Simple Beam with Variable Ix
Simple Beam with Variable Ix
(OP)
Problem:
A person installing my companies product wanted to do field modifications to what amounts to a piece of 3.56in. x 4.375in. x 0.24in-thick tubular steel with a 2.5in x2.5in x 0.25in-thick “strong-back” welded to the back of it. They wanted to remove the strong back all together. I told them No because it would not meet code! They then asked if they could remove 4 feet from each end the strong-back, the total length of the original member is 13 feet. I told them I would have to get back to them…of course they were annoyed.
My shingleys Mechanical Eng. Design #7 does not go into detail of how to calculate a simply supported beam with a point load in the middle, given the beam has a Variable moment of inertia across the member. “The Google” (quote from G.W. Bush) has proved even less useful.
Could anyone point me to an internet resource that addresses this problem?
Or Kick my @$$ in the right direction…
Thank you!
A person installing my companies product wanted to do field modifications to what amounts to a piece of 3.56in. x 4.375in. x 0.24in-thick tubular steel with a 2.5in x2.5in x 0.25in-thick “strong-back” welded to the back of it. They wanted to remove the strong back all together. I told them No because it would not meet code! They then asked if they could remove 4 feet from each end the strong-back, the total length of the original member is 13 feet. I told them I would have to get back to them…of course they were annoyed.
My shingleys Mechanical Eng. Design #7 does not go into detail of how to calculate a simply supported beam with a point load in the middle, given the beam has a Variable moment of inertia across the member. “The Google” (quote from G.W. Bush) has proved even less useful.
Could anyone point me to an internet resource that addresses this problem?
Or Kick my @$$ in the right direction…
Thank you!





RE: Simple Beam with Variable Ix
RE: Simple Beam with Variable Ix
a 1000lb load in the middle
finding max deflection
RE: Simple Beam with Variable Ix
Mike McCann
McCann Engineering
RE: Simple Beam with Variable Ix
Thanks
RE: Simple Beam with Variable Ix
RE: Simple Beam with Variable Ix
Yes, mainly what I am looking for is y (assuming the beam is horizontal) which is dependent on I.
The typical equation being y=(W*l^3)/48E*I)
W= Weight
l=length of span
E= Modulus of Elasticity
I=Moment of Inertia
Although in my case I would be variable across the member.
The I=5 then I= 15 then back to I=5
RE: Simple Beam with Variable Ix
This works very well for members with a varying EI along the length of the member.
It will involve some integration, but will give you the answer you're looking for.
I have it in Hibbeler's text (I think 4th or 5th edition).
I'm sure it's in Timoshenko as well.
If you don't have access to one and would like the info, let me know and I'll scan the pages from the text and post them here.
I won't be able to do that until Wednesday, though. I'm off until Wednesday and my texts are in the office.
RE: Simple Beam with Variable Ix
The strong back is a piece of angle I assume,whats its orientation to the tube underside ie;-
----| or |
| |----
Regards
desertfox
RE: Simple Beam with Variable Ix
Using Strain energy method and a graphical method of intergration, I calculate that the deflection of the beam centre, with 4foot removed from the strong back at each end
will be 29.5mm or 1.161".
This assumes that the strong back is angle and one leg is welded to the underside of the tube ie the angle would be seen as an upside down L.
I'll try and post my working on Friday so you can see what I have done.
regards
desertfox
RE: Simple Beam with Variable Ix
Desertfox.
Close, the strong back is 2.5"X 2.5" sq. tubular w/ wall thickness of 0.25"
using stain energy w/out a strong back, I get 1.06"
y =((W*L^3)/(48*I*E))
E=28.5E6 in^4
I=5 lbs/in^2
W=2000lbs
L=156in
My first calculation with the Castigliano method gave me 0.777in... now I just need to check, everything.
RE: Simple Beam with Variable Ix
Just check your figures I get "I"= 9.67 in^4 without strongback not 5 in^2 as you posted.
In addition when did the load change to 2000lbs your earlier post gave a 1000lbs.
regards
desertfox
RE: Simple Beam with Variable Ix
sorry, a little confusing, the original part was rated at 2000lbs,
so I am trying to prove after modification:
A) 2000lbs is will cause excessive deflection
B) De-Rating the part to 1000lbs will be sufficient.
Sorry again,I had the units backworks...
E=28.5E6 lbs/in^2
I=5 in^4
The geometry of the 3.56in. x 4.375in. x 0.24in-thick tubular steel is a little to complex to decribe in words,
but it reduces the value of I.
RE: Simple Beam with Variable Ix
Like to keep my number crunching and calculus skills in practice when I can.
Well what I worked out won't be much use I suppose, but I assumed the main part was a box section even though I couldn't find it as a standard size in any list and assumed
that the strongback was angle.
Placing the centroids of each section in line vertically I worked out the second moment of area of the combined section
as well as the second moment of area where there was no strong back.
I split the beam in half and like you based it on strain energy, but used a graphical method so it was only an estimate.
If you can give details of the main tube and in addition the position of the neutral axis I'll have another go and we can compare figures.
Can you derate to 1000lbs if service conditions are 2000lbs?
desertfox
RE: Simple Beam with Variable Ix
Is it possible to upload a sketch of the tube.
regards
desertfox
RE: Simple Beam with Variable Ix
The application of the system (luckily) allows for de-rating of the system, other wise I would not consider this modification.
Like you said, I am trying to keep my number crunching sharp and learn new techniques to solve these problems. If it was not Christmas and things weren’t a little slow, I would have told the workers to fly a kite! I normal have better things to do.
RE: Simple Beam with Variable Ix
Okay but seeing you have already given the Ixx as 5in^4
if I knew where that neutral axis was relative to say the vertical depth of tube which I assumed to be 4.375" thats all I would need to compare our calculations.
However I'll leave you to decide what you comfortable with.
best of luck
desertfox
RE: Simple Beam with Variable Ix
I will check with my boss when I get back, I am not sure how things work with regards to such information, I know I have a sheet of info to give customers but it does not go into much detail...so someone couldn't make their own part.
RE: Simple Beam with Variable Ix
To get an exact deflection, calculate M/EI across the section then apply this as a load to the beam. The resultant moment graph is actually the deflection graph. This is a simplified method for the direct integration method.
RE: Simple Beam with Variable Ix
The stiffened part is less then half the span ie:- 13ft o/a
ten take 4ft off each end.
regards
desertfox
RE: Simple Beam with Variable Ix
After my two week vacation....I am just going to take the average method, with a design factor of two and call it good.... cuz their are now about 100 messages that I have to take care of
I did learn a little bit about the Castigliano methodd- intergration method... but will try to get back to it later....
IE: i will forget what I was doing and never do it until it comes up again