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Masonry Arching Action

RFreund (Structural) (OP) 
10 Apr 12 22:50 
Has anyone seen any methods for determining thrust or how much masonry is needed on the side of an opening to consider arching action. It was late and I doodled what I thought may be an appropriate method for determining the length of wall required each side of an opening. Only problem is that it is not much and I'm not sure I have given it enough thought so I apologize in advance if I'm way off. I should also mention I did not apply a live load, only self weight. EIT www.HowToEngineer.com 

If I read it right you are basing the thrust on the moment in the lintel? If that is what you are doing I do not think that is correct. The thrust comes from the load not supported by the lintel( i.e. the load above).
I think you could approximate the thrust as equal to the vertical load that is corbeling(sp?) over the lintel for the 45 degree you show. The flatter the slope you assume the higher the thrusts get. 

RFreund (Structural) (OP) 
11 Apr 12 11:15 
Yeah basically I said you have a 45 degree 'failure line/path' so the load below the 45 degree triangle is the load on the lintel. Then I said that this same triangle acts as a triangular truss  2 compression struts and the bottom being a tension tie. The load on this triangle truss is basically the weight of the masonry that fits into another 45 degree triangle on top of the lower triangle (which is above the opening). I can try to clear this up with an additional sketch. EIT www.HowToEngineer.com 

dik (Structural) 
11 Apr 12 12:08 
Although 45 is common, some references use 60deg, and in Amrhein's book (1st ed), he indicates 30 may be more appropriate... that's the angle I use for determining the shear capacity of the remaining joint.
Dik 

DST148 (Structural) 
14 Apr 12 15:45 
@RFreund : I agree with dik, the dispersion angle could be from 30 deg to 60 deg. We take a very conservative approach: for designing the lintel we assume 60 deg, but for calculating thrust on the pier, we assume 30 deg. For simplicity let us assume 45 deg. Also for discussion purposes let us assume the opening is 8'8" wide, lintel is 10 feet long with 8" bearing on each side. The wall height is 10 feet above the top of lintel. For design of 8" high lintel  self weight + triangular weight of masonry(2000#). Lintel will be designed as a regular concrete flexural member with effective depth of about 6inches. Even if masonry lintel block is proposed, the design approach for the lintel would remain the same. For thrust on the pier on either side, I agree with dcarr82775.  Total weight of masonry for arching = (10' x 10' @ 80  2000#) = 6000#. Thrust on each pier @ 45 deg will be about 3000#. If hollow unreinforced masonry is used for piers, then shear will be calculated using (V.Q/In.b) and not just (V/An). We always use fully grouted reinforced piers. Arching action also requires adequate depth of masonry above the apex of the triangle. Moreover, if floor loads are applied below the apex of the triangle, no arching is considered and the lintel is designed for load from the wall to the underside of the floor directly above and the load from the floor directly above. 

RFreund (Structural) (OP) 
14 Apr 12 19:22 
DST  So basically you are saying the weight inside the rectangle above the opening acts on the masonry arch/truss. Also when you say the shear would be VQ/(In*b). V = thrust against the pier, where b = wall/pier thickness? What I am trying to determine is how much wall is needed each side of the lintel so that arching may be considered. This is why I was using the face shell width only to resist shear/thrust. What are you thoughts on this? Would you say that the pier can resist this thrust? Would you then check the pier as if it had a point load (the thrust) applied at the elevation of the lintel and in the plane of the wall (sorry kinda thinking out load here)? EIT www.HowToEngineer.com 

JAE (Structural) 
15 Apr 12 12:44 

DST148 (Structural) 
15 Apr 12 14:42 
@JAE  Thanks for a very useful link. 

DST148 (Structural) 
15 Apr 12 15:01 
@RFreund: The expression for shear in unreinforced masonry is from ACI 53005. For partially grouted masonry b should be the effective thickness of the masonry at the point in question. 

RFreund (Structural) (OP) 
15 Apr 12 18:20 
Thanks guys. @JAE Thanks I will have a look through the article. I'm trying to finish up that partially grouted shearwall calc. It seems there are many different ways you can skin that cat. EIT www.HowToEngineer.com 

RFreund (Structural) (OP) 
17 Apr 12 22:52 
So the only part I'm in question on is what to use for d or the depth of the arch. Would you assume a 45 (or 30 deg) and use the 'truss/arch' depth. See attached comparison. If you have time let me know your thoughts. Thanks again!. EIT www.HowToEngineer.com 



