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rod that is pin jointed at both ends

rod that is pin jointed at both ends

rod that is pin jointed at both ends

(OP)
Hi

I am using a rod in compression and am fairly comfortable with using Eulers theorem.

However how could I resolve the situation where a compressive force is at an angle - see picture

I believe that this would actually force a torque on the rodding and perhaps should be more of a concern than Euler.

Would I resolve the force into the x and y components relative to the centre line of the rod and the force that is not resolved to the centreline is basically the torque that is acting on the rodding itself rather than transmitting force.

http://files.engineering.com/getfile.aspx?folder=d4bbce14-a853-4515-89fa-c2fa4d7cb705&file=cranks.jpg

I am trying to understand the forces in this rodding as presently it is bending.

regards

John

RE: rod that is pin jointed at both ends

Are all the red circles pin joints? If so, the rod is a 2 force member regardless of what else is going on. Otherwise, you would have rigid body motion.

If however, there is a moment (i.e. they really are not pinned joints at the column ends) then would treat it as a so called "beam-column".  

Brian
www.espcomposites.com

RE: rod that is pin jointed at both ends

Can we see the actual device?
Or a schematic that clearly shows the nature of the pin joints?



 

RE: rod that is pin jointed at both ends

a rod can only carry axial load.  this bears repeating ... a rod can Only carry axial load.

the angles would experience a load along the line of action of the rod.

then draw a fbd of the angles to deermine the pivot reactions.

RE: rod that is pin jointed at both ends

Hi DiscipleofScience

The black arrows are the only force you need to consider acting in a plane of the connecting rod and placing it under compression.

desertfox

 

RE: rod that is pin jointed at both ends

(OP)
yes the red circles are pins

The force placed on the rod has two components, one will be along the plane as desertfox states and the other will will place a torque on the rod I presume?

The cranks are just normal 90 cranks with a centre stud.

regards

John

RE: rod that is pin jointed at both ends

"The force placed on the rod has two components ..."

no, the force on the rod has one axial component, only.

the rod axial force reacts the torque applied.  the pivot point reacts the two forces applied to the cracnk, the rod force and the main drive force.
  

RE: rod that is pin jointed at both ends

i see the problem you're having ... your green arrows are wrong ... the rod does not react the crank torque with a load at 90deg to the crank flange.  the rod reacts axial load, so only a component of this (normal to the crank pivot, along the green arrow) is effective in reacting the applied torque.

similalry at the other crank, the load created in the output is the reaction to the torque applied to the second crank from the rod.

clear as mud ?

RE: rod that is pin jointed at both ends

(OP)
I am struggling yes, its been a long time since I did this last and it was an Electrical Degree too!

I think I understand in that what you are saying is that pin joints do not transmit moments. But what I am thinking about is how the off centre forces are dealt with

In attached diagram I have exaggerated the problem, the cranks are set up for mechanical advantage.

F2 imparts a force, but what happens to its components? Is there an F4? or does it all travel as F7? Then at the other end what happens to F7's components or is it all transmitted through F5?

Have I drawn forces F4 and F3 correctly - what is this doing to the rod, can it be resolved to a moment acting on the bar itself - tending to want to bend it?

http://files.engineering.com/getfile.aspx?folder=118fa985-9f32-49aa-a059-e0a9b4643074&file=cranks2.jpg

regards

John
 

RE: rod that is pin jointed at both ends

(OP)
thanks desert fox I'll shall read it through, I hadn't read your post whilst I was working on my picture.

RE: rod that is pin jointed at both ends

Hi

Yes look at the example of the two force member they resolve component forces horizontal and vertical and then resolve the resultant force along the axis of the strut.
Yes pin joints don't carry moments.

desertfox

RE: rod that is pin jointed at both ends

Technically, a rod can carry a moment, but is an inefficient shape to do so.  It is usually designed as a tension only member, but, in this case, can see both tension and compression, depending on the direction of the forces applied.  Whether or not it sees any moment or torque here depends on the pin connections and their ability to move with a minimum of friction.  The more friction, the more torque, or moment at the connection which will be transferred to the rod.

