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?

 

[apsix]

"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.

 

[rscassar]

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?

 

[BAretired]

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

 

[apsix]

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

 

[rscassar]

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?

 

[rapt]

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.

 

[csd72]

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.

 

[rscassar]

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'.

 

[csd72]

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.

 

[BAretired]

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

 

[cancmm]

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?

 

[BAretired]

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