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MAY BE RECALLED with earlier due date if requested. 1 DATE DUE DATE DUE DATE DUE Geneva 6/07 p./C|RC/DateDue indd-p 1 TMERANIE STRIBSES IN LARGE GRAVITY TYPE DAMS §§****** A Thesis Submitted to The Faculty of The Michigan State College of Agriculture and Applted Science By. Clare EL. Slaughter “— Candidate for the degree, Civil Engineer June 1929 THES‘S Acknowledgement The purpose of this thesis is to develop a method of determining stresses in gravity type dams from consideration of the temperature distribution in the concrete. In order to do this certain data and telemeter readings furnished by the Southern California Edison Company have been used and the permission to do so is hereby gratefully acknowledged. Los Angeles April 21, 1929 103773 9-" .. —— “9.- . ..— mu *7 WW 2‘! fi?L1'.I YLZ‘. ': i H _ -_- . iffiik- Table of Contents Introduction........................ Page 3 ShaanakO Dm;00000000000000000000000000 7 Relation between outside temperature 17 and temperature distribution within.the dam Causes of strains.........................19 Stratus caused bu thermal eXpansion of concrete immediately surrounding the telemeter ....2O Strain due to stress......................21 Stresses induced bu non-uniform temperature distribution................. 26 Comparison of calculated and actual strains..49 conclusionBOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 52 -5 A- INTRODUCTION Immediately after the failure of the St.Francis Dan: in the spring of 1928 one of the first official actions. was to initiate an investigationinto the cause of the failure. The fact that no cut off wall had been provided and that the foundation material consisted of mica schist and red conglomerate which is not the best material for a dam foundation led to the suspicion that the primary failure had accured at this point. This was the report given by the committee after due deliberation and subsequent investigating bodies have taken a similar view. Faulty foundation is the reason ascribed to the failure of most gravity dams. Inasmuchbas the maximum compressive stress as determined by theogfgegheories of design, rarely exceeds 200 pounds per Sq. inch and even the poorest concrete should stand this safely there'is a temptation to blame the foundation as the only remaining cause of failure. However there is a growing suSpicion that high internal stresses and concentration of stress may occur as a result of shrinking and swelling,and deformation due to non-uniform temperature changes. The failure of the St. Francis Dam, eXposing the interior of the structure furnished the startsling evidence. I’ .' C" J. h' E of several extended cracks, shown in Pig. 1. For several days following the failure of the dam water is said to have flowed from these cracks. Moreover the broken faces of the fragments scattered along the path of the flood showed considerable discoloration indicating that failure had occured along cracks that had formed long before the dam was finally destroyed. Such cracks are a common occurance in gravity type dams and their presence indicate s a dangermus condition. Obviously a crack leads to concentration of stress. Water seeping in allows a full hydrostatic uplift to act over the extent of the crack. The surface is lubricated by a film of water so that sliding may occur and water is permitted to gain access to the foundations where it may carry offthe soluble content and soften the material. These