In order to reduce the weight of a bike it is important to explore tube dimensions such as wall thickness/diameter ratios and length/diameter ratios to determine the best dimensions for the purpose. Looking into this can lead to a somewhat interesting (for some at least) foray into stress analysis and buckling theory.Referring to a previous blog on second moments of area, we know that shape of a part greatly affects its mechanical properties and this explains the reason for most engineering shapes used, from simple "I" beams to complex aluminium extrusions. In the world of cycling, round tube is often favoured for it's consistent stiffness and strength in all axis and its traditional cosmetic appearance; but what should the wall thickness and diameter of the tube be for the best performance?In an attempt to answer this we modelled some steel tubes on the CAD system. The starting point was a piece of 50mm steel tube with a 1.6mm wall thickness. This was then compared with a range of other tube sizes all with the same cross-sectional area and hence the same weight. The results would tell us how a given amount of material could best be distributed (shaped) to give the best performance. The simulation parameters were a 50kg load applied at the end of a 600mm long tube.The interesting column is shown in green on the table, this shows the deflection due to the 50kg weight. Deflection was massively reduced by having a larger diameter tube with a thinner wall.Also note that the yield strength of the material (carbon steel) can be approximated to 2.206E+08 N/m2. In all cases the maximum recorded stress (Von-Mises) was above this threshold, but the thinner larger diameter tube was closest, suggesting it is the stronger design.Plotting this data showed an exponential improvement in stiffness as the diameter of the tube was increased.This result would indicate that the larger and thinner the tube used for a bike frame, the stiffer and stronger the bike would be. This explains the use of oversized tubing in off-road bikes where an improvement in strength can be obtained without increasing weight. However this is not the whole story.Very thin walled tube can suffer "buckling" failures. The likelihood of this happening depends on the direction and size of the loads on the part as well as the ratio of the wall thickness to the tube diameter.From other research into buckling failures we can summarise the following points.Buckling only occurs with thin walled tube. As a rule of thumb anything with diameter/wall ratio of less than x40 should not not buckle. However this is only true for short and moderate lengths of tube.Buckling can take two forms.Long columns where the slenderness ratio is >200 can buckleShort column where the slenderness ratio is <50 can crush.Images of these two fail modes can be seen below.A short column crush failure is what you get when you step on a drinks can and crush it; it will typically have multiple folds and creases about the circumference.A buckling failure can be seen when a long column under an axial load suddenly steps out of alignment; this is often seen at a single point along the part.The central columns in the Gothic masterpiece of Salisbury Cathedral show signs of buckling. Although the original 13th century church was OK, the tower and spire were added later increasing the load on the columns by 7000 tonnes. The support columns in the nave can be seen to be buckling under the load.Back to bicycles.Importantly both failure types can happen very suddenly and would be significant danger occurring on a bicycle frame.For a traditional bicycle frame the threat of a bucking failure is mostly eliminated with triangulation. This simple and marvellous engineering shape massively reduces the risk of buckling failures despite extremely thin walled tubing being used on lightweight steel frames.On box bikes where the cargo area is traditionally supported on a cantilevered deck area, the risks are higher and thicker walled tubing must be used avoid buckling. Some designs reduce the risk by using specially shaped sections which have a greater "second moment of area" in the vertical plane, or by adding a deck hoop or lattice sides to front of the bike. The Riese and Muller "Load" is aluminium which has the additional problem of fatigue, but this is designed out of the product with a deck hoop around the load area and some lattice side rails.Other solutions are braces and reinforced areas where stress concentrations or buckling risks exist.We use stress analysis and empirical testing on all our frame designs to find the best performance and a safe balance between weight and strength. Thin walled tubing is the preference but we are wary of the buckling failures particularly on the box bike frame which has an unsupported load deck. Clever design and targeted support braces are used to ensure any stress points are suitably supported.