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curve. Choose scales such that the slope of the diagram near the origin shall be about sixty degrees. Each division of the paper must represent a decimal increment. Plot each point plainly. Draw a straight line averaging those points which precede the more rapid increase in deflection. Tangent to this line draw a smooth curve averaging the subsequent points. Mark on the curve the elastic limit and the load at failure, i. e., the maximum load. If the straight part of the curve does not pass through the origin, draw through the origin a dotted line parallel to the first. This line will represent the relation between the load and corrected deflection.
(2) Compute (a) the modulus of elasticity E by use of formula 4, page 254, Church's Mechanics of Engineering (d and P are taken from any point on the corrected line). (b) R", the fiber stress at elastic limit. (c) R, the fiber stress at rupture. (d) U", the modulus of elastic resilience. (e) U, the modulus of rupturework. To compute the modulus of resilience at elastic limit or rupture, divide the inch pounds of work done upon the beam up to that point by the volume in cubic inches of the part between the supporting knife edges. Also find the values of the exponents x, y, z and w in the following equations pl h
Beams of equal length.
Beams of equal depth.
For equal loads and equal depths. d.
-() = (1)"
P and P" are loads at elastic limit.
d and d, must not be taken beyond the elastic limit, and must be taken from line of corrected deflections.
Compute the weight per cubic foot and the specific gravity, assuming that the per cent. of moisture on the basis of dry weight is 12 per cent.
The Report.-Give a brief description of the method of conducting the experiment. On following pages present the measurements, etc., of the beams; the sketches of cross sections and fractures; the data obtained; the diagrams, and then the computed result in tabular form.
EXPERIMENTS IN TORSION. Object. The object of this experiment is to study the behavior of materials under torsion, and to obtain such data as will enable the shearing strength of the material and its modulus of elasticity in shear to be computed.
Material. The material is to be supplied by the instructor, and may be steel, iron or wood, or other material.
Preliminary.- Carefully measure the dimensions of the cross section and the gauge length. Then adjust the specimen in the heads of the machine, being careful to have the jaws clamped tightly against the specimen, which should be fixed in the axis of rotation of the machine. Then apply the torsion troptometer to the specimen and adjust the clamps of the latter so that the center of the circle of the graduated arc will be in the axis of the machine. Apply a small initial moment of about one hundred inch pounds and set to zero the graduated arc, and also the permanent scale on the twisting head of the machine.
Experiment.-- Apply the loads continuously in increment of -- inch pounds. Read on the graduated arc the movement of the pointer in inches for each increment. When the increase in the angle of torsion is found to be rapid, the elastic limit having been reached, the graduated arc and index should be removed.
If only the elastic properties of materials are to be determined the specimen may be removed. Ordinarily the tests are to be continued until the specimen is ruptured. The whole angle of the twist is read from the fixed scale on the movable head of the machine and should be read for even loads above the elastic limit. The scale should be kept balanced and the maximum load determined.
Computations.- Plot diagrams to suitable scales with the twisting moment in inch-pounds as ordinates and the angle of twist in degrees as abscissa. One of these curves will be drawn with the magnified abscissa and will show the points up to the elastic limit. The other curves will be on a small scale and will show the anglemoment diagram up to the rupture. As in other experiments, the straight line portion in the beginning should pass through the origin. If it does not, a straight line parallel to the straight line passing through the plotted points should be drawn through the origin and terminating at the elastic limit.
Mark the points corresponding to the elastic limit and maximum load on the curve. Compute (1) the shearing strength developed at the elastic limit and the maximum load, using formula
Calculate the modulus of elasticity in shear from the formula
aps Ip Pa
i Using the coördinates of any point on the corrected curve of the magnified scale.
Compute also the modulus of elastic resilience and the modulus of rupture-work.
Report.-The report will contain (1) a brief description of the specimen and method of test, (2) a tabulated statement of the computed and observed results (rule a form to suit the requirements), (3) a description of the fractured specimen, (4) plotted curves on coördinate paper, (5) an ink copy of the running log of loads and deformation.
INSTRUCTIONS FOR TESTING CEMENT.
(Short Course.) The work will include two days in the laboratory, and during this time the student will determine the time of setting, the fineness on No. 100 and No. 80 sieve, and the strength of three to one mortar in the case of a standard brand of Portland cement.
Time of Setting.–Mix up neat cement with enough water to render a paste of such consistency that when placed on a glass plate it will retain its form, and at the same time by striking the glass against the hand
* See Church's Mechanics of Engineering.
the paste can be spread out without cracking on the suface.
Trowel the paste on the glass to thin edges, and set the pat thus made aside in a damp chamber, and observe the time that elapses until (1) it will bear the quarter pound standard needle without appreciable indentation; (2), the weight of the one pound standard needle without appreciable indentation.
Tests for Strength. – Mix up the mortar consisting of three parts standard crushed quartz stone and one part Portland cement, proportion being taken by weight. Mix the sand and cement thoroughly until the mixture presents a uniform color. Gauge with about eight per cent. of water and work over the mixture thoroughly about six times. Tamp in molds in layers, and finish the surface of the briquette. Record the initials on one corner of the briquettes, and leave the briquettes in the molds. They will be taken therefrom by the instructor and placed under water after twenty-four hours.
SECOND DAY's WORK. At the laboratory period one week following, the briquettes are to be taken from the water and tested for strength.
Tests for Fineness of Grinding.–Sift about four ounces of cement through No. 100 and No. 80 sieve and weigh the residue left on the sieves.
The Report.- Each student should report the results of the tests made by him as an individual to determine the fineness of grinding, the time of setting, and the strength of the five briquettes. Reports should be made on blank forms provided for that purpose.
Special instructions are issued to civil engineers.