Problem statements
Solution video - H22.A
Solution video - H22.B
DISCUSSION THREAD
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HOMEWORK 22 - Fall 24
52 thoughts on “HOMEWORK 22 - Fall 24”
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Should I consider the unlabeled point next to A and B that is holding the cable at K?
Yes, you should consider the unlabeled point because it anchors the pulley system that supports the weight W. A downward force of P is applied at this point due to the tension in the cable from the pulley system. While this point does not directly influence the internal forces, the force applied here is important for the overall equilibrium of the structure. Hope this helps!
Yes, it is part of the pulley system and has a downward force associated with it.
Yes as it is part of the pully system
Could someone help explain why the forces in truss members change or remain the same as you analyze different joints? Specifically, when moving from one joint to another, how does the tension or compression in the connected members affect the equilibrium at each joint?
from what i understand the forces in each member, whether tension or compression, remain constant along the length of the member but affect equilibrium differently at each joint. At every joint, the sum of forces must equal zero in both horizontal and vertical directions. As you move from one joint to another, the force in a member remains the same but is applied in the opposite direction at the new joint. This force then influences the equilibrium at the next joint, helping determine the unknown forces in the other connected members. Forces change between joints based on the overall structure and load distribution.
The forces should stay the same no matter where you look at the members from. The only reason they may seem different is when you are finding the moment at different points. This can also be seen if you find a member through the sum of forces in a direction and how you can only get one number (if you do it right) no matter what order or method you use to get the answer.
Each joint in a truss must be in equilibrium, meaning the sum of all forces acting on the joint must be zero. So, when you analyze a joint, the forces in the connected members, either tension or compression, are determined by the requirement that the joint remains in equilibrium. As you move from one joint to another, the forces in the members connected to the joint you just analyzed become known quantities. These forces are then used to determine the forces in the other members connected to the next joint. Hope this helps!
For example, say you determine a member is connecting two joints in tension. When analyzing one joint, the tension will pull outword, where as at the other joint it will be pulling inward, keeping the members at tension. Hope that helps!
Is the easiest spot to split the truss between I and E because its the closest spot to an even cut within the trusses?
This would be the easiest spot to find the force at member 1. I would make a separate cut to find the forces on members 2 and 3. The strategy for deciding on where to section the structure is to find where the cut goes through the members you are trying to solve for. So in this case, cutting laterally between points I and E allows you to cut through member 1 so you can solve for that force.
I split the truss between I and E, E and H, and H and C so that I could have all 3 of the members as forces. By doing this you also have to calculate the force of member EH, but that is not too difficult. You can split it that way too, it really depends on how you plan to attack the problem.
Do we consider the unlabeled point and if we were to, why?
Yeah I think so, as it acts as an anchor for the pulley system. Therefore, a downward force of P would be acting at this point. You will need this for the overall equilibrium of the structure.
How do we solve for the reaction forces Ay and By? I am considering the full truss as a rigid body, but if I were to do a moment, r would be used for some terms but not all and therefore not cancel. Any suggestions?
I'd assume that you would have to look at the location the reaction force of the pully acts on the truss itself and not the ground. So, the reaction force is acting on joint K. And I'm pretty sure you can have the reaction force acting directly on the joint, so you do not need to account for the R of the pully for the perpendicular distance.
How do you tell if something is a zero force member again?
You have to look at the sum of the forces around that point. When you set the sum of forces in the x or y direction to zero, it is usually apparent which forces are equal to zero. You can also use methods from the zero force member lecuture to quickly find which ones are zero force.
How does r (radii of the pulleys) cancel out?
You can look at the types of joints. A T-joint will have a zero member if no external forces are acting on it. This is the same for Y-joints and elbow joints.
To determine if a member has zero load on it, look at the FBD for that joint. Because the truss is in static equilibrium, the sum of the forces in the x and y directions add up to zero. So for the FBD, if there is only one member acting in one direction, then that member will have zero force on it. The easiest example is a T pr Y joint, where there is one member pointing at an angle compared to the other two. The member in that direction will have zero force, unless there is an external load on it. The other two members will have forces with equal magnitude and act in opposite directions.
When it says identify each member as being in tension compression or zero load. Is that asking for each member of the truss or only members 1,2, and 3?
