Concentrated Load Equivalents
Concentrated Load Equivalents
(OP)
I have a project that includes OWSJ's at 4' o.c. supported on a 30 foot W section. The layout is seven joists, evenly spaced. Load per joist is the same, so it's symetrical. My concern is the design of the W section beam.
On small stuff, I like to do the calcs by hand, however the deflection on this one gets a little hairy, so I used STAAD. I know about Table 3-22a in the Steel Manual, but that only goes to four loads per span.
Has anyone developed a rule of thumb where they assume uniform loading if there are so many concentrated loads? The difference between concentrated and uniform diminishes as the number of concentrated loads per span goes up.
On small stuff, I like to do the calcs by hand, however the deflection on this one gets a little hairy, so I used STAAD. I know about Table 3-22a in the Steel Manual, but that only goes to four loads per span.
Has anyone developed a rule of thumb where they assume uniform loading if there are so many concentrated loads? The difference between concentrated and uniform diminishes as the number of concentrated loads per span goes up.






RE: Concentrated Load Equivalents
Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask
RE: Concentrated Load Equivalents
RE: Concentrated Load Equivalents
Although if you wanted to check the deflection with your seven point loads, you could outsmart the manual and its limited tables by using superposition. Calculate the centerline deflection under each of your seven load and add them all up. I bet this is pretty close to your uniform load deflection.
RE: Concentrated Load Equivalents
RE: Concentrated Load Equivalents
Remember that in these situations even if you had a central point load you would usually only have half the udl in that point load.
If this is the case P=wL/2 and M=(wL/2)*L/4 = wL^2/8
As deflection is proportionate to the area under the moment diagram then the deflection in this case would be less than for the udl.
2 to 6 point loads are a bit more complex but also have a reduced load which helps keep the moment down closer to the udl.
RE: Concentrated Load Equivalents
Beam divided into n parts, for n-1 loads P. There are different formulas for even and odd divisions. The first part is the same for both:
CF=PL^3/192EI
When n is odd; dmax=CF.[1-1/n][3-(1-1/n^2)/2]
When n is even; dmax=CF.n[3-(1+4/n^2)/2]
Michael.
Timing has a lot to do with the outcome of a rain dance.
RE: Concentrated Load Equivalents
Deflection is overestimated when "smearing" the point loads to uniform. The moment curve for the uniform load case is outside the point load moment curve between adjacent loads. This means using uniform load is always conservative.
The error can easily be found using moment-area principles. Between adjacent joists, a uniform load would produce a moment of wa2/8 where a is the joist spacing. The area under that moment curve is:
A = 2/3(wa2/8)a = wa3/12
If beam is divided into n parts, then if n is even, there are n/2 areas of A each side of midspan.
Error in using UDL for deflection = (n/2)(A/EI)(L/4) = wL4/(96n2EI)
If n = 8, Error = 0.0125 or 1.25%
n = 6, Error = 0.0222 or 2.22%
n = 4, Error = 0.05 or 5.0%
The case of odd n is not included here.
Using a uniform load instead of point loads results in no error for moment calculation, but a slight overestimate for deflection calcs.
BA
RE: Concentrated Load Equivalents
Take a 12 foot span beam with five 1K loads 2 feet apart on the beam.
Considering the point loads, the moment is 9K'.
1(2 + 4) + 1(12)/4 = 9 K'
But considering the 5K load spread over the 12 foot span, the moment is 7.5 K'. .4167(12)^2/8 = 7.5 K'
That's a 20% difference. You can't make the blanket statement that a uniform load would be the same. It's not necessarily true.
Maybe for longer spans wqith a lot of point loads, but not short ones with a few loads.
Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask
RE: Concentrated Load Equivalents
I personally use UDL over the full length, but the UDL is calculated using the girder's full tributary area width. I know it's a little overkill, but I've almost always done it this way.
tg
RE: Concentrated Load Equivalents
RE: Concentrated Load Equivalents
BA
RE: Concentrated Load Equivalents
The moment and shear will be conservative with the uniform load at .5 klf applied across the entire length of the beam.
Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask