masonry tee beam analysis help

huangyhg

masonry tee beam analysis help
i downloaded many of the tek manuals for assistance in a masonry cmu retaining wall. with a cmu retaining wall, you typically put the reinforcement at the back of the void. for example, a 12" cmu block would have roughly a   d = 8.625".  most of the masonry examples that i have are for walls and they place the reinforcement in the center of the void, therefore a smaller d is present and the kd is magically always in the face shell. where i am going with this, is with a larger d you will typically have a neutral axis nowhere near the face shell and you would need to proceed with the tee beam analysis (referencing tek 14-7a). the value for "k" that i btained from the rectangular beam analysis (eq 10) is positive. the value for "k" using tee beam analysis (eq 14) is negative. can anyone explain how/why this is? this would make the value of "kd" negative. is the negative value supposed to be used in eq 15-21? attached is the tek 14-7a manual.
as an aside, i'm aware of tek 15-7b for cmu retaining wall design. however, the reinforcement is chosen from tables and it also assumes fully grouted blocks. this is a pretty large wall, so fully grouting may not be the most economical solution.
also, using the negative value of "k" results in t not equally c. using the positive value of "k" results in t coming pretty close to c, which i'd guess is a rounding error. with c=d, i end up with a negative mr     this simple design is kicking my but lol   i'm sure i'm over analyzing it, easy for a newb to masonry to do i guess.
you cannot have a negative value for "k" because "kd" is the width of the rectanglar stress block. you must be making an error in your calculation.
yeah that i am aware of, which is why i'm caught off guard. i know this is not the code, but the pdf is attached. the formula for k is below:
k = (-as*n - t(b-bw))/dbw
so there is always a negative value for the first coef as*n and b is always greater than bw, so the second coef will be negative so the entire numerator will always be negative. see where i'm coming from?
i'm just not sure what the reason is for the negative signs in that equation. like i said above, using the absolute value of that k i get a c pretty close to t, which makes sense. t should equal c. using the equation for mr = c(2t/3)-t(d-kd/3-2t/3) gives a negative value for mr. that value of mr ends up matching exactly what i have in some cmu wall charts but the signeage really has me confused. either way i got the answer to match the charts but if anyone is familiar with masonry design and these tek manuals, please let me know what the deal is with this.
check another reference, there may be an error in the tek.
the tek eq 14 is incorrect. an older version of this tek has this equation. the square root term was left out of this printing. hence the blank space.
it should be k = (-as*n-t*(b-bw))/(d*bw) + sqrt((as*n+t^2*(b-bw))^2+t^2*bw*(b-bw)+2*d*bw*as*n) / (d*bw)
i would try to find an older version of the tek.
awesome, i knew it couldn't be correct. thanks for taking the time to type that long equation out lol. steve, is the equation for the mr in eqn 21 incorrect as well? i'm always getting a negative number for the moment capacity, unless there is something i'm missing. i'm using the positive values for c and t. i'll have to check it with the correct "k" value from the equation you listed above. i lack a good masonry manual, so the code and these tek manuals are getting me by until i can get a good reference.
do you happen to have an older tek that you could attach? can't find any others online. any other errors off the top of your head that i should watch out for?
i tried to scan my copy. you might want to talk to your local block supplier and get a copy.
thanks!!
not to beat a dead horse, but have you gotten negative values for the moment capacity (eqn 21)? even with the correct "k" value the second half (tension) of eqn 21 is larger than the first half of the equation (compression).