2 span beam with hinge question
2 span beam with hinge question
(OP)
I have two questions regarding a 2 span beam with a hinge.
The first question is if I have a 2 span beam as show in the attachment, how do I determine the bending moment on the beam if the length of both spans are L=10', the distance from the center roller is X=3' and w=10plf?
The second question is if I have the same beam as described above, how do I determine what X is in order to minimize the moment on the beam?
The first question is if I have a 2 span beam as show in the attachment, how do I determine the bending moment on the beam if the length of both spans are L=10', the distance from the center roller is X=3' and w=10plf?
The second question is if I have the same beam as described above, how do I determine what X is in order to minimize the moment on the beam?






RE: 2 span beam with hinge question
RE: 2 span beam with hinge question
RE: 2 span beam with hinge question
RE: 2 span beam with hinge question
You can probably take it from there...
RE: 2 span beam with hinge question
1) remove the central support, and solve statically; determine the deflection at the mid-support location.
2) without the applied loads, apply a unit load (opposite to the deflection from 1) and solve statically; determine the deflection at the mid-support.
3) then the mid-support reaction is deflection 1)/deflection 2), and find the rest of the reactions (and internal moements) statically.
Quando Omni Flunkus Moritati
RE: 2 span beam with hinge question
This looks like a homework problem but I want to know the answer anyway.
RE: 2 span beam with hinge question
This has got to be a homework problem, and the OP is a sophomore, right?
Mike McCann
MMC Engineering
RE: 2 span beam with hinge question
If you can use class 1 section, steel, and plastic design the moment will be 0.0858 ql^2 and there will be no impact on your max moment with alternate loadings, but your splice moment will change and your splice point should be at 0.172 of your span (I generally use approx 1/6 span).
Dik
RE: 2 span beam with hinge question
RE: 2 span beam with hinge question
RE: 2 span beam with hinge question
Here's some more info:
Mike McCann
MMC Engineering
RE: 2 span beam with hinge question
The second question, I can't answer because it has been so long since I was in University. If I had a need for that concept on a project, I would just set up a simple Excel worksheet and iterate x manually until I got a fairly exact answer. But I don't see how this particular thing would ever be a question on a PE exam.
RE: 2 span beam with hinge question
RE: 2 span beam with hinge question
Dik
RE: 2 span beam with hinge question
RE: 2 span beam with hinge question
Dik
RE: 2 span beam with hinge question
RE: 2 span beam with hinge question
RE: 2 span beam with hinge question
Print it out and turn it around!
Mike McCann
MMC Engineering
RE: 2 span beam with hinge question
The splice location for a uniform load would be at 0.25L. The reaction would be 3/8 the total load with 1.25 being the centre reaction, and the max positive moment would occur at 3/8 of span, or 3/4 of span to PZS. The max +ve moment would be R^2/(2*q). Simple statics for this problem...
Dik
RE: 2 span beam with hinge question
I never heard of Gerber.
It was years ago (before we had computers in the office), we had all these glulam beam roof systems in warehouse type buildings, and of course someone demanded that we come up with the most economical (smallest weight of glulam overall) solution.
We got really burnt out from doing so many of those by calculator and pencil/paper.
RE: 2 span beam with hinge question
RE: 2 span beam with hinge question
I assumed if you made the maximum positive moment in the backspan equal the maximum negative moment from the cantilever, you wouldb minimizing the moment.
From that, using beam tables, I set the moment equations at those two locations equal to one another. You get an equation that has a^4, so I solved with mathcad and got .168L
I ran it in FEA, and got .17355L, so I tried it another way - I noticed in FEA that the positive moment in the beams are equal even when I vary the right span, so I set the right positive moment equal to the cantilever moment, and got 0.1715L, which was still not correct.
So I am stuck...
RE: 2 span beam with hinge question
RE: 2 span beam with hinge question
RE: 2 span beam with hinge question
Years ago I read in Engineering News Record that the greatest structural analysis software in existence is...Excel. I can't disagree.
