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Re: Static Truss -Statically Indeterminate?
Re: Static Truss -Statically Indeterminate? -- Remi	Post Reply	Top of thread	Forum

Posted by: BrokenArrow ® 05/15/2007, 11:15:31 Author Profile eMail author Edit

I realize this student has probably graduated by now, but since others may stumble upon this post, I think it might be expedient to finally solve this problem. There are two pins supporting -4- unknown forces. There are -3- equations, Sum Fx=0 Sum Fy=0 and Sum M=0. In linear algebra, we say the solution set is infinite because it has more unknowns than equations. In Statics, we say the the system is statically indeterminate for the same reason. Ay=-By can have infinite values. You need one more equation to solve this system, but Statics only provides three. You can know the two x forces, but because you can't solve for the two y forces, you can't entirely know the vector sum of the components to compute the shear stress across the face of the cross section of the pins. It was rationalized that the forces in the y direction are zero because there are no applied forces in that direction. There aren't any forces applied in the x direction either, yet there are two solvable x forces, aren't there? This problem can't be solved mathematically, therefore it is statically indeterminate. Modified by BrokenArrow at Tue, May 15, 2007, 11:20:47

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Re: Static Truss -Statically Indeterminate?
Re: Static Truss -Statically Indeterminate? -- Remi	Post Reply	Top of thread	Forum

Posted by: swearingen ® 07/19/2005, 18:20:52 Author Profile eMail author Edit

Using your coordinate system, with the moment about the z axis, the reaction at point (0,0) would be the vector (146.9,0)lb and the reaction at point (0,8.171) turns out to be the vector (-146.9,0), i.e., there is no load in the y direction. As stated before, if the moment is along the x or y axis, the problem becomes much tougher.

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Re: Static Truss -Statically Indeterminate?
Re: Static Truss -Statically Indeterminate? -- Remi	Post Reply	Top of thread	Forum

Posted by: zekeman ® 07/19/2005, 10:50:44 Author Profile eMail author Edit

Is the moment in the x-y plane. If so it is patently obvious that a couple having x forces only is the solution. i.e. 8.171*F=1200 and the y forces are zero. Similarly a pure moment in the y-z plane would result in y forces only and a moment in the x-z plane would be indeterminate requiring a distribution of moment about each opf the bolts.

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Re: Static Truss -Statically Indeterminate?
Re: Re: Static Truss -Statically Indeterminate? -- zekeman	Post Reply	Top of thread	Forum

Posted by: Remi ® 07/19/2005, 12:46:50 Author Profile eMail author Edit

My apologies for not being more specific. The moment is about the z-axis thus creating the statically indeterminate problem. -"a moment in the x-z plane would be indeterminate requiring a distribution of moment about each opf the bolts." - how exactly would i go about the distribution of the moment to each of the bolts so as to be able to then solve for the desired reactions? Thanks.

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forces in bolts
Re: Re: Static Truss -Statically Indeterminate? -- Remi	Post Reply	Top of thread	Forum

Posted by: zekeman ® 07/19/2005, 16:56:30 Author Profile eMail author Edit

Are you sure the moment is about the z axis. Then, if so, it is the first case I discussed and the solution is x forces at the bolts in shear. Post back if this is not the case or if you want further clarification.

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Re: forces in bolts
Re: forces in bolts -- zekeman	Post Reply	Top of thread	Forum

Posted by: Remi ® 07/19/2005, 19:53:24 Author Profile eMail author Edit

It may be that i am not picturing my coordinate system correctly. Further clarification would be great. If you are looking at a flat x,y co-ordinate system on say graph paper, with my three point on it, the moment would be counterclockwise about the third point. I am not sure how you would thus define this moment. When i said that it rotated about the z-axis, i was stupid and didnt mean the orgin, but was trying to reference an individual axis coming out in the z direction form the third point about which the moment would rotate. Am i correct then in thinking that this is the situation that creates the difficulty? I do not see how there could be no y-reaction in this particular case. Thanks! I really appreciate the help thus far. (E-mailed both of you a copy of the drawing to clarify, just notcied that i miss-noted one of the points above based on the drawing. (0,8.171) should be (0,9.000) this just changes the numbers, not the theory that i'm trying to figure out.) Thanks. Modified by Remi at Wed, Jul 20, 2005, 08:30:03

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forces in bolts
Re: Re: forces in bolts -- Remi	Post Reply	Top of thread	Forum

Posted by: zekeman ® 07/20/2005, 09:49:23 Author Profile eMail author Edit

A pure moment has no origin. So it does not matter where you reference it as long as you establish the plane of action. In your case, saying it is about the z axis is the same as saying it is an x-y moment. If you have a pure moment, then you have no y components of force, only the x forces I discussed. I suspect that you don't have a pure moment and if so, could you supply the forces that occur that you say cause this moment and then we could go from there.

