Structures (Civil Engineering) - Help with Planar Truss and Stress Analysis

[allblue123]

Structures (civ Eng) urgent help

Hello,
I've got two resit exams coming up in over a week for Civil engineering first year structures 1a and 1b. I've been attempting several past papers and there were some questions I desperately need help with.

I'm not sure if this is exactly the place for this subject but any sort of help or input will be practically live saving for me at this point.

I have attempted the part (a) of planar truss question (I'll upload my answers shortly) however I have yet to figure out question 2. I suspect that I'll have to use method of sections (free body) but if anyone can guide me through it, please do so.

Again, thank you very much.

 

[PhanthomJay]

You probably should have posted in the Engineering Homework sub-forum for wider viewing. I assume that you will be submitting your work for the first image labeled question 2. after which we will provide comment and assistance, and that you are having a problem getting started with the 2nd image, unnumbered? If so, you might want to web search on zero force members, but generally, always find your reaction forces as a first step.. Start with that. Note that each support reaction has both a vertical and horizontal force component.

And welcome to Physics Forums!

 

[allblue123]

Forces in members

Homework Statement

Determine which members are in compression, tension, and zero force members

Homework Equations

Can you please check the members for me please?

The Attempt at a Solution

Please see the attachment for my attempt :)

 

[allblue123]

Hello thank you for replying, I have made a new thread in engineering help forum for wider viewing as you've suggested :) please take a look at it for me:

https://www.physicsforums.com/showthread.php?p=3467319#post3467319

thanks

Edit: here is my solution to one of my question in case some people are checking out this thread. Please take a look :)

 

[PhanthomJay]

Homework Statement

Determine which members are in compression, tension, and zero force members

Homework Equations

Can you please check the members for me please?

The Attempt at a Solution

Please see the attachment for my attempt :)

Your identification of tension, compression, and zero force members, and the direction of the support reaction components, in the first image, is excellent, nice work. Not many would readily identify those zero force members.

For the 2nd problem, it is not quite correct. What is the horizontal force component at the left support using Newton 1 in the x direction? And don't forget to identify whether it is T or C or 0 force for the middle bracing members.

 

[allblue123]

Your identification of tension, compression, and zero force members, and the direction of the support reaction components, in the first image, is excellent, nice work. Not many would readily identify those zero force members.

For the 2nd problem, it is not quite correct. What is the horizontal force component at the left support using Newton 1 in the x direction? And don't forget to identify whether it is T or C or 0 force for the middle bracing members.

Hello, thank you very much for your help so far. However, I'm very confused with the second problem.

I have come under the suspicion that the left member of the two vertical members in the middle might be in compression.

Perhaps could you please give me more hint as to which members I have labelled right and which one not?

Those questions are not a part of assignment or university homework but from part of practise past paper questions in preparation for an exam I have in a week. I would like to be able to solve as many problems as I can in the mean time. I really am very grateful for your help so far :)

Edit: Below is the solution to question 2. I eliminated zero force members and steel wires that were in compression. :)

 

[PhanthomJay]

Hello, thank you very much for your help so far. However, I'm very confused with the second problem.

I have come under the suspicion that the left member of the two vertical members in the middle might be in compression.

No, it is in tension.

Perhaps could you please give me more hint as to which members I have labelled right and which one not?

most (not all) of them are incorrect. For starters, you must first look at the reaction forces at the left support, as I asked prior. You show a horizontal component there at that left reaction. Can there be a horizontal component of the reaction force there if the sum of external applied or reaction support forces in the x direction must be 0? You must first address this. Then you might want to put some numbers on the loads, identify zero force members (the bottom horizontal chord is not a zero force member), and use the method of joints or sections or combination thereof to find the tension and compression members .
(At the right 1/3 of the truss, your far right vertical member, the 2 diagonals, and top chord member, are correctly labeled).

Edit: Below is the solution to question 2. I eliminated zero force members and steel wires that were in compression. :)

Let's focus on this first problem 107 first so as to not confuse things by addressing 2 or 3 problems at once. Then I ( or another helper) can assist with Question 2a and 2b.

 

[allblue123]

Silly me, I kept thinking there was a horizontal force at top right corner >_<

I think it makes things a lot clearer now. :)

I didn't label the zero force members.

 

[PhanthomJay]

Silly me, I kept thinking there was a horizontal force at top right corner >_<

I think it makes things a lot clearer now. :)

I didn't label the zero force members.

That looks real good now. I'll take a look at #2 as soon as I can.

 

[PhanthomJay]

Question 2: Your forces at certain joints are not adding to zero, but you have the right idea and the correct tension wire configuration. Take a look at your top joint in the center of the truss, where the vertical chord meets the wires at the apex of the triangle, and try to find your error in the joint equilibrium equations.

 

[allblue123]

Question 2: Your forces at certain joints are not adding to zero, but you have the right idea and the correct tension wire configuration. Take a look at your top joint in the center of the truss, where the vertical chord meets the wires at the apex of the triangle, and try to find your error in the joint equilibrium equations.

Sorry for the late reply. Now I've taken a closer look, I noticed that the triangle of forces aren't in equilibrium. For example at the left most members (as in the picture) if I start resolving at 50 kN vertical member, the tension members came out as 70.7 kN and horizontals at 50kN each.

However, when I resolved starting at 25kN left most member, the tension member came out as 35.4 (which is obviously wrong as diagonal has to have biggest value).

Am I missing something here? Have I not got the tension/compression/ zero force members right to start with?

Thanks :)

 

[PhanthomJay]

Sorry for the late reply. Now I've taken a closer look, I noticed that the triangle of forces aren't in equilibrium. For example at the left most members (as in the picture) if I start resolving at 50 kN vertical member, the tension members came out as 70.7 kN and horizontals at 50kN each.

