The video here
shows a rough and ready experiment demonstrating the superior strength under axial load of cylindrical tubes, compared with square tubes (skip to 1:30 if you are not interested in the chat).
The conclusion about the greater strength of the cylindrical tubes is fair enough, but I wasn’t convinced by the explanation that the early collapse of the square tubes was due to the stress concentrations at the corners, so I did a finite element analysis of an axially loaded paper tube:
The contours show axial stress in the vertical direction. It can be seen that the stress is uniform for the first few stages, until it reaches about 0.02 MPa, when the sides start to buckle inwards and outwards in a series of waves. As these waves increase in amplitude there is indeed a transfer of stress from the centre of the plates to the corners, until the maximum stress reaches about 3 MPa, when the corners start to buckle, but the initial change from a uniform stress distribution was the result of the deflections of the plates, rather than the corners causing a stress concentration.
The total reaction force at the base at the final initiation of buckling was 5.8 N (an average stress of 0.29 MPa), which would give a total failure load of 23.2 N (about 2.3 kg force) for four tubes, tying in pretty well with the failure load of something less than 2 heavy books in the video.
The next post will look at the failure mechanisms of cylindrical tubes.
Update 7th July 2011:
Stills from the Surfing Scientist video, showing the square columns at the point of buckling, provided by Georg (see comment below):
Strand7 data files and avi files of the animations may be downloaded here:
The data files need a licenced copy of Strand7 to run, but may be viewed with the free Strand7 Viewer. The avi files can be viewed with a standard video viewer, and are much higher resolution than the Youtube videos.