If the end of a beam, instead of being only supported, be fixed, its strength will be in the proportion of 3 to 2.
From the foregoing results it will be seen that the strength of a rectangular beam varies, as the breadth multiplied by the depth squared, divided by the length, b × d2 1 and if the breaking weight of any material, 1 inch square, and 1 foot long, be found, it will represent a constant multiplier for the above equation.
Thus the breaking weight of a beam of Riga fir, 1 inch square, and 1 foot long (vide following TABLE), is ·164 of a ton; and to find the breaking weight of a beam of any other dimensions, the rule is simply
W = b × d2 1 × ·164.
Example.—What will be the breaking weight of a beam of Riga fir, 8 inches broad, 12 inches deep, and 20 feet long?
8 × 122 20 = 57·6 57·6 × ·164 = 9·44 tons, breaking weight.
Table of constants, for beams of different materials, being the breaking weights of such beams, 1 inch square, and 1 foot long.
| Riga fir | ·164 | of a ton. | English oak | ·248 | of a ton. |
| Red pine | ·199 | ” | Canadian do. | ·261 | ” |
| Pitch pine | ·242 | ” | Dantzic do. | ·219 | ” |
| Beech | ·231 | ” | Teak | ·366 | ” |
| Elm | ·150 | ” | Cast iron, mean. | 1·000 | ” |
| Ash | ·301 | ” | Wrought do. | 1·083 | ” |
From the foregoing rules
Length = b d2 W × constant.