Unreinforced Masonry Shear

[Qrs]

I am looking at the out-of-plane shear strength of an unreinforced masonry wall. My masonry code tells me the formula for the shear load applied is fv=(V*Q)/(In*b) and I understand this is the basic mechanics formula for the parabolic shear. My question would be how do I figure out the Q for my masonry wall?

If it is a solid section, I understand I can use 3V/2A. However, what if the wall is not grouted solid? Would I just do Q=ya, with y being the distance to the center of the face shell and A being the area of the face shell? In doing this, I would be neglecting the shear strength of the webs...I'm not sure the best way to approach this. Are these values tabulated anywhere?

Thoughts?

 

[RFreund]

You could include whatever area is grouted (i.e. full mortar bedding or just face shells, cores) I would think. You just need to take a certain section width to find your values (area, moment of inertia, first moment of area, width etc). The width depends on how regular the repeated pattern occurs. So if you have full motor bedding (web and face shell) then you could use 16" and consider the webs. Just multiply your V by 16/12.

If I remember correctly your width (b) would then be the width 3 grouted webs.

First Moment of Area

The question is what to use for allowable as this is not listed in MSJC. However it is recommended that the same values for in-plane be used.

Actually finding Q would be tough if you had an unreinforced wall where only the face shells and webs were grouted (if you tried to include the webs).


EIT

http://www.HowToEngineer.com

 

[FEM4Structures]

Please review NCMA TEK # 14-1B for the tabulated sectional values of different CMU Blocks. You may be able to find the pdf copy of TEK document on any masonry manufacturer website.

Thanks.

Thanks,

FEM4Structures

 

[Qrs]

Thanks FEM, but I have that publication and it does not list the first moment of area (Q), unfortunately.

RFreund, I think we are on the same page. To simplify, i think I would ignore the grout in the webs/cells, and rely on the face shells only.

So if I had an 8" block with a 1.25" thick face shells, I would say:

y = (7.625/2)-(1.25/2)=3.1875in
A = (1.25*8)=10in2 (for an 8" width)

Q=(3.1875*10)=31.875in^3 *(12/8) = 47.81in^3/ft

Am I missing anything? My justification in ignoring the grout/webs is because 1.) its easier to put in my spreadsheet, and 2.) i think for an unreinforced wall the tension due to bending is more likely to control.

Thanks for your help.

 

[RFreund]

Well at first that seemed right but I don't think it is.
In short, because there is no "shear flow" between the two faces when ignoring the web. When you find Q, you are looking for the first moment of area, of the area outside of your cut (aka the point where you are trying to determine the shear flow). So normally you would cut the center of the web and find the first moment of area using the area above or below this cut (the equation for the first moment of area would be similar to what you stated plus half the web). However in the case of no web I would say half the shear goes to each flange (face shell) and then since each face shell is rectangular I would use 3V/2A.
So in the end I would have fv=3*V/(2*(2*Af)).




EIT

http://www.HowToEngineer.com

 

[Qrs]

Thanks RFreund. I've been pulling my hair out thinking about this and differentiating shear flow and horizontal shear stress from vertical shear stress. I think I agree with what you say, but I am only going to use one face shell (assuming that the other could be in net tension due to bending.)

It's just very confusing to me. I do not understand why the code tells you to use VQ/Ib for reinforced masonry, but allows V/bd for reinforced masonry.

 

[a2mfk]

Why are you checking OUT-of-plane shear?

 

[Qrs]

It is a limit state, is it not?

 

[RFreund]

The reason is that unreinforced masonry is assumed to remain elastic, and that is the formual for the elastic stress distribution.



EIT

http://www.HowToEngineer.com