Design of a Seismometer for Local Earthquakes Citation Kingman, Douglas George (1929) Design of a Seismometer for Local Earthquakes. Master's thesis, California Institute of Technology. doi:10.7907/776b-hm65. https://resolver.caltech.edu/CaltechTHESIS:08202024-215722798 Abstract No abstract. Item Type: Thesis (Master's thesis) Subject Keywords: (Mechanical Engineering) Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Mechanical Engineering Thesis Availability: Public (worldwide access) Research Advisor(s): Martel, Romeo Raoul Thesis Committee: Unknown, Unknown Defense Date: 1 January 1929 Record Number: CaltechTHESIS:08202024-215722798 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:08202024-215722798 DOI: 10.7907/776b-hm65 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16658 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 21 Aug 2024 18:14 Last Modified: 21 Aug 2024 18:14 Thesis Files PDF - Final Version See Usage Policy. 19MB Repository Staff Only: item control page

Design of a Seisometer for Local Earthquakes Thesis by Douglas G. Kingman In partial fulfillment of the Requirements for the Degree of Master of Science California Institute of Technolo gy ?asactena, California 1929 TABLltJ OF CONTJiJNTS Introduction 1 Statement of Problem 4 Procedure 5 Summary 10 Acknowledgments 10 Scale of Earrthquake Shocks 12 Derivations 14 Spring Calibrations 21 Teet data 25 Drawings Plates I - VI I The Design of a Seismometer for Local Earthquakes IN'l'RODUCTION In the design of structures to withstand earthquakes it is necessary to know or to make assumptions as to the magnitudes of the forces involved. The static forces, those due to the weight of the structure itself and to the load which it is called upon to sustain, can be found r 9adily enough from the various Engeneers Handbooks or from the local Building Codes. The values obtained from these sources have been tested by time and anyone using them has no doubt as to their being adequate for his purpose. }/hen it comes to the dynamic loads, thos e produced by the earthquake itself, an entirely difi 8rent picture presents itself. For instead of any well organized, authentic body of information regarding the forces of earthquakes, being available, there is no place to which an engirec:r can turn for any relia iJ le inforrne, tion of t.his nature. All that is left for him to do is to assume sor,, e arbitrary windload and riope that it will take care of actual eurthqu8.ke conditions or else to maim an aeosurnption as to the force of any earthquake which the structure is likely to encounter. Now that more and more attention is bein g directed to the design of structures to withstand earthquakes u.nd to b,0sing this design on more than some unproved a :, su:rnptions it is necessary that there be son;e dependable tables of engineering :i.nforrna tion concerning earthquakes which would be abail ~b le to all interested in the subject and which could be used by one with the asfurance that the values present were at least accurate enough for engineering purposes. 2. Som e of the i tems which i t would be i mp ortant to know are: 1. Nax i mum acceleration of earthouakes at the g round s urface. 2. Comparison of accelerations experienced by a structure 9t different floor levels. 3 . Compa rison of ac ce l erdt ions experienced by structure built on rock and those built upon alluvial soil. 0 i n ce an ear t '.'lquake is a dynam ic affair, the accele.r!:l.tion p roduced can be taken as a measur e of the force acting or of the int e nsity of the shock . ·rhus if the acceleration of an earthquake is known it is possible to have a rather definate i dea as to the int e nsity of' t he qua ke . I n orde r to a s certain t~e values of tne acc e l e rations experienced with defin it eness and accuracy it is necessary to resort to instrumental meas ureme n ts. Su ch an instrument is the seismo g raph wh ic h record s t he mot ion of an ea rth par ticle durin g an earthquake. je isffio g raphs as deve loped for scientific purposes are quite sa t i sfac tory an d are y i e l d in g muc h info rmation which is of inestimab le value in the determin a tion of the structure of the earth . F'rom the vi e,•,vpoint o f the en/2; in ee r, h ovv eve r, there are many dra wb a c ks to t he p res e nt seis mof ra ph. instrument. It is a delica t~, costly, and com plicated Its installs.tion requires g r ea t care and s k ill, and its o pe ration is expens ive a n d a s evere d ra ~gh t u p on the patien ce of the obs e rver. The proba Dility of securin g fro m it a record of an earthquake wh ich i s valua ble to the eneine e r i s usually