II II III I I III III I II urn—u (- r-v-‘r- CALIBRATION OF A BEAM TESTING MACHINE I THESIS FOR DEGREE 0F :3. s. C. J. MITCHELL .W. G. HAGADORN 1926 '- v,‘.vv,._. __'_ ,— .«v “f,_, ‘. ' {THESIS CALIBRATION OF A BEAM TESTING IsmCHINE ----- -ooOoo------ A Thesis Submitted to the Faculty of Hi chigan State College by C. J. Etchell W. G. Hagadorn Candidates for the Degree of Bachelor 'of Science June 1926 -W'~ I " my. ' The fire which destroyed the Engineering Hall and shops on March 5, 1916,~also destroyed all the departmental equipment. The most necessary articles where replaced as soon as possible in order that the college work might continue. One of the things which was not replaced at once was a machine for testing beams. In 1919, H.H.Hiemp baugh and R.L.McGaw, senior students at the college, decided to build a beam testing machine to take the place of the one destroyed by the fire. ' The work was done as a Thesis under the super- wdsion of the Civil EngineEring Department. The machine is composed o: a reinforced concrete base, 16 feet long, 26 inches high, and 36 inches wide, which supports two hydraulic Jacks. The pr0.93 sure is applied by a commercial hand force pump with a one inch plunger. It is connected to the Jacks by a 3/4 inch flexible copper pipe to provide for vary- ing the span between the jacks by allowing them to 10:391.; be moved. The pressure is measured by a gauge placed in the pipe line at the pump. Through the center of the base beam are four steel rods 1 1/4 inches in.dianeter, threaded and de- signed to carry the load by'tying the standard beam to the base bean. The pressure is distributed by two 3" x 12" x 18" cast iron plates, one placed beneath the base beam, the other placed at the top above the beam to be tested. The upper place has a knife edge attached beneath it by a.half inch machine bolt. The upper plate is supported by two nuts placed beneath it at apposite corners. Although this machine was completed in 1919 it has never been calibrated so that it could be used to advantage. For this reason the writers decided to calibrate the machine so it might be used for testing beams in the future. The manner in which this was done follows: Standard Notation Mbdulus of elasticity of steel. Total load at the center. Momen t. of Inertia . Section.modulus. length of beam. bedmum deflection. h 2 Height of beam. If P - load at the middle then \each reaction is g and the moment from the left end to the middle is g . For the portion of the beam between the left ' end and the middle 9 _ E I d” I PX: 652% 2— EI§ I P32 g‘. C I g ' ‘ \ h At the middle from the symmetry of the sides, gee 0.0 C' - -g' “e = e3 - e. At the left support where X = O , Y 3 O .'. 02 : 0 E I y 8 P13 - P121 1'2" IE At the middle where x - é - 3 Y m " P1 - P13 W" W Y max = - P13 43 E I u . ‘ .fl . .. -- ._ A 7 inch - 15# I-Beam was selected as a Specimen for testing. ‘ Length - 9 feet - 0 inches. Total weight ‘ ‘= 155#. E - 30,000,000. I (from Carnegie handbook) = 36.2. S = 10,000# ~ From strength of materials SI - E T - + P 3 431. w Substituting the above values r = 4 x.1o,ooo x.36.2 : 4,ooo# - 9 x.lz x 5.5 Ymax = - P13 (4000) Elos) (1082 . .07" t" D D ' From these calculations it is seen that the maximum deflection.that the beam will stand without permanently deforming it is about .07 of an inch. it rostpgu-n‘ Am 4 The beam was placed on the Bhiele testing machine in the mechanical engineeringlaboratory which is accurately calibrated and capable of ex- erting a pressure of 100,000 pounds. The accompany- ing picture figure # 1 shows how the beam rest on the machine . A dial gauge reading to one thousandth of an inch was placed under the cent er of the beam and pressure applied. The results are shown below. Load Gauge Reading in thousandths of an inch. 220# .041 450 .048 650 .055 790 .0576 1060 .065 1510 .072 1600 .0805 1860 .088 2100 .0951 2370 .1028 2650 .1105 ;. .3. p .‘v (.5 13am. $12.1 that whofiLilIiuM , qualms»! all {an .;. . eel-saw F/G. / I‘-‘ ‘I F/Cy. 6_ These results were plotted on graph paper as shown by graph #1. ‘ The same beam was carried to the machine to be calibrated, usingthe same Span. The beam was placed on the machine as shown by the accompanying photo- graph,Fig.#2.‘..l' ‘ . The first machine in which, we tested the beam was so arranged that the end reactions were stationary and the load applied at the center deflected the beam at the center. In the machine which we are calibrating the lay-out is Just-the Opposite. The two hydraulic Jacks which form the end supports are raised by oil pressure applied through the pump while the center is held stationary.. The results are the same. Two dial gauges reading to. one thousandth of an inch were used. Directly over the hydraulic Jack on each end a gauge was arranged so that any upward movement of the Jack was registered on the dial gauge. A series of tests were run and the averages of the whole lot were plotted on graph paper. Several of the tests are shown below. Gauge Reading ivsr' QQQO’OUPUNI—‘O +4 F’ +4 l4 P’ r4 14 0: en .5 s: on +4 <3 Test #1 Dial #1 Dial #2 Dial #1 Dial #2 ‘1000' 0 .004 .008 .012 1.016 .021 .025 .080 .080 .088 .044 .047 .052 .056 .060 .064 .068 0 .005 .009 .013 .017 .022 .026 .030 .039 .040 .044 .047 .053 .058 .061 .065 .069 Test #2 0 .004 .009 .012 .017 .021 .025 .030 .034 .039 .042 .048 .051 .056 .058 .065 .067 0 .005 .009 .013 .017 .022 .026 .030 .034 .040 .045 .049 .054 .057 .061 .066 .070 in1 I! in # Applied Average Pressure 0 .0045 .0090 .0125 .0170 .0215 .0255 .0800 .0850 .0895 .0440 .0480 .0525 .0565 .0600 .0650 .0685 O 145 290 415 560 700 845 985 1155 1300 1445 1585 1720 1865 1990 2140 2260 Graph # 2 shows the results of these tests. The applied pressure upon any beam may be de- termined by n0t1ng- the gauge pressure and finding the correSponding applied pressure from this graph. Explanati on of Graph # I . The results of tests run on the beam testing machine in the basement of Old's Hall are plotted in Graph 2;“ l. The deflection in inches of the beam are plotted against the corresponding applied pressures in pounds. This machine being assumed as accurate, it was used as the basis of results employed in fur- there tests on the machine which was to be calibrated. From this graph.can.be found the deflection due to a certain pressure or the pressure necessary to produce any given deflection. The method of such determining is easily understood at a glance at Graph # 1. Graph # 1 is a straight-line function and was translated to the origin, as shown. -10... W.“ _- .40...- u. - . .Q-¢”"'¢3“ . *“hh .I. .I.. .A —~..—..r——-—._...__‘ '...p.—......._.— .4... .... . w. 4.0.. We . fA ¢ J .. . a A A .... :1... A A , . _. A ...—...~~.~n_—.~.~_.»--—._~Ap. . 6’49? .. u _ A .. A A A A .A A A . ._ A {U A AA .A . z i. A h n JV. . A i e A A _ . A .. A i. A w... A a . _ A . 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