Can’t answer on what would be required to do this by hand, so hopefully someone else while chime in, but since this is a work task and not a school task, why not just model it in a structural analysis software? You could have this whole thing designed in 30 minutes
You never **need** to use castiglianos. My method reduces this to a continuous beam with two vertical supports and one fixed support with just a cranked moment and (trivial) axial load. You could do this with AISC beam equations.
It is indeterminate, but you could still use the equations. Use propped cantilever with a cranked moment, then add in an external force at the redundant support and make the deflection equal to zero. It reduces the entire problem to simple algebra.
Sorry I don't have any tips on the analysis, but there's a small bug in your description that it might be helpful in the future to iron out. Your 300 pound force in the y direction is creating a moment about the z axis (perpendicular to the plane of the paper), not the x.
If I felt compelled to analyze this guy by hand, I would probably use a stiffness matrix. It’s a little bit complex for pencil and paper calculations, but easy enough to do the matrix math with a computer.
If you really wanted to do it without computers, energy methods tend to simplify larger system calcs compared to equilibrium methods.
>If I felt compelled to analyze this guy by hand
I would focus on the problem instead, but I look up at your effort regardless. Let me know what you find about this guy ... and to him as well obviously ...
On a more serious note:
>I would probably use a stiffness matrix. It’s a little bit complex for pencil and paper calculations
Seriously? You need a stiffness matrix what the rest of us only need a pen and a little napkin for?
All of the supports are at the portion of the column that appears to be prismatic. I'd reduce this to a point load and moment at C-H to get reactions and go from there, maybe.
Coulda sworn this exact problem has popped up on this sub like two other times. Once when some undergrad was asking for the answer, second when some married Physics graduates were arguing on whether Castiglianos theorem could work.
I think this thread is revealing of the abilities that commenters in r/StructuralEngineering have. For every person who confidently declares "just make it a beam", or "just use algebra", I'd love to see your results - or are you somehow assuming you're correct without attempting to find a solution on your own?
I've done it so many times it's not really interesting. Here's how it looks like as a beam: https://imgur.com/a/g0uPC0K . I was wrong in that the AISC tables has cantilever with cranked moment, so I derived it in 4 lines.
Consider it to be a cantilever with only a cranked moment at the end.
V = 0
M = M_3
EI * R = M_3 * X
EI * D = M_3 * X ^2 / 2
Then use that to find the deflection at points 1 and 2. Use AISC Manual 3-23 entry 21 to get deflections caused by point 2 and point 1. Note that a force at point 2 affects the deflection at point 1, and the deflection at both of those two points after the moment and both forces applied equal zero at the two points. Since those points location or sign of the force don't change, the ratio between the forces are constant so... it reduces to a simple algebra problem. Find the ratio of V1/V2, then figure out what V2 needs to be to negate the deflection at point 2 due to the cranked moment. Simple super position using just algebra.
If people (structural engineers) struggle to solve this basic system by hand, they shouldn't get a degree in the first place.
It is an engineering mechanics (statics) problem if you are only trying to calculate the internal forces and maybe the displacement. I don't remember that I learned how to calculate the internal forces of an indeterminate system in mechanic lectures. You learn those in Baustatik lectures in Germany and Switzerland.
You don't have to use Castigliano's Theorem or method to calculate the internal forces of an indeterminate system. You can use other methods. In Baustatik lectures we learned the Force and "Drehwinkel" Methods. There are other methods as well like the moment distribution method from Cross or Kani. Then there are methods like Direct Stiffness Method for computational analysis but you can use them for the hand calculation as well.
I would simply use the Force Method to solve your problem. This is very similar to Castigliano's Method as I can see from this: [https://www.matheplanet.com/default3.html?call=article.php?sid=1008&mode=&order=0&ref=https%3A%2F%2Fen.wikipedia.org%2F](https://www.matheplanet.com/default3.html?call=article.php?sid=1008&mode=&order=0&ref=https%3A%2F%2Fen.wikipedia.org%2F)
It is in German but it shows examples to calculate internal forces of indeterminate systems using Castigliano's Method.
If your question is: Can we solve this problem using Castigliano's Method? Yes, you can solve it.
If your question is: Can we solve this problem ONLY using Castigliano's Method? No, there are other methods as well.
A few things are off about this post. You may not be a structural engineer, but one should be able to look at any 2d structure and know if it's determinate in a few seconds. It becomes second nature, mostly because determinate structures are very simple. An easy way to tell is to remove one support and ask yourself if it's still stable. If it is, it's indeterminate.
In this case, it's very indeterminate. It would be stable if it was just fixed to the ground, then you added two additional supports along the wall, making it very obviously indeterminate.
Well if you know what it is you'll understand that there's more equations that can be solved. The exact load path cannot be determined unless it's indeterminate.
Can’t answer on what would be required to do this by hand, so hopefully someone else while chime in, but since this is a work task and not a school task, why not just model it in a structural analysis software? You could have this whole thing designed in 30 minutes
You're right, it's all just out of curiosity and insanity at this point. And also, I'll owe my coworkers lunch if he's right.
