Length, 16
  Height, 1
  Area Top Flange, 1.0
  Area Bottom Flange, 6.1

In the above formula for cast iron beams,

W = weight in tons. a = area in square inches of bottom flange. d = depth in inches. h = length in inches.

The web uniting the two flanges must be made solid—­as any opening, by causing irregularity in cooling, would seriously affect the strength of the beam.

Example.—­Required the dimensions of a Hodgkinson girder—­for a span of 60 feet—­with a load of 10 tons in the centre.

6 x 10 x 60 x 12
a = ---------------- = 37 inches nearly.
60 x 12
26 x -------
16

[TeX:  $a = \frac{6 \times 10 \times 60 \times 12}{26 \times \frac{60 \times 12}{16}} = 37$]

and the area of the top flange will be,

37
—­ = 6.16 inches—­
6

[TeX:  $\frac{37}{6} = 6.16$]

so that our dimensions will be as follows: 

  Length, 30 feet. 
  Depth, 45 inches. 
  Area Top Flange, 6.16 inches. 
  Area Bottom Flange, 37 inches.

[Illustration:  Pl. 1.]

The thickness of web is usually a little greater at the bottom than at the top, and varies from 1/14 to 1/24 of the depth of the girder.  The bottom rib is usually made from six to eight times as wide as it is thick, and the top rib from three to six times as wide as thick, so that, in the example above given, we could have as dimensions for the parts

Top Flange, 4 1/4 x 1 1/2 inches nearly. 
Bottom Flange, 6 x 2 1/2 inches nearly. 
Web, 1 1/2 inches thick.

The simplest bridge, consisting of a single stick, to span openings of 20 feet and under, is calculated according to the formula

------
/  4WL
d =   / ------ --
\/  5000 b

[TeX:  $d = \sqrt{\frac{4 WL}{5000 b}}$]

Example.—­The depth of a beam, of 12 feet span and 12 feet wide, to support a load of 22400 lbs. will be

------       --------------------
/ 4WL        / 4 X 22400 x 12 x 12      -------
d =   / ------ =   /  ------------------- =   / 215.04 = 15 in. nearly
\/  5000 b   \/        5000 x 12        \/

[TeX:  $d = \sqrt\frac{4 WL}{5000 b}} = \sqrt\frac{4 \times 22400 \times 12 \times 12}{5000 \times 12} = \sqrt{215.04} = 15$]

The following Table was calculated by the above rule—­and the dimensions altered according to the actual practice of the writer.

  Span.  Breadth.  Depth.

4       10       12
6       10       12
8       12       12
10       12       13
12       12       15
16       12       18
18       12       20
20       12       22

These dimensions will give ample strength and stiffness.  Fig. 1, Plate I. gives an illustration of this kind of bridge—­in which a, a, are the bolsters or wall plates, shown in section, to which the bridge