Personally, unless the OP knows otherwise, I would ignore any torque here and just deal with the axial forces the rod sees.

Cheers.

Mike McCann
MMC Engineering
Motto:  KISS
Motivation:  Don't ask

RE: rod that is pin jointed at both ends

no, as described ("pin ended") it can't.  that description implies a single fastener attachment, possible with a spherical bearing.  sure, you can have your static friction moment if you want, but i wouldn't.

RE: rod that is pin jointed at both ends

back to your 2nd pic ... F1*L1 and F6*L6 look clear enough !

the middle bit, loading hte rod looks messed !?  There should be a single force in the rod (F2) offset L2 on one crank and L3 on the other ... F2*L2 does not have to equal F2*L3.  At the end of the day, the sum of the input an output forces = the sum of the pivot reactions.

for a position of the cranks, you have a direction for the connecting rod, a line of action, and an offset from the pivots.

the crank pivot reacts the two loads applied to it.  the crank arms will end up carrying axial load and bending (some transverse component).

do the cranks rotate, under load (changing the geometry) ?

RE: rod that is pin jointed at both ends

rb1957...I think we are getting balled up on semantics.  Yes, as Mike stated, a rod can carry a moment.  With pinned connections, that moment is captive to the rod and is not transferred through the connection.

If the green arrows are acting on the pinned joint, then only their axial component transfers to the rod through the pinned connection.  Unless the cranks can rotate in the opposite direction to each other (producing torsion in the rod), then I would do as you both agreed...analyze for the axial force only using k=1.

RE: rod that is pin jointed at both ends

sorry ron, don't buy "moment captive to the rod".

in a beam, transverse load is reacted by a moment at the far end, yes ?

in a pinned rod, there can be no end moment (as i said, you can have your friction moment, but i don't want it !) ... if there is no moment there can be no transverse force, 'cause there is no free body balance.

this is, IMHO, a really simple mechanism.

RE: rod that is pin jointed at both ends

rb...I agree there's no end moment, but there can be a bending moment in the rod.  It acts as a beam. If it is bending, it has a bending moment.  With a pinned connection, that moment dissipates to zero at the ends.

RE: rod that is pin jointed at both ends

(OP)
rb1957, yes the cranks move, the whole assembly moves in the 2D plane only.

It is a simple mechanism, but as can be seen from the diagram is the off centre forces causing a bending moment?

http://files.engineering.com/getfile.aspx?folder=b5a93792-b2a1-4782-8395-725ab55e3dbb&file=cranks3.JPG


thanks for your help so far on this.

John

RE: rod that is pin jointed at both ends

@ OP:  The off-center forces you are concerned about will not cause a bending moment in the rod.  Assuming frictionless pins, any torque due to any misalignment will be reacted out at the two supports.

@rb:  Just because you do not want a moment to exist in a  theoretical problem, does not mean that it will not exist in the real world.  Parts do wear out and grease does fail, plus countless other imperfections of design.  I am not saying that it is there.  I am saying it can exist.  

And steel rods can take moment, as can any section of any material (just depends how much).  Just try to bend one with your hands.  Cheers.

Mike McCann
MMC Engineering
Motto:  KISS
Motivation:  Don't ask

RE: rod that is pin jointed at both ends

no (again) ron ... you Cannot draw a FBD of a beam with no moments at the ends and only two transverse forces (at the ends) ... a typical SS beam works 'cause there is a transverse load applied in the span, reacted at the ends (in equilibrium).

RE: rod that is pin jointed at both ends

john,

it's a Long time since i've done mechanisms !  structures are easy 'cause they're in static equilibrium.  it relatively easy to relate the movement of the input shaft to the movement of the output shaft. the two cranks are connected by a fixed link.  The question is how much load is created in the rod ?

If it's in static equilibrium, then why does it rotate ?  if it's less why does it stop rotating ?  my "guess" is that the rod in the rod is the static equilirium load, and that the rotation is controlled by the movement of the input shaft.

