133. Another kind of strain to which beams are liable, and which requires particular attention, as the strength of a piece of framing often depends upon it, is that tending to separate or shear the beam in the direction of its fibres.

According to the experiments of Professor Robinson, this resistance appeared to be exactly proportional to the area of the section, and quite independent of its figure.* Barlow made some experiments on this kind of resistance, from which it appears that when the force is parallel to the fibres, the strength of fir to resist detrusion is from 556 lbs. to 634 lbs. per square inch, or about one-twentieth of the cohesive force, in the direction of the fibres.†

Mr. Hatfield gives the amount of the force required to separate the fibres of the following kinds of timber grown in America, when applied in the direction of the length ‡ -

134. To give an example of the application, let A C (Fig. 16) be the lower end of a principal rafter, and C B the tie-beam.

It is evident that if the part D be not sufficiently long, the thrust of the foot of the rafter will cause it to shear off at the line b C. If we suppose the joint to have no tenon, then the horizontal thrust of the rafter in pounds should be equal to the area of the surface in inches that would be forced asunder in case of fracture, multiplied by the resistance of a square inch in pounds.

* ' Ency. Brittinnica,' art. Strength of Materials.

† Essay on Strength of Timber. ‡ American House Carpenter.

In practice, the strain should not exceed, one-fourth of the resistance; therefore, to find the length bC we have the following rule: -

RULE XIII. - Divide four times the horizontal thrust in pounds by the breadth in inches, multiplied into the shearing force of a square inch in pounds, in the direction of the fibres, and the quotient will give the length b C in inches.

Example. - Find the horizontal thrust of a rafter by the principles in Section I. (Art. 40). Let us assume this pressure to bo 5600 pounds, and let the breadth of the tie-beam, which is of Georgia pine, be 6 inches, and the resistance to shearing 510 lbs. per square inch. Then

4x5600/6x510 = 7.3 inches nearly, for the distance 6 to C.

If the beam bad been American oak, the resistance of a square inch of which is 780 lbs., there would be required

4x5600/6x780 = 4.8 inches nearly.

A knowledge of this kind of resistance is useful in ascertaining the length a tenon should be from the pin-hole to prevent the former from tearing out. It was found by Mr. Bevan that a force of 976 lbs. was required to pull out a piece of Scotch fir applied as a tenon in a mortice, and fastened with a half-inch iron pin; the thickness of the tenon being . 87 inch, and the length from the centre of the pinhole to the end 1.05 inch, the lateral cohesion of the wood being the same as in Table V., Art. 83. *

This rule is also useful in regulating the length of the scarfs in tie-beams, and other timbers subject to a tensile strain.

* ' Phil. Mag.,' vol. lxviii., 1826.