_ 5:23,:32::_E_:__:__:__ J .h.“. ,,,,, ..~ 0 3 v9 Ivy-an .‘u ‘11:..U‘Iv.‘ .| \fr I‘v»vb- .IA\uh; .nArt \ .K.olu>ot\tu|-‘oro|.. v I. u. .k; pk; burbbr- Inn»... n‘..‘~‘.n~.‘ w a, ¢ ‘ .. .‘ . ‘ I .32.... 1” .. .. ~51....1..... ..,. a. s! nqnlinou.¢ri.¢4.drll¢.,|ut.fll » :5 .LI. JJAHW J . .. u . . .V. . r THE USE OF POLARIZED LIGHT IN STRESS ARALYSIS. A Report Submitted to the Faculty of the K101113311 Agriculture]. College By Louis higrrieon Candidate for the Degree of Bachelor of Science M. 16, 19“. THEéIs C20 9. \ Acmowlodgncnt is hereby made for the help of w fethoi, Professor Edwin Ron-18021 or the molce Department, without whose suggestions this theeeo could not have boon '1'1 t3“. F‘s 51“ w (:3 was f"\ V Table of Contents. Part I. P88° Introduction 1 Part 11. Theory of Polarized Light 4 Part 111. the Action of PDlarised Light on e Stressed Transparent Iodel 12 Part IV. Deeoription 0: Apparatus need in.the Cater Photo-Elastic Method. 20 Part V. Test: on the Strees Distribution in cement Briqnettee by Photo-Elastic Methods; conducted hy Prof Coker 23 Part VI. Studies Conducted in the Physics Laboratory at E. A. O. 38 Part VII. Conclusions 31 BibliOgrephy 52 - 1 - Part 1. Introduction. the purely eechenicel lethode by which experimentel eclntione ef etreee problue ere etteehed ere both difficult end often quotioneble in their reenlte. One hee to eeeue et the etert thet the etreee ie proportionel to the negnitede of the etrein. Me principle cen hold only within the elee'tic linite of the uteriel end bqond the electic linit theee nethode feil entirely. Further- eore etreeeee within the bob cennot be neeenred by eechenioel devicee. Whetever the errencueent ney be, it ie not pceeible to neeenre the etreee et e point ie the M ie eanected to etreee rerying from point to point. in e neJority of the problem which eriee in ectnel practice the etreeeee chenge repidly fro- point to point end our information hee been obteined either from neinc nechenicel equipment or free eeth-seticei inveetigetioee. w neth-eticel reeeerch it new be poeeible to obtein erect eolntione of e variety of compliceted problem: but even the einpleet of problem offer greet difficulty in eolntion. For exemple, the deteminetion of the etreeeee in hoohe. chein linke, riveted pletee, the effect cf notchee end helee of verione fame in teneicn end compreeeion where, bee-e. pillere end ehefte, the dietribntion of etreee in built up etrnotnree ench ee plete girdere, riveted frnee, melonry dene, etc.. etc. he Opticel nethod of deteuinins etreee dietribntion end inteneity hee proved to be very eccepteble. During the leet few yeere thie eanect hee been ettecned with e very eetiefectory - g - degree of mono by e number of inveetigetore, emong which ere Profeeeore Pilton end Corner end neJcr Low of mglend end I. liceneger of Frence. Perhepe the meet notable epplication of Optical etreee enelyeie hee been nede by neeneger who, from e gleee model. lede e deteninetion of the etreee dietribntion in e bridge of rein- forced concrete to be pieced cfer the river lhone et Belne. Prence. inc General Electric Cal-pew hee done coneiderable reeeerch work elong thie line, in deter-icing the etreee dietribntione in verione typee of eteee turbine bnent deveteine end tenone with different typee of iced. rho hereon of deronentice of the levy Depart-lent hee recently Iede e etndy of e celluloid model of the eirehip “ahenendoeh' by eeene ef photo-electic nethode. me work wee done in the lebore- toriee of the leeeechneette Inetitnte of technology. me levy Deperteent will give no definite etet-ent of the reenlte of the teete. but they heve expreeeee th-neelvee ee being well pleeeed with the dete obteined. nu etete thet the experiuete will be of ndietinct velne end of neteriel eid in the deeign of eirehipe to prevent e repetition of the 'zn - 2' end '30-! dieeetere'. Prof anene who conducted the teete etetee: "w thie photo- eleetio nethod we cen loot into the veet end intricete net work of the dirigible end eee enctly whet it going on when it ie leboringe we cen eee how ehe ie ce‘rrying end dietribnting the loed. We heve Iede en enelyeie cf the 'Shenendoeh'.ehowing exectly how the etreeeee ere tehn up by the “bore cf the frene end the wiree. then we °"_1,:" Lecitqo‘ fxo not-1m) qus chem ,ieloex‘eecig e «or! mag—«g. air: to each“: n a: 303*}.‘6171335 gm .eml’l an 63ch 16??! as“ ‘18? Meet eldccslt .hnoc enob eee the hi enoitndnteib eee'lio ed: urn-Jr guinea“ ban enamel: sew-m - Wee-x ted tnenfleqed war “at: to .. i Weds!