BENDING LARGE BEAMS
Apparatus: A static bending machine (described above), with a special crosshead for third-point loading and a long platform bearing knife-edge supports, is required. ([See Fig. 29].)
Figure 29
Static bending test on large beam. Note arrangement of wire and scale for measuring deflection; also method of applying load at "third-points."
Preparing the material: Standard sizes and grades of beams and timbers in common use are employed. The ends are roughly squared and the specimen weighed and measured, taking the cross-sectional dimensions midway of the length. Weights should be to the nearest pound, lengths to the nearest 0.1 inch, and cross-sectional dimensions to the nearest 0.01 inch.
Marking and sketching: The butt end of the beam is marked A and the top end B. While facing A, the top side is marked a, the right hand b, the bottom c, the left hand d. Sketches are made of each side and end, showing (1) size, location, and condition of knots, checks, splits, and other defects; (2) irregularities of grain; (3) distribution of heartwood and sapwood; and on the ends: (4) the location of the pith and the arrangement of the growth rings, (5) number of rings per inch, and (6) the proportion of late wood.
The number of rings per inch and the proportion of late wood should always be determined along a radius or a line normal to the rings. The average number of rings per inch is the total number of rings divided by the length of the line crossing them. The proportion of late wood is equal to the sum of the widths of the late wood crossed by the line, divided by the length of the line. Rings per inch should be to the nearest 0.1; late wood to the nearest 0.1 per cent.
Since in large beams a great variation in rate of growth and relative amount of late wood is likely in different parts of the section, it is advisable to consider the cross section in three volumes, namely, the upper and lower quarters and the middle half. The determination should be made upon each volume separately, and the average for the entire cross section obtained from these results.
At the conclusion of the test the failure, as it appears on each surface, is traced on the sketches, with the failures numbered in the order of their occurrence. If the beam is subsequently cut up and used for other tests an additional sketch may be desirable to show the location of each piece.
Adjusting specimen in machine: The beam is placed in the machine with the side marked a on top, and with the ends projecting equally beyond the supports. In order to prevent crushing of the fibre at the points where the stress is applied it is necessary to use bearing blocks of maple or other hard wood with a convex surface in contact with the beam. Roller bearings should be placed between the bearing blocks and the knife edges of the crosshead to allow for the shortening due to flexure. ([See Fig. 29].) Third-point loading is used, that is, the load is applied at two points one-third the span of the beam apart. ([See Fig. 30].) This affords a uniform bending moment throughout the central third of the beam.
Figure 30
Two methods of loading a beam, namely, third-point loading (upper), and centre loading (lower).
Measuring the deflection: The method of measuring the deflection should be such that any compression at the points of support or at the application of the load will not affect the reading. This may be accomplished by driving a small nail near each end of the beam, the exact location being on the neutral plane and vertically above each knife-edge support. Between these nails a fine wire is stretched free of the beam and kept taut by means of a rubber band or coiled spring on one end. Behind the wire at a point on the beam midway between the supports a steel scale graduated to hundredths of an inch is fastened vertically by means of thumb-tacks or small screws passing through holes in it. Attachment should be made on the neutral plane.
The first reading is made when the scale beam is balanced at zero load, and afterward at regular increments of the load which is applied continuously and at a uniform speed. (See Speed of Testing Machine, [page 92].) If desired, however, the load may be read at regular increments of deflection. The deflection readings should be to the nearest 0.01 inch. To avoid error due to parallax, the readings may be taken by means of a reading telescope about ten feet distant and approximately on a level with the wire. A mirror fastened to the scale will increase the accuracy of the readings if the telescope is not used. As in all tests on timber, the strain must be continuous to rupture, not intermittent, and readings must be taken "on the fly." The weighing beam is kept balanced after the yield point is reached and the maximum load, and at least one point beyond it, noted.
Log of the test: The proper log sheet for this test consists of a piece of cross-section paper with space at the margin for notes. ([See Fig. 32].) The load in some convenient unit (1,000 to 10,000 pounds, depending upon the dimensions of the specimen) is entered on the ordinates, the deflection in tenths of an inch on the abscissæ. The increments of load should be chosen so as to furnish about ten points on the stress-strain diagram below the elastic limit.
As the readings of the wire on the scale are made they are entered directly in their proper place on the cross-section paper. In many cases a test should be continued until complete failure results. The points where the various failures occur are indicated on the stress-strain diagram. A brief description of the failure is made on the margin of the log sheet, and the form traced on the sketches.
Disposal of the specimen: Two one-inch sections are cut from the region of failure to be used in determining the moisture content. ([See Moisture Determination, page 90].) A two-inch section may be cut for subsequent reference and identification, and possible microscopic study. The remainder of the beam may be cut into small beams and compression pieces.
Calculating the results: The formulæ used in calculating the results of tests on large rectangular simple beams loaded at third points of the span are as follows:
| 0.75 P | |||
| (1) | J | = | -------- |
| b h | |||
| l (P1 + 0.75 W) | |||
| (2) | r | = | -------------------- |
| b h2 | |||
| l (P + 0.75 W) | |||
| (3) | R | = | ---------------- |
| b h2 | |||
| P1l3 | |||
| (4) | E | = | --------------- |
| 4.7 D b h 3 | |||
| 0.87 P 1 D | |||
| (5) | S | = | -------------- |
| 2 V | |||
| b, h, l | = | breadth, height, and span of specimen, inches. | |
| D | = | total deflection at elastic limit, inches. | |
| P | = | maximum load, pounds. | |
| P1 | = | load at elastic limit, pounds. | |
| E | = | modulus of elasticity, pounds per square inch. | |
| r | = | fibre stress at elastic limit, pounds per sq. inch. | |
| R | = | modulus of rupture, pounds per square inch. | |
| S | = | elastic resilience or work to elastic limit, inch-pounds per cu. in. | |
| J | = | greatest calculated longitudinal shear, pounds per square inch. | |
| V | = | volume of beam, cubic inches. | |
| W | = | weight of the beam. |
In large beams the weight should be taken into account in calculating the fibre stress. In (2) and (3) three-fourths of the weight of the beam is added to the load for this reason.