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Concrete Beam Design

Concrete Beam Design

Concrete Beam Design

(OP)
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?

RE: Concrete Beam Design

A sketch would help

RE: Concrete Beam Design

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

RE: Concrete Beam Design

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.  

RE: Concrete Beam Design

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)

RE: Concrete Beam Design

(OP)
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.

RE: Concrete Beam Design

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.  

RE: Concrete Beam Design

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

RE: Concrete Beam Design

(OP)
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?

RE: Concrete Beam Design

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.  

RE: Concrete Beam Design

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

RE: Concrete Beam Design

(OP)
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.  

 

RE: Concrete Beam Design

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

RE: Concrete Beam Design

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).

RE: Concrete Beam Design

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

RE: Concrete Beam Design

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.

RE: Concrete Beam Design

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.

RE: Concrete Beam Design

(OP)
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?

RE: Concrete Beam Design

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.

RE: Concrete Beam Design

"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"

The risk with this is that excessive crack widths may develop due to the tensile reinforcement being located too far from the tensile face.

RE: Concrete Beam Design

I would also have concerns with trying to control the flexural cracks located on the soffit where the distance between the flexural reinforcement and soffit become excessive. I think it should be designed as a beam member, special consideration should be giving to the bearing reactions at the supports.

Has post-tensioning the member been discussed?

RE: Concrete Beam Design

Maybe the best option is to provide a little "cushion" each end of the beam so that arch action is not possible, then design the member as a beam.  This is not exactly an original idea.

BA

RE: Concrete Beam Design

I agree that it should be designed as a beam, but what is the the problem if it acts as an arch despite that?

RE: Concrete Beam Design

No problem, I don't think it would be wise to rely on it. For a span of 30' with a rise of 1' the majority of the design action will be flexure. The element will only be able to arch if the reactions allow it to arch. If the bearings allow a little bit of movement then all the compressive stress which is developed from arching will disappear as the structure relies on flexure to stand.

How is the element supported; Will there be an expansion joint at one end or will it be fixed (horizontally)?

If the flexural reinforcement is provided horizontally at the level h (with allowance for concrete cover), how the the structure be detailed towards the supports?

RE: Concrete Beam Design

BARetired,

No cushions will be required. Look at the amount of compression there will be. The thrust for this angle (1/2' in 15' change in centroid)would be enormous, resulting in very high compression stresses and very large shortening in the section, thus creating the snap-thru that you mentioned in your earlier post. If the shortening under compression is more than the length of the centroid - length of the span, then it must snap-thru. Then it is a beam.

Just design it as a beam and forget about the rest. A lot of bridges have been designed with far larger soffit curvatures and arch action is ignored. It is flexural.

RE: Concrete Beam Design

Yes,

The main bars should continue straight as otherwise it would tend to straighten under tension and could spall your cover. Yes these bars will become further and further from the bottom of your beam but so will the stress reduce as you get further away.

The curved bars are provided purely for temperature and shrinkage and will prevent bottom face cracking. These will attract some bending stress but it will be much lower than the main bars.

Additional side face bars may also be required.

RE: Concrete Beam Design

Quote:

These will attract some bending stress but it will be much lower than the main bars.

How can we make the assessment that the bars further away from the neutral axis will take a lower stress?

The way I see the problem and the acceptable design philosophy as directed by this thread is to design the beam as a prismatic section 3' deep along the entire span. Towards the ends of the spans, smaller bars are provided as face reinforcement to limit cracking.

What other practices are available to limit the cracking to the soffit of the beam where the distance from the flexural reinforcement to the extreme fiber gets close to 1'.  

RE: Concrete Beam Design

kikflip,

The justification is that bar stress is realted to M/d reduce M and increase d and the stress goes down.

There is also an intermediate stage where both sets of bars will be taking stress.

these things were being designed successfully long before engineers started worrying about crack widths.

RE: Concrete Beam Design

rapt,
You are correct.  No cushions are necessary.  

csd72,
The use of straight bottom bars is one solution.  Curved bars enclosed within ties designed to resist radial stress is another.  Personally, I prefer the latter but it is a matter of engineering judgment.

BA

RE: Concrete Beam Design

(OP)
Thanks all for your responses.  

BAretired,
Just to be thorough with this discussion, say the beam was increased in width sufficiently to be be considered a slab.  Span, curvature, thickness, etc. remains the same.  This would obviously preclude the use of ties from a practicality standpoint.  In your opinion, would straight bottom bars be the only solution if this were the case?   

RE: Concrete Beam Design

If thickness remains the same, that would be one heck of a slab.  I would still prefer to use curved bars and ties but there would be more of them.  The ties could be open at the top to facilitate placing the curved bars.

Straight bars are also an option.  A series of straight bars placed tangent to the curve at three or more points could be considered.  They would need to be generously lapped.

BA

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