- ataxia and to :91. We“ ($1 each use HOW od‘.‘ . W .3 $901me in can-ti: ”to 33131891 an: to daemdn‘t r 2 . file m the glued to uricem..: to ed in; “Wm 5:3: 33:13 fl ”1413328 In an“ end-3 at! 3i: 1. ."eeeeeeeie may we '3 - n = mm nu: ‘” acetate nae: end . to rm ten “ennui hm. :anv odd c ”Ciel N 31 ”no 31303 It cut: end ea .bcol end “Mitten was «We en! end vita-axe utmeflsu A; W -‘i t- VI.” (9413 :91: 01‘}. 3 311‘ - 3 .. heer of new forcee which the chip nnet meet in ite venturee over- heed we cen try then out on the model here et fechnology.’ * he eodel coneiete of «veal thou-end piecee of celluloid lechined enctly to ecele end fitted together in e ninietnre deplieete cf the eir ehip. - 4. .. Pl!" IIe rho mory of PolerieedLight. In order to nnderetend the photo-electio nethod eone knowledge Inet be hed of light nvee end of plene polerieed light. it it Of intereet to note thet the phenanmon of polerizetion hee efforded concluive proof thet light wevee ere treneveree wevee. . thet ie the ether perticlee which tree-it light vibrete et right englee to the direction in which the dietnrbenoe ie being propegeted. up: ie refreeted in e definete way when it peeeee fro- eir into glue or other tmeperent enbetenoee. there ere certein cryetele, however, which beheve in e different now towerd light. Bertholinne in 1669 firet noticed thie ee e doubling of en obJect eeen through e perellel eided cryetel of ieelend eper or eeleite. he found thet when e been of light etrihee the enrfeee of ench e celcite plete perpendicularly. one portion of the light goee etreight through in the one eenner it would in e plete ef gleee, while enother portion ie bent eligntiy en entering the firet enrfece. gcee through the plete in thie oblique direction end then bende beck into e direction perellel with the origieel ene ee it leevee the eeoond eerfeee. thie eryetel flieh divided the light felling upon it into two perte. eeeh pert being refreoted ucording to e different lee ie celled e 'donbly refreoting oryetel. the firet of the two perte deecribed ie celled the ordinery rey. becenee it follcwe the ordinery lewe of re'frection, end the eeoond pert ie celled the extreordieeey ray. A netnrel cayetei of celcite ie in the fore of e rhcebohedron .. g .. two cppoeite eolid engiee of ma ere bounded by three ohtuee englee. the opticel enie ef thie oryetel ie perellel to e line dreen through tee of theee eelid eeglee eqnelly inclined to ell three fence. Q J—H- > T“~ I r}: I I I - \ \ \ Lb [71.9. I O <— ----+-- In Figure l. e h repreeente the optical exiet o the ordinelyrqtend I theatreordineryrey. then e plete ie out out of e celcite oryetel ec thet ite feeee ere perpendiculer to the opticel ene, then e rey of light etrihing m feee perpediculerly ie not doubly refreeted. end it peeeee through the plete in e direction perellel to the opticel exie, which ie the enie ebcut which the oryetel ie quetrioel. l cryetel celled touneline note in e einiler nenner to celcite bet in eddition it hen the preperty of ebecrhing the ordinery ray eupletely within e very ehort dietence, while it ie feirly trenc- perent to the extreordinery hey» if two pletee of toumeline ere pleoed open eech other, only the extreordinery rq will get through the firet plete. me will go on through the eecond plete if the opticel enee of the two pletoe ere perellel. If the eecond plete ie - 5 - turned so thet the enee ere not perellel when the extreordinery rey enters the second plete it is divided into two parts, of which the ordinery pert is ebsorbed end the extreordinery gets through. this pert thet gets through becomes greduelly fainter es the turning continues, end diseppeers entirely when the plete hes been turned through 90' from the first position- On peesing the 90' position the light resppeers. end regeine lull brightness et 180'. i1neohenicel eneIOgy will eeplein the phenonen shown by the crossed tourneline orystels. inegine e long flexible rubber tube .A I. Figure 8,‘with.one end.feetensd to the well end the other end held in the bend. By noving the end of the tube held in the bend. A, to end fro it is possible to sense trensverse weves to travel - 7 - down the length of the tube. if e block of wood with e slot out in it is pleoed over the tube. it is evident thet the notion of the tube will not be interfered with so long es the slot is perellel to the direction of notion. If the tube is vibrnted et right engles to the slot the vibreting motion will not be eble to puts the block of wood. Illegine thet the end of the tube much is held in the hend is oeused to