BENDING SMALL BEAMS

0.75P(1)J=--------b hl(P1+ 0.75W)(2)r=--------------------b h2l(P+ 0.75W)(3)R=----------------b h2P1l3(4)E=---------------4.7D b h30.87P1D(5)S=--------------2Vb, 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.

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. 31.)

Figure 31

Static bending test on small beam. Note the use of the deflectometer with indicator and dial for measuring the deflection; also roller bearings between beam and supports.

Preparing the material: The specimens may be of any convenient size, though beams 2" × 2" × 30" tested over a 28-inch span, are considered best. The beams are surfaced on all four sides, care being taken that they are not damaged by the rollers of the surfacing machine. Material for these tests is sometimes cut from large beams after failure. The specimens are carefully weighed in grams, and all dimensions measured to the nearest 0.01 inch. If to be tested in a green or fresh condition thespecimens should be kept in a damp box or covered with moist sawdust until needed. No defects should be allowed in these specimens.

Marking and sketching: Sketches are made of each end of the specimen to show the character of the growth, and after testing, the manner of failure is shown for all four sides. In obtaining data regarding the rate of growth and the proportion of late wood the same procedure is followed as with large beams.

Adjusting specimen in machine: The beam should be correctly centred in the machine and each end should have a plate with roller bearings between it and the support. Centre loading is used. Between the movable head of the machine and the specimen is placed a bearing block of maple or other hard wood, the lower surface of which is curved in a direction along the beam, the curvature of which should be slightly less than that of the beam at rupture, in order to prevent the edges from crushing into the fibres of the test piece.

Measuring the deflection: The method of measuring deflection of large beams can be used for small sizes, but because of the shortness of the span and consequent slight deformation in the latter, it is hardly accurate enough for good work. The special deflectometer shown in Fig. 31 allows closer reading, as it magnifies the deflection ten times. It rests on two small nails driven in the beam on the neutral plane and vertically above the supports. The fine wire on the wheel at the base of the indicator is attached to another small nail driven in the beam on the neutral plane midway between the end nails. All three nails should be in place before the beam is put into the machine. The indicator is adjustable by means of a thumb-screw at the base and is set at zero before the load is applied. Deflections are read to the nearest 0.001 inch. For rate of application of load see Speed of Testing Machine,page 92. The speed should be uniform from start to finish without stopping. Readings must be made "on the fly."

Log of the test: The log sheets used for small beams (see Fig. 32) are the same as for large sizes and the procedure is practically identical. The stress-strain diagram is continued to or beyond the maximum load, and in a portion of the tests should be continued to six-inch deflection or until the specimen fails to support a load of 200 pounds. Deflection readings for equal increments ofload are taken until well beyond the elastic limit, after which the scale beam is kept balanced and the load read for each 0.1 inch deflection. The load and deflection at first failure, the maximum load, and any points of sudden change should be shown on the diagram, even though they do not occur at one of the regular points. A brief description of the failure and the nature of any defects is entered on the log sheet.

Figure 32

Sample log sheet, giving full details of a transverse bending test on a small pine beam.

Calculating the results: The formulæ used in calculating the results of tests on small rectangular simple beams are as follows:

0.75P(1)J=--------b h1.5P1l(2)r=------------b h21.5P l(3)R=---------b h2P1l3(4)E=------------4D b h3P1D(5)S=---------2V

The same legend is used as onpage 98. The weight of the beam itself is disregarded.

Apparatus: An ordinary static testing machine and a compressometer are required. (See Fig. 33.)

Figure 33

Endwise compression test, showing method of measuring the deformation by means of a compressometer.

Preparing the material: Two classes of specimens are commonly used, namely, (1) posts 24 inches in length, and (2) small clear blocks approximately 2" × 2" × 8". The specimens are surfaced on all four sides and both ends squared smoothly and evenly. They are carefully weighed, measured, rate of growth and proportion of late wood determined, as in bending tests. After the test a moisture section is cut and weighed. Ordinarily these specimens should be free from defects.

Sketching: Sketches are made of each end of the specimens to show the character of the growth. After testing, the manner of failure is shown for all four sides, and the various parts of the failure are numbered in the order of their occurrence.

Adjusting specimen in machine: The compressometer collars are adjusted, the distance between them being 20 inches for the posts and 6 inches for the blocks. If the two ends of the blocks are not exactly parallel a ball-and-socket block can be placed betweenthe upper end of the specimen and the movable head of the machine to overcome the irregularity. If the blocks are true they can simply be stood on end upon the platform and the movable head allowed to press directly upon the upper end.

