rebuchet arm fracture

huangyhg

trebuchet arm fracture
                  pivot []
    [==============]
load                [=======================]    projectile   
    [==============]
                    {----5in----}
    {---------8.5in--------}
                    {-----------------17in-----------------}
everything is 3/4in by 3/4in northern white pine glued together and pinned with dowel.
this is the arm of my trebuchet.  i normally have a lead weight (8lbs) where the load is.  i want to attach some springs to that end instead so i can store more energy and as a result, throw the projectile further.  
the problem is i want to put the maximum load the arm can handle (minus a little bit) but i can鈥檛 figure out how to do it.  in other words, how do i figure out how much stress the arm can handle without snapping?  
i don鈥檛 want anyone to 鈥渄o鈥?this for me; if you could just get me started i would appreciate it.
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how far did you get in math class?  this is a calculus problem, for sure.
i've seen trebuchets before, and it appears that the dynamic loads are the higher ones that you must satisfy.  you need a textbook on kinematics and dynamics so that you can model the forces, motions, and accelerations of the structure, first.  after that's done you can move on the the structural analysis.
things to keep in mind are that your lead weight puts a bending stress on the arm when it's horizontal, due to its weight but minus its acceleration as its launching.  if the lead weight isn't the bolt-on kind, such as the "swinging bucket" type, then you have to account for its motion relative to the throwing arm.  if the trebuchet is on free rollers (recommended) when it launches, you have another motion to deal with (can't say if it affects the loads in the arm, though).  the spring alone might be simpler to model than the swinging-bucket load.
i would give some thought to designing the pivot to fail before the arm does, by a simple structural analysis of the arm as it stands.  then you could take the alternate approach of just adding on the weights and projectiles to your heart's content until the pin breaks.  failure of the pin would cause a simple collapse: not too destructive.  failure of the arm = bits of wood everywhere.
stf
i appreciate your input, but the trebuchet is already built.  so i can't really change the pivot design without rebuilding the whole thing.  im entering my senior year at college so i should know how to do this but for some reason im drawing a blank.
also, i realize this is more of a dynamics problem with all of the rotation and forces and whatnot, but i was looking for more of a static solution.  like when the arm is cocked and ready to fire, what stress can it withstand without breaking.  from this, i believe i can "dynamicsafy" the situation.
thanks
draw a freebody diagram.  you know the force in the spring, you know the properties of the material, and you know the distances to the spring, pivot, and the unknown weight your trying to find.  sounds like 1 unknown.  write your equations and solve for the unknown.
pylko-
i dont know the force in the spring.  my goal is to find out how much stress the arm can handle, and then use a spring accordingly.  
thats the part i am confused about.  uts, flexure modulus, youngs modulus, i dont know which to use or how to use it.
thanks for opining though.
3/4" x 3/4" - section modulus (s)= 0.0703125 in^3
northern white pine i dont see in the nds.
eastern white pine (no. 2 or better)-
fb = 575 psi
ft = 275 psi
fv = 135 psi
fc perp = 350 psi
fc para = 825 psi
e = 1,100,000 psi
northern pine (no. 2 or better)-
fb = 675 psi
ft = 350 psi
fv = 135 psi
fc perp = 435 psi
fc para = 450 psi
e = 1,000,000 psi
your maximum bending moment depends on fb and s. your actual bending moment depends on your loads and the geometry (location) of those loads.  with some algebra, you should be able to solve for the max unknown force (spring?).
sounds like a lot of fun to own one...
what are you going to use it for - and to do what to whom?
daveviking-
its just for playing around.  here is the site i used to get the basic design.  i modified it a little.
great website!
the band gwar has a full-scale, working "crap-a-pult" that looks an awful lot like this little trebuchet.