Moment of a perpendicular frame

[whitebalance]

Hi,
I'm a bit new to calculating moments, so I could need some help.
I have a frame as shown in the attachment. The thin blue horisontal and vertical line is the frame made of Bronse.

The frame is connected to a roof by four bolts. The bolts are placed between the a's and the x's (where the black short vertical thin line is).
On the red mark a force of 1kN is loaded horisontally (yellow line shows loading direction)

My question is, how do I find out the force that the horisontal tip (on the top right of the blue frame) apply to the roof based on the moment created by the applied force?

Scenario 1 is when the left bolts are keeping the left part rigid.
Scenario 2 is when the left bolts are not there. (Only bolts on right side).

Any help would be very appreciated.

kind regards
Kris

 

[frv]

This forum is not for students.

 

[whitebalance]

I am not a student, but I don't have a background in structural engineering.

I know the answer probably is easy, but I got unsure on how to calculate it due to the angle in the middle of the frame.

I do not want an full answer for this, but more a tip on how to attack my challenge.

Kris

 

[desertfox]

hi whitebalance

So your not a student, what sort of engineer are you then?

 

[whitebalance]

Dear desertfox,
This was more scepticism than I thought. But I will answer your question, I have a M.Sc. in Materials Engineering. As you then probably figure my background is more material specialized than mechanics.

The case I am looking at is this:

http://www.wesmar.com/images/DualPropThruster.jpg

I understand that the first post can look like student homework, but it's not.
Have I proved my innocence now?

regards
K

 

[desertfox]

Hi whitebalance

Okay sorry for the doubt, your way forward for simplicity
is take moments about the right hand end assuming the bolts there are pivots.

so

Loaded force * Y = lefthand bolts * 2* X


Loaded force * Y/ (2*X) = lefthand bolt loads

bare in mind theres two bolts at each end and I have assumed that the two bolts at each side are in a line, if there not then we need a better diagram with proper dimensions.

desertfox

 

[whitebalance]

desertfox,
thank you for the reply.
you are correct that the bolts are in a line.

the force I'm looking for is the force that acts as a compression load (upwards) on the "roof" on the right side of the bolts.

my goal is to find out what kind of material properties that are needed in the "roof" to withstand the compression force (Fy) from the thruster's loaded force.
please see updated picture

K

 

[desertfox]

Hi whitebalance

There might not be a compressive load through the bolts on the right hand in your diagram, they could all be in tension, it depends on the relative stiffnesses of the components involved.
For simplicity imagine that the thruster is completely rigid and rotates about the right hand corner of the base, both sets of bolts in that case would be in tension, although the load carried by the bolts close to the pivot carry only a small portion of the load the brunt being taken by the bolts on the lefthand side.
I have uploaded a file that will give you a ballpark figure for the tension load in each set of bolts, the tension loads act parallel along the axis of the bolts.

 

[whitebalance]

Hi desertfox,
Hope you had a good easter and thanks for the last post.
I now see that the case is a little bit different.
The bolts are tightened with nuts - so they will not contribute on the compression side. The case is as shown in the attached picture.

The bolt A does not have any other effect than keeping the thruster in place. When the load is applied the tension in the bolt will reduce. How does this affect the Fy compared to your last post?

How do I include the constraint of bolt B? (Bolt B does not yield)

K

 

[desertfox]

Hi whitebalance

Thanks, hope you had a good easter too.

Again it depends on the relative stiffness of the roof and the base of the thruster of which I have no knowledge.
The nuts on the compression side as you call it can contribute as shown in my last uploaded post, all the bolts will be in tension assuming that the base is rigid and pivots at the very edge, but the load carried by the bolts near the pivot will be much lower than those further away, in addition to the tension you will also have a shear force on the bolts which is simply the load F divided by the number of bolts and from which out can workout the shear stress. Your bolt preload needs to be roughly that calculated for bolt (b) in my last posting with a margin of safety.

regards

desertfox

 

[whitebalance]

desertfox,
I agree that the bolts will both be in tension, but the tension in the bolt on the right side will decline when applying the force (Fy). I am not considering the shear in the bolts, I'm only interested in the force that acts on the right side pivot.

The relative stiffness is considered to be equal for the roof and the bottom(thruster). And both structures are very rigid.

I have attached a more detailed picture. When looking at the 3D-model to the right: the top structure is the rigid roof, the shaded area is the material that I'm studying, and the bottom structure is the rigid thruster (which applies the force (Fy))

WIll the calculations you posted still be correct?

