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Distributed Load vs. Point Load
2

Distributed Load vs. Point Load

Distributed Load vs. Point Load

(OP)
I had a SE size a beam for me that will be used to support three steel trusses (columns will sit under the two end trusses).  In his calculations, he assumed that the load from the trusses was distributed over the length of the beam.  The trusses are approximately 14' apart.  I'm trying to understand this.  Were the trusses 16" or 24" OC, a distributed load is easy for me to see.  When sizing a beam or a header, is there a truss spacing at which you would start to consider the loading a point load as opposed to a distributed one?

RE: Distributed Load vs. Point Load

14' apart is a definite point load.

Was the distrbuted load for something else??

RE: Distributed Load vs. Point Load

14' apart... yikes  I dont think the moment diagram nor the shear will even be close if you put it right next to distributed load diagram.

RE: Distributed Load vs. Point Load

I agree that 3 loads at 14' ought to be checked as point loads.

To the other part of your question - at what point can you look at a load as distributed? - it is a question of the length of the beam and the number and spacing of the loads.  For example, a 140' beam with 10 point loads at 14' on center might be assumed a distributed load.  In any case it's a judgment you develop by checking it both ways a few times.

RE: Distributed Load vs. Point Load

yeah, I agree with Millr, 140' with 10 point load at 14' o.c. will probably have moment diagram pretty darn close.  The maximum moment is slightly lower on the distributed one.  

RE: Distributed Load vs. Point Load

(OP)
Thanks, all.

I think I will take his calculated loads and create shear and bending moment diagrams in EXCEL.  I will then convert the distributed loads to point loads and do the same thing.  Then I'll take printouts of the diagrams back to the SE, explain my concern,  and ask him to re-evaluate his design.  Sound reasonable?

RE: Distributed Load vs. Point Load

Excel? sounds like a lot of work.  You dont have a structural analysis program?  Good luck!

RE: Distributed Load vs. Point Load

As far as I can see it, it's just 1 point load in the center, according to your original post.  Maybe you'll have a small distrib. load due to the deck or whatever else may be there.

In either case, you don't need a computer, or Excel to do this.

Just use superposition.

Point load - M= PL/4  V=P/2

Distrib. load -  M = w L^2/8    V = w L / 2

Hope this helps.

tg

RE: Distributed Load vs. Point Load

I like computers as much as the next person but take a step back here, it's an easy hand calc.  For a simply supported beam, 56 ft long with three equally spaced loads P, the moment at the center is 28P.

If we assume the total load of 3P is uniformly distributed along the beam, the moment at the center is 21P or 75% of the true moment.

You tell me if he's being unconservative. OK, OK, I'll tell you. Yes, he is.

RE: Distributed Load vs. Point Load

If the spacing of the trusses is half the span, then the moment ends up being the same.

The reason is that only half of the uniformly distributed load goes to the central point load (the other 2 quarters go to the trusses over the columns.

Therefore

P=wl/2
M = Pl/4 = wl^2/8 (same as a uniform load)

Compare the deflection:

Pl^3/(48EI) = wl^4/(96EI)

Compare this to the udl deflection of

5wl^4/(384EI) = wL^4/(76.8EI)

Point load deflection is actually less!

Shear is also half of the udl case.

The structural engineers calculations are conservative and safe.

RE: Distributed Load vs. Point Load

If the span is broken into an even number of equal spaces, the solution should be 'exact'.  If broken into an odd number of spaces, then the solution is conservative.  for anything other than 3 equal spaces, the degree of conservatism is small.

Dik

RE: Distributed Load vs. Point Load

2
Why not just call him up and ask why it's done that way?

RE: Distributed Load vs. Point Load

I am not following you guys.  Equally spaced point loads are always more conservative than distributed load.  The only time point load is less conservative is if you put it close to the column.

RE: Distributed Load vs. Point Load

COEngineer,

What you say is correct if your point loads add up to the same amount of load as the udl.