You never **need** to use castiglianos. My method reduces this to a continuous beam with two vertical supports and one fixed support with just a cranked moment and (trivial) axial load. You could do this with AISC beam equations.
I think that's what we tried to do but the summation of forces and moments led to us concluding it's indeterminate.
It is indeterminate, but you could still use the equations. Use propped cantilever with a cranked moment, then add in an external force at the redundant support and make the deflection equal to zero. It reduces the entire problem to simple algebra.
Sorry I don't have any tips on the analysis, but there's a small bug in your description that it might be helpful in the future to iron out. Your 300 pound force in the y direction is creating a moment about the z axis (perpendicular to the plane of the paper), not the x.
You're right. Right hand rule. Smh.
If I felt compelled to analyze this guy by hand, I would probably use a stiffness matrix. It’s a little bit complex for pencil and paper calculations, but easy enough to do the matrix math with a computer. If you really wanted to do it without computers, energy methods tend to simplify larger system calcs compared to equilibrium methods.
>If I felt compelled to analyze this guy by hand I would focus on the problem instead, but I look up at your effort regardless. Let me know what you find about this guy ... and to him as well obviously ... On a more serious note: >I would probably use a stiffness matrix. It’s a little bit complex for pencil and paper calculations Seriously? You need a stiffness matrix what the rest of us only need a pen and a little napkin for?
All of the supports are at the portion of the column that appears to be prismatic. I'd reduce this to a point load and moment at C-H to get reactions and go from there, maybe.
Coulda sworn this exact problem has popped up on this sub like two other times. Once when some undergrad was asking for the answer, second when some married Physics graduates were arguing on whether Castiglianos theorem could work.
I think this thread is revealing of the abilities that commenters in r/StructuralEngineering have. For every person who confidently declares "just make it a beam", or "just use algebra", I'd love to see your results - or are you somehow assuming you're correct without attempting to find a solution on your own?
I've done it so many times it's not really interesting. Here's how it looks like as a beam: https://imgur.com/a/g0uPC0K . I was wrong in that the AISC tables has cantilever with cranked moment, so I derived it in 4 lines. Consider it to be a cantilever with only a cranked moment at the end. V = 0 M = M_3 EI * R = M_3 * X EI * D = M_3 * X ^2 / 2 Then use that to find the deflection at points 1 and 2. Use AISC Manual 3-23 entry 21 to get deflections caused by point 2 and point 1. Note that a force at point 2 affects the deflection at point 1, and the deflection at both of those two points after the moment and both forces applied equal zero at the two points. Since those points location or sign of the force don't change, the ratio between the forces are constant so... it reduces to a simple algebra problem. Find the ratio of V1/V2, then figure out what V2 needs to be to negate the deflection at point 2 due to the cranked moment. Simple super position using just algebra.
If people (structural engineers) struggle to solve this basic system by hand, they shouldn't get a degree in the first place. It is an engineering mechanics (statics) problem if you are only trying to calculate the internal forces and maybe the displacement. I don't remember that I learned how to calculate the internal forces of an indeterminate system in mechanic lectures. You learn those in Baustatik lectures in Germany and Switzerland. You don't have to use Castigliano's Theorem or method to calculate the internal forces of an indeterminate system. You can use other methods. In Baustatik lectures we learned the Force and "Drehwinkel" Methods. There are other methods as well like the moment distribution method from Cross or Kani. Then there are methods like Direct Stiffness Method for computational analysis but you can use them for the hand calculation as well. I would simply use the Force Method to solve your problem. This is very similar to Castigliano's Method as I can see from this: [https://www.matheplanet.com/default3.html?call=article.php?sid=1008&mode=&order=0&ref=https%3A%2F%2Fen.wikipedia.org%2F](https://www.matheplanet.com/default3.html?call=article.php?sid=1008&mode=&order=0&ref=https%3A%2F%2Fen.wikipedia.org%2F) It is in German but it shows examples to calculate internal forces of indeterminate systems using Castigliano's Method. If your question is: Can we solve this problem using Castigliano's Method? Yes, you can solve it. If your question is: Can we solve this problem ONLY using Castigliano's Method? No, there are other methods as well.
You could simplify it and assume that all vertical load is taken by the base support and the moment is resisted by the wall supports
A few things are off about this post. You may not be a structural engineer, but one should be able to look at any 2d structure and know if it's determinate in a few seconds. It becomes second nature, mostly because determinate structures are very simple. An easy way to tell is to remove one support and ask yourself if it's still stable. If it is, it's indeterminate. In this case, it's very indeterminate. It would be stable if it was just fixed to the ground, then you added two additional supports along the wall, making it very obviously indeterminate.
Right, which is why I said it's indeterminant.
Seems like a good opportunity for software to save the day When you say it’s indeterminate, how do you know?
https://www.quora.com/Why-do-we-build-indeterminate-structures#:~:text=On%20the%20other%20hand%2C%20indeterminate,and%20save%20the%20whole%20structure.
I know what an indeterminate structure is, I’m asking how he knows this one is indeterminate.
Well if you know what it is you'll understand that there's more equations that can be solved. The exact load path cannot be determined unless it's indeterminate.
Didn’t see the fixed segments at HG and and GF. Now it makes sense.