The Mechanical Properties of Wood Part 11


In instructions for making static tests the rate of application of the stress, _i.e._, the speed of the machine, is given because the strength of wood varies with the speed at which the fibres are strained. The speed of the crosshead of the testing machine is practically never constant, due to mechanical defects of the apparatus and variations in the speed of the motor, but so long as it does not exceed 25 per cent the results will not be appreciably affected. In fact, a change in speed of 50 per cent will not cause the strength of the wood to vary more than 2 per cent.[58]

[Footnote 58: See Tiemann, Harry Donald: The effect of the speed of testing upon the strength and the standardization of tests for speed. Proc. Am. Soc. for Testing Materials, Vol. VIII, Philadelphia, 1908.]

Following are the formulae used in determining the speed of the movable head of the machine in inches per minute (n):

(1) For endwise compression n = Z l

Z l^{2} (2) For beams (centre loading) n = --------- 6h

Z l^{2} (3) For beams (third-pointloading) n = --------- 5.4h

Z = rate of fibre strain per inch of fibre length.

l = span of beam or length of compression specimen.

h = height of beam.

The values commonly used for Z are as follows:

Bending large beams Z = 0.0007 Bending small beams Z = 0.0015 Endwise compression-large specimens Z = 0.0015 Endwise compression-small " Z = 0.003 Right-angled compression-large " Z = 0.007 Right-angled compression-small " Z = 0.015 Shearing parallel to the grain Z = 0.015

Example: At what speed should the crosshead move to give the required rate of fibre strain in testing a small beam 2" X 2" X 30". (Span = 28".) Substituting these values in equation (2) above: (0.0015 X 28^2) n = ----------------- = 0.1 inch per minute.

(6 X 2)

In order that tests may be intelligently compared, it is important that account be taken of the speed at which the stress was applied. In determining the basis for a ratio between time and strength the rate of strain, which is controllable, and not the ratio of stress, which is circumstantial, should be used. In other words, the rate at which the movable head of the testing machine descends and not the rate of increase in the load is to be regulated. This ratio, to which the name _speed-strength modulus_ has been given, may be expressed as a coefficient which, if multiplied into any proportional change in speed, will give the proportional change in strength. This ratio is derived from empirical curves. (See Table XVII.)

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- TABLE XVII TABLE XVII ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- SPEED-STRENGTH MODULI AND RELATIVE INCREASE IN STRENGTH AT RATES OF FIBRE STRAIN INCREASING IN GEOMETRICAL RATIO. (Tiemann, _loc. cit._) (Values in parentheses are approximate) ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Rate of fibre strain. Ten-thousandths inch 2/3 2 6 18 54 162 486 per minute per inch -------------------------+-----------------------+-----------------------+-----------------------+-----------------------+-----------------------+-----------------------+----------------------- C Speed of crosshead. O Inches per minute 0.000383 0.00115 0.00345 0.0103 0.0310 0.0931 .279 M P ---------------------+-----------------------+-----------------------+-----------------------+-----------------------+-----------------------+-----------------------+----------------------- R Specimens Wet Dry All Wet Dry All Wet Dry All Wet Dry All Wet Dry All Wet Dry All Wet Dry All E ---------------------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+------- S Relative S crushing 100.0 100.0 100.0 103.4 100.8 101.5 107.5 102.7 103.8 113.9 105.5 107.9 121.3 108.3 116.4 128.8 110.0 118.9 I strength O N Speed-strength 0.017 (0.006) (0.009) 0.033 0.012 0.016 0.047 0.021 0.029 0.053 0.027 0.039 0.060 0.023 0.049 (0.052) (0.015) (0.040) modulus, _T_ ---+---------------------+-----------------------+-----------------------+-----------------------+-----------------------+-----------------------+-----------------------+----------------------- Speed of crosshead. Inches per minute 0.0072 0.0216 0.0648 0.194 0.583 1.75 5.25 B E ---------------------+-----------------------+-----------------------+-----------------------+-----------------------+-----------------------+-----------------------+----------------------- N Specimens Wet Dry All Wet Dry All Wet Dry All Wet Dry All Wet Dry All Wet Dry All Wet Dry All D ---------------------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+------- I Relative N crushing 97.4 99.0 98.2 100.0 100.0 100.0 105.1 102.1 103.7 111.3 105.8 108.1 117.9 108.6 112.7 123.7 109.6 116.3 126.3 110.3 118.9 G strength Speed-strength (0.014) (0.005) 0.012 0.033 0.014 0.026 0.049 0.026 0.037 0.053 0.033 0.038 0.049 0.014 0.035 0.038 0.006 0.025 (0.023) (0.004) (0.014) modulus, _T_ ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- NOTE.--The usual speeds of testing at the U.S. Forest Service laboratory are at rates of fibre strain of 15 and 10 ten-thousandths in. per min. per in. for compression and bending respectively. -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------


_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.)

[Illustration: FIG. 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.

[Illustration: FIG. 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, above.) 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 abscissae. 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, above.) 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 formulae 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 (P_{1} + 0.75 W) (2) r = -------------------- b h^{2}

l (P + 0.75 W) (3) R = ---------------- b h^{2}

P_{1} l^{3} (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.

P_{1} = 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.


_Apparatus_: An ordinary static bending machine, a steel I-beam bearing two adjustable knife-edge supports to rest on the platform, and a special deflectometer, are required. (See Fig.


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