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Re: forces in bolts
Re: forces in bolts -- zekeman	Post Reply	Top of thread	Forum

Posted by: Remi ® 07/20/2005, 12:10:09 Author Profile eMail author Edit

Let me see if i can explain the exact system. We have a triangular plate(as seen in e-mail) that is held in place by two bolts. I have a pneumatic tool fitted through the plate that when running and engaged generates a torque of 1200inlbs which is thus reacted through the plate as a moment. I'm sending you another e-mail with a rough paint picture of the setup. I can't believe that there are no y-reaction forces because in watching the system run i can see the forces generated. If for some reason this is the case, could you run me through the mathematics that prove it so? thanks again.

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Re: forces in bolts
Re: Re: forces in bolts -- Remi	Post Reply	Top of thread	Forum

Posted by: zekeman ® 07/20/2005, 13:06:48 Author Profile eMail author Edit

What is this pneumatic tool driving;i.e. we need to know the origin of the forces before we can attack the problem.

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Re: forces in bolts
Re: Re: forces in bolts -- zekeman	Post Reply	Top of thread	Forum

Posted by: Remi ® 07/20/2005, 13:47:41 Author Profile eMail author Edit

It is driving a bolt into an assembly. It torques the bolt to 100ftlbs or 1200inlbs.Thus the moment created on the plate should be opposite and equal to the driving torque.

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Re: forces in bolts
Re: Re: forces in bolts -- Remi	Post Reply	Top of thread	Forum

Posted by: zekeman ® 07/20/2005, 14:18:21 Author Profile eMail author Edit

Then it looks like you have almost a pure moment on the plate and therefore the design answer is as ly stated, the two shear forces on the bolts at 0,0 and 0,9 in opposite directions or 1200/9=133 lbs. The y forces are zero. This system then satisfies the vector force summation and moments to zero. If this is a design problem, I would think that these bolt loads are extremely low and your bolt design would depend more on the preload in the bolts than the very low and relatively negligible external load. If you wnat to nitpick the solution, you could ask why doesn't there exist a y component equal and opposite in direction on the bolts? How would a force other than zero be manifested?

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Re: forces in bolts
Re: Re: forces in bolts -- zekeman	Post Reply	Top of thread	Forum

Posted by: Remi ® 07/20/2005, 15:27:57 Author Profile eMail author Edit

I agree with everything that you've stated. That is exactly how i solved the problem initially and the answer that i had. EXCEPT for the fact that i have an equal and opposite y-reaction based on the sum of the forces in the y-direction. I agree that there also exists equal and opposite forces in the x-direction of 133lbs(This was solved from the sum of the moments about the tool begin equal to 0 and knowing that the y-reactions would cancel each other out.) However i do not see how you can assume these reactions to be zero. I would agree that they are opposite and equal, thus canceling out of the moment equation allowing you to solve for the x-reactions but don't see how this allows them to be zero. The reactions still exist, just by consideration of moments around the tool they cancel each other out. Do you see why i am confused? To better see the problem. Assume the joint at (0,0) to be a roller in the horizontal direction, thus it would only have a reaction in the y-direction. The joint at (0,9) would still be a pin and have reactions in the x and y direction. The reaction therefore in the x-direction would be zero, and we arrive at the same delima of not being able to solve for the reactions in the y-direction. You would know that they are opposite and equal, but it becomes statically indeterminate. I have plugged my initial problem into Pro/Mechanica and it informs me that the reaction in the x-direction are 133lbs equal and opposite. It also informs me that the reactions in the y-direction are ~200lbs and equal and opposite. I'm trying to find out why by hand this is so? Modified by Remi at Wed, Jul 20, 2005, 15:39:04

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Re: forces in bolts
Re: Re: forces in bolts -- Remi	Post Reply	Top of thread	Forum

Posted by: zekeman ® 07/20/2005, 16:42:43 Author Profile eMail author Edit

To answer your dilemma, you could have y forces only if in the bolting down of the two bolts you cocked the bolts on the plate in opposite direction causing equal and opposite y forces at 0,0 and 0,9. In that sense that force would be indeterminate. However,your suggestion to impose a horizontal roller at 0,0 would lead to an unbalanced moment when taken about 0,9 since only the 1200 lb in would exist and any y force at 0,0 would have a zero moment arm and thus the system would not be in equilibrium and would rotate about 0,9. I'm puzzled how your program arrived at the y forces you mentioned. I would ignore that answer since it is obviously wrong.

