Is there thrust in a reinforced concrete arch?

[antimatter]

I am designing a reinforced concrete arch spanning 20 feet over a small creek. The creek is not 20 feet wide but the owner wants to be conservative.

I was wondering whether it is correct to assume that since I am designing for aashto loading of H20-44 shears and moments, do I need to worry about horizontal forces at the ends of the concrete arch? I am supporting the ends on 12 inch wide retaining walls with wing walls at each end. I would think that since the arch is designed to handle the moments and shears from the loading, I do not have any thrust. In other words, the arch is not handling the "thrust" like a true arch design, but rather it is designed as a reinforced concrete beam.

Is my assumption correct? Any help is greatly appreciated. Oh, and any recommendations for books on arch design would be nice too. Thanks in advance.

 

[Ron]

Depending on the radius of the arch, there will be some level of thrust. The tighter the radius, the greater the thrust.

 

[antimatter]

When you say tighter radius, are saying shallower arch or higher arch?

 

[Ron]

Higher arch

 

[flamby]

antimatter,

You can design it as a curved beam and you will see lesser reactions at the springing level as compared to those of arch reactions. The distinction of a true arch and a beam is important here. While beam takes up all the load due to internal moments, arch will just transfer the whole load to support by compressive forces only (no moments), thus a thinner section.

 

[StephenA]

Just to add to flamby's comments.

If you put a sliding support at one end, the structure will definitely act as a beam as there can be no horizontal forces.

As an arch you would have to take account of the horizontal movement in the retaining walls due to the horizontal loading from the arch.

StephenA

 

[KarlT]

I always thought (and maybe I'm wrong!) that if you designed an arch as a beam, then you could ignore the thrust at the supports. There may be horizontal loads from things like concrete shrinkage and thermal effects though.

 

[antimatter]

Does anyone have any recommendations for a sliding support. Since all the concrete will be cast in place, I can't really put a roller support beneath the support.

 

[StephenA]

The sliding support depends on the use and life of the structure. What is the arch for. i.e. what is the live loading for example?

To comment on KarlT's comment. The arch/ beam will act the way it wants to and a very curved beam will flex outwards under loading.

StephenA

 

[LPPE]

If everything is cast in place, I would consider both ends as pinned, which would then create a horizontal thrust. I'd imagine your abutments are probably more than adequate to resist the thrust, though.

 

[antimatter]

StephenA - The live loading is H20-44 AASHTO loading.

The rise on this arch is about 24" with a span of 20'. Is there a "rule of thumb" on when one should consider large horizontal forces depending on the rise to span ratio?

I don't anticipate much shrinkage since the span is at about 20' and the minimum thickness at the peak is 12". Is this assumption wrong?

 

[MotorCity]

Ignore thrust at the supports? Maybe I am missing something, but isn't this simple statics? Whether you want to call it an arch or a curved beam there WILL be an outward thrust at each location. The magnatude of this thrust of course depends on the geometry, location, and size of the loads. Once you have determined the reactions you should use your judgement and decide if they are negligible. Also, at least one of the supports must be a pinned or moment connection otherwise it will be unstable (i.e. you cannot have two sliding supports). Be conservative.

 

[connect2]

Right Motor City simple statics, one might also ask suppose the beam is horizontal but the support is inclined, there is a horizontal reaction if the elements or its supports are not orthogonal or if the load is not perpindicular while the element and its supports are etc... in any case all arches have a horizontal reaction component and you can do all the pinned/sliding, pinned/pinned modelling you want etc., etc., The Romans were very successful, after much failure I'm sure, with MASONRY arches which couldn't have a horizontal degree of freedom, ie translation with out failure. Mass was everything from there perspective, and some of them still stand!

 

[flamby]

Motorcity,

Technically, there is a difference when you call something a curved beam or an arch. Imagine you place a C shaped beam 90 degree rotated on a flat lubricated surface. Will it stand or flatten out? It depends on whether its rigid enough to take its own load or whatever load is applied to it on top.

antimatter,

You do not have to provide a real roller to achieve the sliding support. You can keep one end fixed and other end released by introducing a joint, tar felt or steel plate sliding supports. However, do not trust me over internet and go ahead with my advice as I don't understand the exact application. You have to act on your own and also design the beam correctly so that it acts in accordance with the assumptions.

 

[wiktor]

Yes, you can ignore the thrust if you were designing the girder as a curved beam, i.e. ignoring the thrust. In any case, with the ratio of 1:10, it's a very shallow arch, which will work as a beam.
For 20' span you will not need any kind of bearings. Provide pinned connections at both supports (you can use reinforced concrete joints), and let the wall of your abutment flex. You will have to compensate the movement of the structure with pressure relief joints at the ends of approach slabs.

 

[3dboy]

Guys, whether something is a "curved beam" or an "arch" is determined entirely based on the boundary conditions at the supports. If both ends are restrained against longitudinal translation, you have an arch. If one end is allowed to slide you have a beam. It does not really matter which way you go as long as you detail your supports consistently with your design assumptions. This is an area where young engineers often make mistakes so be careful. If you allow one of your supports to translate longitudinally (i.e. pin-roller) your moment will be much higher and there will be 0 thrust, but there will be horizontal translation in the longitudinal direction. If you restrain both of your supports (i.e. pin-pin) you moment will be lower, but you will have thrust. If the detail is screwed up and the bridge is allowed to translate or is not properly restrained then your moment will redistribute and you will have a higher moment than you designed for so be careful. Also you need to look into what lateral loads you might have, is this in the 100 yr flood plain? Is there any likelihood of scour? Will debris get caught in anyway and form an unintentional dam?