Masonry Design: Effective Compressive Width Per Bar 1

[wijgeng]

Hi,

I am studying for my PE exam and I stumbled upon this issue and I cannot wrap my head around it. Can any of you please provide some guidance?

The MSJC-11 Section 1.9.6 defines the Effective Compressive Width Per Bar as the least of:
a) Center to center bar spacing
b) Six times the wall thickness
c) 72 in.

Where does this effective width apply?

I have been looking through my text book from college and there is an example problem on the design of a concrete block wall under eccentric axial load.
The example has four parts:
1.) ASD - Unreinforced
2.) ASD - Reinforced
3.) LRFD - Unreinforced
4.) LRFD - Reinforced

For Part 1, the effective width does not appear to be used, but Anet is calculated per foot of wall.
For Part 2, the effective width is 48" because rebar is spaced every 48". An is not used, but the effective width b is used as 48" in the force equilibrium equation. For example:
P=C-T
2960lbs = 24,000*(4/3)/16*(kd/(7.625/2-kd))*(48)*kd/2-As*24,000*4/3
For Part 3, the effective width does not appear to be used, but Anet is calculated per foot of wall.
For Part 4, The effective width is "defined" as equal to 32" because of the maximum bar spacing, but the book then says, "therefore, b = 12 in./ft of wall." I don't understand why they say the effective width is 32", but then still use b = 12". Anet is calculated per foot of wall. For force equilibrium, they use:
Pn=C-T
659 = 0.8*f'm*0.8*c*(b = 12)-As*fy

Does the effective width as defined in MSJC 1.9.6 only apply to ASD design?

I hope this makes sense. Please feel free to request more clarity. Thank you in advance for any help!

 

[KootK]

I believe that the effective compressive width per bar is getting at the effective width of masonry face shell that can be used as the compression flange reacting against the tension in an individual reinforcing bar when walls are acting in flexure. Similar to T-beam flange width in concrete beams. As such:

1) It applies to both ASD and LRFD.
2) It does not apply to wall that have no reinforcement.

Disclaimer: I wrote this off the cuff rather than looking up the referenced code clause. I'm sure someone will correct me if I'm out to lunch.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[wijgeng]

That seems to make sense to me. My confusion comes from the fact that the LRFD example disregards this. The book recognizes that the effective width equals 32" based on the rebar spacing. Then they say, "Therefore, use b = 12 in./ft which completely contradicts their first statement. Maybe it is a typo and it is causing me angst for no reason!

Thanks for your response!

 

[KootK]

You're most welcome wijgeng.

Then they say, "Therefore, use b = 12 in./ft which completely contradicts their first statement.

There's no contradiction for the common case where the effective compressive width leaves no "gap" along the length of the wall. There, unit width calcs make perfect sense. Where gaps do occur, minor modifications would be required.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[wijgeng]

What would cause a "gap" that you are referring to? It seems to me that there would be no "gap" as long as the reinforcement is spaced less than the minimum of 6 times the wall thickness and 72". Is that correct?

 

[Celt83]

Is the wall in the example fully grouted or partially grouted.

If fully grouted or partially grouted and the effective compression block is in within the face shell then the design would be based on rectangular section and could be reduced down to a per/ft of wall design. If partially grouted and the effective compression block gets beyond the face shell then your into T section design and the effective width plays a roll.

 

[KootK]

Say you hand an 8" wall with bars at 72" o/c. Your max effective compressive width would be 6 x 8" = 48". So between each bar you'd have a gap of 72" - 48" = 24".

It seems to me that there would be no "gap" as long as the reinforcement is spaced less than the minimum of 6 times the wall thickness and 72". Is that correct?

It is indeed correct.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[wijgeng]

Celt 83, they are partially grouted in both cases. It also appears they are assuming the compression is only carried by the face shell for the reinforced examples. The unreinforced examples don't assume that though.

KootK, this makes perfect sense and backs up what the examples assumed. Part 2 states the 6x8" controls so they designed with b = 48". Part 4 assumes the 32" center to center spacing controls so they designed per foot of width.

Therefore, as long as center to center spacing of vertical reinforcement controls the effective width, the wall can be designed on a per foot basis.

Thanks to both of you for the help!