SHEARING STRENGTH
Whenever forces act upon a body in such a way that one portion tends to slide upon another adjacent to it the action is called a shear.[8] In wood this shearing action may be (1) along the grain, or (2) across the grain. A tenon breaking out its mortise is a familiar example of shear along the grain, while the shoving off of the tenon itself would be shear across the grain. The use of wood for pins or tree-nails involves resistance to shear across the grain. Another common instance of the latter is where the steel edge of the eye of an axe or hammer tends to cut off the handle. In [Fig. 10] the action of the wooden strut tends to shear off along the grain the portion AB of the wooden tie rod, and it is essential that the length of this portion be great enough to guard against it. [Fig. 11] shows characteristic failures in shear along the grain.
Figure 10
Example of shear along the grain.
Figure 11
Failures of test specimens in shear along the grain. In the block at the left the surface of failure is radial; in the one at the right, tangential.
| TABLE VII | ||
|---|---|---|
| SHEARING STRENGTH ALONG THE GRAIN OF SMALL CLEAR PIECES OF 41 WOODS IN GREEN CONDITION | ||
| (Forest Service Cir. 213) | ||
| COMMON NAME OF SPECIES | When surface of failure is radial | When surface of failure is tangential |
| Lbs. per sq. inch | Lbs. per sq. inch | |
| Hardwoods | ||
| Ash, black | 876 | 832 |
| white | 1,360 | 1,312 |
| Basswood | 560 | 617 |
| Beech | 1,154 | 1,375 |
| Birch, yellow | 1,103 | 1,188 |
| Elm, slippery | 1,197 | 1,174 |
| white | 778 | 872 |
| Hackberry | 1,095 | 1,161 |
| Hickory, big shellbark | 1,134 | 1,191 |
| bitternut | 1,134 | 1,348 |
| mockernut | 1,251 | 1,313 |
| nutmeg | 1,010 | 1,053 |
| pignut | 1,334 | 1,457 |
| shagbark | 1,230 | 1,297 |
| water | 1,390 | 1,490 |
| Locust, honey | 1,885 | 2,096 |
| Maple, red | 1,130 | 1,330 |
| sugar | 1,193 | 1,455 |
| Oak, post | 1,196 | 1,402 |
| red | 1,132 | 1,195 |
| swamp white | 1,198 | 1,394 |
| white | 1,096 | 1,292 |
| yellow | 1,162 | 1,196 |
| Sycamore | 900 | 1,102 |
| Tupelo | 978 | 1,084 |
| Conifers | ||
| Arborvitæ | 617 | 614 |
| Cedar, incense | 613 | 662 |
| Cypress, bald | 836 | 800 |
| Fir, alpine | 573 | 654 |
| amabilis | 517 | 639 |
| Douglas | 853 | 858 |
| white | 742 | 723 |
| Hemlock | 790 | 813 |
| Pine, lodgepole | 672 | 747 |
| longleaf | 1,060 | 953 |
| red | 812 | 741 |
| sugar | 702 | 714 |
| western yellow | 686 | 706 |
| white | 649 | 639 |
| Spruce, Engelmann | 607 | 624 |
| Tamarack | 883 | 843 |
Both shearing stresses may act at the same time. Thus the weight carried by a beam tends to shear it off at right angles to the axis; this stress is equal to the resultant force acting perpendicularly at any point, and in a beam uniformly loaded and supported at either end is maximum at the points of support and zero at the centre. In addition there is a shearing force tending to move the fibres of the beam past each other in a longitudinal direction. ([See Fig. 12].) This longitudinal shear is maximum at the neutral plane and decreases toward the upper and lower surfaces.
Figure 12
Horizontal shear in a beam.
Shearing across the grain is so closely related to compression at right angles to the grain and to hardness that there is little to be gained by making separate tests upon it. Knowledge of shear parallel to the grain is important, since wood frequently fails in that way. The value of shearing stress parallel to the grain is found by dividing the maximum load in pounds (P) by the area of the cross section in inches (A).
| ( | P | ) | ||
| Shear | = | --- | ||
| A |
Oblique shearing stresses are developed in a bar when it is subjected to direct tension or compression. The maximum shearing stress occurs along a plane when it makes an angle of 45 degrees with the axis of the specimen. In this case,
| P | ||
| shear | = | -----. |
| 2 A |
When the value of the angle θ is less than 45 degrees,
| P | |||
| the shear along the plane | = | --- | sin θ cos θ. |
| A |
([See Fig. 13].) The effect of oblique shear is often visible in the failures of short columns. ([See Fig. 14].)
Figure 13
Oblique shear in a short column.
Figure 14
Failure of short column by oblique shear.
| TABLE VIII | |||
|---|---|---|---|
| SHEARING STRENGTH ACROSS THE GRAIN OF VARIOUS AMERICAN WOODS | |||
| (J.C. Trautwine. Jour. Franklin Institute. Vol. 109, 1880, pp. 105-106) | |||
| KIND OF WOOD | Lbs. per sq. inch | KIND OF WOOD | Lbs. per sq. inch |
| Ash | 6,280 | Hickory | 7,285 |
| Beech | 5,223 | Locust | 7,176 |
| Birch | 5,595 | Maple | 6,355 |
| Cedar (white) | 1,372 | Oak | 4,425 |
| Cedar (white) | 1,519 | Oak (live) | 8,480 |
| Cedar (Central Amer.) | 3,410 | Pine (white ) | 2,480 |
| Cherry | 2,945 | Pine (northern yellow) | 4,340 |
| Chestnut | 1,536 | Pine (southernyellow) | 5,735 |
| Dogwood | 6,510 | Pine (very resinous yellow) | 5,053 |
| Ebony | 7,750 | Poplar | 4,418 |
| Gum | 5,890 | Spruce | 3,255 |
| Hemlock | 2,750 | Walnut (black) | 4,728 |
| Hickory | 6,045 | Walnut (common) | 2,830 |
| NOTE.—Two specimens of each were tested. All were fairly seasoned and without defects. The piece sheared off was 5/8 in. The single circular area of each pin was 0.322 sq. in. | |||