ve ry small as most se ismo g ra phs are built to record li ?nt quive rs and a seve re or destructive shake , w~ic h is of much more en g in ee rin g int e r e st, i s a pt to wr eck the en tire installat ion. Obse rved data, in order to be rnost useful for study and 3 analysis ou ght to be numerous and well distributed over the affected areas. But seismo g raphic obs e rva t ions must, from their costly, complicated, and exacting nature be v e ry f ew and far be*ween. It has therefore been necessary to resor•t to other means of securin g the d e sired data. The method in use at the present time is to classify eartb~uakes accordin g to their effe cts upon persons and u pon their distinctiveness . .Several scales of classification have been brou ght out within the last fifty years. Perhaps the one most generally accepted is the Ros s i-Forel .Scale proposed by Professor di Rossi, of Rome in which quakes are divided into ten classes varying from very weak to extremely strong. This scale is reproduceu on page 12. Professor Omori of the University of Tokio after a series of tests involvin g the forces required to topple columns r1as made an attempt to classify shocks upon an absolute scale of accelerations in ri,rn/sec. His scale is shown on pa ge /2 and a comparison of his scale and the hossi-Rorel on pa8e /3, Wnile these scales are to be commended as attempts at classifying earthquakes, they fall far short of bein g accurate enourh for engineering purposes and it is evident that we rrust rely upon instrumental methods for obtaining the desired knowled p;e . 'l 'o be of r e al service the i ns trument n:us t fulfill the followin g requirements: 1. It must be effective over a great enough range to handle all possible eartnquakes of enginHering importance, w~ich would ran ge from those just barely perceptible to those of the g reatest destructive force. 2. It must have an accurac y sufficient for en g ineering pur pos es. 3. It must be simple in construction and require a r.'1inimum 4of attendance whe n in operation. 4. It must be cheap enou c h th.at installation can be made throughout the entire country in sufficient number to g ive comprehensive data upon any shock t h at takes place and to give a record of the variation in the accelerations experienced from place to place within any locality, such as from floor to floor in a buildin g or from one type of building to the next. 'l 'he desi gn of an ins "crument which will fulfill these conditions is the pur pose of this investi gation. STA'rEMENT OF PROBLEM The problem undertake n in this thesis is that of desi gning and perfectin g a seismograph which will record the maximum acceleration 11 of local earthquakes; which will have a range from .001 g 11 to 11 g 11 , and which can be produced for a b out twenty-five dollars. The lower limit of sensitivity was set at .001 11 g 11 as being one which would be ad e quate to record the slichtest shock which mignt be felt by the avera r: e individual. at 11 ;,: 11 •rhe upper limit was set in order to handle the largest possible shock which mi ght be experienceci.. The cost limit of about twenty-five dollars was thought to be one which would make it possible for the instrument to be distributed in sufficient quantity to insure the securin g of sufficient data to be of value. Of course it was realized that the first model would cost many times the twenty-five doll a rs set as a limit, but it was intend e d to try to perfect the design so that when manufactured on a production basis the cost of t h e apparatus would be within the specified lirnit. 5 PROC.1.:::JUHE Upon undertaking this thesis the assistance of Dr. Sinclair Smith of the Carnep;ie Institute was preferred as vvas also the use cf the equipment of the Institute. An attempt at the solution of tbB problem had already been made by the Carnegie Institute and a model had been constructed. This model was essentially the same as that shown on Plate II with the exception of the indicati:r..g mechanism. ,v'hen taken over this rr,echanism consisted of the primary lever and the pointer which were connected by means of a straight piece of wire. The changes made were; to add a device by which friction could be applied to the primary lever; to substitute a coil sprin 0 connection for the straight wire connection and to introduce oil damping on the pointer. Some difficulty was experiencea in obtaining the proper spring to use as it vvas necessa.ry to have a very iight spring with an elastic elongation of about 100%. Various attempts were made to produce a spring which would be satisfactory using steel or tungsten wire and wrapping