No, the vertical 50 kN force on the lower diagonals splits equally amongst both diagonals. Draw a free body diagram of the joint to confirm this.

However, when I resolved starting at 25kN left most member, the tension member came out as 35.4 (which is obviously wrong as diagonal has to have biggest value).

It is (perhaps not so obviously) right.

Am I missing something here? Have I not got the tension/compression/ zero force members right to start with?

Thanks :)

The T/C/0 force members are correct, you did well here. If you trust the laws of Physics, trust your joint equilibrium equations!

 

[allblue123]

No, the vertical 50 kN force on the lower diagonals splits equally amongst both diagonals.

Ah again, I'm so silly! Makes perfect sense now :)

Almost through the paper! ^_^

I'm a bit confused with question 5, since the two vertical sides of the portal frame are not at the same length, I'm ending up with too many unknowns when resolving vertical, horizontal and moments. At the top right corner is a hinge and I'm aware that the moment there is zero (but perhaps could you explain how that could be of significance?)

I have four equations so far, please let me know if they're correct. Thanks :)

Edit: I did managed to calculate Horizontal forces somehow, HA (Horizontal at point A) came out as negative twelve and horizontal at B came out at zero. This sounds incorrect to me however. :/

 

[PhanthomJay]

I'm a bit confused with question 5, since the two vertical sides of the portal frame are not at the same length, I'm ending up with too many unknowns when resolving vertical, horizontal and moments. At the top right corner is a hinge and I'm aware that the moment there is zero (but perhaps could you explain how that could be of significance?)

I have four equations so far, please let me know if they're correct. Thanks :)

Edit: I did managed to calculate Horizontal forces somehow, HA (Horizontal at point A) came out as negative twelve and horizontal at B came out at zero. This sounds incorrect to me however. :/

It is incorrect, but almost correct. First, you have some plus/minus sign errors in your calcs with your assumed reaction force directions. Beyond that, you need another equation..the ones you have are not enough. You should draw a FBD of the left vertical member encompassing the support at A and the hinge. Looks like a 2-force member. That may help .

 

[allblue123]

It is incorrect, but almost correct. First, you have some plus/minus sign errors in your calcs with your assumed reaction force directions. Beyond that, you need another equation..the ones you have are not enough. You should draw a FBD of the left vertical member encompassing the support at A and the hinge. Looks like a 2-force member. That may help .

I'm really out of ideas with this one unfortunately >_< I did a free body diagram at the left vertical member but I'm not quite sure how I can derive the last equation from it.

I noticed that I had vertical reaction at B the wrong way, which made the previous horizontal force at B positive. Can you help me with the last equation perhaps? :) thanks

 

[PhanthomJay]

The diagram shows a hinge at the top left corner, not the top right corner as you stated in Post 13. I assume the diagram is correct.

Try drawing a FBD of that left vertical member. There are unknown horizontal and vertical forces at the support and unknown horizonatl and vertical forces at the hinge. Try summing moments about the hinge or support, and see what you get.

 

[allblue123]

First question: find the horizontal displacement (extension?) of the horizontal member

My attempt: I have eliminated all the zero force members and calculated forces in remaining.

However, for the work done equation I'm not sure whether to use 200 kN as the force or the total force in the system and also for the distance whether to use only the span of 200kN beam or span of all the non zero force members.

The same as for the strain energy, do I use 200kN force for calculating the stress (force/area) or the total force in the members?

------------------

Second question: Determine the location along the web where the stress state could have been measured.

I attempted sketching the possible deflected shape of the beam and determined which zones are in tension compression. (The answers as I'm aware of are zone 3 and 5 however I'm not sure how to get to that conclusion)

 

[allblue123]

One more attachment :)

 

[PhanthomJay]

Since these questions are not related to the original questions, I suggest you delete these last 2 posts and repost your 2 questions separately under a different topic. You'll get more help from others this way.

 

[allblue123]

Since these questions are not related to the original questions, I suggest you delete these last 2 posts and repost your 2 questions separately under a different topic. You'll get more help from others this way.

Any chance that you could take a look at those question too? Its very last minute for me as I'm taking the paper on tuesday. :)

 

[PhanthomJay]

First question: find the horizontal displacement (extension?) of the horizontal member

My attempt: I have eliminated all the zero force members and calculated forces in remaining.

looks good!

However, for the work done equation I'm not sure whether to use 200 kN as the force or the total force in the system and also for the distance whether to use only the span of 200kN beam or span of all the non zero force members.

The same as for the strain energy, do I use 200kN force for calculating the stress (force/area) or the total force in the members?

Calculate the extension of each member under the actual loading and calculated force in the member. and calculate the force in each member under a virtual unit horizontal load (replacing the 200 N load). Then it's the sum of (all the virtual forces in the member times the individual calculasted extension of the member) to get the horizontal displacement of the horizontal member.. Force times distance is work, and work is change in energy.
------------------

Second question: Determine the location along the web where the stress state could have been measured.

I attempted sketching the possible deflected shape of the beam and determined which zones are in tension compression. (The answers as I'm aware of are zone 3 and 5 however I'm not sure how to get to that conclusion)[/QUOTE]

 

[PhanthomJay]

Second question: Determine the location along the web where the stress state could have been measured.

I attempted sketching the possible deflected shape of the beam and determined which zones are in tension compression. (The answers as I'm aware of are zone 3 and 5 however I'm not sure how to get to that conclusion)

Yes, you are looking for the locations in the web along the length of the beam members where bending stresses are positive (tension) and shear stresses are positive (acting downward on a left hand section).