings are contemplated for use as structural members in a number of environments. For example, in a motor vehicle, a strengthening member as disclosed herein may be used, for example, as one or more of crush cans, front rails, mid-rails, rear rails, side rails, shotguns, cross members, roof structures, beltline tubes, door beams, pillars, internal reinforcements, and other components that can benefit from increased crash energy absorption or the other advantages described herein. In addition, the present teachings can be applied to both body-on-frame and unitized vehicles, or other types of structures.

(75) For example, as shown in FIGS. 14 and 15, twenty-eight-cornered strengthening members with twenty internal angles and eight external angles in accordance with the present disclosure can be a part of or within a vehicle frame and/or a vehicle upper body. FIG. 14 illustrates an exemplary embodiment of a vehicle frame 1400 with several components for which the strengthening can be used. For example, the strengthening members in accordance with the present disclosure may form or be used as a part of a front horn 1402, a front rail 1404, a front side rail 1406, a rear side rail 1408, a rear rail 1410, and/or as one or more cross members 1412. Likewise, FIG. 15 illustrates an exemplary embodiment of a vehicle upper body 1500 with several components for which the strengthening can be used. For example, the strengthening members in accordance with the present disclosure may be formed or be used as a part of a shotgun 1502, a hinge-pillar 1504, an A-pillar 1506, a B-pillar 1508, a C-pillar 1510, one or more door beams 1512, a cross car beam 1514, a front header 1516, a rear header 1518, a cow top 1520, a roof rail 1522, a lateral roof bow 1524, longitudinal roof bow 1526, one or more body cross members 1528, and/or a body cross member 1530.

(76) Moreover, the strengthening members in accordance with the present disclosure may be used as, or form a part of, a vehicle underbody component, for example, a rocker and/or one or more underbody cross members. Also, the strengthening members in accordance with the present disclosure may be used as or form a part of vehicle engine compartment components, for example, as one or more engine compartment cross members.

(77) Depending on the application, embodiments of the present teachings will have varied shapes (i.e. various cross sections) to accommodate specific member space constraints. When used as a vehicle front rail, for example, to achieve optimized axial crush performance, the lengths and thicknesses of the sides and/or angles of the corners can all be adjusted (tuned) to provide optimal strength, size and shape to meet engine compartment constraints.

(78) Although various exemplary embodiments described herein have been described as configured to be used with automotive vehicles (e.g., car, truck, van, ATV, RV, motorcycle, etc.), it is envisioned that the various strengthening members in accordance with the present teachings may be configured for use with other types of vehicles (e.g. aircrafts, spacecrafts and watercrafts) and/or structures, for which it may be desirable to provide increased crash energy absorption. Thus, it will be appreciated by those of ordinary skill in the art having the benefit of this disclosure that the present teachings provide strengthening members for various applications. Further modifications and alternative embodiments of various aspects of the present teachings will be apparent to those skilled in the art in view of this description.

(79) It is to be understood that the particular examples and embodiments set forth herein are non-limiting, and modifications to structure, dimensions, materials, and methodologies may be made without departing from the scope of the present teachings.

(80) In particular, those skilled in the art will appreciate that a strengthening member may include more than one longitudinal section or portion, with each section or portion having one or more of the variations taught in accordance with the present disclosure. Said variation(s) can be made continuously or intermittently along the length of each longitudinal section. In other words, strengthening members that embody combinations of one or more of the above variations to the disclosed tunable parameters, which have not been illustrated or explicitly described, are also contemplated.

(81) 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.

(82) Notwithstanding that the numerical ranges and parameters setting forth the broad scope of the present teachings are approximations, the numerical values set forth in the specific examples are reported as precisely as possible. Any numerical value, however, inherently contains certain errors necessarily resulting from the standard deviation found in their respective testing measurements. Moreover, all ranges disclosed herein are to be understood to encompass any and all sub-ranges subsumed therein.

(83) 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.

(84) 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.