vibrete in e nhber of different directions. If the slot is in e vertioel position. of ell of these vibretory notions inpertsd to the tube only those which ere in s vertioel direction will be trenenitted or peseed through the block. if e second slotted block is pleoed over the tube. those vibretions which pen the first slot will pose the second providing the second slot is perellel to the first. If the second slot is pleoed et right engles to the first, no vibretion will pess. this lseds us to essnne thet ordineiy light «mists of e trensverse weve motion, the vibretions taking plete in neny directions. when such e been pessee throng: e tournelins crystel, only vibreticns in e certein direction ere ellowed to peee, so thet the trensnitted ten differs from ordinery light in thet the vibretory notions of the ether pertioles ere ell in the seas plane. this being the ones, it is evident thet this bees of light cen pess e second tonneline erystnl- only when it is perellel to the first. the been which peesee the first tourmaline plete is seid te be "pleas polerised' end the plete is celled e 'poleriser'. no second plete eote es e detector of the polsrised condition end is celled en "enelyser". - a .. in order to use eeloite es e poleriser or enelyeer it is money to devise e-e neens of getting rid of one of the bone within the orystel. itch tourneline does neturelly. the liool prise wee devised for this purpose end unless use of the principel of totel reflection. ”gt-ens showed thet the double refrection is eosonnted for by the fest thet the ordineey end extreordinery rays travel in the crystel with different speeds. fhet is, celoite hes two different indices of refreotion fer the two bosses. A rhub of celcitensybeont es sheen infiure 8. endthe two helves ere oesented together egeie with Genede belu. edter the two oblique surfeses heve been polished. the refrutive inden of the bele- is internediete between thet of oeloite for the ordinery aid entree finite/fl I/// / 59.3. - 9 - ordineq revs. nae former eeete the beleen file et en engle greeter then the oritioel eagleend is totelly reflected to one eide and new be ebsorbed by some dert eurfsce. We. therefore, here e plene polerieed been of polarised light merging tron the prion, whose direction of vibretion eq be ‘ohenged by roteting the prise. figure d givee en. ides. of the notion of the Nicol prion. it shows. rev of light with its rendoe vibretione before entering the pri- eud eeerging on the ferther side es s re: of pleee polerised light. fl—bmw% 7 WW. F19. 4. I! a plea. p01erited bean of light is pasted through a plete of querte or nice of the prayer thickneee it new be ohenged to e circuler polarised hen. that in, the ether pertioles me in e oireulsr orbit. A thin plete of nice or quarts is out with its optioel erio ‘ perellel to the plete. is e boa of polarized light pessss through this plete. ordinery end extreordinery reye ere egein produced, executing vibretioee in directions 90' to eeeh other. Figure 5 -10- chowc e bean of polarised light which strikes the plete perpendi- euler to the surface of the plete end to the Optical exis. A. B. In this use no bending of either rq occurs. but one is reterded eorc then the other. the difference in reterdetion depending on the thickness or the plete. 2e here. therefore, en eeergent reg of light nede up of two ohponente, the extreordinery re: vibrat- ing in the horizontel plene end the ordiner: in the rerticel plene. If the plete is cut to ouch e thickness thet one of. these rue is reterded e querter or e were length with rsepeet to the other. eny ether particle, sew st P. is nede to vibrete up-end down end side were st the some tine. if one trein ic e qusrter of s pcriod behind the other, the reeultent vibretion is e circular one end circularly poleriecd light in eeid to be produced. In order to produce e seperetion into two perpendiculerlr polsrised regs, es described ebove. the direction or vibretion ef the incident light not mere ouch en engle with the optic exis i h thet neither of the components a or D venieh. These ouponent - n - vibretions not be equel to prodme diroulerly polarised light. i'herefore the direction of ribrstion must nets an eagle of is. with the cptieel exie in order to mete the component ribretions end-1. !he plete now then be pleoed four different positions 90' epsrt to produce circuleri: polerissd light. if the. ends d. 3 shown in Figure 5 see ohenged to the werticel. the incident rw would still nets a engle of is. with this exis, but the reletive reterdstion