Stresses when lifting a beam 2

[maatjie_mike]

Hi,

The attached picture shows a scenario where a beam with 2 lifting points is lifted by a crane by a chain with 2 legs. My question is:

- When considering the beam, is the way I have added the three stresses together correct (Stress_tot)?

Kind regards
Michael

 

[robyengIT]

what about shear ?

 

[maatjie_mike]

Hi robyengIT,

Thanks for the reply, my main focus is on whether the way I added the bending moments is correct or not. To be honest I would not know how to include shear stress into this example. please feel free to show me how to.

Kind regards
Mike

 

[Joe591]

Wouldn't Fv also cause a moment? If you break a force up into components then you must consider the moments caused by both components. Also, I think Bmw will be in the opposite direction that it is drawn in

 

[maatjie_mike]

AJoe591 - Fv is the reaction force to the weight, BM due to the weight or BM due to the reaction force is essentially the same thing. So taking the BM due to the weight is all that is needed. why would the direction be opposite?

 

[rb1957]

Fh will cause a small bending moment on the beam (offset from the NA)

I don't like using a -ve sign for the compression bending stress. the compression bending stress does not have to be the -ve of the tension stress. At least that is what I think the 3rd term means.

I think you haven't combined the stresses correctly. The beam has two stresses acting on any section ...
1) normal stress due to compression (Fh) and various bending stresses, and
2) shear stress.

I would strongly advise a more rigorous approach to analysis.

1) the beam is suspended by the lift. You know the weight of the beam, and so the forces in the lift. Yes, I know you have Fh and Fv for the lift forces, but it helps relating these to w (or W*L)
2) then look at the beam ... a SS beam with a UDL. You can define the moment at any point; note the moment due the weight (w) opposes the moment due to the lift (Fv).
3) define the loads at any point (axial, bending, shear)
4) calculate stresses. Going straight to stress loses some of the connection of the parameters. For example, which stresses combine ? Eg shear stress is maximum at the NA where bending stress is zero (so it combines with the axial load).
5) be very careful about allowable stresses. the allowable for the axial compression is not Fcy, but column stress (Euler, well modified Euler ... a column with an offset load).

The error in your drawing is that you show M due to Fh and M due to w in the same sense ... they are opposite.
I also think your interpretation of (what I think is) von mises stress is incorrect. The axial stress due to Fh is directly additive to the bending stresses rather than being separate terms.
If I'm wrong (won't be the first or last time) please explain your stress calc.

another day in paradise, or is paradise one day closer ?

 

[JStephen]

If this falls under ASME BTH, see if they address stress/load combinations.
Otherwise, I would generally combine loads/stresses via the combined stress equations in the steel codes for a steel beam like that.
Also be aware that lateral buckling may be the limiting condition rather than stress.

 

[maatjie_mike]

Hi rb1957,
Figured this was the easiest way to respond, see green text below.

Fh will cause a small bending moment on the beam (offset from the NA) I know it will, that is why there is a BM_FH. Is there something wrong with this?

I don't like using a -ve sign for the compression bending stress. the compression bending stress does not have to be the -ve of the tension stress. At least that is what I think the 3rd term means. Im not sure what you mean here, I havent made anything negative (in the VM equation the negatives come from the formula not the direction of the variables

I think you haven't combined the stresses correctly. The beam has two stresses acting on any section ... What is the correct way to add them?
1) normal stress due to compression (Fh) and various bending stresses, and
2) shear stress.

I would strongly advise a more rigorous approach to analysis.

1) the beam is suspended by the lift. You know the weight of the beam, and so the forces in the lift. Yes, I know you have Fh and Fv for the lift forces, but it helps relating these to w (or W*L) Im looking for the approach here not the actual values, all I need to know is how to add the BM due to the weight and the BM due to F_H, why does it matter if they are in terms of W or not?
2) then look at the beam ... a SS beam with a UDL. You can define the moment at any point; note the moment due the weight (w) opposes the moment due to the lift (Fv). Yes that is why I have not included the BM due to F_V
3) define the loads at any point (axial, bending, shear)
4) calculate stresses. Going straight to stress loses some of the connection of the parameters. For example, which stresses combine ? Eg shear stress is maximum at the NA where bending stress is zero (so it combines with the axial load). How can I combine shear stress and axial stress without using VM?
5) be very careful about allowable stresses. the allowable for the axial compression is not Fcy, but column stress (Euler, well modified Euler ... a column with an offset load). Im going to use the axial compressive stress to do a buckling calc but I need to do a yield calc as well (one that includes the the relevant stresses (I think I only need to include the BM due to F_H and BM_W and Axial stress F_HC

The error in your drawing is that you show M due to Fh and M due to w in the same sense ... they are opposite. Why are they opposite?
I also think your interpretation of (what I think is) von mises stress is incorrect. The axial stress due to Fh is directly additive to the bending stresses rather than being separate terms. Ive never added a axial stress and a bending stress directly, the whole reason I am using VM is to add the axial stress and the total BM (combination of the 2 bending moments)
If I'm wrong (won't be the first or last time) please explain your stress calc. The stress calc is just plain VM from the text book, Im not sure what you are asking here

another day in paradise, or is paradise one day closer ?

