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Arching action in masonry: a fundamental question of its mechanics. 2

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WARose

Structural
Mar 17, 2011
5,594
Recently I had to design some masonry (which I haven’t messed with for years)……it was a pretty heavily loaded wall that had some openings that needed a lintel above them. For the purposes of the lintel design, I assumed arching action. (There was sufficient masonry above it for such an assumption.)

The literature on this subject (i.e. in most masonry texts) is a bit vague on what this “arching action” actually consists of. (BIA’s Technical Note 31A was somewhat helpful as far as thrust loads go.)

In the case I had, the wall was so heavily loaded that I wanted to follow the load path from stem to stern to be sure I understood what was going on and to get accurate loads. So what I did was declare a zone/area above the lintel as being my “arch”. I made the apex where the lines intersect (i.e. where you come off the end(s) of the lintel at a 45 degree angle) and selected a depth that seemed logical with the geometry. (I didn’t let the depth get into the triangle zone (that the lintel carries) except at the apex.) The thickness was obviously the wall thickness.

Given that, I analyzed the “arch” on some FEA software (modeling the arch only (uncracked), with the proper loading)……got my moment, shears, thrust, etc. I checked the arch itself (vs. the allowables in the code, and not forgetting it is a curved beam for stress calculations) and then checked the adjacent wall for the thrust and other forces. (To my surprise, (given that this was a major arch) some significant moment did develop in the arch, but the axial compression force tended to cancel out the net tensile force from bending [not always though].)

All that being said……does the approach sound right? I would assume this is what is intended with the so-called “arching action” over lintels (i.e. that is the mechanism as to how they are intended to behave)…..but the problem is (in a survey of the available literature), I just don’t see it gone into detail….in this case (due to the loads), I couldn’t just let it go.

Thanks.



 
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I appreciate it, but I have that. In fact, I was looking at it (in addition to my other masonry texts) a few days ago and thinking that's an example of how vague the literature tends to be on this topic.
 
I remember a professor who said that when he was in grad school he had to analyze the mechanics of a classic arch and that he wouldn't wish that upon anyone. At that point I decided not to worry about it any more. Not to dissuade your quest, of course, and I'd like to see the results myself, but there are only so many tasks I have the energy to take on.
 
WARose,

My understanding is that the masonry can only arch if there is enough block on the sides of the opening to provide a horizontal "buttress" force at the lintel level that keeps the masonry stable. Forgive the diagram below (and ignore the periods), but the mechanism I'm referring to is below:

..................o
................o...o
..............o.......o
---->....o............o..<-----
...........^...........^



For traditional (read: older) buildings made from mass masonry, the windows were small, the joints were non-existent, and the walls were massive enough to provide this restraint. So, the lintels could be designed to just carry the triangular load diagram for the masonry that isn't supported by the above mechanism.

BUT. If you are right next to the edge of the building or next to a soft joint in your block... the restraint forces cannot be engaged and the mechanism above isn't stable. Then its up to the lintel to carry the full weight of the brick above it without help.

That's the judgment call. Adding a window into an 100 year old church wall may be different than adding a window into a curtain wall brick veneer.


"We shape our buildings, thereafter they shape us." -WSC
 
I remember a professor who said that when he was in grad school he had to analyze the mechanics of a classic arch and that he wouldn't wish that upon anyone.


Yeah, when I was in Grad school, I did a project on masonry arches. And even going back into the literature I compiled on that subject I really couldn’t find much.

Today though, I was reading some masonry books on line (through Google books) and I came across one statement that basically said my original premise was correct: an arch forms over the lintel and transfers the force to the adjacent wall segments. (With the lintel carrying the masonry between the arch and the lintel.)

But if that is correct, than it isn’t just the horizontal/thrust load (that so much emphasis is placed on) that should concern the designer: it’s also the vertical reaction (which is typically half the total vertical load). If not properly accounted for it could overload the adjacent wall (since the reaction would be a highly concentrated load over a relatively short wall length).

The way most discussions of this are set up though, the vertical reaction really isn’t discussed……makes me wonder if they feel that it will never control….or if it is just one of those things they don’t go into (as academics) but we have to (as engineers).

 
I think that your analysis approach is correct. I would guess that most people do not get into doing a model of the arch, but rather figure out the horizontal thrust and the vertical reaction (by simple hand calcs) and check the adjacent wall for those two components only. At least that's what I've always done. Your moment in the arch does make sense, especially if you consider the two restraints to have some flexibility rather than fixed. To some degree this seems like one of those design approaches that has been validated by time and repetition and therefore most people are satisfied to leave it at that. No harm in doing a model though as you've done - might reveal something that you wouldn't catch otherwise.
 
I would guess that most people do not get into doing a model of the arch, but rather figure out the horizontal thrust and the vertical reaction (by simple hand calcs) and check the adjacent wall for those two components only. At least that's what I've always done. Your moment in the arch does make sense, especially if you consider the two restraints to have some flexibility rather than fixed. To some degree this seems like one of those design approaches that has been validated by time and repetition and therefore most people are satisfied to leave it at that.

The thing about it though is: my "arch" wasn't a slam dunk. It was close to not working in certain areas.....so that's one of the things that got me thinking on this.
 
Forgotten point here though guys - the lintel steel - not only serves to support a portion of the vertical load, but if extended into the sides of the arch, and the associated bond beam, as it should, serves as a tension tie to create a tied arch situation.

Mike McCann
MMC Engineering

 
Forgotten point here though guys - the lintel steel - not only serves to support a portion of the vertical load, but if extended into the sides of the arch, and the associated bond beam, as it should, serves as a tension tie to create a tied arch situation.

That's a good point: it could take out the horizontal thrust internally (if detailed properly).
 
Somewhat shocking at what little real information there is about this. I've looked through probably 20 design guides, manuals, and textbooks, and they all simply rehash the same general points as to when you can assume arching action exists. No more detailed analysis, no empirical investigations.

If anyone turns up something more rigorous, my interest has been piqued.

Brian C Potter, PE
Simple Supports - The history and practice of structural engineering.
ConstructionPic - Send annotated jobsite photos.
 
If you have an expansion joint at the opening, how can you count on arching?
 
That's a condition where I would move the expansion joint if possible. Otherwise, you're right.

Mike McCann
MMC Engineering

 
Didn't T.Y Lin develop some very thin shelled concrete structures? 4" concrete spanning ridiculous amounts is what I recall.
I wonder if doing some research about his designs might lend analysis methods for your masonry arch...

Just a thought.[bigglasses]
 
I suspect Jacques Heyman of Cambridge University will have written sometjing useful and interesting on the subject.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376
 
I suspect Jacques Heyman of Cambridge University will have written sometjing useful and interesting on the subject.



Actually I have his book on this subject (i.e. ‘The Masonry Arch’ (1982))……he certainly goes into detail on arch design itself…..but as far as this behavior within walls: I haven’t seen anything. (I checked again last night.)
 
I had a discussion with an Engineer from the Brick Institute of America. He recommended always adding some ladder wire in the bottom few course of brick to create a rudimentary reinforced masonry beam (in addition to the correctly sized lintel) At some point, if there is enough brick above the opening it is going to act as a deep beam anyway and not even load the lintel. If it did not, we would waaay more issues with brick veneer.
 
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