er the horisontel end wertieel component urgent reps would be reversed in sign. the result is thet the direetion cf vibretion of the circulerlr polerised be. terse piece in the opposite sense. Imerefore in order to reverse the direction of circuler vibrstion in s oireulerly polerised be- it is nerely necessery to rotete the querter were plete through 90' in its piece. If polerised light is peseed through two qusrter were pistes with ens st 90‘ with eech other the effect of one plete is neutrslised by the other, end the rw racins uneltered. lice end querts ere canonly used to m cuerter were pletes. nice being usuelly used in lergs pistes. - 1g . M m. the notion of Polsrised Light on e Stressed frenepereet Iodel. refers considering the notion of s stressed neuter on s rq of eirculerir polsrised light it is secesserr to mow smcthing of stress in gweerel in e W nedin. A etste of stress eee elm be represented by two etrceeee st right engles. end if their directions end eegnitudes ere tum over the whole spool-en the stste of stress is capletely detereined. flees principel stresses. celled the p end q eyet-e sleeps intersect st right eagles end ere nonei end tengent ct bounderiee where there erc no sppiies stresses. figure t shows the primipel < O L {has P Lines F73. 6 - 1a .. stress lines for en ellipticel hole in e menber under tension. it ell free bounderiee thcre cen be no normal strcss so thet either p or q lust Venishe fiese principel stresses always coincide with tho dircotion of serc sheer, so thet the sheer et en: point has a min“ value in pieces st “5' to the principel stress directions. this sheer intensity reries eocording to the sins iew from e maximu- of 1/8 (p - 1) et 45' to sero in the principel stress directions. nose feats hold true for en oyster of piece stress end ere of greet eid in “ti-sting stress distribution. For three dieeneionel stress the sons lees hold true, with on extension to three dimensions, mirt- (l) the principal. stress directions ere represented by three systems of liner nt 90‘ to each other. (a) it ew bounding surface. morn no applied farce: exist one of these directions is normal end the other two coincident with thet surface. (a) m piece coinciding with two of these stress directions in e plene of sec shear. (4) ill plenes st dd’ to these planes ere planes of maximum cheer. (M The cheer rel-ion tron e neximum in these 45' pieces to zero in the principel stress pieces ecoording to the nine law. then s pleuc ctrecsed cpeeilen of celluloid is pleoed in e. ben of oirsulsrlr polarised light. on ection occurs siniler to thet occuring in the querter were plete. an is. the were of - 14 - lifit new be thought of so being sepereted in two polerised coe- ponents with ribretions st rigit engles, end in this one with their directions of wibrstions coinciding eith the principsl stresses eentioned ebore. if the principel stressee ere unequel one of the wibrstions is retsrded with respect to the other end this reterdetion is proportionel to the principel stress differ- enceet the point considered. this in the lsw which connects the lint effect with stress. astheesticelly it new be exprcssed es follows:- Beletire retsrdetion '- e (p - q) t (l) where p - one principel stress n _ u‘w ~‘§‘~ ~~ h u torment x ~~*‘t§§~«‘n* x a”: ‘fi‘ifi‘ 5‘- ?t-‘g‘f‘ 0‘“‘ I: 5". ~§ :N. 32 (S) \l - 15 .. q '- the other principal stress t " the thickness of the specimen c I the Opticel constent for the materiel used. Figure 7 shows e hem of circularly polarized light passing through e stressed specimen. then the light emerges the polarised cnponents st right sngles ere retarded different mounts with respect to one enother scoording to the lew stated above, end therefore the emergent vibretion is plene circular]; or ellipti- osllr polsrised depending on the snount of the relstive retards- tions of the couponents. Figure s showes the verious chenges this vibration goes through for ever: eighth wave length relstive reterdetion. For whole wave length reterdstions the light vibrates Just es the incident: for odd helf wave lengths. 1/2. , 3/2 . 5/2 etc. the vibration is circulsr but in the apposite direction to the incident. for odd querter wave lengths the vibrations ere plene polerised, end for odd eighth were lengths elliptioelly polerised. The reeson for using oirculerly polarised light on the stressed sample is thet no mutter whet the principel stress directions ere. the plene poler .. 15 - ised canpceents perellel to these directions, into which it is separated, lust elways be cf equel amplitude. 