Reinforced Masonry - Partial Grout 2

[RFreund]

Does anyone have any good examples for Partially Grouted Reinforced Masonry Walls subject to axial and bending forces?

I'm looking for one example of a wall subject to in-plane forces (shear walls) and one for out-of-plane forces with Axial Load.

I have read through most of the Reinforced Masonry Engineering Handbook, 6th Edition (great reference btw) however all of the discussion and examples involve solid walls (Except for a partially grouted wall subject to bending and shear only).

I'm trying to develop a spreadsheet or Tedds for word calc that can handle a partially grouted wall subject to in-plane or out plane forces. I believe the calc will be very similar to a solid wall except I need to adjust the compression area so that only the grouted cells, flanges and webs are used. From there I can use basic statics of equilibrium approach for ASD or Strength design.

Thanks in advance!

EIT

 

[RFreund]

Thanks, I'll take a look.

EIT

 

[RFreund]

Damn it. Errata.

Forgot the modular ratio...yikes.

More comments/questions later.

EIT

 

[RFreund]

In regard to strength design I have a few questions:

For walls subject to out-of-plane forces:

1.) The axial load (Pu/Ag (this is really Anet)) must be less than 0.2f'm. If the wall's slenderness ratio exceeds 30 than the axial load must be less than 0.05f'm. Is this correct? Looking at the RMHB 6th edition it appears that the steel does not contribute to Ag, correct? This seams low, what am I missing? For f'm=1,500psi the max compressive stress is 75psi if h/r=30? For ASD H/r=30 the Reduction factor is 0.95 which means the allowable axial stress is 0.95*0.25*1500=356psi.

2.) All walls are designed by an iterative process by checking the moment caused by the deflection due to out-of-plane loads and eccentricity of the DL/LL no matter what the slenderness ratio, correct?

3.) Does the slenderness reduction factor need to be applied? It doesn't seem like it should be applied as we are accounting for P-d and P-D effects.

EIT

 

[RFreund]

Oh crap.

So the slenderness ratio is h'/t not h/r which I was referring to in my example above. This is probably more reasonable - for an 8" wall you would be at about 20' tall.

Ok so my other 2 questions (2.) and 3.)) still apply. Couple additional comments:

2.) Going through the iterative process for checking moment then get deflection then moment again for all walls subject to axial and moment (no matter what the H/t ratio) seems like a lot of work. Unless you make a spreadsheet or something similar, no? So maybe I am missing something.

3.) It looks as thought the slenderness reductions only apply to shearwalls where you are not reiterating the moment-deflection calc.

EIT

 

[RFreund]

For completeness sake there were a couple typo errors.

EIT

 

[MisterBill]

Here is a link to some design calculation. There are alot of examples on this youtube site (Struct2009). They deal with both Masonry/Concrete design and Canadian Codes.

http://www.youtube.com/watch?v=8RliuJNL8Ys

Regards,

 

[DST148]

Late on this thread.....
@hokie66 - Thanks for the link
@JAE - Thanks for posting those two spreadsheets
RFreund - I have ACI 530-05. This is my interpretation of the provisions for strength design of masonry walls for out-of-plane loads:
Your posts dated Jan 12, and Jan 13: For engineered masonry the code does not have any specific slenderness limitations per say. The slenderness is accounted indirectly by:
a) Limiting nominal axial compressive strength of the member per eqns. (3 - 16) and ( 3 - 17)
b) Limiting factored axial stress at the location of maximum moment to 0.2 f'm for h / t <= 30, and 0.05 f'm for h / t > 30
c) Placing limits on mid-height deflections under gravity and combinations of gravity + lateral loads.

Iterations for calculating mid-height deflections are required for loadings under service gravity loads, service (gravity + lateral loads), and factored (gravity + lateral loads). I agree, spreadsheet or something similar is required.

 

[RFreund]

Thanks guys I've just about completed the strength design for out of plane loads.