cracks which are so common in gravity type dams could never result from the comparitively low stresses that are considered in theogjlsieltheories of dam design Their presence is indicative of much higher internal stresses, possibly occuring in tension. For the first time provision has been made for the study of these internal stresses in the construction of Shaver Lake Dam. When the dam was built 93 telemeters were embedded in the concrete in one of the sections and their behavior indicates that unpredicted stresses of high intensity do exist within the Dam. [/er / m: ”AVA/(flu ”Elf/Ira- ,eos ’ p . ~2\\\‘ 4. . a “ \d. O \\'// .3 '/ \A. 4% 29/: P/EC‘E WAS tsp/rum . .‘ \ ‘ // OFF A/l/fl cam/£0 AW4r D 0 1+\_ W ‘ . ' O x‘ \ o o \ ' .. it (7,5 ‘55)? 35,0 .2”. ’-. d I" ' \ o- "-:"uv. ' 'l“.”l' b 4 ' \' .'--<'M§4’1'.2'-T 0. v . .3] A a a 0 -I ‘ '9‘. ' ' x \ , - , j 4* . §\'7 e. r: _ ,, ~ £2: \ _ I .‘ . r Y I /68.6'5 MAX/MUM 65 C 770M 577 Fifi/V675 DAM dflOW/NG C WAC K S fffb’A./VO€/z/i / n ”yd/“Qll/It' E/r/m- '74} Dec. A925 34 3 32 secfion "70 g ' _ . Y A .572» .5290 . 'VeH.“ 5361‘ 2.2 5/0. 6*90 iérz‘ fecz‘ X-Y fiecfion ”/2 D-H +~+- 5667/0”. X—X 5 f X x 66‘ 10/7. " Locavrou-JHA If DAM £004 77 ON & NUMBER5 0F no. ox-cii‘iiTEW‘“ _.-----_.- i“ REVISIONS NOTlx—Locanou euowu mun. - ~ 5 . 75 L f M E TE 8 5 CROSS REFERENCES °"’°"‘° "“3” : °°""*"'° “muxPPROVALs ' cute-(Io In" SOUTHERN CALIFORNIA EDISON COMPANY I u \\ When section 12 of Shaver Lake Dam was constructed, 93 telemeters were installed at the location shown in Fig. 2., at this section the dam is 160 feet high and has a cross section.as shown in the isothermic charts. A telemeter consists essentially of a water-tight tube containing a carbon stack which is held between two bearing plates so that the strain in six inches of concrete is transmitted to the stack. The electrical resistance across the stack is a function of the sum of the distances between the carbon discs. These distances will be affected not only by the strains in the concrete, but also by the temperature of the telemeter itself. A correction must therefore be made in order to determine the actual strains in the concrete. This correction amounts to 0.000016 per unit per degree centigrade. The telemeter is considered as standard at 20° C. and the formulsrfor the correction ds 0: (T—20) 16 x 10-6 C: Correction T= Temp. in Deg. Cent. The relation between strain and resistance was determined by calibration and drawing a calibration curve for each instrument. A temperature coil is included in each telemeter. It is a well known preperty of metals that the resistance varies with the temperature according to the coef. of thermal conductivity. The temperature cod! is merely a coil of fine cooper wire of such length that its resistance will vary 2 ohms for each degree centigrade. The resistance is measured'with a modification of the meridge. Knowing the resistance of each coil at some standard temperature it is possible to calculate the temperature of the coil from its resistance at any time. During the period of nearly two years since the dam has been built a few of the telemeters and temperature coils have become unreliable. Some have failed entirely, possibly due to a break in the circuit or a breaking down of the insulation. While others still seem to be functioning prOperly, but have passed beyond the calibrated range; as in the case of telemeter No. 14. in a few cases the temperature coil failed while the telemeter continued