G4

CALCULATIONS 01' THE STRENGTH

than is absolutely necessary to retain the parts in equilibrium by addingto its strength ; and that under every circumstance, and every descrip-tion of strain to which it may be subjected. This appears to me to bethe ultimatum of every experiment ; and although we may not, in thepresent stage of the inquiry, have attained the same exactitude whichfuture experiments may develope, we have nevertheless acquired certainfixed laws which determine the form and clearly establish the proportionsof the relative strength or distribution of the material in the differentparts of the structure. These may be determined from the experimentsas follows.

On consulting Experiments 15, 16, and 29, on the rectangular tubes,it will be found that they approximate to each other in a certain ratio,as to the thickness of their top and bottom sides. The first, it will beobserved, broke by tearing asunder through the rivet-holes; the secondwas crippled by “ buckling” on the top; and the last was fractured bythe sides tearing from the top and bottom at one and the same time.Now, if we take the mean thickness of the plates used in these experi-ments, I apprehend we shall have a fair proportional of the quantity ofmetal which should be used respectively in the top and bottom sidesof the large tube, in order to obtain the section of greatest strength. Themean of the top and bottom sides of the tubes experimented upon was,—

Experiments.

Area of top sidein inches.

Area of bottor

in inches.

15.

0-142

0-075

16.

0-269

0-149

29.

0-230

0-180

Mean

. . 0-213

0-135

being in the ratio of 213 to 135, or as 10 to 6 nearly*. From this itappears that the top and bottom sides of the bridge should approach inthe areas of their respective sections, as nearly as possible, to the above

* The same result may be obtained in the followingExperiment 15, ratio of the top and bottom areas

manner:—

1*893 :

1

16,

1-805 :

: 1

29,

1-278 :

1

Mean ratio.

1-659 :

1

or

10 :

6