Fixed-Fixed beam with several point loads
Fixed-Fixed beam with several point loads
(OP)
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.
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.





RE: Fixed-Fixed beam with several point loads
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.
RE: Fixed-Fixed beam with several point loads
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.
RE: Fixed-Fixed beam with several point loads
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 !
RE: Fixed-Fixed beam with several point loads
RE: Fixed-Fixed beam with several point loads
-Dustin
Professional Engineer
Certified SolidWorks Professional
RE: Fixed-Fixed beam with several point loads
-Dustin
Professional Engineer
Certified SolidWorks Professional
RE: Fixed-Fixed beam with several point loads
RE: Fixed-Fixed beam with several point loads
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?
RE: Fixed-Fixed beam with several point loads
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.
RE: Fixed-Fixed beam with several point loads
careful about the use of "column" ... usually implies an upright column; i think you mean a beam made up of a round section !?
RE: Fixed-Fixed beam with several point loads
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.
RE: Fixed-Fixed beam with several point loads
RE: Fixed-Fixed beam with several point loads
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?
RE: Fixed-Fixed beam with several point loads
goggle "beam column", this is quite a different structure to the typical beam.