RE: rod that is pin jointed at both ends

OK.  I think that I see what could be the problem .

The OP stated initially that the rod is bending - fact.  

The problem is that the diagram we are looking at is a two dimensional diagram, but the problem is three dimensional.  I think what is happening is that the crank shaft axes and the rod axis are not in the same plane, inducing moments into the pinned joints at the ends of the rod.  A moment has to exist or the rod would not be bending, unless it was bent prior to installation.

Mike McCann
MMC Engineering
Motto:  KISS
Motivation:  Don't ask

RE: rod that is pin jointed at both ends

Mike...exactly!

RE: rod that is pin jointed at both ends

good catch ... i'd missed that ... the next thing is which plane is it bending about (as mike mentions, bending out-of-plane is possible).  it could also be  an onset of buckling ... an enforced displacement on crank 1, a rigid crank 2 would mean the rod would have to change it's length (by bending)  or possibly the ends are not truely pinned ... they might have a single fastener, but they might be clamped up tight so a sizeable friction moment could develop.

RE: rod that is pin jointed at both ends

I don't think the OP is talking about out of plane bending, looking at his diagrams the forces he as resolved are at right angles to the cranks, which then gives him forces on the connecting link which don't run parallel with its axis.
All the OP needs to do is draw a line parallel to the axis of the connecting rod at each crank end, then from that line draw two perpendicular lines one at each end which pass through the crank centre,knowing the torque on the crank and dividing this by the new lengths measured he can find the resultant force along the axis of the connecting rod.

desertfox

RE: rod that is pin jointed at both ends

He has to have out of plane bending.  Otherwise, how are you going to connect the rod to the cranks?

Mike McCann
MMC Engineering
Motto:  KISS
Motivation:  Don't ask

RE: rod that is pin jointed at both ends

I didn't say he didn't have out of plane bending but I believe that isn't forming part of his analysis or question, what he is doing is purely 2D just like the text book 4 bar linkages.
However you can connect two cranks with a connecting rod without out of plane bending by machining each crank with a clevis and fitting the link in between with pins.

desertfox

RE: rod that is pin jointed at both ends

Hi DiscipleofScience

I have uploaded a file that might help, I think your resolving forces in the X and Y directions which is fine, however your resultant force on the connecting link with a simple pin joint at each end is down the central axis between the two pins, one way of getting this resultant is shown in the file.

desertfox

RE: rod that is pin jointed at both ends

(OP)
Hi All

The front crank is the drive end and only ever moves the bell cranks say half a turn either way from the mid point, most of the time it is static, holding the rear crank in position.

This is a simple rod connected by 2 bell cranks, bending is strictly in 2D due to the fixings as desertfox alludes to, it is a a fork type connection.

Because the rod is not square to the bell crank (in order to maximize the mechanical advantage it is futher out on the arm of the seccond crank) this means that the applied axial load is not all in the horizontal plane, relative to the rod, there is a small vertical component  of applied force FB. Is this vertical component lost?

I suppose maximum efficieny occurs when the bell crank is at 90 degrees. Is this too small to be worried about?

Also - why do I have 2 equations for FD?

http://files.engineering.com/getfile.aspx?folder=05eff831-1c9d-483f-b90c-fd95b3e67b5c&file=img001.jpg

regards

John
 

RE: rod that is pin jointed at both ends

Hi DiscipleofScience

Our posts crossed see my uploaded file.

Thanks for clarifying the mechanism.