1911s is true because lineer components of s circulsr notion st right sngles to each other are slows of equal uplitude. therefore it nekes no differ- ence et whet sngle the specimen be turned in e plene perpendiculer to the light direction, or whet direction the principal stresses 1) end 4 thb. the vibretions of the liglt emerging fruit the specimen ere sleeve of the some character and therefore like the forms shown in Figure 0. me engle of the .srging plene end ellipticeliy polarised light. however, does depend on the stress directions, end changes so the supple is rotated in its plene. On referring to Figure 'I the two ellipses shown rill turn so the s-ple is turned. After trensnission through the suple es expleined shove the light is of the ohsreoter shown in Figure 7. lbs direction of the oupcnent vibrstions depending on the principel stress directions. but the relstive retsrdstions depending only on the difference in eegnitude of the principel stresses for e spool-en of given thick- sees. eccording to the lew ststed in Iquetion (i). if this light is trensnitted through enother qusrter weve plete end enother licol prise polsriser, the result is thst- for ell points of the specieen where reistive retsrdstions of integrsl weve lengths (see Pigure d) ere produced the light is ell out off: for odd hslf weve lengths it is ell trenseitted, end the snplitude of vibrstion veries cocci-ding to the sine lew for intensediete points. This lew is expressed esthnsticelir es follows:- - l7 «- .i ' An sin '7' A where A - amplitude in - maximum smplitude )— I relative retardation of vibration components in wave lengths. The intensity of light varies as the square of the amplitude and we have:- I ' 1‘ sin'rrA where I - intensity of illumination 1. - minus intensity. All the light transmitted through this ascend Nicol prism is of course polarized in one plane. The above discussion is true only for e single wave length, or nonochronatie light only. If red light were used, the light projected on e screen would cOnsist of s castes: of black and red hands. Second end higher orders of red would sppeur when the difference between the principal stresses p and q wee greet enough. Where p end q were equal or where the stress wee zero the red would all be out out and black would result. also}: would elso result where p and q differed by an mount which produced on even wave length relative retardation. For odd helf wave length relative retsrdstions the maxim rod would appear. annilsr results ere produced.hy sny single wave length or color, but different colors are retarded different amounts by e given stress. the result is that the system of bands of one color do not exactly overlap those of another color. they are - 1g - shifted with respect to esoh other ad for several colors the shifting results in repented series of colors in piece of whet wss e single bright end desk bend in the ones of e single color. nu. is illustreted in figure 9. which shows e series of colors obteined fro- ectuel observation, st the Gonerel Electric storetories, on e couple of celluloid 0.1. inches thick end 8/. inches wide. rho . I Stress in lbs, per 5a. In. F79 . 9. stress wee curled up to coco pounds per squsre inch. four different colors ere shoes with their chsrssteristio verietions of intensities snpsrinposed. which gives s series epproxinting the mm. the: indicete the we; the color series is produced. is 1) end «1 differ nors end nore this series of color nu peso through nore then one order. As (p - q) sboreeses (Iquetion l) the colon posses through drfinits series. for celluloid this sequence is shout es follows: beginning er (p - q). block. strss. orsnge, red. blue green. end sgein straw. crenge, rm blue green. etc. rho color effect gives s sensors of (p - 11) only, end not the velues of p or q. - 19 .- In order to hsve n complete determination of the stress it is neossetsy to have (p + q) elso. mic is msde by means of an exten- suseter measuruont. only color observations are necesseiy, how- mr. shore p or q venish. an. principel stresses p and q ere elwsys nor-cl. end tangent to free edges and also there can be no noml stress at s free edge. Therefore, p or q must vanish end the remeining stress is tengent to the edge. it ell free bounderiss, therefore. in e plene stresses specimen the order of color is e direct meesursnent of the stress magnitude. since edges ere ususlly regions of nexim stress this is e fect of ilportenoe. For e simple reotsngulsr tension esmbber or for parts of e