to give fairly consistant results. This was probably due to the fact that a slight break in the insulation causing a slight decrease in resistance would cause a much greater error in the temperature coil than in the telemeter, the resistance of the former being about ten times that of the latter. In practically all cases, however. there have been. enough consistant temperature coils in each group to determine the temperature of the concrete at that point with certainty. hr 3 . esrvnALNfla AazLLAoA/7ZASC faf7? wwf TEMFEI'FA 77/175” F ". 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DECEMBhR I STRA/IV W M/AL/O/V7'fld‘ PER U/V/7'I JANUARY PEIRUARY MARCH APRIL MAY .1011: JULY ‘ Auausf ‘ Oman-u OCTOBER 5 1o 15 20 25 5 1o 15 20 25 5 1o 15 to 25 5 1o 15 to :5 5 NOVEMIER Dunn“ 10 IS 20 25 8 10 13 2° 28 IO ‘5 IO 28 8 5 IO 18 2O 88 B 1013 2018 5 IO IS 20 25 8 10 I! 20 28’ 8 IO 13 20 23 1. ‘1 * v, a QA Q #00 1-300 TEMPEPAVUPE W F ..... 4' v“ 1 f b . 510152025 _51o152025 510152025 JANUARY FEBRUAR! “ARCH v .i .. w- I 'Q 15 :0 25 5 10M15 20 25 5 10 1s 20 25 5 10 15 20 25 5 1o 15 to 25 5 1o 15 20 25 5 1o 15 20 25 5 1o 15 20 25 5 IO '5 20 25 AER! AY JUNE JULY august septa...“ QCIQBER NOVEMBER DECEMBER O '1 1'1 IIO — JANLIAQY .MBER DECEMBER 5 ‘1') ‘5 20 23 5 1‘ 1? DO 25 5 20 25 +209 ~ ~v »——~+~~v~ - v - 5 v v .' I ' U 1. 3‘.c-. . 'oo 0" a .. I ' ' ' ~ .. ...... ..... w .. ‘ n . ‘ I .I ' ~9- ,.... 9: u n I 0' 1' ' ' o. .. .-~.¢ o I ‘ V . I v . ‘‘‘‘‘ -> 1‘ 7- - .. ., . ., . a .. . Lo-‘c-b-ow.-_——_.-.,---__.-.-..1 ., . .. .. 1. .. . . . .... . .. . . ~ . - . 5 .,. 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JANUARY FEBRUARI 5 MARCSO 3" 5 1° 15 20 25 5 10 15 20 25 5 IO _15 20 2‘9 5 IO 15 go 25 :5 no 15 20 25 .5 IO 15 20 25 5 IO 15 20 25 5- IO 15 20, 25 5 ‘IO 15 20 25 _ AER"- . MAY JUNE JULY August - . SEPTEMBER QCIOBER NOVEMBER ' DECEMBER \ O . . -‘_‘-_. .1 J-NUARY DECEHBB‘ 9 4,. 3“ H ’Il'? 9"".0‘lllrl|'.llah.h| ‘1; Q l ‘ a C I ‘ \-.a \ J\.\§\J\!\I: .V IN V / {,k| ( x _ \\A ,) A \Tkwv J x I ckr wwwkx {MK {Nan .2 W» Z‘VC 5' 5 {k 1;. .-fiH; L'O UELtMUEH ') Iu JANUARY FIIRUARY _ MARCH Anal. luv JUN! JUL? Aucurr ‘ III-TIMI!!! ocroun lawman ' Duncan 3 1o 13 20 23 5 IO 1s 20 as a 10 1s 20 as a 10 as to a! a so 15 20 as a 10 13 20 as s 10 15 202: 5 IO 18 20 as s 10 as 20 as s to :5 20 as a 10 15 20 2‘51 9 to I! 20 23 ‘t R Q Pf}? U/Y/ 7' t l 8‘ a I \ Q ' -/so arfiA/N ——"‘ M/LL/O/VTHJ ‘‘‘‘‘‘ TEMPERATURE w 1"” ' ;. .... L.l. 5 1° 15 20 25 5 1015 20 25 5 IO 15 20 2.5 JANUARY FEBRUAR! MARCH f o . 51015 20 25 s 101520 25 5 IO 15 20 25 5 10 15 20 25 8 IO 13 20 25 .5 IO 15 20 25 5 IO 15 20 25 5 10 15 20 25 U 5 IO 15 20 25 Mann. MAY JUNE ' Juu Aucusr SEPTEMBER QCIOBER NOVEMBER DEC-EMER- E i l i 1} D‘CEMBER 'J ‘ ”50f -;;;,- O—A A. H: .-§r our. 4; ’14”.- 1 ‘_‘ Yfi‘? Er‘: ‘- 4 . ' ‘ g " g: :0 I :_';O‘.: 4‘ I" mWiu.’ “5+1 311.1132. ‘7 ‘ w 7‘ \ g ‘k \ -.. 9“; JV _-:).2 T;0_.¥_: ‘ ‘0 15 » JANU’,‘ 5 K315 20 25 DECEMBER E’fi4” ' “mpu, “7‘ 1'5 17 The strains, corrected fior thermal eXpansion of the concrete, and the average temperature of each group of telemeters have been incorporated in the accompanying charts which embody all the essential data that have been collected since the measurements started on April 16, 1927. RELATION BETWEEN OUTSIDE TEMPERATURE AND TEHPERATURE DISTRIBUTIFN WITHIN THE DAM. This relation has received some attention in similar structures. In the Arrow Rock dam near Boise, Idaho, temperature coils were embedded in the concrete and