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Re: forces in bolts
Re: Re: forces in bolts -- zekeman	Post Reply	Top of thread	Forum

Posted by: Remi ® 07/20/2005, 17:20:44 Author Profile eMail author Edit

I understand what you're saying about the suggestion. I was just trying to quickly think of another way to present our dilemma. What i do not understand is the mathematics you use to prove that y-reactions are equal to zero. SUM(Fx)=0=Fx1+Fx2 THEREFOR Fx1 = -Fx2 opposite and equal SUM(Fy)=0=Fy1+Fy2 THEREFOR Fy1 = -Fy2 oppoisite and equal Assume counterclockwise to be positive SUM(Moments about Tool)=0=Fx1(0.829) - Fx2(8.171) - Fy1(4.187) -Fy2(4.187) Since Fy1 = -Fy2 they cancel out in the moment equation, BUT this does not mean that they are equal to zero. I can see how there is the fact that the x-reactions account for the entire moment created by the tool, now based on your new equation where the y's cancel out, and thus you could i guess assume that your y-reactions are equal to zero because of this? But mathematically i don't see how you can really prove that the y-reactions are equal to zero since they just drop out of the equation. Zero or not, they still drop out of the moment equation, and thus i can't prove anything either way.

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Re: forces in bolts
Re: Re: forces in bolts -- Remi	Post Reply	Top of thread	Forum

Posted by: zekeman ® 07/20/2005, 18:25:41 Author Profile eMail author Edit

Reread my last post. I showed that lateral preload in the bolts could account for the equal and opposite y forces you mention. Therefore , zero is a solution, only if the assembled condition does not cause the lateral preload. If it does, then you would need a strain gauge to detect the amount. No way does the introduction of the moment cause a y component of force.

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Re: forces in bolts
Re: Re: forces in bolts -- zekeman	Post Reply	Top of thread	Forum

Posted by: swearingen ® 07/21/2005, 16:27:17 Author Profile eMail author Edit

zekeman is exactly right. There are no external forces creating a force in the y direction, therefore they must be zero. Theoretically, if instead of the bolts, you put rollers there that allowed BOTH fix points to move in the y direction and resist force in the x direction, the rollers would feel the lateral load BUT NOT MOVE in the y direction, even though they are free to do so. There are no EXTERNAL y reactions. However, there are stresses internally to the plate in the y direction. They just cancel themselves out by the time they get to the bolts. To further confuse this issue - it does not matter how you arrange the three points, as long as they are in a triangle, if you apply a torque to one point and hold the other two, you will get no reactions along a line drawn between the two held points and equal and opposite reactions perpindicular to this line.

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Re: forces in bolts
Re: Re: forces in bolts -- zekeman	Post Reply	Top of thread	Forum

Posted by: swearingen ® 07/21/2005, 16:25:52 Author Profile eMail author Edit

zekeman is exactly right. There are no external forces creating a force in the y direction, therefore they must be zero. Theoretically, if instead of the bolts, you put rollers there that allowed BOTH fix points to move in the y direction and resist force in the x direction, the rollers would feel the lateral load BUT NOT MOVE in the y direction, even though they are free to do so. There are no EXTERNAL y reactions. However, there are stresses internally to the plate in the y direction. They just cancel themselves out by the time they get to the bolts. To further confuse this issue - it does not matter how you arrange the three points, as long as they are in a triangle, if you apply a torque to one point and hold the other two, you will get no reactions along a line drawn between the two held points and equal and opposite reactions perpindicular to this line.

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Re: forces in bolts
Re: Re: forces in bolts -- swearingen	Post Reply	Top of thread	Forum

Posted by: Remi ® 07/22/2005, 08:56:25 Author Profile eMail author Edit

Thank you all for your help, it has been greatly appreciated!

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slight alteration
Re: Re: forces in bolts -- Remi	Post Reply	Top of thread	Forum

Posted by: Remi ® 07/22/2005, 12:53:58 Author Profile eMail author Edit

say you were to offset the points just slightly. Would you then just get an incredible small reaction at the two points or would you get an infintisimally large reaction? With machine shops there's never a guarantee that any holes made are exactly in a line.

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Re: slight alteration
Re: slight alteration -- Remi	Post Reply	Top of thread	Forum

Posted by: swearingen ® 07/22/2005, 14:04:50 Author Profile eMail author Edit

If you offset the bolts, you can still draw a line between them (center to center). There will be no force along this line. The only forces will be perpindicular to this line (equal and opposite at each hole).

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