64 thoughts on “HOMEWORK 23 - Fall 24”

    1. Personally, I like to make my division that splits all the members that I need to find. In this situation, I started my line between joints DE and ended it between joints NO. There are a ton of different ways to solve this problem however so take my strategy however you please!

    2. I would recommend first finding all the members carrying zero load by looking for Y, T, and elbow joints. This will also help determine which members carry equal loads. Once you have determined as much as you can without doing any math, you can make a division by splitting all of the members you want to find. Then, you can use the moment equation and sum of the forces in the x and y directions to find the loads carried by members 1, 2, and 3.

    3. I split mine in a way to keep the unknown members but to get rid of the constraints on the right side. This way you can use the external forces to help solve for the unknown members without having to deal with the constraints.

    4. I personally like to cut my FBDs in a manner that goes through all the forces I'm trying to solve for, that way they become external forces and can be used when calculating sum of forces and moments. Additionally, when deciding which side of the cut FBD to use, consider using the side without the constraints as it will lead to having fewer unknowns. It may seem harder to use one side over another, but by identifying the zero-force members, the calculation will be simplified. Hope this helps!

    5. Initially, it seems that the best way to split this FBD would be to consider the right side of the split (assuming you cut a line that goes through one two and three. However, this way would be more complex as you have to consider the reactions at points I and Q, which is more complex. So, I would recommend cutting a line that goes through members 1,2 and 3, while considering the right side of the structure.

    6. I split mine so that the 2 and three members were split in the process. This allows you to determine their tensions/ compressions with the forces on one side eliminating the other unknowns. When you split a support the goal is to minimize the unknowns and constraints. After you compute the tensions you can then plug those back in to find the other unknown of 1.

    7. Personally, I like to draw a line that divides all the members I need to analyze. In this case, I started my line at DE and ended it atNO. There are many different ways to approach this problem, so feel free to use my method or find one that works best for you!

    8. I found that the best way to solve this problem was to "cut" along member 1, 2, and 3 and make your free-body diagram with the truss to the left so you don't have to solve for the reaction forces at I and Q

    11. In most problems like this, I've focused on finding some mutual segment between the segments I'm looking for. From there, you can cut there. In a case where there are three segments you're looking for, I look for the shared point between two of the segments and then find (from that shared point) the segment that connects to one of the points of the other needed segment. If you can't complete those steps due to the segments you need to find, it may be worth doing two splits.

  2. Before splitting I recommend identifying which members carry 0 load by identifying the type of joint where those members connect, that would also give you a good idea on where to split the FBDs

  3. I agree with the points made above. I found in the last homework that the best way to make a cut and ultimately solve the problem is making one cut exposing all of the desired members. From there, it then became relatively simple to set up the moment and force summations and solve for the various force values.

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  4. Could we use the sectioning way to solve? This would allow you not to have to solve for the reactions. Also, do we have to mathematically prove the zero forces, or can we answer based off inspection?

    1. Yes, the sectioning is the most efficient way to solve this problem. I don't believe that we have to prove the zero forces, but just answer them and give a small explanation of why.

    2. I think identifying the zero-load members based on FBD would be enough, as using method of joints to mathematically prove it would be way to long for a homework question!

    1. I think you should be fine just labeling them. Proving each zero-force member would require the method of joints which would be extremely tedious for this problem

    2. The best way to do this would be like shown in class. Adding a circle to the truss that is a zero force member. To add on, consider using the X joint, elbow joint, y joint, and t joint strategies to solve in a more efficeint way.

    1. I'd say we most likely can't assume symmetry of the triangle, and it's not really necessary to know the length of JK in order to solve the problem.

    2. For the specific loading that we are given, we don't really need to care about the specifics about any part of the left hand side of the triangle, as we aren't trying to find the forces in those members. Instead, you can just focus on using the method of sections correctly and splitting it in a way where that doesn't matter, and where you also don't need to care about the reaction forces at I and Q, although this method would also work, but it would require more equations and more work.

    1. I just labeled them for my solution, with no mathematical proof. If you'd like, you could probably say what type of joint is present that makes it a zero force member.

  8. I didn't prove the zero forces mathematically, but I drew small FBD's of some of the joints as proof for where my logic came from. Not sure if that is necessary though.

  10. On an FBD in this situation do you have to label what the joints are that you used to find zero force members? An example being would I have to write "t-joint at __" if that was used? In class we just did the equals and marked the zero force members but also made sure to explain what joint we did them around, so is that necessary on the FBD?