But in cases such as trusses, part of the udl will be supported by trusses outside the span. (i.e half of each purlin/batten load goes to each truss).

Follow my maths above, it is correct!

Shear will be higher though, if trusses were spaced close to one end.

RE: Distributed Load vs. Point Load

Two differing interpretations of the problem are used in the previous posts. One analysis assumes a 56 foot span with 3 points loads at L/4, L/2 and 3L/4 and the other assumes a 28 foot span with points loads at the ends and at L/2. csd72 assumes something different all together.  A restatement of the problem will have all engineers getting the same answer.

RE: Distributed Load vs. Point Load

You consider point loads as distributed when it doesn't make a significant difference.  For instance, the difference between the calculated moment using a single point load and using the point load as distributed over the beam is 100%.  that's significant.  When you have 7 point loads, the difference is about 14%, much more reasonable but perhaps not enough for some.

RE: Distributed Load vs. Point Load

Civilperson and UcfSE,

You both need to sketch the area up(including the trusses on each side of these trusses (i.e. 5 trusses total).

Follow the loads from roof level all the way down to the beam.

With a 28 foot span and trusses at 14 foot, each truss only picks up 14 foot worth of load. Your point load is then equal to wl/2 as noted above assuming w is taken as the average roof load per foot.

All my numbers are correct for this case.

RE: Distributed Load vs. Point Load

csd72, I was not addressing you and I do not need to review your "maths".  My post was directed to the OP who asked a general question.

RE: Distributed Load vs. Point Load

If, as described in the OP, the 3 trusses are 14' c.c. and there are 2 support columns, one each under the 1st and 3rd trusses, there is only a point load from the 2nd truss at the center of a 28' span.

M = PL/4 which will be greater than the moment from a distributed load.  P = the load from the center truss.  L = 2 x 14' = 28' (not 56').

As trainguy said, you don't need a computer.  You can use M = PL/4 and V = P/2.  You can also easily draw the shear and moment diagrams to get the design values.

RE: Distributed Load vs. Point Load

Example (with made up truss loads):

Load per truss = 10 kips
3 trusses at 14' c.c.
Support columns under 1st & 3rd trusses. Span = 28'.

M = 10 kips x 28 / 4 = 70 kip-ft
V = 5 kips
R1 = R2 = 15 kips

If the SE designed as a distributed load, he MAY have used the following:

Total load = 3 ea. x 10 kips = 30 kips
w = 30 kips / 28' = 1.071 klf
M = 1/8 x 1.071 klf x (28 x 28) = 105 kip-ft (> 70 kip-ft)
V = 0.5 x 28' x 1.071 (or = 1/2 x (3 x 10 kips) = 15 kips
V = 15 kips (> 5 kips)
R1 = R2 = 15 kips

Big differences between the point load analysis and the distributed load analysis (assuming the SE distributed the loads like I assumed).

As JStephen said, call and ask the SE.

RE: Distributed Load vs. Point Load

I suspect the engineer was distributing loads the same way as cds72 (but with 3 trusses not 5). If this is the case then the centre truss load is wL/2 and peak moment is wL^2/8.

RE: Distributed Load vs. Point Load

Ignore the bit about "3 trusses instead of 5". I misunderstood cds72's phrase.

RE: Distributed Load vs. Point Load

Why are the trusses 14' apart?  Are these holding up some kind of roof?  SIP's, I hope?

RE: Distributed Load vs. Point Load

depending on the load, 3" deck will span 14' continuously

Dik

RE: Distributed Load vs. Point Load

(OP)
Thanks for all the replies.

The reason I did not just go back to the SE for clarification was that I wanted to get it straight in my head first.

COEngineer was correct - getting the shear and bending moment diagrams out of Excel was alot more work than I anticipated.

Yes, Michfan, these trusses are holding up a roof.

