THESIS PRE BE MO) RSE OKA F VETO Jo C. H. PETERSON & A. L. SAYLES 1915 ” _ ; f - | _ Cs oS 1 aks Qep IEE “7 . , . . ro _—_— - . & i : ' ' C_ ct. y ( f a ; le. A Y . We AL te \ po, 1s \ v - Af. f, y (y AN > QIAL ACY ~~ ( ‘ : . . oN po SY oN ~- } ' \ ’ rr | t) o+ b, peu bee too ‘ (, he a2 eet 28 oe woof - waa This thesis was contributed by ‘ Mr. C. H. Peterson under the date indicated by the department stamp, Be to replace the original which was destroyed in the eo fire of March 5, 1916. " ede ge ed fo of ee apne ee os Siar Pewee ow ~ 1 | | | b INVESTIGATION OF STRESSES In BAST LAGSING WATER TOWhR. e+ * A THESIS SUBMITTED TO THE FACULTY OF MICHIGAN AGRICULTURAL COLLEGE by wk’ . “ ‘ ‘ oe | uh : ae CG. He Petersen Ae Le Sayles Candidates for the Degree of BACHELOR OF SCIENOE. June, 1915, LOGS SE ITHDES ; Introduction pase 1. Specified Loeis Se Specified Unit Streseas be Loads Te Stresses 9. Make-up of vecign 12. Max, Unit otrecces 1S. summary | Ze General Conditions «ni Vormenship - ole Acknowledgnoe cts ana 3eforences 22e Protegraph:: Biueprints vyery wen Aye TO QaAT FAT OUTLIN: Set a LL INa et @ Gates ans see Qng eee ee oo ee Ae History. B. ‘“pecified Loads. Ce “neckfied Unit Stressed. D. Loads - 1. Tankfaull - sgouare wind re tanxfull <= viactonsl wind Se Genk empty - sauara wind 4. Sank enuoty - diagonal wind Le otresses - le 2Olumn, taximun 2e Horizontal Bracing Se vertical Bracing 4. :nchor Bolte 5. ieasonry - 3Jearing on Resist to uplift Press on soil 6e side rlate Pl. 7. Spherical Bottom Pintes Po F. Make-up of Design - 1. Colum ) 2. Horizontal Bracing ) 3. Vertical Bracing a. Main section 4. /mchor Solts be Riveted connesotions 5. Masonry ) of Lacing 6. Side Plates P ) 7e Spherical 30ttom plates ) G. Maximum Unit Stressea - 1. Column ) Ze Horisontal Bracing 3- Vertical Bracing a. On main sections. 4. inchor Bolts be Riveted connections 5. liagonry Ce Lacing Ge Side Flates P 7. Spherical Bottom Flates ) He Te Je Outline of Procedure, Conti. SUMMaPry - le Based on Crisinal Sections a. tienbers overstrained bd. Eorcente ozcoe3ss overstrzuined ce Loading vroducing excess. Ze so2erel vonaitions end torkmanship icknowledgmenta aml Technicsl references. Miscellaneous. 00-6 0. This work of analysis was undertaken not in any spirit of fsult finding or of criticising the design er construction but in order to gain knowledge of steel construction ond experienes in analysis. le INFRODUCTION. Prior te 1909 the City «@ East Lansing had no public water supply but depended on the individual system instd led in private residences or from the College. ir. Chase had erected a private tower and from this supplied ea few in the immediate vicinity, but this was entirely inadequate to supply mere thm @ wery few surrounding him. As the city expanded the need of an adequate water supply fer domestic and fire purposes became very pressing. A number of emall fires algrmed the city council ani they realised that they could not depend on the City of Lansing for their water as they had done far their lights. They first tried to obtain water from the College, as Mr. Bira on Grand River Aveme had done, but failed, as Mr. Bird had no legal right te use the College water. A comnittee was appointed by the council to in- vestigate the various systems in use ani suthorized to summit plans for a system to be used in Bast Lensing. Professor Haddon,then of the Civil Engineering De- pertment of the College, was secured to draw up design of tower. These plans were sutmitted for bids and the eentract far building was let to Whitehead and Kales Ze Iren Werks of Detroit, Michigan, in January, 1909. The original site of this tower was the present location of the pumping station, but before the erection was started the present location was secured on Forest Hill Avenue. This had been originally selected as the building site but the price asked by the owners was almost prehibitgry. | By changing the location te the top of the hill an ina ease in head of about thirty feet was gained, but necessitated the pusping of the water about three hundred feet further and thirty feet higher. Construction was started on the tower late in the spring of 1909 and finished in the sumer of the same year. The system had so far been entirely satisfactery. Other improvements were meadé after the tower was erected which depended on a good water sapply, the ehief being en extensive sewer systen. The tower is 118 feet high ani has a capacity & 10,000 gallens. SPECIFIRZD LOADS. Dead Loads. Weight of structure. 