Measuring the deformation: The deformation is measured by a compressometer. (See Fig. 33.) The latter registers to 0.001 inch. In the case of posts the compression between the collars is communicated to the four points on the arms by means of brass rods; with short blocks, as inFig. 33, the points of the arms are in direct contact with the collars. The operator lowers the fulcrum of the apparatus by moving the micrometer screws at such a rate that the set-screw in the rear end of the upper lever is kept barely touching the fixed arm below it, being guided by a bell operated by electric contact.

Log of the test: The load is applied continuously at a uniform rate of speed. (See Speed of Testing Maching,page 92.)Readings are taken from the scale of the compressometer at regular increments of either load or compression. The stress-strain diagram is continued to at least one deformation point beyond the maximum load, and in event of sudden failure, the direction of the curve beyond the maximum point is indicated. A brief description of the failure is entered on the log sheet. (See Fig. 34.)

Figure 34

Sample log sheet of an endwise compression test on a short pine column.

In short specimens the failure usually occurs in one or several planes diagonal to the axis of the specimen. If the ends are more moist than the middle a crushing may occur on the extreme ends in a horizontal plane. Such a test is not valid and should always be culled. If the grain is diagonal or the stress is unevenly applied a diagonal shear may occur from top to bottom of the test specimen. Such tests are also invalid and should be culled. When the plane (or several planes) of failure occurs through the body of the specimen the test is valid. It may sometimes be advantageous to allow the extreme ends to dry slightly before testing in order to bring the planes of failure within the body. This is a perfectly legitimate procedure provided no drying is allowed from the sides of the specimen, and the moisture disk is cut from the region of failure.

Calculating the results:The formulæ used in calculating the results of tests on endwise compression are as follows:

P(1)C=-----AP1(2)c=-------AP1l(3)E=---------A DP D(4)S=-----2VC=crushing strength, pounds per square inch.c=fibre strength at elastic limit, pounds per square inch.A=area of cross section, square inches.l=distance between centres of collars, inches.D=total shortening at elastic limit, inches.V=volume of specimen, cubic inches.

Remainder of legend as onpage 98.

Apparatus: An ordinary static testing machine, a bearing plate, and a deflectometer are required. (See Fig. 35.)

Figure 35

Compression across the grain. Note method of measuring the deformation by means of a deflectomoter.

Preparing the material: Two classes of specimens are used, namely, (1) sections of commercial sizes of ties, beams, and other timbers, and (2) small, clear specimens with the length several times the width. Sometimes small cubes are tested, but the results are hardly applicable to conditions in practice. In (2) the sides are surfaced and the ends squared. The specimens are then carefully measured and weighed, defects noted, rate of growth and proportion of late wood determined, as in bending tests. (See page 95.) After the test a moisture section is cut and weighed.

Sketching: Sketches are made as in endwise compression tests. (See page 102.)

Adjusting specimen in machine: The specimen is laid horizontally upon the platform of the machine and a steel bearing plate placed on its upper surface immediately beneath the centre of the movable head. For the larger specimens this plate is six inches wide; for the smaller sizes, two inches wide. The plate in all cases projects over the edges of the test piece, and in no case should the length of the latter be less than four times the width of the plate.

Measuring the deformation: The compression is measured by means of a deflectometer (see Fig. 35), which, after the first increment of load is applied, is adjusted (by means of a small set screw) to read zero. The actual downward motion of the movable head (corresponding to the compression of the specimen) is multiplied ten times on the scale from which the readings are made.

Log of the test: The load is applied continuously and at uniform speed (see Speed of Testing Machine,page 92), until well beyond the elastic limit. The compression readings are taken at regular load increments and entered on the cross-section paper in the usual way. Usually there is no real maximum load in this case, as the strength continually increases as the fibres are crushed more compactly together.

Calculating the results: Ordinarily only the fibre stress at the elastic limit (c) is computed. It is equal to the load at elastic limit (P1) divided by the area under the plate (B).

(P1)c=-------B

Apparatus: An ordinary static testing machine and a special tool designed for producing single shear are required. (See Figs. 36and37.) This shearing apparatus consists of a solid steel frame with set screws for clamping the block within it firmly in a vertical position. In the centre of the frame is a vertical slot in which a square-edged steel plate slides freely. When the testing block is in position, this plate impinges squarely along the upper surface of the tenon or lip, which, as vertical pressure is applied, shears off.

Figure 36

Vertical section of shearing tool.

Figure 37

Front view of shearing tool with test specimen and steel plate in position for testing.

