Moment Beam Problem - Fixed End and Propped Cantilever

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1. Hey, I am really struggling to derive the formula for M2, for Figure 17 of this site:

http://www.awc.org/pdf/DA6-BeamFormulas.pdf

How the hell do you do it?
2. Start by deriving the bending moment equation, then use the deflection equation.

Actually, that's probably of no use to you for deriving a formula. That's how I was taught to do such questions, but I never had to do any derivations; just find answers.
3. What?
4. (Original post by LukeySherlock)
What?
If you have already got the other values correctly (specifically R1 and R2) then it should be pretty simple to work this out by imagining a cut just where the cantilever meets the wall and taking moments here.

If you are starting from scratch... you need to begin to consider deflection boundary conditions, as with any statically indeterminate problem. You know that the end deflection must be 0 as it is propped. You can superimpose two solutions, one for the load, one for the propping force - use Figure 14 for the load (which will be an expression with P in it), Figure 13 for the prop (upside down of course - this will be an expression with R1 in it). Equate the two end deflections from each of these (as one exactly cancels out the other) and solve to find the relationship between R1 and P. Then resolve vertically to find R2 and find M2 as above.

This is assuming you are allowed to use the results from Figures 13 and 14! If not, these aren't too difficult to derive, and I will assume you already know how to do this. You could also get to the solution without using these results by writing down an expression for M(x) (in terms of R1, P etc), integrating twice to find deflection and rotation and setting boundary conditions for deflection and rotation at the wall and the prop.
5. Make sure you have your internal and external sign conventions consistent throughout.

First just equate the reactions with any external forces. Then, working from left to right along x of length l, relate the end reaction (and include any force as you come to it) with the internal forces. You can also do the same with bending moment diagrams too, but as I mentioned before, remember your sign conventions, particularly the internal ones.
6. (Original post by Smack)
Start by deriving the bending moment equation, then use the deflection equation.

Actually, that's probably of no use to you for deriving a formula. That's how I was taught to do such questions, but I never had to do any derivations; just find answers.
Only because you're doing a rubbish degree.
7. (Original post by Dorian10)
Only because you're doing a rubbish degree.
Given that my university wipes the floor with your university in terms of both graduates who are employed in graduate jobs and as engineering professionals we can safely say that that is not the case.
8. (Original post by Smack)
Given that my university wipes the floor with your university in terms of both graduates who are employed in graduate jobs and as engineering professionals we can safely say that that is not the case.
ROFL. The only sound engineering institutes in Scotland are Edinburgh and Glasgow. You attend neither of these, and you think your university beats ICL. Hilarious.
9. (Original post by Dorian10)
ROFL. The only sound engineering institutes in Scotland are Edinburgh and Glasgow. You attend neither of these, and you think your university beats ICL. Hilarious.
I'm pretty sure you're the guy who was doing a BEng and then wanted to follow it up with an MSc right? And you're also a civ eng at Imperial too right?
10. (Original post by Dorian10)
ROFL. The only sound engineering institutes in Scotland are Edinburgh and Glasgow. You attend neither of these, and you think your university beats ICL. Hilarious.
You applied for law at Swansea for 2009 entry. I checked a while ago to see what where you were studying engineering at and, well, I loled.

I got this when I searched for your posts again to show you the exact post where you said you applied for law at Swansea:

So I clicked on it and to show you the exact post and oh look:

Notice when you last edited it? Straight after you made this post.

So you do not study at Imperial (and if you had the grades to consider engineering at Imperial then you would not be considering law at places like Easy Anglia and Leicester), nor do you even study engineering.
11. (Original post by Peel)
I'm pretty sure you're the guy who was doing a BEng and then wanted to follow it up with an MSc right? And you're also a civ eng at Imperial too right?
No. He's a guy that is neither studying at Imperial or engineering.
12. (Original post by Smack)
You applied for law at Swansea for 2009 entry. I checked a while ago to see what where you were studying engineering at and, well, I loled.

I got this when I searched for your posts again to show you the exact post where you said you applied for law at Swansea:

So I clicked on it and to show you the exact post and oh look:

Notice when you last edited it? Straight after you made this post.

So you do not study at Imperial (and if you had the grades to consider engineering at Imperial then you would not be considering law at places like Easy Anglia and Leicester), nor do you even study engineering.
Lol buuuuuuusted! Another interesting point: Imperial civil engineering department does NOT do BEng. For some reason this guy reminds me of RBarack a lot - he also applied for law, went to Swansea and considered them to be undoubtedly "top 5" for engineering and he also previously applied for law, applied to very similar universities if I'm not mistaken too....
13. (Original post by Smack)
No. He's a guy that is neither studying at Imperial or engineering.
14. (Original post by Peel)
Lol buuuuuuusted! Another interesting point: Imperial civil engineering department does NOT do BEng. For some reason this guy reminds me of RBarack a lot - he also applied for law, went to Swansea and considered them to be undoubtedly "top 5" for engineering and he also previously applied for law, applied to very similar universities if I'm not mistaken too....
I think that he is actually RBarack.

RBarack liked to follow me around and nearly every post that Dorian has made in the engineering forum has been directed at me.

They both go to Swansea.

Both idiots, and very argumentative ones at that.

And someone that mentions engineering institutions in Scotland without Heriot Watt or Strathclyde clearly knows not what they're talking about.

Looks like I checked his posts just in the nick of time. I clicked "find posts by user" just a fraction of a second before he had time to save that edit. He came close, but no cigar.

15. Just before he edits, here's him claiming he got a 1st in his first year in the BEng ... at a university that doesn't even offer a BEng!
16. (Original post by Smack)
I think that he is actually RBarack.

RBarack liked to follow me around and nearly every post that Dorian has made in the engineering forum has been directed at me.

They both go to Swansea.

Both idiots, and very argumentative ones at that.

And someone that mentions engineering institutions in Scotland without Heriot Watt or Strathclyde clearly knows not what they're talking about.

Looks like I checked his posts just in the nick of time. I clicked "find posts by user" just a fraction of a second before he had time to save that edit. He came close, but no cigar.
Yeah Im quite sure it is him, but if it isn't sorry RBarack! The thing that sticks out in my mind is that both of them have an unhealthy obsession with university rankings. I also remember RBarack also saying he was on for a 1st, and that he'd go to the library after uni and work solidly for 3+ hrs to get that first as "2.1s were too common", which is pretty admirable but he got a 2.1 in the end. Pretty sad I actually know all this but he struck me as someone very career obsessed and seemed to have a bit of a chip on his shoulder about things.
17. (Original post by Dorian10)
Only because you're doing a rubbish degree.
Oh FFS. This is completely irrelevant to the thread.

Smack's original reply, "Start by deriving the bending moment equation, then use the deflection equation", is a completely valid way of going about this, if described perhaps a bit too briefly for someone who is struggling with a question. The final paragraph of my reply is basically explaining this method too just in a few more words!

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