_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