fixed or simply supported boundary condition

huangyhg

fixed or simply supported boundary condition.
a 5" width, 1" thickness, 12" clear span plate, exerted a load p. i guess most people will consider case (a) as simply supported boundary condition, and case (b) as fixed boundary condition.
my question: is there any statement in any code which can justify above assumption?
should there any limitations for the weld size so that below certain weld size, the steel plate beam can no longer considered as fixed end. or this limitation has to be based on load balance calculation?
i will be interested to hear others' opinions, but i am looking at this and thinking it is fixed.  if you want it to behave simple then don't provide the welds?  why are you providing them?  do you want it to behave fixed?  the only way for it to behave pinned is for the weld to fail, so if that is how you want it to behave, just don't provide the weld.
i should say that my comment above depends at least partially on the length of bearing of the plate, but it looks to be a decent distance (probably 2.5" or so).  this is not insignificant given the 12" span
suppose this bearing length is very small, say only 0.5", and weld is only tw=5/8", weld leng is only 2 of 1/2" (just imagine an example), does it still reasonable to consider it as fixed boundary? or you have to prove your weld will not fail?
the weld is serving no purpose that i can see other than to lock up the end and make it behave fixed.  the load is going into the supports by bearing.  if you wan't want it to act fixed, then don't weld it.
certainly if you weld 1/2" of the 5" dimension it will act more like a pinned support, but why are you welding it?
if you're preventing the ends from rotating, it's fixed.
the "answer" does not have to be limited to either "simple support" or "fixed support", it can be somewhere in between. unless there is test data, that is where engineering judgment comes in.
since maximum moment for simple supports = p x l / 4
and
for fixed supports = p x l / 8
for what you have shown in the sketch i would estimate the following:
case "a" (bolted connection) m max = p x l / 6
case "b" (welded connection) m max = p x l / 7
just an opinion based on the assumption that the overall length of the plates in cases "a" and "b" is identical.
i would wager, because l is so small, that the end condition is irrelevant and design should be based on shear instead of flexure
i would analyze this as a 3 span continuous beam on pinned supports.  that way, you would get the shear in the weld, as reactions at the end supports.  those end reactions might be surprisingly high.
i second miecz's response.
good point. i think miecz gives an accurate analysis method. while slideruleera gives an quick estimation method.
thank you both very much.