Regards

desertfox

RE: rod that is pin jointed at both ends

hi

Just looked at your calculations, firstly once you have Fb you need to divide it by Cos Alpha that gives you the force in the connecting rod that then transfers its force to Lc, then if you take the force in the connecting rod and draw its line of action perpendicular to the pivot point at Lc you can workout the torque acting on it.
Lastly the moment where Lc is you have:- Fd*(Lc+Ld) I think that is completly wrong.

desertfox

RE: rod that is pin jointed at both ends

(OP)
desertfox,

thankyou for the sketch, yeah I think I am getting there with this, we are on the same lines

the fact is the small horizontal component has reduced the force from end to end, maximum efficieny is when the angle between F2 and FR (on your sketch) is zero. This horizontal component doesn't travel down the rod but is reacted againts the primary force (the vertical force)

Plugging in some numbers:

Force 2kN
L1 = 0.3m
L2 = 0.4m
angle of crank relative to the rod (angle between F2 and FR) = 10 degrees

LR = 0.4 x Cos 10 = 0.39

so FR = 2x103 x (0.3 + 0.39) = 1.38kN

a loss of (2x103 x (0.3 + 0.4)) - 1.38x103 = 20N (1%)
 

RE: rod that is pin jointed at both ends

(OP)
Sorry - had a rethink there! Just to make a correction about FB


It should be (2x103 x 0.3)/0.4 = 1.5kN

take away the horizontal component

The horizontal component (to the rod) is 1.5x103 x Cos 10 = 1.477kN

A reduction of 22.7N

 

RE: rod that is pin jointed at both ends

(OP)
desertfox - I think you are right about the moment about C

FC = FD x LD / LC and it acts directly on the pivot

so FB x LR x Sin 40 = 0, which I think it means its trying to say that there are no moments at all on C

regards

John

RE: rod that is pin jointed at both ends

Hi John

Fr in my sketch should be greater than F2 because the right angled distance from the line of action of FR is smaller than the distance than L2, therefore to find Fr divide F2 by the Cos alpha angle which in your case is Cos of 10 degrees.

desertfox

RE: rod that is pin jointed at both ends

like desertfox said, a couple posts back, the force in the rod is Fb/cos(alpha).

looking at your sketch i think there's a problem in your understanding of torque the torque of Fa is Fa*La Only if La is perpendicular to Fa (which it doesn't look to be in the sketch)

the torque arm at crank 2 of the rod force is less than Lc ('cause the rod is not normal to the arm of crank 2).

similarly Fd.

but none of this explains why the rod is bending (in real life).

RE: rod that is pin jointed at both ends

your solution of sum moments @ C is completely messed up (i'm way less dipolmatic than desert fox) ...

Fb creates no moment about C since it passed thru C.

it'd be Way more rational to take moments about the pivot of crank2.

RE: rod that is pin jointed at both ends

i'm not sure that alpha, as shown in the sketch, means anything at all.  you need the perpendicular distance between the pivot point and the force.  this is not the length of the crank arm (unless the force is at 90deg to the crank arm).  it is the crank arm*cos(angle) ...   

RE: rod that is pin jointed at both ends

(OP)
thanks rb1957, you make a good point that the input and output forces are also not perpendicular to the crank arm, again it will be a case of resolving horizontal and vertical components relative to the crank arm, with the horizontal force being reacted back (lost) at the crank stud.

I am with you also on the Force*Cos(angle)

working with your desertfox's sketch

LR = Sin (90-alpha) x L2 = Cos (alpha) x L2

So basically FR = (F1(v) x L1) / Cos (alpha) x L2

(v) denotes vertical component

[Interesting to note that as alpha decreases FR increases)

please tell me I'm right winky smile

cheers

John

I agree my attempts at taking moments are lame - thanks for





 

RE: rod that is pin jointed at both ends

Hi DiscipleofScience

Using your diagram earlier with the enlarged view of the crank and Fb, if Fb as drawn is perpendicular to the crank and the rod on the otherside is at an angle alpha, then the force in the rod is given by Fb/Cos Alpha, now imagine just altering the rod angle alpha (everything else staying the same) so that instead of being 10 degrees it is now 30 degrees, therefore as Alpha increases then the force in the rod FR increases, if Alpha decreases then the force FR decreases, I think your statement in brackets is the wrong way round.

Your statement in your original post:-

"I am trying to understand the forces in this rodding as presently it is bending".