it about diff~rent sizes of mandrels. The most successful seemed to be those made of tungsten wire .ool 11 or .0025 11 in diameter wrapped around a wire .04 11 in diameter. .1fter the wrapping, the tungsten was heated in a flame until it became a cherry red and then quenched in wa tcr. ;rhis treatment preserved the shape of the spring after it was removed from ttie mandrel and permitted of the high elongation required. The indica~or after the changes had been made is shown in ?late I and the cornijlete instrument as set up is so.own on Fla.me II. The purpose of the oil damping was to prement the pointer from developing iromentum which would carry it past its rightful position. The friction was a ppli e d to the primary leve r to enable it to ma int a in its positition against the pull of the spring. The princi ple of its o pe ration is that the arm with the ,veight activat e s the p rimary lever which moves t o it s a µp ropriate position and r ema in s t here by virtue of t h e friction on the shaft. The sprin g is e lon ga ted and put in a state of s~ress ~ hic h is r emo ved by the slow mo tion of the po int e r t h rou r;h t he damping oil which continues until all of the stress ha~ be e n r err oved from t h e s p rin g and the pointer has reache d its rightful p osition. 'I'he pointer arm is balanced about the shaft so that it vvil l have no terniancy for mo tion because of the quake. In order to test the s e ismo g ra ph as simply as possible it was deterrr:in e d to app l y va :e ious a cce lerations by a pp lyin g differe nt forces to the wei gh t arm. From the expres s ion f=rna it is seen that in order to apply diffe rent percentages of "g" acceleration to the instrument it is nec e ~,sa ry to ap ply a force of the same percent of the we i ght of the arm and wei e;ht to the we i gh t arm. a cceleration of . 001 11 g· 11 it 'r hus for an is nec e ssary to ap p ly a force equal to .001 of the mass of the arm ar.d weight combined. I' o r:,ake it possible to apply an accurat e ly measured force it was de cided to us e calib r ated sp rin gs . Thre e sprin g s we r e obtained and cali brated for e lon p;a tion a ga inst force. of these springs are shown on pages 2./ , 'l'he cali b ration cur•ve s 22 ,and Z3. I n testin g the seismo g raph the p rimary leve r was so arran ged t h at it just rested a ga inst the we i [(n t t1.rm at a p oint about . 2 of its length from the sha ft. 'r he fo rce necessary to p roduce a p redit e r mined ac cele ration wa s a p plied t o the arm and the d eflection of t he pointer not e d. In order to facilit ate the transfer from forces to acc e lerations a force acc e leration curve was drawn which i s shmm on pa r e Z4. 7 Tests were just made using a spring of tungsten wire .0025 in diameter. The observed data of this test is shown in tabular form on page 2.5 and in graphical form on pae·e 26. From the curve of deflections against accelerations it it seen that an acceleration of .043 "g" is necessary to overcome friction in the indicating mechanism. It is also seen that the apparatus can not record one greater than .265 11 g 11 without going off the s c.ale. Since the instrument will not record accelerations less than .043 "r,n or more than .265 "r," the problem presents itself of selecting a new arm which will respond to an acceleration of .001 and will handle all values up to 11 11 g 11 g~t In order to accomplish this the work was organized as folLows: 1. Compute the normal deflection of the present spring arm under a force of .043 g. 2. Compute the actual deflection of the arm. 3. Determine the difference in deflection due to the frictional resistance of the pointer. 4. Determine the force of the frictional resistance. 5. Determine deflection of spring corresponding to deflection of pointer of 1 mm. 6. Assume different spring sizes. 7. Calculate length and weight for period of 1/6 sec. 8. Calculate force in grams for acceleration .001 g. 9. Determine normal deflection for .001 g. 10.Determine decrease in deflection due to friction. 11.Determine actual derlection of spring. 12.Determine actual deflection of pointer. 8 The develO f)rnent of the diffe rent formulas necessary in the carr y in g out of the above pro g ram is shown on pa ge J~ and the d e termination of t h e mass required is shown on pa ge /6, The calculated weight neces sa ry, 45 lbs., was thought to be too large for convenience, so another test was run on the seismo g raph usin g a tun g sten wire sprin g .001 in diameter in place of the .0025 in. sprin g used before. pa ge c5 The results of this test are tabulated on and are shown in graphical form on pa ge 2h. Up on calculatin g the mass necessary to produce a deflection of 1 mm for an acceleration of .001 g it is found that a wei ght of 25 lbs will be required. This work is shown on pa gel7. Since 25 l b s s eemed a r e asonable wei ght to use, it was d e cided to as sume different sizes of arms and t o calculate the len c ths and deflections. 