![]() In general a large diameter circular tube is the most efficient shape under axial loading. This is probably offset by the fact that a circle would deflect projectiles better. The hexagon may be more resistant to localised impact, particularly if that impact occurs at a corner. localised buckling of tubes under bending (not a straightforward analysis - especially for the hexagon).Some factors which I have not considered: So this basic analysis shows that a hexagon of equal area and wall thickness would be weaker under bending and have a lower buckling load. Again, the circle is more resistant to buckling since its $I$ is larger. ![]() The axial stiffness is $EA$, where $E$ is Young's modulus which depends on the material (assumed to be the same in this case) and $A$ which is the cross sectional area.Ī hexagon with an equal cross-sectional area to a circle of radius $r$ and (thin) wall thickness $t$ must have side lengths of: $a=\frac $, where $L$ is the length of the tube. For them to be the same strength (and weight) they would have to have the same cross-sectional area. If it is assumed that both the round and hexagonal tubes are extruded (which is likely for a bike frame) we can ignore any cold-forming or welding issues. Hexagonal tube is likely to be much more expensive as it is a non-standard shape. I can't think of much advantage to using a hexagonal tube, except perhaps cosmetic - but this is subjective. It seems likely to me that hex tube would be a fairly poor compromise between square and round/elliptical section tube. Of course there are other pragmatic considerations to be taken into account for example square or rectangular tube is much easier to join than round as square tube can just be mitred to the required angle with a saw whereas round tube needs to be notched with a specialist machine or painstakingly hand fitted. ![]() Although this is, in most cases, impractical for fabricated frame structures. An ideal structure will have a smoothly varying section with section size proportional to the stresses on it, in fact bones are an excellent example of this. It is a fairly good rule of thumb in structures that any sort of discontinuity represents at best an inefficiency and at worst a potential failure point. If the section has a uniform wall thickness then it certainly means that some of the material is effectively wasted as the corners will encounter yield before the flats and at worst it can lead to crack propagation points and fatigue. With tubing this can be a double effect that you potentially have work hardening from the manufacturing process concentrated at the corners as well. Where F is the force (15 kips) and d is the distance from the base of the tube to the point of application of the force (0.15 in).An additional factor is that any section which has defined corners will tend to concentrate stress at the corners rather than it being evenly distributed throughout the section. The moment can be calculated using the following formula: Step 3: Calculate the moment (M) caused by the 15-kip load. For the loading given, determine: a) the stress at points A and B, b) the point where the neutral axis intersects line ABD. The distance from the neutral axis to point a is 0.65 - 0.3 = 0.35 in, and the distance to point b is 0.65 in. The tube shown as uniform wall has a thickness of 10 mm. The neutral axis is located at the center of the square tube, which is 0.65 in from the top and bottom edges. Step 2: Calculate the distance from the neutral axis to points a and b. Where a is the outer side length and b is the inner side length. The moment of inertia for a square tube can be calculated using the following formula: (a) sigmaA MPa sigmaB MPa (b) Neutral axis: mm above point A Posted 2 years ago View Answer Q: An extruded aluminum beam has the cross section shown. For the loading given, determine (a) the stress at points A and B, (b) the point where the neutral axis intersects line A B D. The structural tube has a square cross-section with side length 1.3 in and wall thickness 0.3 in. The tube shown has a uniform wall thickness of 14 mm. ![]() Step 1: Calculate the moment of inertia (I) of the structural tube.
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