been of unifon cross section. there exists only one set of principel stresses end here else the color gives the stress directly. no neutral eeis of the been my show es s derl: bend. For meny ceses, however derk erees will represent erees where p on Q have finite vslues but ere equel. the stress nsgnitudes corresponding to perticuler colors one be reed directly from the color. A sample of the same meteriel es the specimen under investigetion is taken and the vari- ous colors ere celibreted in tons of stress. Another method is to belmce out the color until e dark field is produced, using a piece ef the some meteriel. on which the intensity is honoured by e spring balance. .. go - Part IVs Description of Apparatus and in the Baker Photo-Elastic hethod. P G E '- : .8 c. a z’ - _--—7 -_.—u— - \ ’r 6 H ” ”<5 fll HI Mb ‘, 1:}:318’i‘ \\ -___ _-__- I’ K ‘~ $3114" ‘:::== ” I Figure 9 is e disgrmtic representation of the optioel epper- etns used end shows the path of the light reys. The epperetus des- crited is in use et the cenerel slectric Oonpeny's neseeroh storetories. Light from s source A pesses through e condensing lens 3 end e weter screen 0 to reduce the heat rays. It is then passed through e poleriser D. this unit consists cf two 4. 1/2 inch condensing lenses end two smell conceve lenses errsnged es shown in Figure 10, in combination with e licol polerising prism of celcite. the inter is less then one inch in disaster, but with the combinetioe of lenses gives e d 1/: been of polarised light. ) I I) Nic A o/ 9'13”? F73. /0 no plans polarised light is then pessed through e quarter weve plete of mice J, which changed it to circularly polarised light. This is pessed through the trensparent specimen under investigation. This specimen is in the plene marked ,1". The light then pessee through lenses 3. 1' mid G end through the quarter were plete I which is similar to J except that its axis is st 90’ to that of J and therefore counteracts the effect of J. m. resulting light is analysed by the polariser u with its plans of polarisation 90‘ to thet of the polariser D. m light is finally projected upon the screen i so that points in either the plane P or Q in which ever the specimen is placed. ere brought to e focus on this screen. The colors produced depend directly on the stress distri- bution in the specimen. The models are usually made of celluloid on eooount of its greet flexibility and toughness and the ease with which it been be drilled, turned or meohined. this materiel hes e value of l - 355,000. more is no very pronounced elastic limit end the .. 32 - stress defornetion curve is very nearly ttreight up to e load of 1900 pounds per square inch, which mq be taken so the elastic limit of the meteriel. Part 1 gives the results of one of e number of experiments conducted by Prof. echer by this method. - 23 - PIN Vs Tests on the Stress Distribution in Consent Briquettes by lhoto-Blsstic liethods . rho stress distribution in sweat briquettes is of a very com- plex nature. The loads are applied very obliquely to the contour at four points end the shape of the briquette invites much complexity. m. is at once evident from the 1121.. of principal stress in the British standard form in fiich the contact loads applied by the grips produce a complicated stress system which would be practically impos- sible to unravel emocpt by experiment. ‘ In experiments conducted in 1913 hot. Coker found it impossible to messure the stress distribution completely, but an ettmpt was made to find the stress difference (p - (1) across the minimum and principel section end thereby fix the relation between the maximum stress there and the mean spplied load, since at the contour 1 must be sero at every place untouched by the grips. sass earlier measurements on the British standard briquette indicate that this meximm stress is about 1.75 times the value cf the mean everage stress soross the section, and in the standard American form of that date the corresponding value was found to be 1.70. while in the continental form it appeared to rise to about 1.95 times the mean stress. mess measurements have been repeated and amplified recently, so that it is now possible to give a better idea of the actual stress systems at the central sections of each fans, and Figure 11 - 24 - shove the distribution obtained at the minim sections of each briquette. is will be observed the distinctive feature of the distri- bution in each case is an eatr-ely variable tension p across the ainiau cross-eestin sees-paid Iv a variable