'rhis work is shown in Plate III. The arm selected as b est mee tin g the requirements is 1/4 x 1 1/2 x 18 9/1 6 with the c enter of the mas s 1 3 5/16 in fro m the s u pp 0 r t. The mass is to consist of two cast iron wei ghts each 5 in. diameter by 1 31/32 in hi gh. When the d e flection of the arm was computed for an acceleration o f 11 g 11 the value obtained, 0.371 in, wa s much too g reat for the pointer to stay on the scale. S ince the allowa b le deflection of the pointer was known, the maximum permissable deflec t ion of the a rm was found b y assumin g a value for t h e ma gnification of the indicator from the curve on pa ge 20. The p roblem the n pre sen ted its e lf of cu tt in g do wn the maximum deflection of the arm to such an a mount as would keep the point e r on the scale and at the same time to maintain the valu e of deflec t ion corres pondin g to an ac c elera tion of .001 " g 11 • The most feasible wa y of doin g this seemed to be in having some me ans by g which the effective len g th of the arm could be decreased at the higher accelerations. The easiest way of accomplishing this appeared to be in having two curve d surfaces, one on either side of the arm so arranged that as the amplitude of the motion increased, the arm would bear upon the surface nearer to the mass, thus decreasing its effective len g th. The calculations involved in selectin g the proper curvature for the two surfaces are shown on pa ge 19 . From the results of the calculations it appeared that it would be necessary to have a radius of curvature of 4000 in. Since the production of such a radius of curvature is beyond the realms of prac tical machine work, this plan was abandoned as impractic~l. An alternative idea was to allow the arm its full deflection and to reconstruct the indicator mechanism to take care of this, In order to make t h is change, it would be necessary to make the primary lever longer on the side where it touched the arm and to arran ge the p ointer so that it :JVould be free to make seve ral rev0lu tions. A g raphical an~lysis of such an arrangement as shown on Plate IV shoNed the scheme to be entirely satisfactory. By utilizing this idea it was possible to draw· up plans for a new instrument which would fulfill the specified conditions. These plans are shown on Plate V and the accompanyin g force ac ce leration curve on pa ge E7. Professor R.R. Martel of the California Institute of Technology thought it would be well to draw up plans of another intensity meter which would not attempt to cover such a wide range as the one just ment ioned but which would deal with accelerations to 1/2 11 g 11 and which would be even varyin g fror,; about 1/20 ngtt simpler than t he other. This suggestion was carried out and resulted JO in the design of a seismometer consisting of a horizontal pendulum with a pencil at the end bearin g upon a piece of paper . 'l'he displacement of the pendulum and hence the len r th of the mark on the paper varies from about 1/16 in. at an acceleration of 1/20 acceleration of " g n. page /7 II [ 11 to 1 in. at an The calculations of this design are shown on and the plans on Plate VI The work done in the course of this thesis consists of: 1. Perfecting the design of a magnifying, indicator mechanism . 2. Constructing and testing a seismo g raph. 3. Apolying the results of this test to the design of a new seismograph which will fulfill the specified requirements. 4. Desi~ning an additional seismograph of limited ran ge and simpler construction. Acknowledgment is g ratefully made of the kind as s istance and helpful sug ~estions of Professor R.R. Martel of the California Institute of Techn ology who was always ready with a su p.:gestion whenever a difficult problem presented itself. tr /'- 'l'o Dr. Sinclair Smith of the Carnegie In s tituti ' goes acknowled gment for much aid derived fro r:1 discus sin g with him the various problems which arose durin g the course of the work and for the generous financial aid which he secured with which the ~odels were constructed. Credit is due to t h e members of the staff of the Seismolo g ical \ ,<. / •• Laboratory of the Carnegie Institut~· of Washington for the use of II their tools and other facilities and for the kindly interest which they displayed in the work. Ro