    1. Everything in this course is stable. However, I believe the better way to do this problem is an approach where doing the reaction x y forces in I and Q don't matter, because we would have to find 4 equations and solve all of them, which would be much more work than splitting it and using the left hand side of the split with the P and 2P forces and doing the moment, and the x and y sum of forces to get 3 equations to solve for the 3 unknowns.

  12. On this question would it be useful to draw out three FBDs, one to represent the entire system, one that represents the entire system without the zero force members, and one to use method of sections? I think this would greatly simplify using method of sections.

    1. I think that that would certainly be helpful to understand and solve using the method of sections. You could also consider using 2 free body diagrams instead: one that is the overall system, with all of the zero force members labeled, and another that is your section. That way, you would get to your equations faster, but your method would make the understanding of the problem more clear.

    2. Yes, sure you could just draw one but if you split the system out and draw each section separately solving it will be much clearer and easier to follow through incase you forget something or considered the same system for 2 different things

  13. Is it reasonable to assume that Iy and Qy (the y-component reactions at point I and Q) are equal to one another? I used two different equations that both resulted in Iy + Qy = 2P, but I don't know where to go from there.

    1. No, it is not reasonable to assume that Iy and Qy are equal. However because we are not asked to find these specifically we can treat them as just Iy + Qy = 2p. Meaning in equations this term will appear and you can subsitude (Iy + Qy) to be 2p. For example this appears in the moment EQ as Mn: .....+8d(Iy + Qy) ==> Mn: ....+8d(2P).

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  15. If you split up the truss through EH and NO. I would take the moment at N, allowing you to get the F1. Then I would take a second moment at H in order to find F3. You would most likely have to consider two-moment equations for this problem.

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  16. You are able to take the moment at point N to find F1, however the second moment equation at point H isn't necessary. When you write out the equations of Net Force in the X and Y directions, you'll see that the only unknowns are F2 and F3, which there means the equations are solvable.

    2. Yes, if you look at big picture. When you look at the whole structure, you have the reaction forces and the applied forces that are acting on the whole structure, so they would be considered when you take a moment about a point on the structure.

  19. I don't understand, most people seem to be cutting at EH down through NO, wouldn't that mean you'd need to solve for ALL the joints on the left side to find force 1? I don't see how it would be involved in the moment equation either

    1. Yes, AJ and AB would also be zero-force members since that is an elbow joint with no external load at either joint. Since the angle between them won't equal zero, the only way for either component to equal zero is if the magnitude of each force is equal to zero. This can also be determined when summing up the force equations about joint A which isn't necessary but helps show how that relationship plays out. Hope this helps!

  21. Would it be simpler to split this into three sections using 2 straight cuts or just using one curved cut? I've been using 2 cuts for examples like these but would it be easier to solve for all three forces at once? That way we only have 2 FBDs, although those will be more complicated.

    1. Using one curved cut can solve for all three forces at once with fewer FBDs, but the equations will be more complex. Two cuts would allow for smaller equations and require more FBDs.

    2. For me it was easier to split this by using a single cut. If you cut diagonally between DE and NO, you are able to single out all of the forces. From this point you can take the moment at N to solve for F1, and then use equilibrium equations to find F2 and F3.

  22. I found making one cut, through all the desired members was very doable. the equations I ended up with were pretty simple. Originally I choose to look at the wrong side of where I cut but once I looked at the other side it was pretty chill.

    1. To find a zero force member there are two ways to identify one to my knowledge, if there is a joint which has only two members connected to it and there is no external load applied to that point, then that is a zero force member. Also, if there is a joint with three members but two of them are parallel and there is no external force acting on the joint, then the member that isn't parallel to one of the other members is a zero force member. Hopefully this makes sense.

    1. Yes, AB and AJ are zero-force members. To figure this out, I believe that the easiest way to do so is to use the method of joints. Therefore you can calculate the forces at point A and determine whether or not the forces of AB and AJ are zero-force members.

    2. I think you can tell that AB and AJ are zero force members because join A is a Y joint with no external forces. The sum of forces in the x and y direction is 0.

  26. I am studying for the final exam and i was wondering for problem b why the joints at a not included as a zero force vector if we say that all off the masses are negligible?

  27. The mass is negligible; however, the force from the external force will be transferred down to points A and B. This means that there will be a force at A, so you can not call it a zero-force vector.

    1. Yes, if you are referring to the number of zero-force members, there are many due to T-joints. For example, member OH is a zero-force member as it is a T-joint and there is no external force applied to it.

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