Quoting the author, that “destructive criticism is of no value unless it offers something in its place,” and in connection with the author’s tenth point, the writer offers the following formula which he has always used in conjunction with the design of reinforced concrete slabs and beams.  It is based on the formula for rectangular wooden beams, and assumes that the beam is designed on the principle that concrete in tension is as strong as that in compression, with the understanding that sufficient steel shall be placed on the tension side to make this true, thus fixing the neutral axis, as the author suggests, in the middle of the depth, that is, M = (1/6)_b d_^{2} S, M, of course, being the bending moment, and b and d, the breadth and depth, in inches. S is usually taken at from 400 to 600 lb., according to the conditions.  In order to obtain the steel necessary to give the proper tensile strength to correspond with the compression side, the compression and tension areas of the beam are equated, that is

1        2                d
---- b d S = a x ( ----- - x   ) x S  ,
12                          2       II        II

where

a = the area of steel per linear foot,
x{II}_ = the distance from the center of the steel to the outer
fiber, and
S{II}_ = the strength of the steel in tension.

Then for a beam, 12 in. wide,

2                   d
d S = a S  ( ----- - x ) ,
II     2       II

or

2
d S
a = --------------------- .
d
S ( ----- - x )
II 2 II

Carrying this to its conclusion, we have, for example, in a beam 12 in. deep and 12 in. wide,

S = 500, S{II}_ = 15,000, x{II}_ = 2-1/2 in. a = 1.37 sq. in. per ft.

The writer has used this formula very extensively, in calculating new work and also in checking other designs built or to be built, and he believes its results are absolutely safe.  There is the further fact to its credit, that its simplicity bars very largely the possibility of error from its use.  He sees no reason to introduce further complications into such a formula, when actual tests will show results varying more widely than is shown by a comparison between this simple formula and many more complicated ones.

GEORGE H. MYERS, JUN.  AM.  SOC.  C. E. (by letter).—­This paper brings out a number of interesting points, but that which strikes the writer most forcibly is the tenth, in regard to elaborate theories and complicated formulas for beams and slabs.  The author’s stand for simplicity in this regard is well taken.  A formula for the design of beams and slabs need not be long or complicated in any respect.  It can easily be obtained from the well-known fact that the moment at any point divided by the distance between the center of compression and the center of tension at that point gives the tension (or compression) in the beam.