cross-stress c at right angles of considerable aacnitude. In the sritish fen. hr sample. with , a load giving a seen average stress of Soapoundspersquareinch. thehicheet valueof p atthe outer contour is .70 pounds per square inch, or 1.74 tines the value of the sen stress, ahich sinks to £05 pounds per square inch at the center. or slightly acre. than to percent of the lean average value. In addition to this stress there is a cross-stress which rises rapidly frus a care value at the contour to a value of about 838 ponds)" square inch for the central sin-tenths of the cross- eestion. so that the lunar of loading and the fora of the section - 25 - ealls into ply a cross-stress of 47 per cent of the neamaveraae stress due to pull. more. a heater of this form is certainly not in pure tension. and the color beads ahieh are observed on the medal will iadieate this quite clearly. It is important to show that the stress distribution in a scent briquette is similar to that in a transparent model and recent experiaents show that the an of the principal stresses (p a a) at the waist are also» exactly the sees as those found in a transparent nodal . when the briquette has been lads for acne tines his is what my be expected, for it is veiy probable tht the stress in a sunset briquette of considerable age is of exactly the sense kind as experilente on transparent nodele show since old snout has very perfect elastic properties. be fast that sound vibrations are tran-itted very readily through e-ent partition sells and floors shows this, and in another direction it has been proved that such scent possesses very perfect them-elastic properties. this latter property is not, however, possessed. or only iaperfeotly so, by s-ent inch has been recently aouldsd, so that so far as this evidence can be tahen into account it points to the conclusion that briquettes tested in seven days and in twenty eight days. as 1. provided for in standard specifications. will not be under exactly the one type of stress as transparent aodels show. ihey are in fact ncst probably in a semi-elastic condition in which the stress distribution is less variable than in a purely elastic state, so that any provisions found necessary - u - fro- eaperiaeats ea elastic bodies will lore than cover the require- aents sought. no older the briquette the lore nearly the stress distribution approximates that of the elastic condition of the trans- parent nodal. the chief bar to uiforsity appears to be in the varying shapes of the briquettes themselves. but it does not appear iapcseible to devise a siaple neans dies-sly this difficulty can be - overcue without the necessity of a telesale scrapping of eeiet- iag testing eashinery. Briefly. Ref. coher's proposal is to ensue as- m- utter-iv or testing can be obtained by naiatain- iagiaeverycasetheeaistiagforasoftheeadsandlengtheniag the central part by addition of a parallel part of the least possible length which will eatisq the condition that stress in that part is a unifor- teuein. use if we take the British standard briquette. Figure is sad introdue into it a defin-te ‘b v. Q {a b £73. I2 - 27 - parallel length, the part in pure tension is at once defined by the serc iscclinics as shown in Figure having established this length I by experiment, and this has already been done, it is a sinpls natter to snake the length in pure tension any quantity considered desirable, and this need only be a .all fraction of an inch. Further sxpcrincnt will be necessaq to find in the cenent briquette the stress distribution.at the waist at various ages. It has been established by recent neasurenents that there is unifcrnity of lateral contraction under load in each type of briquette lengthened in this way, therein indicating the rehability that uniforn tension exists at these central cross- sections. Should therc be no farther difficulties it would any be neces- sary to alter the neulds new in use to obtain not only unifornity in the conparison of results, but also a real tension test of ceaent which there is sue reason ts believe has never yet been attained under existing conditions. owing to the variable tension at the waist. and the cent of correspondence of this variability in briquettes of different patterns. - gg .. Mb "a Studies Conducted in the Pivsics Laboratory 3: “e ‘e 0e Owing to difficulties encountered in obtaining apparatus for use in the Boxer Ehoto-hlastic method, w father, Prof. liorrison, has devised another method. Instead of evaluating the stress in terns of color, which is