Is it actually bending on the actual mechanism or are you thinking its bending because of your forces in your diagrams.
If its bending for real then what might be happening is that its buckling under the compression forces, we could determine that but would need the forces in the mechanism and the connecting rod sizes.

desertfox

RE: rod that is pin jointed at both ends

(OP)
Yes it is bending and its due to Euler type compression forces, I have based calculations for sizing the new rod on the output force so say it delivers a maximum of 6kN to the back then that is what I have based my calcs on with a Factor of Safety of 4.

I just need to develop the free body diagram.

RE: rod that is pin jointed at both ends

Hi John

Look at the example on the link I left you earlier and the sketch I uploaded recently.
From what you are saying I believe the links just buckling, have you considered using a circular connecting link ie uniform 'I' value in all directions.

desertfox

RE: rod that is pin jointed at both ends

how readily does crank2 turn ?  you've said that crank 1 rotates.  if crank2 is seized then that'll cause problems for the rod.

have your calcs shown that the original rod buckled ?

alpha is defined two ways in your sketch, as the angle between the rod and the normal to the crank1 arm, and as the angle between the rod and the crank2 arm ??  are the cranks parallel ?

if alpha (=a) is the angle between the rod and the crank1 arm, note this is not your definition, for you have alpha as the angle between the rod and the normal of the arm; i think you need three other angles defined ...
the angle (=b) betwwen the input for and crank1 arm,
the angle (=c) between the rod and the crank2 arm, and
the angle (=d) between the output force and crank2 arm.

then using the arm lengths A for crank1 at input force,
B crank1 at rod attmt,
C at crank2 at rod attmt, and
D at crank2 at output force.

then Prod*B*sin(a) = Pinput*A*sin(b)
and Prod*C*sin(c) = Poutput*D*sin(d)

RE: rod that is pin jointed at both ends

(OP)
hi desertfox - yes thankyou I have studied the example and the sketch very carefully and tried to use the same principles to produce the free body diagram for the pivot of the first crank - which gives me the force in the connecting rod.


hi rb1957
The Euler equation bears what we are seeing. I have attached a free body diagram which hopefully explains it better, this is a difficult to get across with text!

I can use the same principle for the rear crank, there's really no reliable dimensionable relationship between the position of the front and rear crank except the force travelling down the rod. So I almost have to treat them as seperate entities.

At least now I have a formula for the force in the rod/link thanks to you guys.

http://files.engineering.com/getfile.aspx?folder=3353765f-4f91-4772-a416-ba34d5a69d1e&file=img002.jpg


 

RE: rod that is pin jointed at both ends

(OP)
just to be a pedant, I need to point out in the summation of moments bit: one should be negative so that it becomes positive value when moves to the other side of the equation.

RE: rod that is pin jointed at both ends

if the arrows are taken as +ve directions then it works, just that the math is a little sloppy.
Sum Mb = 0 ...Pav*0.305 = Pbh*x (why is x a variable ?)

the reactions at the pivot are wrong ... there are contributions from both forces (Fa and Frod) in both directions.

RE: rod that is pin jointed at both ends

(OP)
hi rb1957 -

x is variable to suit the installation (a sleeve on a crank arm)

I have the reactions for FA as FA Vertical and FA Horizontal similarly for FC (the rod) FCV and FCH - all relative to the crank. The moments (FCH and FCV) don't act on the centre pin.

I have drawn the pin reaction arrows the wrong way around.

 

RE: rod that is pin jointed at both ends

the pivot reacts the forces applied to the crank.

Fa has h- and v-components, both these are reacted at the pivot.

can you draw a free body diagram ?  sum forces in both directions ??

i'd've thought x was known (since you've already got this thing built, no?)

RE: rod that is pin jointed at both ends

Your summation of moments is fine.  For summations of forces you need to sum all forces in the chosen direction, e.g.,

ΣFx = 0 = FAx-RBH-FCy

RE: rod that is pin jointed at both ends

(OP)
Terio - would I include FCy since it is not acting on B directly (B is a pivot), but is a moment around B?

