Fixed-Fixed beam with several point loads 4

[bwanamukubwa]

Good day everyone,

I'm working on a support beam for a vessel and trying to determine the maximum deflection. There are several point loads at various positions between the fixed-ends of the beam.

I seem to have forgotten how to use the principle of superposition; can someone be so kind as to guide me on how to combine the deflections from all the point forces? I seem to recall something about checking if it is statically determinant.

Thanking you all in anticipation,

Ahmed.

 

[Ussuri]

I would recommend getting any structural analysis or mechanics textbook. They will cover it. Alternatively, try searching the internet.

The principle of superposition states the total deflection due to a number of applied loads is equal to the sum of the deflections if the loads are applied separately. It is only applicable if your load-deflection relationship is linear and any deflections are small (large deflections introduce second order effects).

Your structure is statically determinate if you can solve the system using the equations of equilibrium alone. If you cannot, it is statically indeterminate. Again, this is covered in the text books.

 

[GBor]

...the effect produced on an elastic system by any final state of loading is the same whether the forces that constitute that loading are applied simulatneously or in any given sequence and is the result of the effects that the several forces would produce if each acted singly.

In other words, add up the results...it's that simple. There are some exceptions. For instance, an axial load on the beam will increase the bending if a transverse load is applied that adds an eccentricity. This all also only applies to elastic situations.

 

[rb1957]

apply each load separately and sum the displacemnts.

you'll probably need to calc these from first principals, since roark or similar texts only give you the maximum deflection. but this isn't too hard.

if calcs fail, apply FEA !

 

[rb1957]

try excelcalcs.com, they might have the displacement solution for a doubly fixed beam with a point load

 

[ShaggyPE]

There are some good tables in machinery handbook and AISC steel manual for many statically indeterminate beam cases. I have a few pdf excerpts that I have attached to this post. I put them together when I was preparing for the PE.

-Dustin
Professional Engineer
Certified SolidWorks Professional

 

[ShaggyPE]

Here is the other pdf.

-Dustin
Professional Engineer
Certified SolidWorks Professional

 

[rb1957]

looks like case 17 in shaggy's 2nd post is it ...

 

[bwanamukubwa]

My first post to eng-tips and i got 7 replies within 5 hours! Many thanks to everyone, i really do appreciate everyones' altruism. I look forward to being of service in the same manner in the future.

Just one final point i need to clarify: with case 17 in the pdf, do i add simply take the deflections at each 'x' location along the length of the beam and sum them up? From experience, we know that the column diameter is approx. 5m, and with the loads, the max deflection in the center is approx. 5mm. Can this be considered small enough to ignore non-linear effects? What is a good rule of thumb to keep in mind in general?

 

[GBor]

I want to confirm that you are saying the diameter is 5 meters with a deflection at the center of 5 millimeters. If that is what you meant to say, then the deflections should absolutely be linear.

As for your statement with regards to the summing process, here's a simplification:

1 2
X_________________X
A B

X's represent the fixed supports
numbers represent loads at points A and B, respectively.

Load 1 causes a displacement of 'y' at point A
Load 2 causes a displacement of 'z' at point A

Total deflection at point A is y+z

You would have to examine the displacements at a specific point along the beam caused by each load and sum those point-specific displacements.

Hope this clarifies a bit.

 

[rb1957]

yeah, pretty straight forward ... for piece of mind calc the moments too, but if 0.5mm is all the deflection you're getting then there won't be a problem.

careful about the use of "column" ... usually implies an upright column; i think you mean a beam made up of a round section !?

 

[bwanamukubwa]

Basically a customer has asked us to verify static calculations that the vessel manufacturer has provided them. The process is in an upright column; it's either VCM or NH3 scrubbing, but the I-beam is welded to the vessel support ring.

So essentially, i would be looking at deflections at the center of the beam caused by all the individual loads. I think it's str8 forward from here.

Thank you once again to everyone for the replies.

 

[rb1957]

how much column load is the column supporting ?

 

[bwanamukubwa]

There are several packed beds and liquid distributors, but the greatest one is apporx. 29,000 kg. This load is the wet weight of the packing on the profile support grids. I'm not sure if you are familiar with profile support grids but i have attached two different illustrations of them. The ones i'm working on are similar in design to the one in the drawing, M350, whereas the one in the model shot is M165, a smaller profile.

At any rate, the profile rests on the support ring and the beams, so i figured it would be good enough to simulate the points of contact of the beams as point loads, so each profile has 2 point loads on each support beam. Advanced vessel design manual 3rd edition discusses weight distribution for beams and supports if you are interested in how the total weight of the packing is to be distributed on the profile support grids.

Do you have any experience with column/vessel supports?

 

[rb1957]

so the column load is comparable to the lateral loads ?

goggle "beam column", this is quite a different structure to the typical beam.