Perhaps a silly question, but would one consider the tension on the left pulley acting directly at point K, or by a difference of the radius, r?
I think it would be directly at K since the edge of the pulley is not attached to the truss, just the center.
Is it ok to still use the method of joints to find the loads in the members in this problem or do is it the method of sections make the problem more concise and faster?
Using the method of joints is possible and would ultimately result in the same answer, but I believe it would be a lot more work. Instead, I first solved for the moment about point A and used equilibrium equations to find the reaction forces Ax, Ay, and By and then made two splits (horizontally through 1, and horizontally through 2 and 3) to solve for the loads using the method of sections. The method of joints may work, you would just need to start from the outside of the truss and work your way inside to these three points, which would require solving many more systems of equations.
Could there be multiple ways of solving this problem? Are there different ways to section it, and is it possible to do it with just one break?
There are multiple ways to solve the problem, but I don't think it can happen with just one break since 1, 2, and 3 don't all share one line where there could be a break. Try using two separate breaks, such as one for 1 and another break for 2 & 3.
How would treat the weight from the pulley/cables whenever you split the truss at point 1?
For member 1, I think you can ignore the weight from the pulley/cables since it should factor into your calculations for the reaction forces at A and B.
Would you sum the moments at H, C, and E?
If you are trying to find the total moment about point A, then you should find the moments from the forces in DH, CH, and DE (although I think that the moment from DE will be equal to 0 since the force intersects point A). You can use this to solve for the force in CH.
Can we essentially ignore everything happening with the pulleys since we can select a smaller section of the entire system to find the load carried by members 1, 2, and 3?
It depends on what part of the system (the smaller section) that you work on. If you are focusing on the top part of the system after you divide it, then no, you can not ignore everything that is happening with the pulley cause there is a force tension acting on it... but you can neglect R.
When writing the full equilibrium equations to solve for By, Ax, and Ay, do we consider any forces from the unlabeled point as well?
Yeah, it seems like the consensus is that there is a downward force at that point due to the tension in the cable.
Is it possible that the forces FDE and FIE are associated such that FDE = -FIE. This would prevent having to do multiple cuts and such and I figured it would be okay because any forces acting on those two compents dont act in the vertical direction
Can we do this problem using the forces at the joints or do we have to do it by splitting up the component?
You can do it either way, but I believe splitting up the components would take fewer calculations!
Do we find the forces due to the pulleys using the pulley tension equations (T_L / T_S = e^(mu × angle))?
That would not be necessary for this homework as we don't care about the loads in the cables of the pulleys. Just the truss components and the load from the pulleys onto the frame.
How are we supposed to determine the forces caused by the pulley's, and would those effect the way that we are solving this question if we are just going to use sections?
You can solve for the forces in the y direction for the pulley with the block, then you'll find that Tension = P. This will then help you when solving for the forces with the different sections.
Is the downward force acting at point M equal to W (2P) or is this value different since there is another pulley connected to the pulley at point M?
Yeah when calculating the moment about A, can we just consider a force acting downward with a magnitude of 2P?
I am not sure if the equilibrium equations should be taken with the entire truss system in mind, or as we go member by member/section by section. The approaches seem to lead to different answers.
Should we take into account the unlabeled points when solving?
Yes, more specifically the unlabeled anchor point next to point B at least.
Yes, you should take into account the unlabeled points when solving. Specifically the point directly below K. This is because when you solve for the moment at H (or whatever point you choose) and plug in to find the equilibrium equations, you will need to include this unlabeled point as there is a tension force acting on it.
is there a force at K due to the pulley system or just at M. I'm not sure how to break down the forces of the pulley
So for the pulley system, there is the block of mass W which is 2P, and it has two strings attached to it, so each one of them has a weight of P. For the long string that goes across both pulleys, that one has a weight of P across the whole thing, resulting in a P force going down on the left side of the pulley at K. So there is not a force at K, but r distance away from K, and the same for the right pulley. But there is a force P at M because it is directly connected to that point.
I’m wondering how to incorporate the K and M pulley radius in our equation. Does it have to do with our moment or reaction forces for just the pulley system? The Truss system? Or both?