RE: rod that is pin jointed at both ends

FCy acts on B because a shear force equal to FCy acts on all cross-sections of the arm between B and C.  To see this cut you free body diagram somewhere between B and C and look at the forces (and moments) that would have to act on the cut section to keep the part with C from flying away.

RE: rod that is pin jointed at both ends

No ...

sumFx = 0 ... Fbh = Fax-Fcy

your diagram is not incorrect, but it is very sloppy ... you're using "datums of convenience" ... it's "better" to have a consistent +ve direction and to measure angles to the same datum. 'cause then the math works out better.  with your approach, you need to be looking at thepicture to understnad why you're combining x- and y- components, +ve and -ve signs.

 

RE: rod that is pin jointed at both ends

btw, as a nit-pick, the rod looks as though it's attached to the cranks by some brkts.  the line of action of the rod force is thru the pins that attach the rod to the brkts (and not where the brkts attach to the cranks).

RE: rod that is pin jointed at both ends

(OP)
rb1957 - not sure what you mean by 'datums of convenience', which datum should I use? Do you mean instead of referring to say FCy I should in fact state 'Fc Sin thetaB'?

I have swapped the labels around for FCy and FCx - schoolboy error!

Okay Terio and rb1957 I'll take it as read that FCy and FAy should be included so therefore amended diagram is attached.

rb1957 - I'm probably overegging this anyway by taking account of 'theta A' angle since is it is only a few degrees at most, for this purpose I'll keep it simple since I am seem to be struggling with this as it is smile  

http://files.engineering.com/getfile.aspx?folder=1537e14d-20f9-42fe-a234-f11f2ef26b36&file=img004.jpg

RE: rod that is pin jointed at both ends

"This is a simple rod connected by 2 bell cranks, bending is strictly in 2D due to the fixings as desertfox alludes to, it is a a fork type connection."

Yes,if you "see" the rod bending in that 2 dimensional structure it is due to the dynamics of the problem , i.e. acceleration in the mechanism and friction.

If the mechanism is dead slow or almost stopped, then the static case is in play and there can be virtually NO moment carried in the rod, even with friction present

  

RE: rod that is pin jointed at both ends

hi DiscipleofScience

It appears to me that your summation of moments in your last post is incorrect Fcy doesn't have a moment it is a vertical force going through the pivot at B and the force you have actually found in equation 1 is not Fcy but Fcx.
I will try to help you some more on probably Friday.

desertfox

RE: rod that is pin jointed at both ends

he's relabelled Fcy as Fcx ... corrected one equation, forgot the other.

"datums" of convenience" ... your +ve direction for each force suits the direction you think the force will be acting ... Fax is +ve in one direction, Fcx the other.  "Normally" you'd start by defining a +ve co-ordinates system x +ve to the right, and Fc will be a -ve number.  The advantage of this system is you can say Fax+Fbx+Fcx = 0 (instead of Fax-Fbx-Fcx = 0);  i suspect Fbx is negative.

not sure how this helps answer your original problem ... why is the rod bending ?  If the calc'd load exceeds the euler buckling load, you then have to ask yourself, what's controlling the displacement of A ? ('cause if the rod buckles, it's stiffness goes to zero and the crank'll rotate, unless A has soe displacement control).

RE: rod that is pin jointed at both ends

I wrote
"Yes,if you "see" the rod bending in that 2 dimensional structure it is due to the dynamics of the problem , i.e. acceleration in the mechanism and friction.

If the mechanism is dead slow or almost stopped, then the static case is in play and there can be virtually NO moment carried in the rod, even with friction present"
------------------------------------------------------------------------
Firthwer comment:
While the dynamic situation would  cause some bending in the rod I do not believe it to be of the magnitude to cause the "observed " bending.

So, I basically agree with the conclusion of others that since there is NO moment acting at either  end of the rod  there cannot be any  bending within the rod. As a consequence, if the OP observes bending then it's cause is Euler buckling due to a single compressive force in the rod, period.

I think the OP should post the forces and rod dimensions so we can put this to bed. If the numbers suggest Euler buckling then case closed. If not, then we have to look for something in the pin connections that could "clamp" one or both ends and thus cause the "observed" bending.

