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## 56 thoughts on “Homework 23.B”

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Can we assume that point L a horizontal distance d away from M?

Bridget, you have enough information to calculate the angle formed by AMC. Once you have that angle, you can find the perpendicular distance from L to MJ. Hope this solves your question.

Can we assume that there is a T joint at L, that is, that MK is perpendicular to LJ? I ask to determine if LJ is a zero force member.

I did not assume that MK is perpendicular to LJ, but I did get that LJ is a zero force since there are only 3 forces at L, and ML and LK are colinear, which means that LJ is 0.

I did that too.

Hi Kate. Point L actually forms a Y joint which acts the same as a T joint, just instead of the 0 force member being perpendicular it is at an angle. Because we know the angle is not 0, the member LJ must carry no load so that the forces balance. Hope this helps!

Hi Kate, you do not need to determine whether LJ is perpendicular to segment MK because LJ is the non collinear member of a Y-joint. This means that LJ will be a zero force member. Hopefully this is helpful.

When you find a force that is a compression force, do you plug in the negative or positive value into other equilibrium equations?

What I did is still assuming tension in the equilibrium equation and use negative value, so this will bring us consistency and avoid getting confused.

I draw the forces pointing away from the point of interest (tension) and then plug in all the calculated values, without changing the sign. This should keep all the signs in order.

There are multiple ways to go about approaching this problem, however, I would probably draw the forces pointing in one direction, in order to keep the signs consistent throughout the remainder of the problem.

When finding the angle for EI, why are you supposed to find angle IED and not IEH?

You need angle IED if you want to find the horizontal and vertical components of the load in EI. This is the angle made by the member with the horizontal line, and hence components would be dependent on this angle and not angle IEH. Hope this answers your question.

My guess here is that by finding angle IED, you can then use geometry more effectively to find angles such as angle IEH, and angle EIH. I believe this also allows you to find and equate angles DEC, HIE, JKI, and so on, going up the structure.

Do you need to solve for the reaction forces here? I know it is not asked for it in the problem but do we need them to solve for what is asked?

This problem can be solved without solving for the reaction forces at A and C.

You do not need to solve for the reactions and you will only need to use the loadings at the top at point V to be able to solve for the members we are looking for

Im not sure how to approach this. Am i supposed to solve for the reaction forces or not?

If you take the upper part of the truss it might be easier as you don't have to find the reaction forces. However, if you take the lower part then you will have to find it.

I was able to solve the problem without solving for the reaction forces. I suggest making a cut through JH, HK, HI, and IE. This will expose 4 members, some of which are zero force members. So after you find which ones are 0, you can just solve for the rest using moment equations or sum of forces equations. Hope that helps!

I solved it without the need for reactions, if you take the FBD cut to not include the points of reaction, you should not need the forces. I have found this is usually the easiest way to solve the problem.

Do final answers need to be given in terms of the magnitude and then tension/compression, or should we include the sign (+/-) as well?

I leave my answers in terms of +-, and then just explain whether this means tension or compression. I think you can do it either way.

As stated by others, I do believe that it is your choice to include the (+/-) signs or to just list the magnitudes and state the nature of the forces. Personally, I just list the magnitudes of the forces and state whether they are in tension or compression.

The final answer should include the sign (+/-), from this you will state if the element is in tension or compression.

When solving these sorts of problems does it make a difference if the problem asks for the load at IE or EI? I know in other contexts, the order of the letters signifies the direction of the force so therefor IE=-EI but is that the case here as well?

The order doesn't matter in this question in my opinion. Naturally, you find all the zero-force members before cutting through the leftover forces you have to find. What matters is the direction you point those forces in when you attempt to find them. If you point them away from the FBD and the solution is positive, it is a tension force and vice versa.

The order doesn't matter in this question in my opinion. Naturally, you find all the zero-force members before cutting through the leftover forces you have to find. What matters is the direction you point those forces in when you attempt to find them. If you point them away from the FBD and the solution is positive, it is a tension force and vice versa.

The order doesn't matter in this question in my opinion. Naturally, you find all the zero-force members before cutting through the leftover forces you have to find. What matters is the direction you point those forces in when you attempt to find them. If you point them away from the FBD and the solution is positive, it is a tension force and vice versa.

For our work and calculations for the problem, are we required to show calculations for the zero-force members? Or can we just state that we visually "performed" the method of joints and found which members were zero-force members that way?

I didn't show the work out for the zero-force members but I did give the reason why the members were 0. For example, member LJ is only connected to two other links, so it is a zero-force member.

By using trig you can solve for the top angle. And then by similar triangles you can solve for the length of HI. This then allows you to find the moment easily.

In this case, would we need to consider the reaction forces at A and C? I could obtain my answers without them; however, I am unsure. Can someone please explain this?

You can ignore the reaction forces at A and C if you choose the FBD that has the loads at M when cutting the structure into two.

Would it be possible to use the reactions in this problem? Rather than just the forces at point M.

Hi Dominic. I think that is a safe assumption to make that we would need to find at least a couple of the reaction forces in order to solve this problem. For my solution, I ended up not needing them in the end, it really just depends on where you place your cut when solving with the method of sections.

From my professor, it seems that you can almost always (in this course) find a way to go about solving without needing to worry about the reaction forces. For me and others that I have talked to, they weren't needed.

How do we use trig to find angle HIE? I've seen suggestions to solve the top angle so for that do we awesome like KJ is a length of 2d? I think maybe I am just overthinking this.

Hey Hannah! If you want to solve for HIE, try solving for HIK first. Since all of the lines inside of the entire system (aka a giant right triangle) are parallel, you can assume that HIK is equal to ACE. Using the given vertical and horizontal lengths of the entire triangle, you can solve for ACE which ultimately gives you HIK. From there, you should be able to find HIE. However, when I solved this problem I didn't need HIE - only HIK.

Alternatively, if you do not want to get involved with angles in your solution process, you can use similar triangle proportions to find the length of moment arms. This will allow you to find the value of HJ using moments. Afterwards, you can solve for the x and y values of EI using the sum of forces in the x and y directions, then you can calculate the magnitude of EI using the Pythagorean theorem.

For the sum of the moments in H, you will solve for the force of IE, what is the best way to find the angle of IE?

Hi Ricardo, you can find angle IE using similar triangles. You will then see that angle IE is the same as angle AMC.

For this problem I just want to help people out by saying that this whole truss system is a giant right triangle. So you can find the angle of that giant triangle, and the angle will carry over to smaller triangles within the system. Use can use this hint to help solve for the y component of Force IE.

How many non-zero forces are there including the loads asked for in part b)?

*zero-force members

I got 5 total, and the way I approached it is starting at joint L and then moving down. You should be able to find all 5 one after another.

I followed the same methodology as Mitch and also got a total of 5 zero-force members. Hope this helps!

Do we need to show any specific work for finding zero force members or can we just list out the ones that are fairly obvious?

Hi Andrew. I suggest you show the force at each joint and then also include a x y diagram showing their directions. That's what I did if they were obvious. If not, maybe show the sum of forces in x or/and y. Hope this clarifies things.

Why Isn't DE a zero force member?