Preparing the material: The specimens are usually in the form of small, clear, straight-grained blocks with a projecting tenon or lip to be sheared off. Two common forms and sizes are shown in Figure 38. Part of the blocks are cut so that the shearing surface is parallel to the growth rings, or tangential; others atright angles to the growth rings, or radial. It is important that the upper surface of the tenon or lip be sawed exactly parallel to the base of the block. When the form with a tenon is used the under cut is extended a short distance horizontally into the block to prevent any compression from below.

Figure 38

Two forms of shear test specimens.

In designing a shearing specimen it is necessary to take into consideration the proportions of the area of shear, since, if the length of the portion to be sheared off is too great in the direction of the shearing face, failure would occur by compression before the piece would shear. Inasmuch as the endwise compressive strength is sometimes not more than five times the shearing strength, the shearing surface should be less than five times the surface to which the load is applied. This condition is fulfilled in the specimens illustrated.

Shearing specimens are frequently cut from beams after testing. In this case the specific gravity (dry), proportion of late wood, and rate of growth are assumed to be the same as alreadyrecorded for the beams. In specimens not so taken, these quantities are determined in the usual way. The sheared-off portion is used for a moisture section.

Adjusting specimen in machine: The test specimen is placed in the shearing apparatus with the tenon or lip under the sliding plate, which is centred under the movable head of the machine. (See Fig. 39.) In order to reduce to a minimum the friction due to the lateral pressure of the plate against the bearings of the slot, the apparatus is sometimes placed upon several parallel steel rods to form a roller base. A slight initial load is applied to take up the lost motion of the machinery, and the beam balanced.

Figure 39

Making a shearing test.

Log of the test: The load is applied continuously and at a uniform rate until failure, but no deformations are measured. The points noted are the maximum load and the length of time required to reach it. Sketches are made of the failure. If the failure is not pure shear the test is culled.

The shearing strength per square inch is found by dividing the maximum load by the cross-sectional area.

(P)Q=---A

Apparatus: There are several types of impact testing machines.59One of the simplest and most efficient for use with wood is illustrated inFigure 40. The base of the machine is 7 feet long, 2.5 feet wide at the centre, and weighs 3,500 pounds. Two upright columns, each 8 feet long, act as guides for the striking head. At the top of the column is the hoisting mechanism for raising or lowering the striking weights. The power for operating the machine is furnished by a motor set on the top. The hoisting-mechanism is all controlled by a single operating lever, shown on the side of the column, whereby the striking weight may be raised, lowered, or stopped at the will of the operator. There is an automatic safety device for stopping the machine when the weight reaches the top.

Figure 40

Impact testing machine.

The weight is lifted by a chain, one end of which passes over asprocket wheel in the hoisting mechanism. On the lower end of the chain is hung an electro-magnet of sufficient magnetic strength to support the heaviest striking weights. When it is desired to drop the striking weight the electric current is broken and reversed by means of an automatic switch and current breaker. The height of drop may be regulated by setting at the desired height on one of the columns a tripping pin which throws the switch on the magnet and so breaks and reverses the current.

There are four striking weights, weighing respectively 50, 100, 250, and 500 pounds, any one of which may be used, depending upon the desired energy of blow. When used for compression tests a flat steel head six inches in diameter is screwed into the lower end of the weight. For transverse tests, a well-rounded knife edge is screwed into the weight in place of the flat head. Knife edges for supporting the ends of the specimen to be tested, are securely bolted to the base of the machine.

The record of the behavior of the specimen at time of impact is traced upon a revolving drum by a pencil fixed in the striking head. (See Fig. 41.) When a drop is made the pencil comes in contact with the drum and is held in place by a spring. The drum is revolved very slowly, either automatically or by hand. The speed of the drum can be recorded by a pencil in the end of a tuning fork which gives a known number of vibrations per second.

Figure 41

Drum record of impact bending test.

One size of this machine will handle specimens for transverse tests 9 inches wide and 6-foot span; the other, 12 inches wide and 8-foot span. For compression tests a free fall of about 6.5 feet may be obtained. For transverse tests the fall is a little less, depending upon the size of the specimen.

The machine is calibrated by dropping the hammer upon a copper cylinder. The axial compression of the plug is noted. The energy used in static tests to produce this axial compression under stress in a like piece of metal is determined. The external energy of the blow (i.e., the weight of the hammer × the height of drop) is compared with the energy used in static tests at equal amounts of compression. For instance:

Energy delivered, impact test35,000 inch-poundsEnergy computed from static test26,400 inch-poundsEfficiency of blow of hammer75.3 per cent.

Preparing the material: The material used in making impact tests is of the same size and prepared in the same way as for static bending and compression tests. Bending in impact tests is more commonly used than compression, and small beams with 28-inch span are usually employed.