measurements were made during 1913-1915. High and low temperatures of the air for short periods had no influence 3 feet below the surface. It took 4 and 5 days for a continuous high or low temperature to appear within the dam. In the Boonton dam the transmission 6f the exterior heat into the dam is eXpressed by Professor Merriman as t c = t -.L -5 _ applicable for 0.5 {a <20 ft. when t a = 75° F. - Ayerage yearly temperature difference of the air. d = distance from the face of the dam in feet. In the Kensico dam, New York, the law expressing 18 I0 the transmission of temperature was found to be t c = 48 - 12. 3 105 e d. applicable for d\.wk\<\ .xxtewt em. khan “0me {\J hbhfikb. 3. 3 ..e , DR fiW 9k) 3%.. ON QVV §°\ OD) O§ $1 m, k .fiz \\ .UZ\ N “QR \ m ”(Mk NW3 Q\ em em, 3. v.9 em an ch om, M5 zesy~ a]; VM JO «an?! 26 Substituting (4) 2 R.= V cos a: cere (8) STRESSFS INSUCED BY NCNUNIFORM TFKPERATQBE_QI§E§§§UTION The maximum change in stress due to the overturning moment of the water load, Just discussed, is generally considered a controlling factor in dam design. However, it is only a small part of the change in stress that has occurred, as an example consider the situation at telemeter 13 (vertical). So far the maximum stress due to water load, and neglecting the weight of the concrete which is constant is 27 lb. per sq. in. which assuming a modulus of elasticity of 4 x 106 for concrete of this class would result in a strain of only 6.75 millionths. As a.matter of fact the actual change of strain due to stress has been 145 millionths representing a change of stress of 580 pounds per sq. in. or over twenty times that due to water load. Similar uneXpected stresses exist throughout the dam. The object of the following analysis is to eXplain the relation between strain and non-uniform temperature distribution 27 For this purpose the time since April 16, 1927, when the lower telemeters were covered to the present time, has been divided into periods, as follows: 1 U1 .h-U h) KOCOWIOS 10 10 ll 12 13 14 15 - Aug 15 16 17 April 16 - 20, 1927. April 20 - May 10 May 10 - May 11 May 11 - May 13 May 1 3 - May 17 May 17 - Rune 9 June 9 - June 23 June 23 - Aug. August 4 - Sept. 39 Sept. 30 - Nov. 29 Nov. 29, 1927 - Jan. 24, 1928 Jan. 24 - April 14, 1928 April 14 - JUne 15 June 15 - Aug 16 Aug. 16 - Oct. 1 Aug. 1 - Nov. 16 Nov. 16 - Dec. 29 These periods are of such length that the changes in temperature and strain during any one period are not too great to handle conveniently. The following charts were constructed by plotting the change in average temperature of each group of telemeters that occurred during the period. Lines were then drawn connecting points of equal change of temperature. In this discussion these lines have been called isotherms. April 16 - April 20, 1927 4i / 1%, ,3 I _/ I, I . April 20 - May 10, 1927 K" SE: .12.fi::fi?§§%§§§i::fgjjfg;;J{ if? \h? _ vz‘r‘ //, // . rd _ 44 /‘ . .... ... ‘3’ 4.2.2 ’ ,. , . 7” \‘\' I: ”3;" 0 cm 4.0 W .4’Z/‘CI/A . K“ " ..- n _ \\ fi//2,-’:f/.‘\\ ,- - f. ‘ / ////',i’/’ -' ., // l,’/..l‘//'/. / "O ‘\ 1/ / /I 'I "'4’ 1/ \‘l / \\ ’ J / -‘ /,;-’// ' _’/" -..At",’/ :. / I ‘|\ V.:_': .. -- . - . ,, . ’ \ \\\ \’} \ 4 Sit; ’ May 10 - may 11' 1927 I. 1 May 11 - May 13. 1927 //é\\\\\\‘ k\\\ ' \ - -r’ -\ \‘z 4” - ////:'<\’<'2>.\\27;{({ \\ May 13 ' 38y 17. 1927 . ,/7 ” .l ' I \ ’- x. . . l.‘(‘\\\\'//\\‘\\_< I I’ '. ' ‘ I a May 17 - June 9, 1927 t, -.4' I'rl'l‘ I -I‘///-I// //, — e _—-...A.— ‘* t '5? 1.;- - 1:": - ...