K = for yellow pine, 10; for red pine, 13; Memel, 12; spruce, 12; English oak, 15.

(N.B. These strengths as given in Molesworth do not agree with those given by Unwin, and they must be regarded by the student rather as indications of differences in strength than as correctly representing the exact relative value of various timbers.) 4KBD2 L

Rule.-W=

Example.-Let B 6, D6 L = 72 (6 feet), and K = 10;

then

=

W =

4KBD2
L

4 X 10 X 6 × 62

= 120 cwt., or 6 tons

72

This rule may be simplified when K = 10, as follows:-
W breaking weight in tons; then-

=

This is easy to remember, as most of the figures are 6's. Thus, beam 6 inches wide, 6 inches deep, 6 feet long; breaking weight, 6 tons.

Rule for strength of round beams is given by Molesworth as follows:

R = the radius, or half-diameter, of the log in inches.
The following example shows how the rule is worked :-
Let K =

10, as in the foregoing example; let the diameter be 8 inches, the radius 4 inches, and L be 72 inches; then

or, roughly speaking, an 8-inch bar 6 feet between the supports will require a load of 8 tons in the centre to break it.

It will be seen that this rule agrees approximately with some results obtained by testing mining timber with the 100-ton testingmachine at the Yorkshire College. The tests were made by Professor Goodman and the writer upon bars of ordinary mining timber in their ordinary condition before use, as taken from a pile out of doors. The results are shown in the following table. A simple rule for the breaking weight of round beams is given in the last column.

Remarks.

TABLE XIV.-TIMBER TESTS.

10'64

W =

Here W is

The strength of rolled steel girders of H section (see section, Fig. 417) may be calculated by the following rule :

W

=

breaking weight in tons in centre of span.

x = tensile strength of material in tons per square inch.

A = area of one flange (either top or bottom) in square inches.
depth of girder from top to bottom in inches.
span in inches.

=

D

L

Then W =

4x × AX D
L

For rolled steel joists, x = 25 tons,1 and 4x = 100 tons. The safe load in structures is of the breaking load, or for rolled steel girders the safe load is say 5 tons per square inch. Therefore the formula for a safe load for a girder supported at both ends, and all the weight in the centre, and ends free, would be— 20 X AX D

W=

If the load were distributed evenly throughout, the girder would safely sustain double the above load, or 8 tons; and if the ends were built in very firmly to a length of at least 18 inches, with a heavy load on them, and the load distributed, it would bear 50 per cent. more, or 12 tons.

The following table gives the breaking load and safe load of rolled steel H girders :

128 to 30 is, perhaps, nearer the figure, but 25 tons is within the mark.

For wrought iron, x = 20 tons.

In order to determine the strength of timber props, the writer procured a number of specimens of oak, larch, and Norway props of the size and condition commonly used in mines. These were put in the testing-machine, and subjected to an end pressure till they crushed, The results are shown in the table on the

following page.

The

It will be noted that there does not appear to be any serious difference in the strength of the three kinds of wood as tested but the oak props were not so straight as the larch, and the larch was not so straight as the Norway. It will also be noted that the 7-feet props crushed with a less weight than the 4-feet props, and these again with a less weight than the 2-feet props. weight that would be required to crush a prop longer than 7 feet can be ascertained roughly from the above tests by calculation. Assuming that the long prop was quite straight, it is probable that the crushing load will not fall much below 1 ton per square inch, if the length does not exceed twelve times the diameter.

Professor Unwin, in his book on "The Testing of Materials of Construction," quotes experiments by Professor Lanza, according to which the crushing strength of posts 7 to 10 inches in diameter, 12 feet long, and 2 feet long, of yellow pine, was very nearly 2 tons per square inch. It is probable that this was an excellent quality of seasoned timber. Professor Lanza also made tests of posts up to 30 feet in length, from which it appears that a yellow pine post, of which the length is fifteen times the diameter, requires a crushing load of 13 tons per square inch; and with a length from thirty to forty times the diameter, the crushing load is 1 ton per square inch; and with a length fifty to sixty times the diameter, the crushing load is ton per square inch. With white pine the strength is less. With a length ten times the diameter, the crushing load is 1 ton per square inch; and with lengths from ten to thirty-five times the diameter, the crushing load is about ton; while with lengths forty-five to sixty times the diameter, the crushing load is about 0'44 ton per square inch. The permanent or safe load is, of course, much less than the loads above given in all cases.

9 10

It would seem, from the various observations above recorded, that the strength of a straight prop or strut is in some measure proportional to the relation between length and diameter, and that a prop 12 inches in diameter and 12 feet long will bear approximately as great a load per square inch as a 6-inch prop 6 feet long. The relation of the ratio of the length and diameter of props and the crushing load per square inch, as worked out from the Yorkshire College tests, is given in Table XVII.

The test-pieces consisted of round timber props, neither hewn nor sawn, but just as grown and cross-cut, the ends not squared, the oak without bark.

The following were tested as struts as follows: at the top and bottom of each prop a piece of board about inch thick was placed, to give a level bedding, the compression was applied through flat and level iron plates at the top and bottom, the prop being vertical.