 

[desertfox]

Hi whitebalance

Go back to my post on the 25th march and see the file I uploaded.
The bolts on the righthand side closest to the pivot, see a reduced tensile load proportional to the distance from the pivot point, also those further away from the pivot see maximum load, there is no further reduction, Fy creates a moment about the base of the thruster.
The calculations in my file will be correct for your case, at least they will give a good approximation.

desertfox

 

[honat]

1- How does a bolt connection keep any part of this frame rigid? do you mean privides fixity at that connection?
2- Are we to ignore the weight of this sytem?
3- are these element rigid?
4- The easiest steps in determining the forces in yout
system (ignoring the weight of), is to first assume two eparate free body diagrams.
a) the vertical portion as a cantilever beam type with of course a fixed end (Shear=1.0k and moment reactions at the connection point with the horizontal element=1.0y)easy to find.
b) Take the reactions from the fisrt free body diagram in a)and analyze the second free body diagram, the beam part axxa,(horizontal portion with two cantilever ends with(horizontal shear and torsional bending or torque at the mid-section). Get your reactions at each of the bolted supports (couple and shear). That is all you need to do.

 

[whitebalance]

Thank you for all the help so far.

I have now calculated the tensile/compressive forces acting.
But I now got a bit concerned with the shear forces that occur.

Is it correct if I take the F that is applied in the end of the lever and divide by 4 bolts and then the area of each bolt?

Do you see any other stresses that need to be considered for this construction?

whitebalance

 

[desertfox]

Hi whitebalance

I am glad you resolved your tension forces, but what compression forces have you calculated? or do you mean reduced tensile force as we discussed previously.
Anyway to answer your question yes just divide the thrust by the four bolts to get the shear force and then divide by the area to obtain shear stress.
I don't recall you ever posting what the thrust force was, however once you have the shear stress and tensile stress in the bolts, you need to combine them and calculate the resultant stress.
Finally your last diagram indicated that the thrust acted central to the bolt within the bolt pattern, if in reality the thrust acts outside the bolt pattern then you will have bolt shear stresses due to a torsional effect.

regards

desertfox

 

[whitebalance]

desertfox, thank you for the reply.
The compression force is as you say the reduction in the tensile force. But, correct me if I'm wrong, if the thruster force increases, resulting in a tensile force above the pre-tension. Then it would only be a compressive force acting on the 'roof' and zero tensile forces in the bolts. My concern is not the bolts, rather the material the bolts go through.

The thrust acts in the center of the pattern, so the off center torsional stress does not apply.

I will see what I can find regarding the resultant stress.

Thanks again,
whitebalance

 

[desertfox]

Hi whitebalance

If the thruster force exceeds the bolt preload your bolts will stretch and the thruster base will seperate from the housing and you will want to avoid that.
Have a look at this site it will give you formula for resultant stress,scroll down toward the bottom of the page.

http://www.roymech.co.uk/Useful_Tables/Screws/Bolted_Joint.html

If you want to upload some sketches and your calcs I don't mind taking a look.

One more thing to say is that, if the thruster exerts a force at right angles, at any time to that shown in your sketch, then you would need to recalculate the bolt loads all over again.

desertfox

 

[whitebalance]

desertfox,
this is the sketch I'm working on.
Calcs:
Pre-tension:
tensile stress = Pre-tension pr bolt/area pr bolt

Tensile force:
F*dx = Fx*dz
tensile stress = Fx/area

Shear stress:
Each bolt withstands a vertical shear force:
Fnv = F/4
shear stress = Fnv/bolt area

Resulting force:
Each bolt also withstands a shear load
Fnm = F.R.*rn/(r12 + r22...rn2)
The total horizontal force on each bolt
Fth= Fnm*vn/Sqrt(hn2 + vn2 )
The total vertical force on each bolt
Ftv= Fnv + Fnm*hn/Sqrt(hn2 + vn2 )
The total shear load on each bolt
Ft= Sqrt(Fth2 + Ftv2)
The resulting bolt shear stress
?t = Ft/A

whitebalance

 

[desertfox]

Hi whitebalance

The formula you are using are from the Roy Mech site, however they are the wrong formula for your case.
The formula you have quoted are for torsional shear due to the applied load being outside the centroid of the fixings, which I mentioned in my previous post and you confirmed that your applied load was at the centroid of the fixings.
Look at the case below it talks about bolts under bending forces and I believe that suits your case better.

desertfox