- —-s¢-'b'—' -4 ... ---4 -—-,..--,c -- w l. O O o fiJd’ _ “/0: o/‘/ /--z 4 /‘ {p \ “h w x}. I June 9 - June 23, 1%? (3’ O ‘ I: 74. V '1 ,;/,:71,;$\7/ :3? //‘ ”Hf I {I \\\C II 7 ;<\\ HT August 4. Bod .— \- ‘,' \ \" ’/~\ ’H‘; ' // I 1 {:-‘\\\“\\\\fi: INF August 4 - September 30, 1927 \O / I. l,‘ . / 1/1/ I .- .gefl ~36 /\‘- \ Ab: 1942p o . lf'é/[r 7 I ~54 V@/// 4 ~ ’lfr/fl',’ T. / V ’ / 1/; ’y I " 1' £"'?r,//7W/ a j ’aw/ U ‘) "‘ . - ‘.. - LmW‘~.-‘i ,Ei II .....I September 30 - November 29, 1927 _ 0"”; II I4 1' I 1‘ l .. .. a I .. v x \ s \ » | e H v. . .. IO~ ». I .w x. .. . . .\ «V .\x , . , , . ,. . .~ ~z.\ . a x. _ e ,. . ..x. I . .a . . ... ... u 1 f o 0 1 , .. I: i II -..-III... ).| I. y! 0 - 14- 7 \ 38 on: °\‘f \ '3V’l'fli o "Q/W’7‘ November 29. 1927 - January 24, 1'29 / 1/ ’/ g; 1' 7, I 7, 7 7' \'~ Vl/// /// 7 \ // r //// ;’_.“\ /, /‘;/ 7/ -' ,/////'/ "/17 //,/2’* flat / " 4V 1/ ‘ n . 5i. 'Iil'lu. . . ..Il II I“, .i- x i a , v. 1 uEil‘iIiI’h) :tlaw.l¥.lll. «L...— -‘. .- - — .? r-I/o .\ \ .» 1/ i '/ I « > / /// / ‘ ‘ L— . 3' . \\ 7,4,.” '. 1’7 _ R; /’l"/’/ . /,/. K. .4,’ . ‘ ‘//(\x ‘1 I . .\ C . ' ‘ '. \ ,/ -xr 7.x, III ‘ ., I A l ' . , Tanuary 24 - April 14, 1929 _ . __‘.__-..-._. 3“. “: ..4 U1 $13; «#3,- W5": ‘\ " \\\ ' ,1 I / /’:;\\‘\ . 1 J ’ - .a’ fi/yc'. /.g‘ ‘f‘ “*—4‘-§:=é June 15 - august 16, 19?: i.ul.r|‘ni .b II III: . Eats... .x-’. '5' i _ -‘//,\‘- v I I, //‘.‘ 1“ / , i :—'I' ' ""3“ ”‘égg . 'QQVH“9>/’ / -—- / / ; August 16 - October 1, 1928 ‘ // - \\> // {/7 IZ:\’HV/’ “ // A . . N I October 1 - November 16, 1928. ._J // hrf ci\ /\ i\ \ a \ , ix/Qt. T ,\\ \ L a // Sex/in .wflfl TV + \ / , EA r . ... ... 1T... N.N_Ml+fl+1+lfinw\._ EMT T _ _ I \ / moo \ TR .\/\\/\ / em \ \ we I. / \/V.\\/ /\cfl W ca \A / \A / M W7 \4\«\/\> ,\« my a nu 6N ”/ am //V 677041467? LAKE DAM v, /// 11“...” 1 I'll a“. '1 ~ I. ’ V ’14 —\ L I! c u t _ . I .‘h‘ / x/ / - f 4.. \ Illi‘l'i I, V E71. \ FJI 45 The method of determing stress due to nonuniform temperature distribution is illustrated by the following specific example. Let it be supposed that the change in stress at telemeter 51 during the period of September 30 to November*29, 1927 is desired. Fig. 5 represents the isothermic chart for the period in question. Section E. F. is drawn at right angles through the telemeter. The change of temperature indicated by each isotherm is then projected as an ordinate at the point where the isotherm cuts the section. In the element y d x the change in temperature is represented by y. If the coefficient of thermal eXpansion is 3.x 10'6 then 5 x 10'6 y 3 Strain. This strain is made up of actual and potential strains caused by change of temperature. If the DIAGRAM IS REFERRED TO SCALE B the ordinato, y will represent the strain in millionths directly. The term, potential stra in, is used here to denote a deformation which would occur in a body if it were free to eXpand and contract. This deformation is supposed to be caused by some internal condition such as change in temperature. (7)771/71‘ If the body is partially éenferred the deformation that cannot occur, by reason of the confinement, is called potential strain. This potential strain manifests itself as a stress which is eXpressed by the following relation 48 S = E S = Stress 5’: Potential Strain E = Modulus of Elasticity Due to the influence of the potential strains the section E F will move to some position E" .F" Fig. 6. This movement will be sufficient to bring about equilibrium of the stresses acting