Masonry - radius of gyration and section properties 3

[BurgoEng]

Intially, I was going to simply post a question about how to obtain the radius of gyration(r) for a masonry wall, because it is needed per ACI 530 for axial load capacity. I managed to finally find a table from the NCMA manuals (TEK 14-1A), that gives the "r" value for various reinforcing spacing, which is exactly what I was looking for...although I am still not sure how it's obtained.

The problem/question I have now is that these tables also provide Area, I, and S values for walls, but the values in the tables do not match other tables I had previously been using for Areas (net or otherwise) except for the fully grouted/sold wall numbers which are a perfect match.

For instance: say 8"wall grouted at 40". TEK gives Anet=42.8in/ft, Aavg=51.2in/ft but my other tables gives A=58in/ft. Which numbers are correct...and why does it seem like Masonry design standards are all over the place when it comes to procedure, equations and properties.

 

[USFEngineer]

From what I can remember the radius of gyration (r) is calculated from square root of (I/A). For example an 8" wall with grout spacing of 40" on center (walls assumed to be 55% solid) Area = 57.00 in^2/ft. and I = 377.08 in.^4/ft. r = 2.57. Note: that average values should be used to calculate r.

As far as the difference in the values I would look closely at each table. For some tables it could be for the differnce in block densities i.e. light weight block, medium weight or normal weight. Also, in the NCMA-TEK tables I have found several values that are incorrect.

 

[concretemasonry]

BurgoEng -

The tables in the NCMA TEK Notes are very conservative. Generally they use the minimum face shell and web thicknesses required by ASYM C90. For the net cross-sectional properties in Table 3, there is no additional structural credit give for the average thicknesses, corner radius, core configuration (1,2 or 3 cores), etc. In reality, these always exist and do contribute to integrity.

The other tables you have, they may have been based on the average values for a particular manufacturer's units that are dictated by market demand and not just ASTM minimums. This could be why your only agreement was for solidly grouted walls where the individual element dimensions and configurations are not a factor.

If you have major use, you should contact a local supplier to determine the availablity of different units and strengths. If it is a minor use, the NCMA tables would be more than adequate.

There is actually no one standard 8" block. a typical block producer may have 4 or 5 units that could be used. This is due to local market demands and not the minimal outdated ASTM requirements. The same applies to the strength of a block. A producer cannot afford to make a minimal strength unit, so the typical cured strength may be 50% above the ASTM requirement. Other manufacturing aspects produce the higher strengths without regard to the ASTM standards. If you actually need very high strengths most producers can easily produce units 2 to 4 times the ASTM minimum strengths if required.

Masonry design is somewhat different than some other designs where you are analyzing individual elements. - That is one of the reasons for prism tests that are based on the actual units used to construct the wall. This test is a prime example of the lack of effect of mortar strength on the compressive strength of a masonry wall where a 50% lower mortar strength will actually have a minor effect (5%?) on the prism or wall strength.

Unfortunately, the structural design and use of masonry in the U.S. has lagged behind some other countries. In some areas, the construction of 15 to 20 story loadbearing concrete masonry buildings using 6" "partially grouted/reinforced" block has been common for the past 20-30 years using codes essential the same as ACI 530.

USFEngineer -

For the structural properties, the figures are independant of the density since all block must meet the same ASTM loadbearing standards. Due to some "quirks" in the ASTM C140 testing procedure two block, made in the same mold, of different densities will have very minor differences in the percentage of solids. The measurement of the block elements is not affected by the density.

 

[lkjh345]

ConcreteMasonry:

Thanks for taking the time to explain all of this. Very informative post.

 

[BurgoEng]

concretemasonry,

Phew, that was a mouthful. Thanks for all the info. To be honest, I don't know exactly where the tables I have with the larger values originated. There are copies, of copies from someone I used to work with, and there is no reference on them. Having only really just begun designing with masonry, I have only just discovered the TEK's and was concerned. I read through the TEK again and saw where it was assuming (2)square holes, minimum face shells, etc... so it sounds like you were correct in saying TEK assumes the worst....which isnt' always a bad thing, in being conservative.

 

[Galambos]

If this can be inferred from the previous posts, i apologize. per ACI 5.13.2 and 5.13.3 the Moment of Inertia and Radius of Gyration used in stiffness calcs are calculated based on the average net cross sectional area, whereas, the Area and Section Modulus for strength calcs are calculated on the minimum net cross sectional area.

In other words for strength, we dont consider the webs because they aren't necessarily buttered (i believe). However, it is permissible when dealing with stiffness calcs to consider the web.

It would be nice if someone could explain why it is permissible for stiffness. anyone?

 

[Tomfh]

Stiffness is a function of all cross sections combined whereas strength is a function of the weakest cross section.