cantilever problem.
cantilever problem.
(OP)
hallo everyone,
I have a cantilever with a point load at the far end e.g 10N and a spring of know stiffness e.g 100 N/m attached perpendicular to the beam at 1/3 of the beam from the fixed point. can somebody please help me know how i can calculate the deflection at the cantilever tip. I will appreciate
Thank you!
I have a cantilever with a point load at the far end e.g 10N and a spring of know stiffness e.g 100 N/m attached perpendicular to the beam at 1/3 of the beam from the fixed point. can somebody please help me know how i can calculate the deflection at the cantilever tip. I will appreciate
Thank you!






RE: cantilever problem.
or you can solve this iteratively ...
first solve the cantilever without the spring, calculate the delection at the spring point;
with this defelction you know the spring force,
solve this cantilever (with two forces, at the tip and at the spring)
calculate deflection at the spring point, and revise the spring force.
anticipating that the solution will oscillate (the cantilever alone will predict a large deflection at the spring, applying the spring force = to this deflection will probably produce an opposite deflection). if it does, i'd replace the spring force with 1/2 the first deflection, and see how that works out.
there are closed form solutions to the elastic support, but solving DEs is probably out of the question.
RE: cantilever problem.
Then work out the deflection of a cantilever 2L/3 long with a 10N load, call this d2
The total tip deflection is then 10/(k1+100)+2L/3*alpha+d2
Another way would be to do a work equation.
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: cantilever problem.
RE: cantilever problem.
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: cantilever problem.
Thank you in advance, am really learning a lot from all this discussion.
RE: cantilever problem.
still a "basic" problem ...
draw a free body, it looks like you'll have three reactions (shear, moment, and torque) due to the applied load.
now you can solve the basic beam equations ("double integration") to get deflections of the beam generally (as equations);
get the deflection of the spring attach pt.
then set up a 2nd free body for the spring force, some unit value, 1?, applied as the spring force would act, opposite the deflection due to load;
calc the deflection of the spring pt.
now you can set up an equation to determine the spring force, F, ...
d1 = initial deflection of the pt (+ve), with only tip load,
du = deflection of the pt with a unit spring load (-ve),
ds = deflection of spring = ds = d1+F*du, ds = d1+(k*ds)*du
RE: cantilever problem.
I have attached a file, if you have some time, you can have a look at it and give me clue of the way forward.
N/B the material is Allum hence E= 70GPa. am looking forward to your reply.
RE: cantilever problem.
same deal ... you can calc the stiffness of the cantilever (i think someone did it here already, but try it for yourself first)
calc displacements of the loaded cantilever (double integration method). that'll give you displacements along the beam.
"all" you have to do is match the displacement at the common point ...
RE: cantilever problem.
What is the length of the beams?
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: cantilever problem.
hand calcs have the advantage that the engineer is frameing the question ... neglecting things that are IHO negligible.
hand calc have the disadvantage that because they are framed by the engineer, he may not include a feature that is relevent.
computer solutions have the advantage that they have defaults so the engineer doesn't have to think much (in fact more thought is spent on getting the damned thing to work)
computer solutions have the disadvantage that because they don't require much thought, generally not much thought is given.
pick your poison !
(it'll kill you either way)
RE: cantilever problem.
RE: cantilever problem.
I was interested in how much difference it made having a moment connection between the two beams.
With a moment connection I get much the same result as you (0.136 m) and releasing all rotational restraint where the transverse beam joins the longitudinal beam that increases to 0.173 m, which is what I'd expect you to get with a hand calculation (just done it, that's what I get).
By the way, the simplest way to check the computer output is to take the forces from the computer and apply them to two separate cantilevers, and see if the deflections at the connection point are equal.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: cantilever problem.
now maybe (maybe !) if the joint is 15cm from the fixed end of the 40cm (so that the two fixed supports are equally 15cm from the common point), then possibly (i'd expect) that the two beam will deflect the same, and the inner portion of the longer beam is deflecting at though it has double the inertia (assuming both beams have the same section). but that'd be a special solution and i think it's better to understand the general solution.
RE: cantilever problem.
my other idea is to try and find the force acting at the junction but the problem is, the force acting at that point is shared by the two arms of the beam.
any ideas, will still be welcomed cause its my most crucial point to proceed.
Thank you!
RE: cantilever problem.
RE: cantilever problem.
(1) solve the long cantilever, reactions (simple equilibrium equations) and displacements along the length (double integration method).
(2) now that you've solved a cantilever, you can solve the short cantilever with a load P at the tip
(3) now you can solve the long cantilever with two forces applied, the tip load and a load P at the join of the two cantilevers,
like (1) reactions and displacements (ok, they're generalised 'cause you don't have a value for P)
(4) now guess a value for P, say 1/2 the tip load. is the displacement of the end of the short cantilever (2) the same as the long cantilever with two loads and the common point ?
(5) adjust your guess accordingly.
this isn't that hard (IMHO), any text book should cover it.
RE: cantilever problem.
Force F acts upward on Beam A and downward on Beam B. The solution can be found using strain compatibility. Beam A deflects downward an amount delta due to force P at the end combined with force F at the connection point. Beam B deflects downward an amount delta due to Force F acting at the connection point. One equation is required to solve for F.
If you consider the members connected rigidly together, then the torsional rotation of each beam must be considered as well. At the connection point, there will be an unknown vertical force F as before, but there will also be two unknown moments Mx and Mz. These can be solved directly using compatibility equations, which is what your computer program presumably did. You will need three equations to solve for three unknowns, namely delta, alphax and alphaz representing the vertical deflection, and the rotation about the x and z axes respectively.
BA