 

RE: rod that is pin jointed at both ends

(OP)
zekeman - The mechanism spends majority of its time in static equilibrium. Your last comment is bang on ist Euler buckling due to single compression, probably very worn cranks and friction - I just wanted to understand the magnitude forces in the rod. I understand Euler formula is for ideal conditions too (perfect surface, no in-built stresses, perfect axial load etc), so it is reccomended to use a factor of safety.

rb1957 - I understand what you mean about negative and positive forces, and yes FBx will be negative to how I have drawn it, since FCx >> FAx I can virtually eliminate FAx.

I have now at least arrived at a Free Body Diagram which provides the compression force in the rod, thanks to all who pointed me in the right direction and having patience!! Especially rb1957, desertfox, Terio and zekeman. The rear crank will follow the same pattern.

Once I understand more I can search for relevant information and found some great resources:

How to add moments in a 4 part series: http://youtu.be/MUMcn-VJsOc, use the simpler method!!

How to solve FBDs: http://youtu.be/vNwOcEUU7Jg

I have now answered my original question of what is the force in the rod, which is really determined by the load, the actuating force just increases to meet the demand. It is my opinion that the off-axis load tends to accelerate the situation once the critical Euler load has been exceeded.

thanks all


http://files.engineering.com/getfile.aspx?folder=08681acb-94b3-4449-a512-8d5c72c15ec7&file=img005.jpg

RE: rod that is pin jointed at both ends

Hi DiscipleofScience

Sorry I thought the thread had ended which is why I didn't post anymore, anyway if your happy with your anwsers now goodluck and your welcome.

desertfox

RE: rod that is pin jointed at both ends

well I Really dislike neglecting Fax ... why ?

it's really simple to solve the problem correctly ...
determine Fc from sum of moments about B.
determine the pivot reaction from Fa and Fc.

neglecting terms as early as you have will get you into trouble.  And these no reason to.

sorry, but IHMO your final sentence shows you haven't learnt anything.  there is No off-axis load in the rod.

and you penultimate sentence implies that maybe the applied loading is a displacement (rather than a defined load) and a seized crank2 could explain the behaviour of the rod.

desertfox,
three times "your" should be "you're"


 

RE: rod that is pin jointed at both ends

ok, 2 out of 3 !

RE: rod that is pin jointed at both ends

(OP)
ok rb1957, I have effectively done what you have said - I have summed the moments about B to arrive at a value for FC

Removing FAx is to help me investigate the suitability of the crank pin.

Again, I agree, you can't have an off axis load through a pin - I do learn rb1957! Have faith winky smile I do think though that when the rod (carrying FC) is actually bending its a different matter.

 

RE: rod that is pin jointed at both ends

"Removing FAx is to help me investigate the suitability of the crank pin" ... don't understand ?  the best i can think of is since Fax and Fcx act in opposite directions then it's conservative to say Fbx = Fcx ('cause it's really = Fcx-Fax) ... but that's not what you wrote.

still wonder if this column buckling ... if the rod was buckling then the rod would lose axial stiffness and crank1 would rotate freely.

but maybe this is a displacement load ?  does a move x" controlled by the linkage attached to it ??

RE: rod that is pin jointed at both ends

(OP)
no x is static, it can be moved for setting up, but after that it remains 'as is'.

I know that angle thetaA is probably 5 to 10 degrees at the most so FAy is relatively small, similarly with thetaB.
 

RE: rod that is pin jointed at both ends

still don't think euler buckling explains the rod bending.

are the fasteners at the ends of the rod clamped up tight ?

really dumb question ... is the rod too long ?

RE: rod that is pin jointed at both ends

Hi rb1957,
Thanks for correcting my mistakes - didn't know this was an English class, thought we were in an Engineering forum (grin). By the way "and you penultimate sentence" should be "and your...."?
Regards,
desertfox

RE: rod that is pin jointed at both ends

touche (imagine the accent)

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