Concrete Beam Design

[cancmm]

I've been asked to look at designing a concrete beam that varies in cross-sectional dimensions. Essentially it has a flat and level top surface while the bottom surface is a shallow arch which results in a reduced beam depth towards mid-span. Would this configuration be analyzed as a simply supported beam or an arch? My problem with a shallow arch is that the lateral reactions are huge and I need this to be simply supported. The ends of the beam are restrained. Any thoughts?

 

[frv]

A sketch would help

 

[dcarr82775]

A sketch would be helpful, but is sounds like a tapered beam, not an arch.

 

[ToadJones]

sounds like you may be able to design it as a simple beam and if you dont need the arch depth, treat it as superficial.

 

[cancmm]

Sketch is attached.

I'd prefer to design it as superficial, but I don't want it to behave in a different manner and have the arch try to spread...

 

[frv]

What are your support conditions, and is this drawn roughly to scale?

I'm inclined to agree with ToadJones here, unless you have some funky support condition that would necessitate accounting for thrust (I can't really think of any, though)

 

[cancmm]

Not to scale, this is more of a general query at the moment. The ~3-4' deep beam would be approximately 30' long with a 1' rise in the middle.

The beam is simply supported (pinned at both ends) and therefore will be subject to thrust loads if applicable.

Do others concur with frv? I can't seem to come up with a good explanation as to why this would be designed one way over the other.

 

[ToadJones]

Well, I guess I would say this...with a slight arch on the bottom you are not likely to see any compression forces in the "arch" portion except for maybe very near the ends and therefore the beam is not really an arch.

 

[slickdeals]

If your sketch is to scale, I have a hard time picturing it behaving like an arch. But that's me. I am curious as to what others think. You can always design it as a beam and have a small vertical joint at the ends where the arch like portion meets the support if you are too concerned.

We are Virginia Tech
Go HOKIES

 

[cancmm]

Here's another thought on this. I think it's necessary to consider the alternative configurations to understand this one. See attached file.

Case A
This is the beam in question. Does it behave like an arch or like a simple beam? So far undecided.

Case B
This is clearly an arch. The only difference is that it has a little more concrete in the compressive zone at midspan of the beam as opposed to Case A.

Case C
This is clearly a beam. The additional concrete on top of the beam could be assumed as superficial.

Conclusion
To me, it seems that the orientation of the flexural steel is what governs the behavior of the beam. By slightly arching the steel over the span in Case A, you induce some compression into the steel as it is no longer perpendicular to the span. It then becomes a beam-column. This compression is transferred to the pinned supports as thrust. It is interesting to note that the compression will partially offset the tensile forces in the steel resulting from bending, which acts in a similar manner to prestressing.

How does this sound to everyone else?

 

[ToadJones]

From a classical standpoint an arch is 100% compression and would require no tensile steel.
IMO, none of the cases you show are necessarily an arch.

 

[rowingengineer]

complex and confusing.
The thrust can only be developed if the supports are rigid like abutments, if the supports are rigid the thrust will develop not matter what the shape, as long as the stiffness is correct.however to get check if a beam is an arch best to do a strut tie diagram.

An expert is a man who has made all the mistakes which can be made in a very narrow field

 

[cancmm]

TJ,
Agreed that this is not a classical "arch", but I used the terminology in describing the behavior for lack of a better one.

Rowing,
The supports are definitely rigid and the magnitude of the thrust would need to be calculated if it is an issue. My concern is that from arch theory: the shallower the arch, the higher the thrust. I hadn't thought about the strut-tie on this one as I rarely have the need to use it, but its definitely something to look into.

 

[BAretired]

With rigid supports, the member will try to act as an arch. If the large horizontal reactions are too much for the supports, they will move outward and the member will start behaving more as a beam.

For a very shallow arch, there is a danger of snap through, in which case the member must be designed as a beam.

BA

 

[htfptm]

As ToadJones suggested above, it is a beam unless it can't be. If you have the depth at center to be a beam, it's a beam. Like a scissor truss, just because it has the shape of an arch doesn't make it one (and that's a good thing).

 

[rowingengineer]

cancmm,
Are you sure the supports are rigid, as you have noted the force generate if these are rigid is high. so if the supports are not designed for this force they will deflect and not be rigid, and the arch will be a beam.

I have a feeling that this is a simple problem turned into a science experiment and we are not point this out because we don't have all the information.



An expert is a man who has made all the mistakes which can be made in a very narrow field

 

[csd72]

I have done this type of thing before.

Treat the top section as a rectangular beam with straight bars designed for bending.

Provide additional curved bars for temperature and shrinkage.

 

[ishvaaag]

Also, if the beam had not reinforcement, you would see the arced stresses within it by elasticity analysis. Adding the stirrups and rebar allows the structural member to behave (and be designed) as a beam. The corbel-like slope at the roots could classically be counted to reduce the required shear reinforcement at ends, something less likely in current design. more aware of compressive strut capacity.

 

[cancmm]

cds72/ishvaag,

Just to clarify, you are implying that the primary flexural reinforcement being continued straight through the beam? Then, additional reinforcement be placed on the bottom face to account for shrinkage and crack control?

 

[ishvaaag]

no, cancmm

I was remarking that the solid described when without reinforcement would contain inside the arch as the mechanism of resistance. By adding the rebar, that may follow of course the top and bottom faces for the longitudinal, and the stirrups, we allow the mechanism of Mörsch to form and then design it as a beam.

Of course one could decide to take only part, say a prismatic rectangular inscribed beam, and then hang the rest of the beam as dead weight.

In practice, in the same way than for sloped roofs, the arcing action will develop. Inclined roofs push the walls, and arced beams show inclined reactions on unyielding supports. You can't entirely fool nature by just adding reinforcement. However, once the necessary yield (lateral movement at the support) has occurred to relieve the push, this member if well reinforced as a beam would start to work entirely so.

Note that in the classical way of reinforcing these reinforced concrete beams, even the inclined push of the root corbels or arcing showed, for it was used to reduce the shear at the section, and so contributed to the vertical transmission of the load, then divided in shear and vertical component of the push. My seventies' copy of the reinforced concrete treaty by Montoya, Meseguer, Morán had quantification for the proper relief of shear to be taken when wanting to so account.

I assume in later years it was understood accounting this reduction of the shear due to the push was an unnecessary complication and then all the shear reinforcement was being dimensioned without any reduction from any inclined push. Then, also, only such (the total) shear was contributing as reaction on the column.