s s r-~nR~L SCALF ow EARTHQUAKF 8HOCKS I. Microseismic shock: recorded by a single seismograph or bv seismographs of the same model, but not by several seismographs of different kinds; the shock felt by an experienced observer. II. Ex tremely fe ebl e shock: recorded by several seismographs of different kinds; felt by a small number of :persons at rest. I II .Very feeble shock: felt by several fersons at rest; strong enough f'or the direction or duration i:.,o be appreciable. IV. Feeble shocl'": felt by persons in motion; disturbance of moveable objects, doors, v.rind.ows; cracking of ceilings. V. Shock of moderate intens ity: felt generally by everyone; disturbance, furniture, beds, etc. ringing of some bells. VI. Fairly strong shock: general awakening of those asleAp, rPnPral ringing of bells, oscillation of chandeliers; stopping of clocks; visible agitation of trees and shrubs; some startled persoms leave their dwellings. VII . strong shock: overthrow of moveable objects, fall of plaster; ringing of church bells; gene~cal panic, wi thou.t damage tobuildingso VIII. Very strong shock: fall of chimneys, cracks in the wall s of buildings. IX. F.stremPly strong shock: partial or total destruction of some buildings. X. 8hock of extrerr.e intenF:ity: r:reat disaster, ruins, disturbance of the strata, fissures in the ground, rock-falls from mountains OMORI'S ABSOLUTE SCALE OF DESTRUCTIVE EARThQUAKES No .1. Maximum acceleration == .300 mm. per sec. p er sec. The motion is sufficiently strong that people generally run out 01~ doors. Brick walls of bad. construction are s.l i ~h tlv cracked; :furniture ov erthrown; wooden houses so much sh::,.ken that cracking noises are p:roduced; trees visibly shaken; waters in ponds rendered slightly turbid in consequence of the disturbance of the mud; pendulum clocks stopped; a few factory chirr.neys of' very bad construction damaged. No . 2. Maximum acceleration =- 900 rrun . per sec. per sec. Walls in Japanese houses are cracked; old houses thrown slightly out of the vertical; tombstones and stone-lanterns of bad construction overturned. In a few cases changes are produced in hot springs and mineral waters. Ordinary factory chimneys are not damaged. 18 No. :3. Maximum acceleration= 1200 mm. per sec. per sec. About one factory chimney in every four is damaged; brick houses of bad construction partially or totally destroyed; a few old wooden d.vrelling-houses and warehouses totally destroyed; wooden bridges slightly damaged; roof tiles o1' wooden ho1.J.ses disturbed; some rock f'ragments thrown down from mountain sides. No. 4. Maximum acceleration= 2000 rnrn. per sec. per sec. All factory chimneys are bro1cen; most of the ordinary brick buildings partially or totally destroyed; cracks two or three inches in width produced in low and soft grounds; embankrnents slightly damaged here and there; wooden bridges partially destroyed. No. 5. Maximum acceleration = 2500 mm. per Bee. per sec. All ordinary brick houses are very severely damaged; about three per cent of the wooden houses totally destroyed; embanlcments severely damap;ed; railway lines slightly curved or contorted; cracJ::.s one o:r two feet in width produced along ri,1 er banks; waters in rivers and ditches thrown over the banks; wells mostly affected with changes in their waters; landslips produced. No. 6. Maximum acceleration =4000 mm. per sec. per sec. Fifty to eighty per cent of the wooden houses totally destroyed; embankments shattered almost to pieces; roads made through paddy fields so much cracked and depressed as to stop the 1->assage of wagons an<i horses; railroad lines very much contorted; large iron bridges destroyed; wooden bridges partielly or totally destroyed; craclc.s a few feet in width formed in the ground., accompanied sometimes by the ejection of sand and water; low grounds, such as paddyfields, 1rery greatly convulsed, both horizontally and vertically; sometimes causing trees and vegetables to die; numerous land-slips produced. No.7. Maximum acceleration much above 4000 mm. per sec. per sec. All buildings except a very few wooden houses are totally destroyed; some houses, gates, etc., projected one to three feet; remarlcable Janclslips produced, accompanied by faults 0.nd shears of the ground. COMPARISON OF SCALJ!:s ABSOLUTFI SC.A.LE AccmJ F:RATI ONS INTENSITY ROSSI-FOREI.i SCALF. Slight 1 2 weak ?; 4 5 strong1-300 2-900 3-1200 4 2000 5-2500 s 7 Violent 8 9 10 /4 DEVELOP MENT OF FORMULAE Half period of Simple Harmonic Motion of cantilever beam ( 1<1irth & Buckinp;he.m - Vibration in Engr. ) m =mass f /d = force :r-equired for unit displacement I t::fT✓~d t: 11v4m1 3 3EI By dimensional reasoning: n, = "FT 2. slugs E -- -'F'z L I=- 1 L 4 feet 4- feet L == L Which check s . ~onverting the units: m in lbs.;. 