RE: 2 span beam with hinge question
we've got two 10' spans, yes? total load = 105*20 = 2100
LH+RH = 435+1231 = 1666 ??
if the RH beam is effectively SS, then the LH is statically solvable, with a tip load of w(10-x)/2 (and the UDL)
then LH reaction will be w(10+x)(10-(10+x)/2)/10 - w(10-x)/2*x/10
and the moment (in the LH beam) will be M(y) = LH*y - wy^2/2
maximum at y = LH/w = (10+x)(10-x)/20 - (10-x)x/20 = (10-x)/2
Quando Omni Flunkus Moritati
RE: 2 span beam with hinge question
Archie264,
Yes, and the irony is I refused to learn it at first because I thought it was simply accounting mathematics - oriented, and had no idea it had all the Boolean logic and table lookup (and even some database) functions we need. But back in those days we used Enercalc a lot.
RE: 2 span beam with hinge question
Sorry, I forgot to write divide by 2 for the half-span. =But the 435# applied at the cant end is correct.
RE: 2 span beam with hinge question
gjc
RE: 2 span beam with hinge question
We were approaching this as an academic exercise. It took me less than as minute to iterate the x-value. Now that I have it set up, I can use it in the future with ease.
RE: 2 span beam with hinge question
Yeah, I prefer Excel to MathCAD. I find it easier to use and even think it might be more powerful. Others' mileage may vary...
RE: 2 span beam with hinge question
There are several other things to consider in this beam arrangement problem. You should consider the potential of unbalanced loading. For all the fine tuning of the moment and splice location, you may not be able to find a W17.83x60.326 which has the exact Sx you need; and then you will not want the spice to fall at the exact location where a joist or truss frames onto the beam, since you don’t want a truss seat right on the splice. You don’t want a bunch of different length beams in the same area, so you’ll pick a few common splice locations. And finally, you have to pay attention to beam bracing at the canti. tip and over the column, at the -M.
RE: 2 span beam with hinge question
The first question seemed to be a basic EIT test question, and the second one, I doubt would be on the PE exam.
In defense of Excel vs old-fashioned thinking and slide rules, since I used slide rules in University until my senior year, I agree...however there's a lot of thing that Excel can be set up to check that would be too time-consuming to do even by slide rule or design chart.
I probably forgot the rules of thumb of which you are familiar, because I haven't done a cantilever system since 1980. But I still do cantilever beams on Excel, because in my type of work they have horribly complex loadings.
The skip loading is easy in Excel because it is a piece of cake to apply and remove span-specific loads.
What you advocate is typical of engineering practice before Excel was popular, but I guarantee you that it ensured that I was working on weekends instead of with my family.
On the other hand, I agree 100% that any engineer that uses STADD or Excel exclusively without never doing the old-fashioned methods will become merely an input technician. The trick is to find a good balance.
I used to like tables and charts but in my line of work, the loadings are just too complex to ever allow those to be accurate.
RE: 2 span beam with hinge question
BA
RE: 2 span beam with hinge question
hmmm, just noticed that - I didn't see that before. What I did was write down the problem in my own fashion, and correctly wrote down L-x.
RE: 2 span beam with hinge question
The load on the cantilever is equivalent to a concentrated load of wL/2 at the tip, so Mcant = wLx/2.
Moment will be minimized when the negative moment at Support 2 is equal to the positive moment in the other two spans,
i.e. when wLx/2 = w(L-x)2/8
Solving this quadratic equation, we find that x = 0.1516L which was found by dhengr above.
BA
RE: 2 span beam with hinge question
2nd part, iteration is good but complicated (for me) by compression face bracing field location limitations.
RE: 2 span beam with hinge question
It doesn't depend on the tools, it depends on how you use them. You can use Excel to plug numbers into someone else's spreadsheet, or you can use it to work from first principles, or anything in between. You can use STAAD to do a complete design for you, or you can use it to understand how the structure behaves under different conditions. The same applies to "hand calcs"; you can plug numbers into a formula found in a book, or you can work to improve your understanding of how the structure behaves.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: 2 span beam with hinge question
RE: 2 span beam with hinge question
I got 0.1715L by plugging into Excel, and structSU10 got 0.168, 0.1715, and 0.1735 depending on what computer method he used.
Was your 0.1516L a typo?
RE: 2 span beam with hinge question
The thing I like so much about Excel is you can goal-seek or adjust the inputs so easily to see what changes in how the structure behaves
RE: 2 span beam with hinge question
BA
RE: 2 span beam with hinge question
x = L(3 +/-√8)
= 5.828L or 0.17157L with only the latter value within bounds.
BA