The following rules laid down by Tredgold will be useful to those who are unable to find the direction and amount of the stresses on various parts of a roof; and thus by a more accurate method to arrive at the sizes necessary for the different members.

The student should observe that though these look like complicated formulae, they are very simple, being merely letters substituted for words, as in Hurst's Pocket-book, and they require nothing but ordinary arithmetic for their application.

B=Breadth of piece in inches. D = Depth of piece in inches. A = Area of section of piece in inches=BxD. L - Length of piece in feet. S = Span of roof in feet.

## Tie Beam

u = Length of longest unsupported part in feet.

When the tie beam has to support a ceiling only.

D = - x 147 for fir, or x 1.52 for oak.

When there are rooms above, the tie beam must be calculated as a girder (see p. 102, Part I.) Ceiling Joists 12 inches from centre to centre.

D = x 0.64 for fir, or x 0.67 for oak.

## King Post

A = L x S x (0.12 for fir, or x 0.13 for oak.

## King Bolt

Diameter in inches = x 0.2. Queen Post. - t = length in feet of part of tie-beam suspended by the queen post. A=L x t x 0.27 for fir, or x 0.32 for oak. Queen Bolt. - Diameter in inches = x 0.29. Struts and Braces. - r = length of part of principal rafter supported by the strut, in feet.

D = x 0.8 for fir.

B = 6/10 D.

### Principal Rafters

Supported by struts over which the purlins rest.

## In King-Post Roof

D = L2 / B3 x .096 for fir.

## In Queen-Post Roof

D =L2 / B3 x 0.155 for fir.

The thickness is generally the same as that of the tie beam and king or queen posts.

## Purlins

C = distance in feet that the purlins are apart. D = x 1.0 for fir, or 1.04 for oak.

## Common Rafters

D= x 0.'72 for fir, or 0.74 for oak.

## Straining Beam

In the best form for strength the depth is to breadth as 10 to 7.

D = x 0.9 for fir.