Bending moment of I section beam

[cjdfromclm]

Homework Statement

Hi everyone this is my first post. I am having a problem with the bending moments of the beam (see attached files). I cannot for the life of me seem to get the bending moment to finish at 0 so I can draw the bending moment diagram. I know this is generally quite a simple process but I am stumped with this one. Please help :)

Homework Equations

I have attached a file with all relevant forces etc that I have worked out to get to this point

The Attempt at a Solution

I have also attached a file showing my attempt at adding the bending moments. As you will see BM@K =3 and it should =0?View attachment Q.pdf

View attachment Q..pdf

 

[PhanthomJay]

Hi there, welcome to PF!
You have rounded off the support reactions and thus get the non zero result at K. Even at J, you should see that starting from right to left, the moment should be 1500(1) = 1500 N-m, where you got 1497.
When finding support reactions, always sum moments about one support to find the reaction at the other, then sum moments about the other support to get the first support reaction, then check the results using your sum of forces = 0. In this way, you check your work to see if you made a math error.

Be careful drawing the moment diagram at the UDL piece ...you should draw a shear diagram first.

 

[cjdfromclm]

Hi Jay thanks for the reply.

I have tried using the full answer i got for the support reactions which are RA=3071.428571 and RB = 2178.571429 which results in me getting the answer BM@K =0.000003 is this close enough to zero? I am pretty sure it should be a flat zero I don't know where this 3 is coming from.
Note I have gone from left to right A-K working out the bending moments

Thanks Chris

 

[cjdfromclm]

I have also drawn the shear force diagram with the numbers rounded off and it comes back as zero. I had done this first so thought my figures were right rounded off.

 

[PhanthomJay]

Hi Jay thanks for the reply.

I have tried using the full answer i got for the support reactions which are RA=3071.428571 and RB = 2178.571429

reverse that

which results in me getting the answer BM@K =0.000003 is this close enough to zero? I am pretty sure it should be a flat zero I don't know where this 3 is coming from.
Note I have gone from left to right A-K working out the bending moments

Thanks Chris

The bending moments at the free ends of the beam (at A and K) must be 0. Using BM@K = 0.000003 is pretty close to 0, but using that answer would be wrong. In a problem with just a couple of significant figures, final results for the bending moments at various points in the beam should be rounded off to 2 significant figures before the decimal point. Or at least get rid of the decimals, please.

 

[cjdfromclm]

If I get rid of the decimals does this not leave me with RA=2179 and RB=3071 which results in me having BM@K=3??

 

[PhanthomJay]

If I get rid of the decimals does this not leave me with RA=2179 and RB=3071 which results in me having BM@K=3??

If you got the shear diagram to balance, use those values. Or else leave the values as is, except for the BM at K, it must be denoted as 0, same way you denoted the BM at A = 0. If you use any other value of the BM at A or K besides 0, whether it's 3, .00003, or .000000000000000001xx, your answer is wrong. At the other points, a few Newton-meters round-off doesn't matter much, but if you don't get it exact at A and K, it indicates you may not quite be fully understanding engineering concepts.

 

[cjdfromclm]

I used RA=2179 and RB=3071 for the shear force and it balanced. I've tried all sorts of rounding up and down and different decimal places and I can't get it to balance at zero for BM. It's got to be something to do with the decimal place.

Like you say it has to be zero I keep thinking I must be missing something but I've been over and over it. Surely I can't just make the result for K up.

 

[PhanthomJay]

I used RA=2179 and RB=3071 for the shear force and it balanced. I've tried all sorts of rounding up and down and different decimal places and I can't get it to balance at zero for BM. It's got to be something to do with the decimal place.

Like you say it has to be zero I keep thinking I must be missing something but I've been over and over it. Surely I can't just make the result for K up.

Don't make it up, prove it by working from right to left instead of left to right. Alternatively, note that 21500/7 = 3071.42857142857142857..., and that will get you closer to the 0 you are looking for. Or just leave it as is even leave it at 3, and make a note: "Due to round off error, this value should be 0, since the bending moment at the free end must be 0", and that might impress someone and earn you extra points.

 

[cjdfromclm]

View attachment Assignment q..pdf

I have attached my SF and BM workings for you to look at. showing BM answers both RtoL and LtoR. Working RtoL seemed to have solved the problem as the answers were all -3 of the LtoR workings up until BM@D that is when it all went wrong again.

I think it might be time to email my tutor and ask him what he thinks as I don't want to hand it in and get a low mark. This is straight forward stuff but its holding me back and I need to crack on.

 

[PhanthomJay]

View attachment 52791

I have attached my SF and BM workings for you to look at. showing BM answers both RtoL and LtoR. Working RtoL seemed to have solved the problem as the answers were all -3 of the LtoR workings up until BM@D that is when it all went wrong again.

I think it might be time to email my tutor and ask him what he thinks as I don't want to hand it in and get a low mark. This is straight forward stuff but its holding me back and I need to crack on.

Values of shear and moments look ok, and are not exact due to rounding off, but so what, they are supposed to be rounded, you already are off by a percent or so when assuming g is 10 instead of 9.81. Just be sure to denote the BM at K is 0 as I have already explained, and the
Tutor should be as happy as I would be, unless he or she wants to see more rounding to less sig figures.

 

[cjdfromclm]

The question said to assume g=10 so it might be that he expects us to round everything off. I've emailed him anyway no reply yet. Thanks for your help I'll let you know the outcome.

Cheers Chris