6 - 6" Channels @ 8# / ft. LOS high » 6600f same 4- 8"x > plates @ 6.84/ft 51° * 8 TLOfS (1504- lé"x 3" vers @ .65f ea. 7 5/16" long = 1000f fotal ------ 6351 Of | 200° & lox 1g” x 5/16" @ 1.0¢/ft = 860f 100 round bars @ 1.28 ea. = 1206 fotel ----- 4508 Bori- ( 16 Le a$"x 8° x &" @ 35.606/2t60.5 2 960F sontal - Bracing! 144 bare 19" x4" x 14" @ 1.64 cn. _- 2505 l frame ---- 122 OF ————S fetal frames --- 38650 8 ~ 1" Rods 50° long @ 2.64/26 = 620F Yertical ant (8 - 2" ° 28° * @ 2.6#/2t = S8OF lateral trace (8- 7/8" " 26° " O8¢ /ft = 415f reas. ~------- (8 - 7/6" " 25° *" @2# /ft = 400f 4-3/4" " 13° * @1.53/ft= TeF (4 -~ 3/4" " 10° * @1.58/ft = 60f (4- 3/4" " 8° * @1.55/2t a 48f fetal -—-—— s201f wank pe plates 8'x48"x3/16" @ 50.6#/ft «2950f 4 °° 8*x28"x3/16" @ 17.85¢/ft _= 560F | fetal -----~ 3510f Tank Reof (18 plates No.12 . | , 60°x24"xi /10" @ 490%/Cu ft = 410f 1 Plate 75%x3/16"x6'S" © 46.8f/ft 2 300# S * 48°x5/16"x4' ¢ 50.6¢/ft _= 9608 fet al ----- 1280f ms | fotal, Weight of Tenk ------------ ---- 52008 de Tetal Dead Load Estimates - 4 Columns 631 0F 1 ladder 4804 S Cress Prenes S650f Vertical & Lateral reds s201f Tank 8 200$ Total ------ 196214 Use ------ 20000 Aaa 20% for rivets, etc. --_ 4000 Total Dead Load --~- 24000f Feight sf Contained Vater in Tepk- 10000 Gals. =z 1540 Cu ft. @ 68b¢/ou ft. = 84000$ Total Dead Load ef Structure and Contained Water = 1080008 208000 = 27000f DL. en each column Wink leads SOf/aq-ft. of exposed area 150f/ Lin. ft. of height Specified Unit Stresses. fension in Tank plates 12000#/sq.in. net area Tension in other parts of structure 16000%/ 3q.in.net area Compression 16000//sq.in. (reduced) Shear on shep rivets 120007/ sq.in. = © #42104 * 90004/sq.in " {ff plates 10000f/aq.in. (Grose area) For ecupression members the permissible unit stress of 16000f shall be redwed by the formula P 2 16000 ~ 70 i Yr where P # permissible working stess in compression in pounds / sq.in. 1 = length of membor frem center to center of connections in inches. Yr 2 least radius of gyration of section in inches. The ratie L/r shall not exceed 120 for main members ani 180 for struts and reof construction members. Unit compression on conerete sub-structures = S50f/ sq in. Unit masonry bearing on soil « 2 tons/sq.ft. ah Ss, Wing on reefs - (Print No.2) 2/3 »h x 30#/aq.ft. 2/8xz12%4x 30 « 960F Wind en Drum 2/85 bh x SOf/aq.ft. 2/8 x10x13 x 30 @ 2600f Winé en Bell 2/35 bh x 504/aq ft 2/8x10x6&x30= 1000f Wind en Tower (Prints Nos. 2 and 3) Diagoneally per foot of vertieal height Area = 8"+ 8+ 6" 6" = 21/8" + 2.86 = 5el7® 5.17 x 50 x1 = 1548/ft of height. Squarely on Tower. Area a 4 : 10 =-- 3.33' + 2' = 5.33* 5.38 x 30 x1 = 160#/ft of height. Load on each section (Print No.3} 25 x 160 = 4000/ Te AR SR G8 SG With tenk full, the loads on leewnrd side are izn- oreased by the weight of the water in the tank £609 1000 4000 4500 4000 Ding. Wind. 960 8600 1925 2006 S850 S850 3860 1926 9. unetGnenenenae Stresses in Column Analytical Solution. Stress due to wind = M/fr for four column structure where M is maximum moment of each section due te wind and vy is the radius of a cirele passing through the center of the columns. Thus: | sito about base in the plane about the diegonal v of the structure = 0 3 a (f4000 x 25)+(4000 x 50)+(4000 x 75)+ 000 x 100)+(2600 x 106.5 )+(960 x 114.85) 17000 x 96)]e(15 x 2) S = 428337 due to wink. S = 27000f due te weight of structure and water fetal stress- 69833; This compares favorably with wind otresses es shown in graphical solution in Print No.3, that giving max. stress as 45000 + £7000 = 72000f. This being slightly greater the graphical solution was used for final results. Colum Stresses. Member Wind Stress Deed Load Stress Max. Stress C1, 62 45000 27000 7Z000 CS, C4 32500 26000 58600 C5, 06 20600 25000 455800 07, 68 10200 24000 34200 10. Horizontal Bracing Member _ Max, Stress. Sl. 7000 . $2. 