on the section and will consist of two parts. '(1) A translation along the neutal axis to position‘l"F' (2) A rotation about the neutral axis to position E "F" The translation will be sufficient to fulfill the requirement- ,//y 53.: o The position of the section that fulfills this requirement is obviously at the mean height of the diagram. The rotation about the neutral axis must be such that the moment of the vertical stresses on the section will be zero. EXpressed mathematically The above expression is represneted graphically by the moment of area E "F" CHI about the neutral axis which must also equal zero. 49 A. Moment of area B "F" CH! 'F' sHI Moment of area E 'E"JF"F' Moment of area Fits] Moment of area "F" GHI = 0 Therefore. Moment of Area E 'ETDQF' = Moment of Area E'F' GHI Moment of Area E'E "Jr"ré E'E"_x s‘r' 6 E'E" = F"F" = 6 E'F' Moment of Area TF' GHI after determining the final position of the section at E "F" the distance from the section to the curve at any point represents potential strain. The actual stress at this point may be obtained by multiplying the potential strain by the 'modulus of elasticity which for concrete of this class is about 4 x 106. A comparison will show that this potential strain calculated entirely on the basis of the change in temperature distribution during the period of September 30 to November 29, 1927 agrees very well with the actual strain measured by the telemeters. COXPARISON 0F CAECULATED AND ACTUAL STRAINS_ The two charts immediately following are intended to show the relation existing between the potential strains calcuhited on the basis of non- uniform temperature distribution and the g 5 ,. “"9“" _ 1 I """A'" I "“9" "Wk. luv Jun: ‘ Jun-r _' anew -' ' annulus oc‘ronn : -. "cleverness ascend-uh. ' - ' 3 ‘0 '3. 80' ’ 8.40 "I 20 25 to is 20 as s so I: 9.023 s to a 20 as s to u no as s to 18 no I! I Io u :01. so I. 201: s 3013 no 23, "£8 10 a 2-0 as s «e is 3018' l. ' “qt ’D 4 ...- 4...; 1° 1'20 83“" - s ‘10 is no as. , . ' ‘ ‘ ‘ ' JANUARY , annuAnv' s .‘ZAcho as 5 ‘0 ‘5 2° 25 8 to ‘5 20 as s 10 ‘5 20 25 s 10 15 20 as a as Is to 25 " 5 IO Is 20 as a 10 15 so as s to Is 20 as 5 IO II 20 as ' . - 5"“ WW JUNE JULY amt - autumn menu: uovmasa _ Decal-an V JAWARV ' 'nlauanv ‘ and? -' _ 8' WI. HAY .1qu MY AUCUI‘I’ IMIHIII OCTOBER MOVINIER I DEC!" BER .15: I so. '20 as '. _ , . e 1015 sets a to i! so“ is so as 21 1'. u so a Io 11:02: so :5 toss a so 13 2025 51015 2023 51013102! ,5 1.13 20 2-3 1 i ' s I \ JmA/W" M/ZZ/fl/i/ 7545' 745'}? {/AK/7’ ..... i . ‘ . ' |' .‘ . .. . . 4»- . . . ’ . . , . 4? ~94 "-..- I} l ‘; ' ’ l._> A. I p . .. .... . . . . 1 V . ' . » ‘r'-‘ ‘ YT‘Y . ...,1‘ ,:._\..-.¢ , -‘, .. teen - . ‘° ‘5 2° 25 5 ‘9 ‘5 2° 25 5 1° ‘5 20 25 s to Is 20 as is to 18 so as s to is 20 as 5 10,1: 20 25 s :o 15 20 as 5 10 is so 25 5 lo 15 20 25 5 :o 15 20 as 5 1° 15 20 2: JANUARY FEBRUARY MARCH, AW!"- NAY JUNE JULY AMT scenic-an OCTOBER novcussn _ Dacsusea la 1' 1‘. JANU‘RY 8 1° .15 20 23 v- 5 10 15 20 23 JANUARY "IRUA‘RV 10' 13 20 85 ‘ z _ _ l. 5 10 15 20 25 FEBRUARY .. 10 13 20 25 MARCH " AVRIL to '8 1.0 8‘ 9—4 ' ‘ f . 1 5 10 15 2.0 2 APRIL MAY 10 is no 19 ‘0 ‘5 20 38 MAY JULY w 13 to as 10 18 20 25 JULY AUGUST t 15 20 25 10 ‘5 20 25 AU“? 5 SIP?!“ Ill 10 15 20 23 3;”. ti"; 8. , so 15 20 25 SEPTEMBER 10 OCTOBER 10 IS 20 25 a .4-..‘ QMOBER 10 18 20 2. 15 20 2.5 MY AUGUST IMINDKR OCTOBER NOVEMBER ‘ DECEMBER 10 13 20 25- 8 IO 18 2° 25 8 10 15 20 25 5 1015 20 25 5 ‘0 I. 20 3' 5 1. 