32 = m in slugs 2 lbs.fin. x 144=lbs./ft. I in in! ;. 20,736 = f t f Lin in;3;. 1728 = rt.3 Ji: in then t :rT. mL 207 36 (32)(1728)(3)(E)(l44)(I t = 1T lrriL3 ~4 =7T m 13 1152FI for the half period VF.I for the whole period AFJsu.mptions: t = .166 t 2-= 712- mL 3 from F, (I ) =30,000,000 (I) 17a.EI L 3 2 w m L 2 = 17·~\ EI = 290 - (289)(.166 )EI= 24,390,000 I ,,-r2.m m (II) /5 deflection of cantilever beam with concentrated load at the free end (Boyd-Strength of Materials, pl48 ) l 3 = 24,.'390,000 1.. E = 50,000,000 m d = 24,390,000PI = (3)(30,000,000)Im . 271 P m (III) Deflection due to acceleration of .001 11 g 11 ll'=.00lrn=P d= ( .271)( .OOl)(m) = (IV) .000271 in. m Deflection of ~ointer Magnification assumed Displacement assUined Displacement of arm 500 1 mm. .1 ( 500 )( 2. 54) .0000787 in. per mm. of pointer (V) FORMULAE USF,D IN THEr :SFLECTION OF THE ARM (Ii) Length to weight from support= 290~ m Weight of arm= Length+ 3 x wt from p49 Carnegie Pocket r,omp. 12 Period of' arm= .:JI.. 17 /mL = .1847 ✓ Irlli EI F.I 3 3 Deflection of acceleration 2 cl== P(l - a) (2l+a) (I) (Boyd-Strength of Materials pl49) 6EI Deflection of friotion d = Pl 3 ( BOYQ - page 148) 3'F'I Deflection of pointer= displacement of arm . 0000787 mm . /6 COMPUTATION OF WEIGHT USING SPRING .0025" in diam. Asswne that the weight arm makes contact with the primary lever .2 of its length from the pivot. From the curve the magnification is seen to be 500. ~rem tests the movement of the pointer corresponding to an acceleration of . 073 11 g" is 3. 02b cm. The deflection of' the arm actuated bv this force woulo. be = deflection of pointer ~ map.:nification. 8inne the weir.ht arm changes its position relative to the lever, Wf! will assume an average maP,:nification of 200. Deflection of arm= 3.025 = .01513 cm. or .00595 in. 200 Deflection of arm, no friction: z. d = P(l-a) (2l+a) 6F.I 1=6.687 a= 2 437 0 I= .00000533 P E = 30,000,000 = 39g =.086 lbs. 2 d ; (.086)(4.75)((2)(6.687)-2 437) = . 02!16 in. (6)(30,00 0 ,000)(.00000533) 0 Difference in deflection due to frictional resistance: Diff. = .0256-.00595 = .01965 in. Value of frictional resistance: P = (3)(30,000 1 000)(,00 00 0533)(,01965) = .0319 lbs.=14.5g 6.6875-3' Gheck; From curve, force to overcome friction = .073 11 g 11 or 23g Assume the force is applied at the center of gravity Fiqui valent force at end = ( 23 )( 425) =14. 6 P:. 6.6875 Deflection due to f::riction from (III) d = ( 271)( 0?119) = .00865 in. 0 0 m m From(IV)deflection of acceleration= .000271 From (V) displacement required= .0000787 Normal displ.-f::rictional displ. = required displ . . 000271 . 00865 - . 0000787 m m(.000192~) = .00865 m = 45 lbs. 17 r:OMPU'l' ATI ON O'F' WEIGHT USING SPRIUG • 001" IN DI AM. From curve, force required to overcome friction equals .Ol54"g" W~ich is 8.2 ~o or .01806 lbs. Deflection due to acceleration = . 000271 in. from (IV) From (I1I) deflection of friction= (.2?1)(.01806} = .00489 m m From (V) displacement required= .0000787 in. Normal defl. - defl. oi' 1'riction = required 1er'l. .000~71 - m .00489 = .0000787 m = 25. 45 lbs. CAL0ULATI0NS FOR APPROXIMATE SEISMOMETER .3 wrom derivation of' (II) L = 24,390, OOOJ. m For different values of T, 3 1 == 24,390,000 I when t t = .166 2 m .166 2 Since the equation for the deflection, d = . 271 P is of the f'orm m 3 the deflection for other values oft will be: d ::::: _fl ' 3EI 2. d = . 271 P t z. m.166 wor a force of 1/20 "g" it is desirable to have a ,:1.e!'lection of To get this, let Pin the above equation equal m/20, substitute different values oft and solve ford. .063 in. Values oft Corresponding values of d .01:355 .166 . 20 .01965 .30 .04425 . 40 .0755 L .; 513n m Assume f'rictional force = 20g or . 0319 lbs. der,l. of' friction "" ( 1. 51 )(. 0319) = . 0482 m Assume necessary det~lection equals . 0755-. 0482 m m • 06Z 11 = . 063 m = 3. 8fi or say 4 lbs. JB L = 51~3/r .314 y ··· = '2,23y"I I .Assume L = 18 11 -vr,,, -1:_ 323 = .000174 Assume an arm 1/8" thich, then a width of 1-1/16" will be required giving a moment of Inertia of .0001733 AfJsun.e v✓ eigh ts diam. then length of the arm = 20 in. 4" in Weight of arm= (,425)(20) = .'708 lbs. 12 l\.ioment of (.708)(10) ( 4 )( 18) Total = arll1 Moment o:i:' weight'"' e.g. 3 Period. = .1847 ~ = = 7.08 72,00 = '79.08 79.0 8 = 16.8" 4.708 9 = .1847 ✓( 4. 708 )( 16. 8' ) F I ( 3 0 , 0 0 0 , 0 0 0 ) ( .0 001733) Defl. for acceleration 1/20 11 g 11 d d 2 2 6FI (180,0 00 ,000)(.0 0 01733) =P ( J. - a ) ( 21 +a ) = (.235)(16.8)(43.2) = . 