Method: In making an impact bending test the hammer is allowed to rest upon the specimen and a zero or datum line is drawn. The hammer is then dropped from increasing heights and drum records taken until first failure. The first drop is one inch and the increase is by increments of one inch until a height of ten inches is reached, after which increments of two inches are used until complete failure occurs or 6-inch deflection is secured.

The 50-pound hammer is used when with drops up to 68 inches it is reasonably certain it will produce complete failure or 6-inch deflection in the case of all specimens of a species; for all other species a 100-pound hammer is used.

Results: The tracing on the drum (see Fig. 41) represents the actual deflection of the stick and the subsequent rebounds for each drop. The distance from the lowest point in each case to the datum line is measured and its square in tenths of a square inch entered as an abscissa on cross-section paper, with the height of drop in inches as the ordinate. The elastic limit is that point on the diagram where the square of the deflection begins to increase more rapidly than the height of drop. The difference between the datum line and the final resting point after each drop represents the set the material has received.

The formulæ used in calculating the results of impact tests in bending when the load is applied at the centre up to the elastic limit are as follows:

3W H l(1)r=-----------D b h2F S l2(2)E=-----------6D hW H(3)S=-------l b hH=height of drop of hammer, including deflection, inches.S=modulus of elastic resilience, inch-pounds per cubic inch.W=weight of hammer, pounds.

Remainder of legend as onpage 98.

Abrasion: The machine used by the U.S. Forest Service is a modified form of the Dorry abrasion machine. (See Fig. 42.) Upon the revolving horizontal disk is glued a commercial sandpaper, known as garnet paper, which is commonly employed in factories in finishing wood.

Figure 42

Abrasion machine for testing the wearing qualities of woods.

A small block of the wood to be tested is fixed in one clamp and a similar block of some wood chosen as a standard, as sugar maple, at 10 per cent moisture, in the opposite, and held against the same zone of sandpaper by a weight of 26 pounds each. The size of the section under abrasion for each specimen is 2" × 2".The conditions for wear are the same for both specimens. The speed of rotation is 68 revolutions a minute.

The test is continued until the standard specimen is worn a specified amount, which varies with the kind of wood under test. A comparison of the wear of the two blocks affords a fair idea of their relative resistance to abrasion.

Another method makes use of a sand blast to abrade the woods and is the one employed in New South Wales.60The apparatus consists essentially of a nozzle through which sand can be propelled at a high velocity against the test specimen by means of a steam jet.

The wood to be tested is cut into blocks 3" × 3" × 1', and these are weighed to the nearest grain just before placing in the apparatus. Steam from the boiler at a pressure of about 43 pounds per square inch is ejected from a nozzle in such a way that particles of fine quartz sand are caught up and thrown violently against the block which is being rotated. Only superheated steam strikes the block, thus leaving the wood dry. The test is continued for two minutes, after which the specimen is removed and immediately weighed.

By comparison with the original weight the loss fromabrasion is determined, and by comparison with a certain wood chosen as a standard, a coefficient of wear-resistance can be obtained. The amount of wear will vary more or less according to the surface exposed, and in these tests quarter-sawed material was used with the edge grain to the blast.

Indentation: The tool used for this test consists of a punch with a hemispherical end or steel ball having a diameter of 0.444 inch, giving a surface area of one-fourth square inch. It is fitted with a guard plate, which works loosely until the penetration has progressed to a depth of 0.222 inch, whereupon it tightens. (See Fig. 43.) The effect is that of sinking a ball half its diameter into the specimen. This apparatus is fitted into the movable head of the static testing machine.

Figure 43

Design of tool for testing the hardness of woods by indentation.

The wood to be tested is cut square with the grain into rectangular blocks measuring 2" × 2" × 6". A block is placed on the platform and the end of the punch forced into the wood at the rate of 0.25 inch per minute. The operator keeps moving the small handle of the guard plate back and forth until it tightens. At this instant the load is read and recorded.

Two penetrations each are made on the tangential and radial surfaces, and one on each end of every specimen tested.

In choosing the places on the block for the indentations, effort should be made to get a fair average of heartwood and sapwood, fine and coarse grain, early and late wood.

Another method of testing by indentation involves the useof a right-angled cone instead of a ball. For details of this test as used in New South Wales seeloc. cit., pp. 86-87.

A static testing machine and a special cleavage testing device are required. (See Fig. 44.) The latter consists essentially of two hooks, one of which is suspended from the centre of the top of the cage, the other extended above the movable head.

