Longitudinal Reinforcement for Torsion, ACI 318-14, 9.6.4.3 - Units 2

[MGMtulsa]

Ref:
1. ACI 318-14, 9.6.4.3, equations (a) & (b)
2. ACI 318-11, 11.5.5.3, equation 11-24

Reference 2 limits the distribution of reinforcement, A[sub]t[/sub]/s to a minimum ratio of 25*b[sub]w[/sub]/f[sub]yt[/sub]. The distributed quantity is the area of torsional reinforcement and the spacing of the same. b[sub]w[/sub] is the width of the concrete section (web) and f[sub]yt[/sub] is the yield strength of the reinforcement.

The problem is that the units for the limiting ratio are incompatible with the distributed area. The distributed area results in units of inch. The ratio results in cubic inches per pound, whereas the expected quantity is "inch". (The complete equation has units of area for the final result.)

Reference 1 provides two equations, the minimum area is taken as the lesser of the two equations. It is simply a restatement for that shown in Reference 2.

I do not find any correction in ACI.

What am I missing?
What is the solution?

Thanks.

 

[JAE]

At/s is in units of (sq. in)/(in.) which, in your result is just inches.

For the limiting ratio (25bw/fyt) the value of 25 has inherent units in it.
Here's an example from PCA (old one based on 318-02) but same equations:

 

[MGMtulsa]

JAE:
Thanks for the solution. Your notion of inherent units with the constant '25' is what I missed.
You have made me recall such notions that constants can carry units. But, that was in the days before spreadsheets and worksheets, of which now units are mandatory.
Have a great day.
MGM