JAE - thanks for the spreadsheats however they appear to be for full grout.

MisterBill - thanks for the video it was helpful. The codes are slightly different but helpful non the less.

It seems odd that the compressive stress is limited to 0.2f'm for any slenderness ratio and that you always have to use the iterative deflection process. I should note that for out-of-plane axial and bending it does not appear that the reduction factor for slenderness applies so I guess that's why you must use the iterative deflection method.

I will post the Tedds calc on Monday and I may turn it into a spreadsheet however I find that the 'Tedds' calc is easier to follow. Like a mathcad calc.

EIT

 

[DST148]

@RFreund: Your last post, "I should note that for out-of-plane axial and bending it does not appear that the reduction factor for slenderness applies..."
Though the code does not directly impose any limit on slenderness, the reduction factor for slenderness does apply. For strength design of reinforced masonry walls subjected to axial load + out-of-plane loads, instability due to slenderness is accounted for by ensuring that the factored axial load on the wall does not exceed (phi * Pn) given by equation (3-16) for h/r <= 99, and eqn(3-17) for h /r > 99.

 

[RFreund]

@DST148 I thought that the slenderness reduction (eq 3-16 and 3-17) would apply as well but for out-of-plane wall subject to axial and flexural loads I do not think they apply (for shear wall yes).

Here are my reasons (I only have an older code in front of me '02) Walls are addressed in section 3.2.5 where they address the limit to axial loads as 0.2f'm and 0.05f'm then stability is addressed with the P-D iterative method and they do not refer to eqn 3-16 and 3-17. However in section 3.2.6 they address walls for in-plane load where they do refer to eqns 3-16 and 3-17. Also in the reinforced masonry engineering handbook's design example of a wall subject to out of plane forces they do not use the slenderness ratio. They use the iterative P-D Method.

But now I'm left to wonder how do you handle columns or piers...Use the P-D method or enforce the slenderness reduction factor? The 2011 code and designers guide should be out soon...I may have to look into that..

EIT

 

[DST148]

@RFreund - I agree with you. Section on strength design of walls for out-of-plane loads does not refer to eqns. (3-16) and (3-17) directly. However,.....
I have Masonry Designers' Guide - 5th ed. which is based on ACI 530-05. There is a solved example for Strength Design of Masonry for out-of-plane loads., EX 10.4-5. It's a single story structure. Wall thickness, f'm, steel placement is assumed, and (phi.Pn)- (phi.Mn) interaction diagram is drawn. Check for adequacy of the section for strength is made after applying reduction per eqn. 3-16 or 3.17 to the interaction diagram. Then the adequacy of the section is checked for secondary effects per section 3.2.5, again using the interaction diagram.
For walls subjected to low axial loads, the author suggests that a moment-magnifier method would be more rational than the approach presented above in the Guide.

 

[RFreund]

Attached is the calculation I came up with following the reinforced masonry engineering handbook 6th edition. In this method you iterate the position of the neutral axis similiar to developing a P-M interaction diagram however you are also considering the secondary effects when iterating so you must also iterate the deflection of the wall. The required eccentricity should match the design (or section) eccentricity. Then check if phi.Pn and phi.Mn are > Pu and Mu.
Feel free to comment.

DST- so your saying that in the MDG they create an interaction diagram with phi.Pn and phi.Mn which does not account for secondary effects then they reduce these values by the "slenderness reduction factor" (eqn 3.16 and 3.17). Then they follow the PD method (per 3.2.5) to get a magnified moment and check this vs the interaction diagram but this time they do not the "slenderness reduction factor".
Then after this the author says that a moment-maginfier method would be more rational for small axial loads. Do they suggest a what the maginifer should be (equation)? My Nawny concrete book (end has masonry design) suggests b=1/(1-(Pu/(Anf'm*(70*r/h)^2))) for 45< h/r <60 but I'm not sure how it applies as it is not presented very well (IMO).



EIT

 

[RFreund]

and Tedds calc

EIT