hard to estimate, this nethod will make use of the varying wave lengths of light in detemining stress intensity. i'he apparatus, Figure 18, consists of an adapted horrenburg Polarisccpe. Light frm a ice ntt lanp 1 passes throng: a standard ray filter 3 which will give a been of light of E9. /5. a go - wave length. This beam is polarised by means of a glass plate 0 and is reflected vertically and passes through the quarter wave plate h, where it is circularly polarised. After passing through the nodal I being studied, the beam is focused into the licol analysing prim h h means of the lens I of 16 centi- netcrs focal length. a quarter wave plate is placed between the lens and analyser. A picture of the effects produced is taken Iv neans of a camera I. he nethod of procedure will be as follows. a standardiaing been of glass or celluloid will be placed in a clamp as shown in Figure it. w placing weights on the lever are a known load may be concentrated at the center of the been. fine loaded been will then be placed in the apparatus at point 8 and a picture will be talcen of the stress distribution, usinga light of/u, wave length. .. 30 .. rho load on the beam will then be changed and another picture taken. The standard ray filter will then be changed to one giving light of a wave length ,uz and two pictures taken using the same leads as before. Therefore, by measuring the width of the stress lines produced and knowing the wave lengths of the light used and the loads used it will be possible to compute the sx-xount of the stress at an point in terms of wave lengths of light. N placing a model made of the same material as the the stand- ard beam in the apparatus, and loading the model to produce an unknown stress distribution, and by taking picturesusing the standard ray filters it will be possible to evaluate the stresses. The two pictures show the stress in a mall piece of unan- nealed glass. me apparatus has Just been set up and further study will be ”Ce .- 31 - Part VII. Conclusions. The photo-elastic method has been used to show stress distri- bution and to measure the stresses themselves by the Amsrical Navy. A prominent engineer in France has analysed the stresses in a reinforced concrete bridge which has been actually constructed over the Rhone by this method. a great industrial concern lilos the General Electric Company has used this method in designing steam turbine buckets. ‘ Experiments conducted in the Hayaics Laboratory at ii. A. 0. have shown the possibility of using this method. From the above statements it is to be seen that the photo- clastic method of stress determination is being used more exten— sively and is deserving of further study. .. 32 - Bibliography. 1. Cr. The General Theory of Polarized Light hasten: Theory of Light. mod: msical Optics. hillihan and killer Electricity, Sound and Light. haunt Advanced Optics. Duff: A i‘cxtboot of Physics. ‘Ihtsons A Textbook cf Physics. Edsert Light for Students. Franklin and hachutt: Light and Sound. 11. (hi the Application of Polarised Light to Stress Analysis. hesnager: Determination of the Stress Distribution in a Reinforced concrete Bridge over the Rhone at Balms. Prof. I. G. Coker: Polarised Light and its Applications to mineering. tridey Evening Discourse. Royal Institute, 1916. the Optical Determination of Stress. PhilosOphical hagasine, Oct. 1910. Photo-Elasticity. Engineering, Jan. s. 1911. the Keasurcment of Stresses in Materials and Structures. Canton Lectures, Royal Society of Arts, 1913. Presidental Adress to Section G (Engineering) of the British Association at Sydney, B. A. Report, 1914. Experimental Determination of the Distribution of Stress and Stndn in SOlidle Be ‘e Report, 191‘s - 33 - Photo-Elasticity for Engineers. Sir lectures delivered at the General Electric Company at Schenectm, New York. General Electric caspany's magmas, 1920 a ll. £30.... .1 at . I. 1 II «I I u , , .1. ..u........ u Tu..— I’. 1' A . n M ‘1 . a. 1.8.2 £1.93). . . .. .3. . . . i \u . ‘ . V. , . 3.4 ... u. . 1.11.1... .. 1. .V..P.i..~-nuhk NLnH ‘ .. , . V . . .. . . l... 1:83.212”? 5.3.}.35Ivvnrfi,’ _ . . I i : . i . . .. .. ? . . .lw. ,u....|..1»nvn.vk.i {Jug—J .— .. .. r . . A . .. . .. .13.. ...la._.1.xj . ._ s. . 1:...” . u. . ‘~§.N§iha‘n..._ur. nor 3.»... V ‘ ...:......,:..::.Jrl!flullr‘r . . . . u . T. . . .2 .. re . 2.. nln . W!” M USE 033:” a (3 E a 7"T""‘ " ,_ if.» +111. . 1 15%. J ,.V.+.w,.w..l.\w.\...hfl.lul.4 1.1:." at. .J..~.h._1r-.1..:n:r :1. . . .., . 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