PEinc - you got about the same result in 7 or 8 lines that it took me all afternoon to arrive at.  Using point loading, my maximum moment was 142 kip-ft.  The SE got a maximum moment of about 200 kip-ft using distributed loading.  This result was counter-intuitive to my way of thinking.  However, I am now convinced that his beam will work.

RE: Distributed Load vs. Point Load

So, if my assumed-for example 10 kip load per truss gave a point load moment of 70 kip-ft, your 142 kip-ft moment must have been caused by a 20.28 kip truss reaction.  Correct?  Your span between columns was 28ft?

RE: Distributed Load vs. Point Load

(OP)
The truss reactions were roughly 16 kips.  There was a small (relative to the truss load) distributed load that made up the difference (also, one of the columns is not centered directly under a truss - it is offset to the inside by 18").  I didn't mention it before because I didn't think it mattered in the overall scheme.  I was trying to understand what was done.

I still don't quite understand why a distributed load was used for the three truss loads.  True, it gave a higher bending moment and maximum shear which results in a larger beam being selected.  So it was more conservative.  But was it too conservative?  I'm not going to ask that it be changed, but it seems to me like a point-loaded beam gives a more realistic analysis.  I guess it was just a short cut to save time on the part of the SE.

RE: Distributed Load vs. Point Load

PatBethea,

You are looking at it from a mechanical perspective where you may be doing a design for 100000 cars(say) and even 1% would make a lot of difference.

In Structural engineering we are always designing 1 off structures and the additional time it takes to cut things down to the bare bones usually outweighs the savings. The material cost is only a proportion of the total build cost.

knowing the shortcuts is a big part of our profession.

RE: Distributed Load vs. Point Load

If we were talking about one or two beams, I might agree.  But if many beams are 30% over sized, pretty soon the dollars add up!

RE: Distributed Load vs. Point Load

If it's early in the design of the building, he might have used a conservative shortcut to leave room for error and revision down the line.

RE: Distributed Load vs. Point Load

I interpret the problem as a beam with a truss at midspan of the beam and a truss at each end where the beam is supported.  I would design the support beam using a discreet point load at midspan equal to the middle truss reaction, not a uniformly distributed load.  The moment would be equal to PL/4, where L = the beam span.

RE: Distributed Load vs. Point Load

What the SE did was perfectly acceptable.  Provided that you follow the correct tributary areas for each element, the PL/4 moment from the truss rxn is equal to the wl^2/8 moment that the supporting beam sees.  From the posts above, the most common mistake is dividing the point load by the length of the beam to get the equivalent distributed load.  
This will not work.  

Turn over an envelope:

Use easy numbers:

Draw a 10'x10' bay with columns at each corner.
Bisect the bay with one intermediate beam.
Use 50psf roof load
Analyze the south beam.

Using the point load:
Wtrib for intermediate beam = 5'
RXN from intermediate beam = wl/2 = 50x5x10/2=1250#
PL/4=1250*10/4= 3125#'

Dist. Load:
Wtrib of south beam=5'
w=50x5=250plf (NOT the 1250 from above divided by 10)
wl^2/8=250(10^2)/8=3125"'

Same moment.  Size beam, check shear and deflection.  done.

Take it further if you wish... try non-square bays, try multiple intermediate beams, draw the moment diagrams, and here's what you'll find:

Even number of spaces between intermediate beams means the udl moment will equal the point load moment.  Odd spaces mean a slight disparity, but the UDL moment is slightly more conservative, but it is much easier and quicker. I always use UDL unless there are 3 spaces.  

dik's above post said the same thing, only more succintly.

RE: Distributed Load vs. Point Load

If you have a point load, why not analyze it as such?  It's much easier to design the beam for a point load than to explain and prove that an assumed distributed load gives the same answer - sometimes.

RE: Distributed Load vs. Point Load

I agree... but the point to my post is that it doesn't matter which way he analyzed it.  Both methods yield the same answer.  I would have done it the same way as the SE.  

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