Stiffness method for fixed end moments

[PEin2010]

In the CERM 9th edition, example 47.6 talks about a beam with fixed ends and 2 hinges in between. I am not able to follow why the Moment, M AB = 2EI/L ???

They are using the stiffness method. I am following it until they find out the restraining moment vector. For the M AB, they are calculating nonzero moment at the ends of the bars corresponding to a unit rotation at Point B on the beam...I know it is to do with the moment curvature relation, i just don't know how curvature is coming to be equal to 2/L!!!

Any help is appreciated!

Thank you!

 

[civilized_naah]

In the CERM 9th edition, example 47.6 talks about a beam with fixed ends and 2 hinges in between. I am not able to follow why the Moment, M AB = 2EI/L ???
They are using the stiffness method. I am following it until they find out the restraining moment vector. For the M AB, they are calculating nonzero moment at the ends of the bars corresponding to a unit rotation at Point B on the beam...I know it is to do with the moment curvature relation, i just don't know how curvature is coming to be equal to 2/L!!!

Any help is appreciated!

Thank you!

I hope you are NOT spending a lot of time on time consuming methods such as Stiffness Method, Slope Deflection, Moment Distribution etc. if you are taking the Civil exam. There is no way you will be asked to do that in 5 minutes. If you are just trying to refresh the concepts out of intellectual curiosity, or from the point of view of the upcoming 16 hr Structural exam, where part of the exam is constructed response, then go for it.

To answer your question, if you look at the attached image, showing the slope deflection equations, you will notice that the near node response (effect) of a unit rotation (theta_n) is to produce a moment = 4EI/L times theta_n (which is =1 UNIT ROTATION), while the response at the far node is 2EI times theta_n. If you look at the layout of the solution to Example 47.6, they are constructing the terms for a unit rotation at B. So MAB will be 2EI/L while MBA will be 4EI/L.

It is not exactly the moment curvature relationship, which relates the bending moment at a point to the induced curvature at the same point. Not disconnected, but not exactly the same either.

 

[PEin2010]

In the CERM 9th edition, example 47.6 talks about a beam with fixed ends and 2 hinges in between. I am not able to follow why the Moment, M AB = 2EI/L ???
They are using the stiffness method. I am following it until they find out the restraining moment vector. For the M AB, they are calculating nonzero moment at the ends of the bars corresponding to a unit rotation at Point B on the beam...I know it is to do with the moment curvature relation, i just don't know how curvature is coming to be equal to 2/L!!!

Any help is appreciated!

Thank you!

I hope you are NOT spending a lot of time on time consuming methods such as Stiffness Method, Slope Deflection, Moment Distribution etc. if you are taking the Civil exam. There is no way you will be asked to do that in 5 minutes. If you are just trying to refresh the concepts out of intellectual curiosity, or from the point of view of the upcoming 16 hr Structural exam, where part of the exam is constructed response, then go for it.

To answer your question, if you look at the attached image, showing the slope deflection equations, you will notice that the near node response (effect) of a unit rotation (theta_n) is to produce a moment = 4EI/L times theta_n (which is =1 UNIT ROTATION), while the response at the far node is 2EI times theta_n. If you look at the layout of the solution to Example 47.6, they are constructing the terms for a unit rotation at B. So MAB will be 2EI/L while MBA will be 4EI/L.

It is not exactly the moment curvature relationship, which relates the bending moment at a point to the induced curvature at the same point. Not disconnected, but not exactly the same either.

Thanks!!! That clarifies it. Also thanks for the tip on not wasting time on those in-depth stiffness method, moment distribution etc, I think I was getting bogged down by the fact that I didn't know certain things and it was unnerving and so I just had to find out. Anyway yea I'm not going to waste more time on it. I'm really nervous about taking the structural depth portion, a lot of people have discouraged me saying its too difficult! .....Thank you

 

[IL-SE]

The structural PM is difficult but not impossible if you prepare for it. There may be one FEM problem out of 40 total, if even that. A good strategy on the exam is to skip any problems that you think will take more than 5 minutes, even the ones you know how to do but will take a while to solve. Then when you are finished with the shorter problems, you can see how much time is left and hopefully you'll have more like 10 min/problem rather than 6. Don't miss easy points because you are stuck on a problem.

More than one time during the exam I literally told myself "let it go!" I knew how to do the problem, but I just couldn't get one of the answers on the exam. When I worked a few more problems, I realized my mistake and went back and solved it. Time management is critical.

One other strategy I used was any problem I didn't really know how to do (or could maybe eliminate 1-2 answers), I just guessed and moved on. If it was something that I thought I might be able to look up, I'd spend 2-3 minutes, but that would be it. Don't save these all until the end or you might end up frantically bubbling all the unanswered questions. Remember if you have time you can always come back to it (that's what erasers are for).

 

[Hromis1]

IL-SE and others, in regards to your comments about time management and solving for fixed end moments, slope deflections etc....I agree, That advice is good for the civil structural exam,

But regarding the future 2 day structural exam format: Has anyone on this board gotten a good sense of the impact of the new test format with regards to long format answers? So many of the example problems use multiple techniques that take a lot of extended work. Simply solving for the rigidity in a frame can chew up a lot of time. (IE lot's of siesmic problems, story drift etc).

That is where I am currently spending most my time studying. I would like to hear other peoples input regarding this.

 

[IL-SE]

The NCEES SEII sample exam is a good indicator of content/format (make sure you download the errata). My understanding is the the content isn't changing much, just the format (combining multiple choice and essay into both days instead of keeping them seperate). The essay questions were fairly straightforward and didn't need any "fancy" analysis other than the portal method for moment frames. There may be some areas where you are asked to graphically sketch your solution (beam reinforcing, foundation wall, steel connection, etc.), but again they were straightforward.

I'd say the biggest thing on the essay questions is to state your assumptions (assume the deck fully braces the beam top flange, etc.) and cite your equations (AISC Table 3-11, ACI 8-32, etc.). It doesn't add that much more time and having an easy to follow solution goes a long way. If you interpolate between two values in a table, then write that.