statically indeterminant problem
statically indeterminant problem
(OP)
Hello
I wonder if anyone can help/guide me with a problem i have, the figure below shows a free body diagram of a brake caliper, the force on the body acts at 30 degrees from the vertical at point C, I resolved this to get the two forces shown in the x and y direction.

I have determined the values for v1 and v2 but i cannot decide how to get the values for h1 and h2, they cannot be the same due to the direction of the force. The problem appears to be statically indeterminant so is there another way i could solve this problem?
Any suggestions appreciated
I wonder if anyone can help/guide me with a problem i have, the figure below shows a free body diagram of a brake caliper, the force on the body acts at 30 degrees from the vertical at point C, I resolved this to get the two forces shown in the x and y direction.

I have determined the values for v1 and v2 but i cannot decide how to get the values for h1 and h2, they cannot be the same due to the direction of the force. The problem appears to be statically indeterminant so is there another way i could solve this problem?
Any suggestions appreciated





RE: statically indeterminant problem
this means that the forces intercept at a point
this should remove your redundancy
RE: statically indeterminant problem
e.g.: sum moments about B = 0 = braking force * its moment arm - resultant force at B * its moment arm
Ted
RE: statically indeterminant problem
RE: statically indeterminant problem
If one of the joints is a roller/slider, then it is determinate. Assuming your pivoting point is A and slide point is B, there should be no H2 at all. If H2 is a frictional force then it is an externally applied one and is dependent on motion of the rubbing member, so it has to be calculated from the normal force V2 (easy to find) and the coefficient of friction.
Don
Kansas City
RE: statically indeterminant problem
RE: statically indeterminant problem
better would be an FEM, particularly if "A"and "B" are those groups of 3 fasteners (capable of taking some moment).
RE: statically indeterminant problem
RE: statically indeterminant problem
I am just looking into the use of the three force body method
RE: statically indeterminant problem
Here's why. If both joints are perfectly fit, with zero tolerance (and they won't be), and the holes in both members are spaced perfectly the same (and they won't be) then there is no net force between them. But then if the temperature changes by a half a degree, there is, because the disk and link will expand or contract by different amounts. There is no way to simply measure this linkage and determine the forces on A or B since forces are invisible.
So, what if one hole is snug and the other is loose? Well, first of all, now they are technically not "fixed". If joint A is snug and B is loose then the angle at which the journal B acts on hole B depends on the clearance and the accuracy of the hole/journal centers. If the holes are .001" farther apart than the journals are, and the clearance at joint B is .002", then the bearing point of contact can be geometrically calculated...and it *won't* be tangential to the arc about A...depending on tolerances, it might not even be close. And, again, when the temperature changes, all bets are off and the angle could change radically.
As you can see, there can be no definite answer for this situation, since it is statically indeterminate. If B were designed as a free roller on a flat surface then the forces at B would not change with tolerances or temperatures and could be determined easily with statics.
Don
Kansas City
RE: statically indeterminant problem
RE: statically indeterminant problem
as regards FEA, yes, it may be a good option, but:
1- if you schematize it as "two-beams" (for an extremely simple system like that you can even do it by hand), you will have to make assumptions about the stiffnesses of each beam
2- if you analyze the whole "thing" as a solid model, then you will need first of all a FEA package, then a little time and lastly a lot of attention about boundary-conditions' application.
Regards
RE: statically indeterminant problem
So, my contention is that if the friction handles the load, then it is patently indeterminate, but if not, the geometry determines which bolt wins the total load battle. And if this is a design problem, then you designe each member to take the full lateral load.
RE: statically indeterminant problem
RE: statically indeterminant problem
RE: statically indeterminant problem
RE: statically indeterminant problem
As I stated before, the problem with any mathematical solution for a loose connection is that the direction of bearing contact can vary widely depending on variances in hole diameter, bolt diameter, hole spacing (both parts) and even hole/bolt runout. And the closer the fit, the more radical the changes in free-body component forces and direction for even small manufacturing variations and temperatures. This could vary a lot from assembly to assembly and under differing field conditions.
If one bolted connection is *really* loose, then you could probably approximate a solution by assuming that the loose journal acts in a tangential direction along the arc about the fixed joint. Perhaps this is sufficient for your purposes.
Don
Kansas City
RE: statically indeterminant problem
if the disc has a directional stiffness (stiff in one direction, weak in another), if the connections are more fixed than pinned, then FE would solve these issues.
RE: statically indeterminant problem
Don
Kansas City