13 30 28 '4‘ “gnaw nonuny Inca '- ”an. an .1qu a 10.13 2025 s so 13 sou .3 10 152.625 316181013 5 sous aoas 3‘0132'616 ‘1 C .\ . smeygz/Mrfl: 2°52? l/IY/f s :0 35-2913 5 101: no 2&4 *3 1o 13 an as' Mama! . runwm‘v ‘ ‘ ‘ MARCH "-'i°- 13:02: I‘_sosa‘ac as' a 1.1320 as s to as 202: a to as to u “5 10,1; :9 as 8 10.13 2025 510 1530.13? 5 ‘°" "2' 5"“- . WW . _ was: .mtx- » - M j 8mm“ 0070'“ NOVfiM'IR ‘ oscaum ,I . ‘ "<-« «A, 50 actual strains as measured by the telemeters and corrected for thermal eXpansion of concrete. ”or purposes of comparison the calculated and actual curves are placed in coincidence on or shortly after August 4, 1927 on which date construction of Sec. 12 was completed. In the case of telemeters 51 and 78 in the first chart the relation between the calculated and actual curves is very striking. In the case of telemeter 51 the divergence prior the August 4 is due to the increasing weight of masonary during construction and other factors such as shrinkage. Tea lesser degree the same effect is seen in the early part of the curves for telemeter 78. In the next chart telemeter 13 of the lower row has been treated in a similar manner. Here the two curves shwo a very close agreement up to the time when the face was submerged on November 15. From this time on the "strain due to stress” curve continues as indicated by the dotted line. However the actual strain curve diverges rapidly and attains a difference of 59 millionths within a month. This is evidently due to the swelling of the concrete. It will be noticed that the face is submerged at a time when the curve is on an upward trend and the concrete is probably under some tension. Horizontal hair cracks probably formed allowing the water to seep some distance into the concrete causing this swelling. A correspondingswelling is observed in No. 12, the horizontal telemeter at this point. If horizontal cracks have formed at this point the concrete would be free to eXpand in a vertical as well as horizontal direction. 51 Indeed it would seem that water might enter the cracks and cause a progressive swelling which would continue for a long time. For the sake of comparison the swelling of 40 million- ths observed in the horizontal telemeter has been added for the corresponding period to the strain curve. This accounts for the rapid climb of the curve after November 12, but from that time on the curve of actual strain runs practically horizontal showing no appreciable change in strain. This is exactly what would be eXpected'if a horizontal crack or series of small cracks had formed near the telemeter for in that case the telemeter would be subjected to no stress and consequently no strain due to stress. And the only strain registered by the telemeter would be that due to swelling. It is the writers belief that, if at some time in the future it is possible to examine the upstream face at this point, these cracks will be found. 52 Conmlusions Four important conclusions may be drawn from this thesis. (1) Unpredicted stress changes of considerable magnitude occur in large gravity type dams. (2) These stresses are chiefly due to non-uniform temperature changes tithin_the dam. (3) These stresses are most pronounced near the upstream and duwnstream faces. (4) The change in stress, over a period of time may be determined from consideration of the change of temperature within the dam as described on pages 45-49 HICHIGQN STQTE UNIV. LIBRQRIES llHIIILIIINHIIHII1|"lll!|H|||lIllIIIIIHIIIIHIIIVIUHI 31293500234665