 

[maatjie_mike]

Hi JStephan,

I dont have any of those codes so I cannot check, thanks though.

 

[saplanti]

Never put lugs in that direction for the shackle connection of the cable/chain lifting with angle. That will likely be cut the lug under bending and tension since it is in the weak axe direction.

In case you correct the lugs by rotating them by 90 degree of angle, the beam will be under axial load and the bending moment.

You need to check your local steel structure code or crane code or both, and design the beam in accordance with the action above with some certain of safety factor(s) to the code requirements.

The beam will likely fail under the actions by lateral torsional buckling before getting the allowable stresses.

Additionally you may need to involve shackle/pin joint calculation as well.

It seems, from your sketching and question, you are not familiar with structural design. I suggest you either consult a structural design engineer or give the job to one of them.

 

[maatjie_mike]

Hi saplanti,

The lug design is not considered here , the sketch is not accurate WRT the lug orientation, that is why I asked the question

"When considering the beam, is the way I have added the three stresses together correct (Stress_tot)?"

can you answer that question?

 

[rb1957]

I think your approach is flawed, because you're not following the typical analysis sequence.

Your approach, as I see it ...
1) sketch the loads applied (ok, nothing wrong with this)
2) deduce some loads produce bending or axial stress
3) combine these stresses with what looks like von mises equation

I think you should ...
1) sketch the loads applied. I'd use a FBD (Free Body Diagram) approach so you can see that each part is in equilibrium. I'd include the weight acting at the top of the lift. This'll allow you to see the load in each of the lift cables is W/sqrt(2) and Fh = Fv = W/2 (assuming 45 deg lift angle, but for any angle Fv = W/2).
2) Now determine the critical internal loads. Plot the SF, BM along the beam if you like (it is instructive). The key element here is the beam loaded by the UDL (w), so maximum moment is wL^2/8 (+ Ph*x). But looking at the plot you'll see maximum bending happens with zero shear, and maximum shear happens with zero (or small in your case) bending.
3) Now calculate stresses ... bending stresses are +ve and -ve and combine (sum) with the axial (compression) stress. You should track both stresses, but you can see compression is likely to be critical.
4) I'd combine stresses with principal stress equation.
5) Determine the appropriate allowable stress and resulting MS.

I think you're learning this material (to ask how to combine bending stress with axial stress is telling). I'd study a Strength of Materials text (rather than rely on what random people of the internet say).


another day in paradise, or is paradise one day closer ?

 

[maatjie_mike]

I think your approach is flawed, because you're not following the typical analysis sequence. I am not posting the entire 294 page design report that shows the whole sequence, I am obviously only posting the specific part I need help with

Your approach, as I see it ...
1) sketch the loads applied (ok, nothing wrong with this)
2) deduce some loads produce bending or axial stress
3) combine these stresses with what looks like von mises equation

I think you should ...
1) sketch the loads applied. I'd use a FBD (Free Body Diagram) approach so you can see that each part is in equilibrium I have done this. I'd include the weight acting at the top of the liftI am in no way interested in the weight acting at the top. This'll allow you to see the load in each of the lift cables is W/sqrt(2) and Fh = Fv = W/2 (assuming 45 deg lift angle, but for any angle Fv = W/2). this is obvious and I dont need help with this part
2) Now determine the critical internal loads. Plot the SF, BM drawing the SF and BM plots means I need to know how I should combine the 2 BMs which is one of the questions I am asking along the beam if you like (it is instructive). The key element here is the beam loaded by the UDL (w), so maximum moment is wL^2/8 (+ Ph*x)this is not the case because there are 2 BMs which AGAIN is one of the questions I am asking. But looking at the plot you'll see maximum bending happens with zero shear, and maximum shear happens with zero (or small in your case) bending.
3) Now calculate stresses ... This is the question I am asking bending stresses are +ve and -ve why is one positive and one negative? and combine (sum) with the axial (compression) stress and I did this using VM. You should track both stresses, but you can see compression is likely to be critical.
4) I'd combine stresses with principal stress equation. I have combined them using VM, why is this wrong?
5) Determine the appropriate allowable stress and resulting MS.

I think you're learning this material (to ask how to combine bending stress with axial stress is telling). I'd study a Strength of Materials text (rather than rely on what random people of the internet say). sorry I didnt know this was a platform to post things you fully understand instead of a place to ask questions about things you dont understand

 

[3DDave]

It could make sense if those components are orthogonal, but the diagram and equation have no vector components, just scalars. This is usually shown by unit-vector subscripts.

