(3) It is inversely proportional to the span for beams of the same breadth and depth and not to the cube of this dimension as in stiffness.
The fact that the strength varies as the square of the height and the stiffness as the cube explains the relationship of bending to thickness. Were the law the same for strength and stiffness a thin piece of material such as a sheet of paper could not be bent any further without breaking than a thick piece, say an inch board.
| TABLE IX | ||||||
|---|---|---|---|---|---|---|
| RESULTS OF STATIC BENDING TESTS ON SMALL CLEAR BEAMS OF 49 WOODS IN GREEN CONDITION | ||||||
| (Forest Service Cir. 213) | ||||||
| COMMON NAME OF SPECIES | Fibre stress at elastic limit | Modulus of rupture | Modulus of elasticity | Work in Bending | ||
| To elastic limit | To maximum load | Total | ||||
| Lbs. per sq. in. | Lbs. per sq. in. | Lbs. per sq. in. | In.-lbs. per cu. inch | In.-lbs. per cu. inch | In.-lbs. per cu. inch | |
| Hardwoods | ||||||
| Ash, black | 2,580 | 6,000 | 960,000 | 0.41 | 13.1 | 38.9 |
| white | 5,180 | 9,920 | 1,416,000 | 1.10 | 20.0 | 43.7 |
| Basswood | 2,480 | 4,450 | 842,000 | .45 | 5.8 | 8.9 |
| Beech | 4,490 | 8,610 | 1,353,000 | .96 | 14.1 | 31.4 |
| Birch, yellow | 4,190 | 8,390 | 1,597,000 | .62 | 14.2 | 31.5 |
| Elm, rock | 4,290 | 9,430 | 1,222,000 | .90 | 19.4 | 47.4 |
| slippery | 5,560 | 9,510 | 1,314,000 | 1.32 | 11.7 | 44.2 |
| white | 2,850 | 6,940 | 1,052,000 | .44 | 11.8 | 27.4 |
| Gum, red | 3,460 | 6,450 | 1,138,000 | |||
| Hackberry | 3,320 | 7,800 | 1,170,000 | .56 | 19.6 | 52.9 |
| Hickory, big shellbark | 6,370 | 11,110 | 1,562,000 | 1.47 | 24.3 | 78.0 |
| bitternut | 5,470 | 10,280 | 1,399,000 | 1.22 | 20.0 | 75.5 |
| mockernut | 6,550 | 11,110 | 1,508,000 | 1.50 | 31.7 | 84.4 |
| nutmeg | 4,860 | 9,060 | 1,289,000 | 1.06 | 22.8 | 58.2 |
| pignut | 5,860 | 11,810 | 1,769,000 | 1.12 | 30.6 | 86.7 |
| shagbark | 6,120 | 11,000 | 1,752,000 | 1.22 | 18.3 | 72.3 |
| water | 5,980 | 10,740 | 1,563,000 | 1.29 | 18.8 | 52.9 |
| Locust, honey | 6,020 | 12,360 | 1,732,000 | 1.28 | 17.3 | 64.4 |
| Maple, red | 4,450 | 8,310 | 1,445,000 | .78 | 9.8 | 17.1 |
| sugar | 4,630 | 8,860 | 1,462,000 | .88 | 12.7 | 32.0 |
| Oak, post | 4,720 | 7,380 | 913,000 | 1.39 | 9.1 | 17.4 |
| red | 3,490 | 7,780 | 1,268,000 | .60 | 11.4 | 26.0 |
| swamp white | 5,380 | 9,860 | 1,593,000 | 1.05 | 14.5 | 37.6 |
| tanbark | 6,580 | 10,710 | 1,678,000 | 1.49 | ||
| white | 4,320 | 8,090 | 1,137,000 | .95 | 12.1 | 36.7 |
| yellow | 5,060 | 8,570 | 1,219,000 | 1.20 | 11.7 | 30.7 |
| Osage orange | 7,760 | 13,660 | 1,329,000 | 2.53 | 37.9 | 101.7 |
| Sycamore | 2,820 | 6,300 | 961,000 | .51 | 7.1 | 13.6 |
| Tupelo | 4,300 | 7,380 | 1,045,000 | 1.00 | 7.8 | 20.9 |
| Conifers | ||||||
| Arborvitæ | 2,600 | 4,250 | 643,000 | .60 | 5.7 | 9.5 |
| Cedar, incense | 3,950 | 6,040 | 754,000 | |||
| Cypress, bald | 4,430 | 7,110 | 1,378,000 | .96 | 5.1 | 15.4 |
| Fir, alpine | 2,366 | 4,450 | 861,000 | .66 | 4.4 | 7.4 |
| amabilis | 4,060 | 6,570 | 1,323,000 | |||
| Douglas | 3,570 | 6,340 | 1,242,000 | .59 | 6.6 | 13.6 |
| white | 3,880 | 5,970 | 1,131,000 | .77 | 5.2 | 14.9 |
| Hemlock | 3,410 | 5,770 | 917,000 | .73 | 6.6 | 12.9 |
| Pine, lodgepole | 3,080 | 5,130 | 1,015,000 | .54 | 5.1 | 7.4 |
| longleaf | 5,090 | 8,630 | 1,662,000 | .88 | 8.1 | 34.8 |
| red | 3,740 | 6,430 | 1,384,000 | .59 | 5.8 | 28.0 |
| shortleaf | 4,360 | 7,710 | 1,395,000 | |||
| sugar | 3,330 | 5,270 | 966,000 | .66 | 5.0 | 11.6 |
| west, yellow | 3,180 | 5,180 | 1,111,000 | .52 | 4.3 | 15.6 |
| White | 3,410 | 5,310 | 1,073,000 | .62 | 5.9 | 13.3 |
| Redwood | 4,530 | 6,560 | 1,024,000 | |||
| Spruce, Engelmann | 2,740 | 4,550 | 866,000 | .50 | 4.8 | 6.1 |
| red | 3,440 | 5,820 | 1,143,000 | .62 | 6.0 | |
| white | 3,160 | 5,200 | 968,000 | .58 | 6.6 | |
| Tamarack | 4,200 | 7,170 | 1,236,000 | .84 | 7.2 | 30.0 |
Kinds of Loads
There are various ways in which beams are loaded, of which the following are the most important:
(1) Uniform load occurs where the load is spread evenly over the beam.
(2) Concentrated load occurs where the load is applied at single point or points.
(3) Live or immediate load is one of momentary or short duration at any one point, such as occurs in crossing a bridge.