Figure 44

Design of tool for cleavage test.

The specimens are 2" × 2" × 3.75". At one end a one-inch hole is bored, with its centre equidistant from the two sides and 0.25 inch from the end. (See Fig. 45.) This makes the cross section to be tested 2" × 3". Some of the blocks are cut radially and some tangentially, as indicated in the figure.

Figure 45

Design of cleavage test specimen.

The free ends of the hooks are fitted into the notch in the end of the specimen. The movable head of the machine is then made to descend at the rate of 0.25 inch per minute, pulling apart the hooks and splitting the block. The maximum load only is taken and the result expressed in pounds per square inch of width. A piece one-half inch thick is split off parallel to the failure and used for moisture determination.

Since the tensile strength of wood parallel to the grain is greater than the compressive strength, and exceedingly greater than the shearing strength, it is very difficult to make satisfactory tension tests, as the head and shoulders of the test specimen (which is subjectedto both compression and shear) must be stronger than the portion subjected to a pure tensile stress.

Various designs of test specimens have been made. The one first employed by the Division of Forestry61was prepared as follows: Sticks were cut measuring 1.5" × 2.5" × 16". The thickness at the centre was then reduced to three-eighths of an inch by cutting out circular segments with a band saw. This left a breaking section of 2.5" × 0.375". Care was taken to cut the specimen as nearly parallel to the grain as possible, so that its failure would occur in a condition of pure tension. The specimen was then placed between the plane wedge-shaped steel grips of the cage and the movable head of the static machine and pulled in two. Only the maximum load was recorded. (See Fig. 46, No. 1.)

Figure 46

Designs of tension test specimens used in United States.

The difficulty of making such tests compared with the minor importance of the results is so great that they are at present omitted by the U.S. Forest Service. A form of specimen is suggested, however, and is as follows: "A rod of wood about one inch in diameter is bored by a hollow drill from the stick to be tested. The ends of this rod are inserted and glued in corresponding holes in permanent hardwood wedges. The specimen is then submitted to the ordinary tension test. The broken ends are punched from the wedges."62(See Fig. 46, No. 2.)

The form used by the Department of Forestry of New South Wales63is as shown in Fig. 47. The specimen has a total length of 41 inches and is circular in cross section. On each end is a head 4 inches in diameter and 7 inches long. Below each head is a shoulder 8.5 inches long, which tapers from a diameter of 2.75 inches to 1.25 inches. In the middle is a cylindrical portion 1.25 inches in diameter and 10 inches long.

Figure 47

Design of tension test specimen used in New South Wales.

In making the test the specimen is fitted in the machine, and an extensometer attached to the middle portion and arranged to record the extension between the gauge points 8 inches apart. The area of the cross section then is 1.226 square inches, and the tensile strength is equal to the total breaking load applied divided by this area.

A static testing machine and a special testing device (see Fig. 48) are required. The latter consists essentially of two doublehooks or clamps, one of which is suspended from the centre of the top of the cage, the other extended above the movable head. The specimens are 2" × 2" × 2.5". At each end a one-inch hole is bored with its centre equidistant from the two sides and 0.25 inch from the ends. This makes the cross section to be tested 1" × 2".

Figure 48

Design of tool and specimen for testing tension at right angles to the grain.

The free ends of the clamps are fitted into the notches in theends of the specimen. The movable head of the machine is then made to descend at the rate of 0.25 inch per minute, pulling the specimen in two at right angles to the grain. The maximum load only is taken and the result expressed in pounds per inch of width. A piece one-half inch thick is split off parallel to the failure and used for moisture determination.

Apparatus: The torsion test is made in a Riehle-Miller torsional testing machine or its equivalent. (See Fig. 49.)

Figure 49

Making a torsion test on hickory.

Preparation of material: The test pieces are cylindrical, 1.5 inches in diameter and 18 inches gauge length, with squared ends 4 inches long joined to the cylindrical portion with a fillet. The dimensions are carefully measured, and the usual data obtained in regard to the rate of growth, proportion of late wood, locationand kind of defects. The weight of the cylindrical portion of the specimen is obtained after the test.

Making the test: After the specimen is fitted in the machine the load is applied continuously at the rate of 22° per minute. A troptometer is used in measuring the deformation. Readings are made until failure occurs, the points being entered on the cross-section paper. The character of the failure is described. Moisture determinations are made by the disk method.

Results: The conditions of ultimate rupture due to torsion appear not to be governed by definite mathematical laws; but where the material is not overstrained, laws may be assumed which are sufficiently exact for practical cases. The formulæ commonly used for computations are as follows:

Back to Index Next