0918 in. Assume force of .0368 lbs. Defl. of friction 1 = (,0368)(8000) (180,000,000)(.0001733) Net deflection .0918 . 00944 acceleration 1/20 11 g 11 • 08 2 36 in., Net deflection acceleration d.e:el. .00944 in. .0918 X 1/2 11 g 11 10 ::::. - .918 .00944 • 90856 in., accel. 1/2 11 g 11 /9 y ~ ► l x,y -----------.:::-... f' r --- -- --- r Lei d= ----- ~ y d '°' y + P(l.-x) !?Y (l - x) f- t o fa/ derlec flon l = l en9lh x,y.; po1rd -x cf' arrn -longency OT r = radius or cu,,-volvre 3 3EI dx .., X x-== r .:sin ¢ .s in i ton</,= sin</:, - rX + ,I;- rz x co-s¢ cf --=- i I - s/n 2 <f CC-5 r 2 L,- ::: 1 ::: c'::-x ..... 1 r~ X 11' ,r L_,Xz._ y =-r-·rcos ¢> :. r (/-co.5 cp) = r(J -,(rz-,52-) == r- ir -xz. 2 r r--y r -x d = 2 2 -t- (?-x) + P9: - x)_ 3 X y r -x 2 3 2 CALCULATION No. r I ;c 2 2C- p 3EI 2 X ~-+_12,9 .0001236 /2.9 .a:::o/2'36 15 3 cO e 4 /OC 5 5 /00 B 6 200 B -·--- - - ····· · I OF r2-,)(Z CURVATURE ,' r'-.xz l-X !Hx (l-)() P{.l-.xl 3 75 B.66 7, 9 375 /9 . 36 -·- - - 4.56 0,06/ 5.961 79 _______ L 2.04 006/ 2.741 4.9 i 2.c4 I 18.33 d ..3EI I rz.-,r• -· 001175 --- ·- ··--- /2 ,9 .000/c?-:36 33G 12,9 ,00OIE36 9,975 99 .87..5 7. 9 I I I 0.395 0061 C. 5 8 1 12 .9 .0001236 9,936 99.6 79 4.9 I /2.9 .OCJ0/£'36 39,936 199.84 - - - - -·· ---· -·-- · - 3.92 , 4.9 ! 0.393 0.01175 07Eb 0 , /9 6 0.011?.5 036G .0001236 89,936 299.894 4.9 , O.l.:31 0.01175 Oc49 ,00()/£36 249,936 14-99.935 4-.9 !I 0.0784 0. 0//7.5 0. 155 00827 00407~ 0./60 00826 OOE'53 0.1569 ·-- _ _ _ .,!...._ 7 - .:300 B 1 12.s 8 sec B -9 6CC 6 12. 9 ,0001236 249,.964 499,96.3 6. 9 /0 5CO 7 12.9 ·.0001236 24~9!5/ 14-99.95/ I/ /C-00 e 1£.9 .00012..36 99Q936 999.967: 4 .9 ·· I - ·----- ·- ,.._._-- - ·· - ·· t · · - - - - - - - - - - - - - - ---- ·----- ----- -- ···- - · --- · ' .. ·· - --- ; lc.9 ·- -----·-- 6.9 I 003 9e 00//7!5' 0026/ OOl/7S 0 .0..598 0084 ,_.i,. , le / .500 B / 2.9 ,00012.36 2,249,936 1,499. 9781 4-. 9 13 2000 8 12.9 .000/£36 l:1,9.99,936 1,999,984 4.9 I z. 999. 992, 4 9 ·--- Q O/Q G 001/75 0.047.:3 ..___. 0.0130.6 0 011 75 0 0326 ·- · 0.0098 0 001175 O.Oc/55 /4 3000 B 129 .G00/236 8 ,999,936 15 4000 8 12. 9 .000/~36 V5,99Q936 -'.:!, 99Q99,:',I 4 . 9 /6 5000 8 129 4.9 ! .000lc36 24,999,936 4,999.993- -· 000784 001175 0.01959 17 4500 B 12.9 .OOOJe.:36 20,24.9,936 4,499.99£' 4 . .9 O.OOB?E 0.0117.!:Y 00c'Q4.7 IB 5500 8 12.9 .OOOIE?36 3{),c49,936 5,499 .993 4 .9 0.007/Eb 0. 01/7:;> o .01e07 /8 6000 B 129 .0001236 3.5,999,93t 6 000 0.006.!53 0,01/7.5 001838 ---! - -- -- ··----- .. 4 .9 .. . --- ---·-·· --- - - -- 20 ,.: z ai 0 :f~~-•]'.;:_:iAA,tJ:tc~lt~Fm;: ••t· ,·:12:r'! 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I\ _._: \ . . .. : \ ~~ - -- _ ~ : .,., . : • ' - L;·'.·: I --i---;-- + - - - , t - - - 1 - ----4-....-l--:_:_: -:---::t~-t::-:-::t-:~-t---t---'-+-·-'-t+'---lf--'-:_;.+~..;__-,+.:_:_:_; • • :'\ f - ' t':~h--'-J~:-t-·,_;_•+i\-\;:-":.:_.+__:.~i-:-:...:.i:.;.:;,:_'.:.:;:+t:::.':. . ,:·_;_J:.:_:_;_.:..j_;•_;_•.;...' : -: . : i ::.. ••• • 11 _ :\ ~Hi TJi!ST No. Spring OF SEISMOGRAPH spring Measurements Af'ter Lengths Before Front Back Front Back Before After Elong. Force Acc. Derl. Spring made :from .0025 11 tungsten wire. 1 1 2 1 ~ 2 4 7.55 1 ..'35 . 5308 .001 0 1.00 9.60 8.60 2.40 1.0616.002 0 2. '7 5 10.65 7.35 7.90 .55 2 2.90 11.'75 8.85 1.50 .18 7.00 5 2 2.90 11.75 8.85 1.50 .18 7.25 6 2 3.10 12.70 9.60 2.25 . 265 7.70 .70 6.90 2. 65 10.00 1.00 8.55 6.20 . 073 :S.02!'3 Spring made from . 001 11 tungsten wire . 6.3 8.4 2.1 .8 .., .00155 0 3. 75 11.10 7.45 7.53 . 08 507 2 3. 60 11.30 7.70 .25 15.2 . 0285 1. 46 2 3. 63 11.50 '7.87 .42 24.0 .045 2.45 2 3. 73 12.50 8.77 1.32 74. 6 .140 5.36 7 1 .80 8 2 3.45 10.9 9 10 ,, ..1...I. 7.1 1.10 9.5 0,- ;) .0105 .65 ! ·-•--·· :----- : -· i - --~- - --~----- '--- ! • I I t . ' I i : _i . -I ! ; . ' ; I / -~J·•---~--J___J __+'---+---+--1 I • -1 i l i 1--l--1 i i . . l \, t ·_.. ·+--+----;--t--+---+---+--+-1--+-~-;---+--+--+--+--+-_;,___+---'---+-! --_· ••,__ ;-- --1 -·-t_ -··--+------+---+-l----+-----i--;..---+,---i !- . i i- -- :----1---r- ---- - • ! : r • - ·-:r·-- r - T l .1. I l ! -- -··-r----r------·· i• ---··r-·-r-. .1---~-. 27 : -• f- : t _,· T::":-: .. ·•· •--'-'+--.,.+~-4--'-1----'..J.... . :l ' .C: y~ , . . ; . ; _: . ' J -.~--+--4--,...I • ·- ' · ·_, ·.:-~-t~t-:-:--t:--:r--t:--'.+-:---r~+--:-:+___;_~d-+--+_;_;_+:-t_;_;_-+-~~ij_s5:..;..!~L...:J ... , ; \ _:_ .:~i.. rI :i . n~t-r4±t~f:d~~~~-,:j;~~~~+-+--+-----+-~~~~~ . • ! .•. I 1 I PLATE.I I 2.· I I ,-...;:: 0. 4£' ··-> C.18 . r r /c f /on Arm /L:n9.sren vv1re. C c. ii .sp ~lng c?-66 F lot Fillisft=r Head tv1. 