Loading on Studs 1

[slickdeals]

Folks,
Please see attached sketch. It is a situation where a steel beam is hung from underneath a slab to pick up a cantilever load.

Will the first row of studs see all the loads or will there be a different distribution? I would have analyzed this as a propped cantilever and got the resulting reactions and designed the studs for T/C loads. But would there be a different behavior in the stud group?

Your thoughts are welcome.

 

[Splitrings]

BAretired is correct, my assumption was that the slab and beam are infinitely stiff. I should have mentioned that in my post.

The only way the studs in each group carry the same load is if they are beyond the elastic range (plastic range).

 

[dhengr]

BA & Paddington:

Can I hijack this thread for a moment? I guess I just did. But, I’ll add that I think the above thread and this kind of question is a very good use of this forum. Whereas the thread below boarders on dangerous, and it may even be irresponsible on our part to respond to the latter, unless the person is told to go to his teacher or boss with this type of question. That teacher or boss should be right there, to guide that person and keep them from getting further into trouble, or to prevent them from doing something dangerous for total lack of understanding. One would hope that the boss knows what his/her underling does not know, so as to guide the underling properly, and our participation on this forum should not inhibit that from occurring at their office.

What ever happened to the thread with the simple beam with different length cantilevers at each end and the convoluted formulas, funny sketch and bad notation for calculating stresses at different locations “x” along the beam of total length “L”. Someone suggested that the moment must then be zero, for some reason, at one of the supports. Only a mathematician like Paddington could start to unravel that mess; and BA, you said that seemed like ‘a mighty difficult way to go about a simple problem.’

I saw that thread and started a response, then looked back at his sketch and formulas, and you two had already stolen half my thunder. You two guys are too quick for me. But, in addition, I was going to suggest that he calc. the two reactions, then draw the shear diag., and from that the area under the shear diag. would allow him to draw the moment diag. Then he could calc. the stresses anyplace he wanted. Rather than mix it all together with a bunch of funny notation and not have the vaguest idea what he was doing. The next time I looked, to post my thoughts, I couldn’t find that thread. Where does this stuff come from? And, where did it go? That is an awful way to do engineering or teach structural engineering concepts and expect the structure to remain standing.

 

[BAretired]

dhengr,

I know the thread you are talking about. Didn't realize it had disappeared. Could be a variety of reasons for pulling it. One could be abusive or inappropriate language on the part of one of the contributors.

BA

 

[BAretired]

dhengr,

Re your earlier post. I don't think there is any difference between the two theories. You are assuming that each stud in a 3 stud group carries equal load. Your statics for that assumption are correct, but you get the same result using Splitrings' assumption, i.e.:

A = 6, I = 3(3^2)2 = 54, P = 10, M = 85;

P/A +- My/I = 10/6 +-85*3/54 = 6.388 or -3.055
Multiply these by 3 and you have 19.167 or -9.167, same result as the "non-nutty dhengr".

The assumption that bolts in a group carry equal load is not correct for rigid bodies. For flexible slab and flexible beam, the correct answer can only be found when the relative flexibilities are considered.

BA

 

[hokie66]

There are a variety of reasons members redflag posts, and management makes them disappear if the reasons are sound. I don't recall the post in question, but it sounds like student homework, which is disallowed.

 

[paddingtongreen]

I remember the thread. I wasn't going to answer it, I just clarified which were the variable dimensions as they might be unclear from the diagram.

I worry that for as long as good computer programs have been available, engineers and designers don't get the chance to ask their structures all the intimate questions about their behavior that we dinosaurs used to have to do, so I only point the way and hope they will dig.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[paddingtongreen]

Back on subject, an additional support point in the interior span would control the slope of the beam at the support at the cantilever.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[slickdeals]

Lower the slope/rotation of the beam at the cantilever support, the more equally distributed the loads on the studs at that location. Right?

Assuming the supporting slab was rigid, the way to ensure uniform loading of a stud group would be to make the beam as stiff as possible.

Won't there have to be a compatibility of deformations in the stud group? Meaning if the first stud deformed/elongated a little, would'nt the load now want to go to the stiffer element (which would be the adjacent studs) and so on?

 

[Teguci]

Q1 - Will the studs see equal loading?
A1 - Only if the concrete fails.
Q2 - Will 2 studs (1) resist all of the loading?
A2 - No

My approach - Right (not left) connection is designed to take tension and any transverse loading of the beam - Use single plate turned perpendicular to the beam length for beam to slab connection. Design stud group for steel plate plastic hinge (weak direction)and max tension of steel plate to yielding. Failure is now isolated to the steel plate.

 

[Splitrings]

slickdeals,
You are correct. Two of the three studs would have to enter the plastic range and start to yield in order for all 3 studs to carry the same load.

 

[Splitrings]

With the strength reduction factors required for bolts and or studs you won't enter the plastic range under design loading. Therefore each bolt will carry a different load.

 

[BAretired]

slickdeals,

Assuming the supporting slab was rigid, the way to ensure uniform loading of a stud group would be to make the beam as stiff as possible.

That is not true. Making both slab and beam rigid ensures the stud loads are not equal.

Won't there have to be a compatibility of deformations in the stud group? Meaning if the first stud deformed/elongated a little, would'nt the load now want to go to the stiffer element (which would be the adjacent studs) and so on?

Yes, I agree. Strain compatibility will determine the various stud loads. The concrete slab, the steel beam and the studs are all straining, so they would all have to be considered.

In the case of the concrete slab, creep deformations would scuttle any attempt at calculating a precise answer.

BA