In a typical FBD the beam would be sectioned at the location where the stress was being evaluated, usually with the expected stress distribution graphically depicted.

 

[rb1957]

Ok, did not know (that this is a summary of a 294 pg analysis). Often what people post here is what they have.

No, you have not drawn a FBD.

Ok, you may not be interested in the weight acting at the top, but the structure is. And this is why your understanding of what's happening in the beam is so "limited".

And you are asking a very basic question (how to combine axial stress with bending stress, how to combine different bending stresses) so that raises my eyebrows ...

You can't draw a SF BM diagram ? You don't understand that the "two moments" are entwinned together, inseparable. There aren't two bending moments in the beam, just one (with two components).

The maximum moment in the beam IS wL^2/8 +Ph*x ... wL^2/8 is the combination of the UDL and the lift load.

"sorry I didnt know this was a platform to post things you fully understand instead of a place to ask questions about things you dont understand" ... no need to get snarky. This is meant for professional engineers who should know ...
1) how to sum moments together, and
2) von Mises isn't the answer to every stress combination.
Thus I suggested getting a Strength of Materials textbook which will cover these questions.

to answer your original question ...
"- When considering the beam, is the way I have added the three stresses together correct (Stress_tot)?" ... the answer is "no".

another day in paradise, or is paradise one day closer ?

 

[desertfox]

Hi Mike

I have done an analysis of a beam with lifting wires but I had to assume a neutral axis position in order to get the stress equation, I don’t think you need Von Mises stress ebquation for this and from my experience in lifting steel beams it’s only usually stress due to bending in the beam and the loading on the lifting points that matter, although I don’t have any information on the beam you are trying to lift. Anyway provided it’s not made of concrete or wood or some other composite material the analysis should be similar to what I have posted below.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

 

[saplanti]

Maatjie_mike,

I guess you did not read my post completely. Of course, the shackle connection is part of the design calculation, and your question was not on it.

First, you did not explain the problem adequately. You presented a picture and asked us a question that does not see the entire picture. So I felt that I needed to warn you. If you respond the responders as you did here you may not get answers any more. I see that you are new attender to the forums, I ignore it for this case.

Second, every structural application forces the designers to comply with safety rules all around the World. Therefore I suggested you to check the code rules to comply. I mentioned that there are other thing perhaps you need to involve, such as adequate load calculation, code load multiplication or safety factor to increase the load for your application, adequate derivation of axial load and bending moment. I have to remind you that you have not mention of the lifting mass/load yet. As it is the cable system is lifting the self weight of the lifting beam only.

Third, if you read the structural code you will find which stresses you need to consider for comparison to code allowable. As mentioned above, if you are following working stress method, you will have axial stress, bending stress and shear at several locations. Perhaps the beam centre will take the maximum bending moment and the axial stress. Bending moment will produce max compression stress at top and max tension stress at bottom face of the beam. The maximum compressive stress will be additive of axial stress and max compressive stress. However, codes will have allowable comparison in the different way. Therefore you need to check the code rules. You may have to additionally check the beam for lateral torsional buckling.

The last you may have to check the deflection of the beam to be able to work under small deflection theory, such as 1/250, 1/500,.... depending on your application suggested by the code.

I hope it helps.

 

[1503-44]

Your diagram and stress looks fine. But you don't seem to be considering lateral buckling. If its a round tube or square tube section, you're likely to be OK, but if its a WFlange, lateral buckling could be your most important consideration.

Statements above are the result of works performed solely by my AI providers.
I take no responsibility for any damages or injuries of any kind that may result.

 

[desertfox]

Hi 1503-44

I doubt lateral buckling would be a problem in this case because it’s only self weight of the beam that’s involved, there is because of the offset of the lifting points a constant bending moment but it’s about 25% more than if the lifting forces were just vertical.


“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

 

[1503-44]

Steel structural design (AISC) has minimum requirements for lateral bracing regardless of the applied load, just as they do for a KL/r ratio maximum for a 0 loaded column design, It seems misdirected to do a complete stress workup for ... self weight, yet simply assume we're good for lateral buckling. That should be checked before ever delving into stresses. Could save a lot of time with that simple pass/fail criteria, Structurally you still need to check it anyway because, if below minimum, allowable bending stress Fb has to be reduced to 75% of that for a compact section. The point being that maximum combined stress is not the only design criteria.

Maybe also worth a mention is that structurally (AISC), this is a beam-column, due to compression and bending load, so it also would need to meet minimum criteria of column buckling length, of which a 5m length could be significant, possibly reducing allowable compressive stress Fc.

Statements above are the result of works performed solely by my AI providers.
I take no responsibility for any damages or injuries of any kind that may result.