3. -, -< 0. /0 ),,, r P o ,nfe r A rm ' - - - - ~ ~ - - - - - - - - , - - - - - - - - - - - E..25 ,n. long f------------i--------------1-------1-------~ y- INDICATOR Dr. D . K In Dote n--,an Moy 23,192.9 .s._a /e - B x n c rrnal PLAT£...ZZ .___--------------------,------------~-- L - 12 - ' y 00 INTC:NSITY METER Dr. D . Kinqrnan Dede May , 17, 192-9 .Scale 6"= l'-0'' PLATE J7Z srLCCTION OF ARM No. Wt Arm Center of Gravity Feriou Derleclion or Gravity rricfton Nef Der/ rbrce 2-a Z2ra Der/ rorce Der/. Del/ Poinle, I 25# 2in .375ir, 19.85 4.28 .008 4..96 490 5450 2925 18.6 ./64 .02328 166 49.95 ,000352 .0//47 .000/90 .000162 2.06m~ 2 25 ;i_ .25 IZ.40 1635 .tJtJ/95!5 310.0 IZ.6 322.6 26.64 12. I 3 25 2 .4375 23.85 6.66 .01.3~ 596.0 895 685..5 31,66 21.68 ./633 .0.3166 2/68 5887 .00034S .01/47 .CCOl7J .ca:J/7? c./9 4 25 2 .500 26.9{; 846 .020 67Z.5 /c'6.7 7992 3346 Z390 ,/62 ,03346 2390 65.8 00t1J49'i .01/47 ,tZ0/7<0 ,tml7S 2275 5 25 2 .562.5 2970 /044 . OP96~ 7425 17/0 91..3.5 35.44 25.75 ,/53 .03544 2575 72.35 Oa2318? .01/47 ,a:<?/52 .tm/68 2./35 6 25 2 .cso 12.48 1.768 ,002 7 25 2 ./875 /02/ 1403 .a:71097 2.550 9.26 264.?6 26.40 /000 B 25 2 9 25 /0 25 Width Thick Lenqlf, Wei9hl I Mofwt Wofarm Tofa/M lota/wl c.q. ./658 .02664 12. / 34./ .a?0.3X5 .0/147 .000236 .000140 /78 3/ZO 13.68 325Gc. c6.77 /2./6 ,/662 .Oc677 12.16 3428 .000371 .01147 .tm?366 .CllJ/4tJ4 1.765 ./66 .OZ64t /0.00 296.3 .0a7396 .0//47 .<'.'.WE6:S .tmlcB 1.627 .lc5 6.BE 0.695 .CW325 1705 3.41 /73.41 2569:. 6.75 ./666 .0257 6.75 22.7/ .00045,j .0//47 .aJJ372 .O:W73 0.928 ;J .125 6.75 0605 .a:oc84 /68.8 2.95 V7l.75 25.61 6.70 .1758 ,02561 6.70 22.55 .00t)50J .0/147 .@417 .a:12J90 1143 ;J ,250 1305 /99 .mcc8 326.0 15.97 341.9? 26.99 12.66 .16!53 .0269!; 12.66 3.5.49 .0::037.2 .01/47 .w231 .caJ/44 183 ··- -· .375 /9.55 4./9 .CXJ768 488.0 47.E5 .535~ 29./9 /834 ,/63 .029/9 18.34 49.3/ .az85/ .01/47 ,OZJ/93 .a::.o/56 1984 II 25 1: /2 25 ;J ,5CO 26.05 721 .01823 6Z6.C°J /04.70 7307 32.21 2270 .l.536 .03c£1 22.70 6445 .@326 .01147 ,aJJ/7/5 .tm/55 1.97 - /3 25 I .zso /085 0983 .001303 27/0 /4 25 1: .250 / l.65,/.c0B .00/628 2914 8.74 3a?./4 c6.21 11.45 ,/66 /5 25 2}. .250 14 cO 2.740 .0029.3 355.0 c..3.55 p78.5.5 27.74 /364 ./656 .0Z77 /364 37.98 .0003/2: .01147 .ClZJcZI .mJ/.51 /.92 6.81 277.81 e5.9o /0.6B ./666 ,0260 10.68 30.87 .caJ39/ .0114? .We~ .atl/3/ 1665 .026Z 1145 32..50 .000.39tE .01147 tmc46..5 ,(lZl/.36 1.727 . -·--- •- - - I /. 7/ /.34.9/ zo.35 6.63 .166/ Oc'035 6.63 22.35 .a::mss .0/147 .CJ:ZJ47/ /6 20 /z .125 G.66 0354 .@£445 /33.Z 17 20 ;j ,t?!50 /335 1736 ,t:o/9:55 e67.o 14-.2 281.2 2174 /2.92 ./65 .02174 IE.92 36./3 ,a:2J37.c.5 .01147 .a:oe85 ,{M87S /./IE IB 20 ,375 ?000 318 .a7659 4CJO.O 36.6 436.6 e.3/8 /8.BZ ,/634 ~02318 1882 50,/8 .0:034? .0/147 .twc/4 .a:lJl/c /.424 /9 20 ;; Ii .500 20 20 1J ,c5o 13.375 1.74 .00195.5 cGB.o /4.E6 k?Bc.26 21.74 12.97 ,/664 ,02/74 /2.97 3916 .a:o4tJJ .01/47 .a2?c6'6 ,Cl:Z1/ZI /537 21 20 Ii .250 V33lc'5 1733 (lJ/955 266.0 /4./4 280./4 21733 1290 ,/653 .02173 lc.90 36.03 .CW37/ .01/47 , tlm8'3 ,arlJ88 11/8 22 26.70 5.66 .Ol!J63 534.0 84./ 001 me c~s .. - c:. ~1 618./ E5.G6 24.10 ./6/6 ,02566 24./0 65.0 .tm..344 .01/47 .a:oc/4 .tll:J/30 165 21.73 lc..90 36.03 037/ .0//47 .Oa?c~ 0.371 55.?ln PLATE .BZ" 0CALE OF DEFLCCTION.S A cce/er. 03 71 ° Di.sp/. 332 ° 4.35 0./q 441° 0.2 527 498 0 .3 56/ 5E'7 0.4 06 08 584 602 6/3 550 562 0. / I I / / ,/ \ I \\ I \ \ \ \ ------- ~ \ i' \~ 0. I \ o. / \ \ / \ \ / 0./ \ I I o.3 \ \ \ \ 0. I. • ··-- -------------1.0 -// -- - Derleclion or 109 =-0.37/in. ANAL Y.:SI.S Detlecfion or IOq ==- 0185 in. or .:Scale-1.c''~G" RE."CORDING May 10, /929 ACTION D.Kinqrnan I 7=LATE. JZ 1 L:J' · / /(b ~ A - A- Cb 'l(\J --.. '{ - y_ ' - j x.!:J Bolf · -24I C ounfarwe,ihl Poinfer ~ -13 /1: cj lcr_ig "' ~Ccnsf Iron .... -:j x j f--lol head MS. " 6 0- .,. -Sprinq i - l------------------7------- gx;j jx/ U.5.5 Bolf..s USS Bolf y -3 I 8 x/4Cap Screvv ' 'tff-x/ USS Bolf..s INTENSITY METER Dr. D. Xinqman Scale 6 "=/'-0" PLATE. J2T A I I -< A - - ..3 ► I I 0 0 0 01 PAPE.:f=:r ,- I ' II ~J ' iol(b i ,: I L~ ..... " I - 0 4 I ' I, I I i l I:I I I I y - 4 I I, I 'c">tro .L x/_j_ ' r:n, rm-, , I ' ~j r~ ~ ~ I I I X- I -~ ~ ~ ,f rlafheacl MS~ _£ Jfj _(_ /6 2 U . .S.S. Bolls - 01 0--0 -· y_ I -c -1:/ _!I,.. 8 i y I -27 • - Pencil_ ,., Ca,5f Iron /8 =--< I -ee- Weight_ .Sprin9 S feel Arm • -------- j -- _\,...______________-1.>:.../- - - - - - -- - - - - - - - - - -- - - - - - - , ~=--=:-1- ,f\lJ C e 0 -0 - x- - - - - - - - - - - - - - 1 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - , - - - - - - -. U ..S.S. Bo/ t.s ' INTENSITY METEf? Dr. D. Kingman .Scale J Size Do/-e l'vfoy E.5,1929