The following images are taken from Mechanics of Materials, Ferdinard Beer et al. 6th ed (2012) Just wondering that why the effective length of the column is taken 0.7 L (highlighted in the sample problem) ? Souldn't it be 0.5 L since in the xy plane we have two plates supporting the column with a reaction force in the y direction and a moment (which is the same as if the column were fixed at both ends). Any thoughts would be appreciated.
The text says... "smooth and rounded fixed plates". So although the plates are fixed, they are not rigidly attached to the column. They will restrain translation in the y and that is all. So for all intents and purposes you can consider the top support to be "pinned". And the effective length can be determined from The first figure, condition c).
In real life cases these diagrams are all highly exaggerated to convey the idea that effective length has to do with the inflection point and or, it starts at a pin support.
Otherwise for all intents and purposes the smooth rounded edge of the two plates are close enough to a pin support at that joint.
Now if we want to be too fussy, even if the two plates are too tight and fit to the column, under the load they yield just a smidge to make it a pin connection. And we would see the yield line as shiny horizontal score lines after.
