The euler-buckling generator
9 essays call
euler-buckling. The drawing above is what it returns with no arguments at all; every
call below passes it something, because a placement that passes nothing draws whichever
member of the family the generator happens to default to rather than the one its essay
argues about.
Where it is called
Changing this generator changes every one of these figures.
Depth is the cheapest strength there is
Doubling the depth of a truss halves its chord forces without adding a gram of material to the chords. Nothing else in structural design is that cheap, and almost every structure has already spent it.
Sections and stressThe material far from the middle does nearly all the work
A strip of steel contributes to bending stiffness in proportion to the square of its distance from the centre. Move the same steel outward and the section gets stiffer for nothing.
Sections and stressThe same steel in a different shape, and a factor of forty
Four sections of identical area, identical weight and identical cost. The stiffest is dozens of times the stiffest of the flattest, and the only thing that changed was the arrangement.
Sections and stressThe point that is not in the section
A channel loaded down its web twists. To stop it, the load must be applied through a point outside the steel entirely — in the air beside the section, where nothing can be attached.
StabilityStrong enough and still falls over
A column can fail at a fraction of the load its material could carry, by going sideways. Buckling is a failure of stability rather than of strength, and it is decided by geometry.
StabilityThe ends decide the length that matters
Four columns of identical height and section, buckling at loads sixteen times apart. Nothing differs but what is holding the two ends.
StabilityThe load that makes itself worse
A structure that has leaned carries its weight off the axis, which makes it lean further. The amplification is one over one minus the load ratio, and it runs away long before the buckling load.
StabilityThe column that was never straight
Euler's load is the load at which a perfectly straight column becomes indifferent to being bent. No column is perfectly straight, so no column ever reaches it — and the load it never reaches can still be measured.
StabilityThe brace that need not be strong
A brace holding a column at mid-height carries almost no force. What it has to be is stiff — and the stiffness required is exact, large, and reached at a knee past which more buys nothing at all.