Dissipating load
Dissipating load
(OP)
I am trying to figure out how to mount a bar that will dissipate the forces from a torque.
The bar will be slipped into a hollow square beam that is located 6" from the point where the torque is applied and it extends 8". There will be 3 bolts placed along the hollow square beam at 2", 4" and 6"
The calculation to find the forces at bolts A, B and C would be T = A*8 + B*10 + C*12
Since I only have one equation and three unknowns how can I calculate the force at each bolt?
Attached is an image of the situation.
The bar will be slipped into a hollow square beam that is located 6" from the point where the torque is applied and it extends 8". There will be 3 bolts placed along the hollow square beam at 2", 4" and 6"
The calculation to find the forces at bolts A, B and C would be T = A*8 + B*10 + C*12
Since I only have one equation and three unknowns how can I calculate the force at each bolt?
Attached is an image of the situation.





RE: Dissipating load
RE: Dissipating load
a) equilibrium along horizontal axis: 0=0, an identity equation, so unuseful;
b) equilibrium along vertical axis: Ay+By+Cy=0;
c) rotation around axis perpendicular to the plane, the same equation you wrote above.
So you have 2 equations and 3 unknowns. The problem is one time statically indeterminate or hyperstatic.
This means that you have to introduce one further equation which should account for the way the beam buckles under the load, like Virtual Work principle or elastic line equation.
The problem here is that since the active force is only a pure moment, surely one of the costraint forces is upward and not downward as you are showing in your attachment. Furthermore, you need to take into account the stiffness of the bolts (but at first you can model them as simple rigid supports).
It goes without saying that using only 2 bolts would make your life easier.
Hope it helps.
Stefano
RE: Dissipating load
RE: Dissipating load
"Strength of bolts withstanding torsion generated shear loading"
http://www.roymech.co.uk/Useful_Tables/Screws/Bolt...
RE: Dissipating load
How are you getting a pure moment on the bar? Pure moments are not often seen. Are you sure there is no x or y loading?
RE: Dissipating load
RE: Dissipating load
As of differential equation, equation of elastic line is clearly useful here to find the value of the hyperstatic unkown.
RE: Dissipating load
RE: Dissipating load
"On the human scale, the laws of Newtonian Physics are non-negotiable"
RE: Dissipating load
If you really want to be conservative, you take the pair with minimum distance, which is the smaller of x2-x1 or x3-x2 so that
F1=-F2=T/(x2-x1)
or
F3=-F2=T/(X3-x2)
and take the maximum F
RE: Dissipating load
The other thing to point out, do the bolts shear due to failure by torsion similtaneously? As pointed out by TheTick, forces are distributed, yet you infer dissipation as in some sort of work-energy.
I see the problem of three distibuted bolts holding input torque of a six inch bar, bolts are 2, 4 and 6 inches off the LHS face of that rectangular sleeve holding the bar. Is this correct? And do the bolts shear by torque similtaneously?
Regards,
Cockroach
RE: Dissipating load
Yes shearing of the bolts will be something to consider but that was going to be taken into consideration after I figured out the forces acting at the bolts (need the force to determine if the bolt will fail). Also the bolt would not have to fail simultaneously.
I have the intention of analyzing two parts of this set up. First would be to design the bar with the torque on it so that limited bending will occur. The second part is to figure out what the forces on the bolts would be, and where there locations should be to help distributed the load from the torque.
The hollow square beam that it is mounted in then should distribute the load from the torque over a larger area?
RE: Dissipating load
Not that the the more complicated three-screw attachment loading can not be calculated. Just might simplify the problem.
Ted
RE: Dissipating load
Otherwise, Desertfox give you a very good link to one method of analysis of the bolts.
RE: Dissipating load
So I give HyTools the star. You need to C,BORE a series of set screws, brass of course, to resist torque. The rod is necessarily circular, the housing may be whatever, square being the worst choice. The rod carries torque equally distributed over the span of shear screws.
Regards,
Cockroach
RE: Dissipating load
Also if more of the bar is in contact then is the determining the load along the length of the bar/tube becomes more a problem of determining the relative stiffness of the bar within the tube?
RE: Dissipating load
Ted
RE: Dissipating load
Im having a little bit of trouble figuring out how to model the elastic line equation. My inclination is to model the edge contacts as a simple support such as a roller, however that would imply that the deflection at the edge contact points should be zero however the contact form the edge point is created by the deflection at those points. Or perhaps working out the elastic line equations and then specifying the deflection at the edge contacts points?
RE: Dissipating load
RE: Dissipating load
To start the outer tube will be .5" higher therefore giving us the .25" in clearance between the bar and tube. There will be two .25"x.25" bar inserted in between the bar and tube at the location you specified. The middle bolt will remain to hold the bar in the tube. One question I have is that would we assume that the bolt has no reaction forces?
I also noticed from your earlier post that you have asked if there are any other load involved with the bar. This is where the situation become tricky because yes there are other forces on the bar and it would be very wrong to not include them.
Here's more description of the situation. The piece being analyzed will be mounted into a longer structure to hold it up. The torque on the left end of the bar comes from a torsion bar that has already been twisted. (I am unsure if it is correct to treat that as a moment at the end of the bar.) I have included a picture to help show what I am describing.
I still think the advice you gave will be useful for the situation.
RE: Dissipating load