5750 a3. 4450 Yertios] Bracing Member Maxe Stresas DL 11000 De 10000 . DS 8600 m4 6750 Aneher Bolts _ fwo ancher belts in eack pier take the tension due te wind on empty tank, minus 1/4 weight ef tank. Max, Stress = 45000 - 6000 = 195800 Masonry Bearing « The masonry takes both the compression on the lee- ward side and the dead load coming on it from one leg, or Max. Stress = 45000 4+ 27000 = 729004 ile Searing on Seid 45000 + 27000 s 78000f Bearing due te tewer 157 Cu ft @ 150f/ou ft= 235008 Wt. of one pier 9B500f 88 ou ft Zarth © 100F /ou ft = 68800; Wt. of earth above 1043007 Tide Plates - Fl « (See Print No.) Stress is thst due te taxk fall of water. Stress per sq. in. of plate hs height in feet = 14‘ 4 = Dimmeter of Tank in feet = 10° t = Thickness of plates in inches = .1875* S = 226 £34 510 = 1940%/square inch. Spherical Plates Stress fT. = Ee6 hy /Sq.In. h = height in feet = 19° radius of tenk se §° % = thickness in inches = .1875" T =_2:6 519 25 = 1520#/Sq in. WAKE UP OF DESIGN. Columns, (Plate Bo.5) he columns are made up of two 6" channels, the two lower ones having a 3/8" x 8" plate on one side ani Single laced on the other side by 1-1/2" x 1/4" bers. The two upper ones are single laced on each side. 5/8" rivets are used in all columns. Horisontal Bracing. (Plate No.6) The horisontal bracing is made up of four angies 2-1/2" x 2x 1/4", twe in each set and joined by 1-1/4" x 1/4" laced work, 5/8" rivets. The tie rods of the horizontal bracing are of 3/4" round rods, bolted to the columns. Yerti@al Bracing, (Plate No.5). The vertical bracing in the two lower panels are of 1" round rods; that in the two upper panels are of 7/8* round rods. | Ancher Bolts. (Plate No.6) These are of 1-1/4" =x 4° long stock firmly imbedded in concrete. L3e Yesenry, (Plate Ne.6) The piers are of solid cenerete made in three stages, the lower ene being ¥° x 7‘ x 2", mid@e one 5° =x 65 x 2° and the tap one 8S’ x 3° x 1°. Side Plate - Ph). (Plate #5) These are of 3/16" 0.H-Steel, &@1 rivets 1/2". The Plates are bent to the radius of the tarzk. Spherical Bottom Plates. (Plate 0.7) These are aleo of 3/16" O.N. steel, using 1/2" rivets, stamped te conform to their sphoricsal shape. MAXIMUM UNIT STRESSES. Colums. (Refer te Plate No.8) | Stress in 61 - C2 - C3 - C4. S=P4¢P.9,.0. ~ a . = 720008 a 4.76 43 = ¥e.76 Sqein. s 4.35" = 1.35" 14 4.19 ry 2.32" Ss 73000 + 72000 x 1.35 x 4055 = 19500//sq. in. ee af PF WwW $0 ite Unit Compressive stress = 16000 -~ mi. where 1 is length (unsupported) in inches and ris least radius of gyration = 16000 ~- 70 x 25 x= 12 allewed stress - 16000 - 9000 = 7000#/a@. in. 12 should not exceed 120 but in this ease it is in ex- odes of that amount. 2 = 3% = i129 a Boon rege $n o olin C5 - 06 - OY - cB. Sa P Pe 458003 z Ae 4.76 sq.ine a 00 = 96502 8q in. 48800 / rs (k I 2 25-9 r ~-2.34 Aw 4.76 =i" ™ Should not exceed 120 Allowea Unit Compression » 16000 -_70 31 r = 16000 - 9000 = 7000#/sq in. Lacing on Colums (Print No.9) 9000 2 704 4 fr Lace bar Shear e2 9000 ar” x 4 a/e2 L Max. Stress in Lacing « 93000 x $x Seo 0 2 15. where A = 7.76 sq.in. = 2.32" 7.25" 3O0" o tp oot) Angle between lace bar and horisontal 3O@Ce Os 1.33 Shear 2 9000 x 7.76 x 5.38". 4__ = 11807 7205/2 350 Stress in bar = 1180 x 1.33 = 1570; Divide by area of bar 1-1/2" x 1/4" « 3/8" 8/3 x 1570 = 4200#/sq. in. Cheek (From Xetchums) Stress = 280 Ar Csc e, A 70765 sqeine P= 2632" C = 4035" Cae @e 1.33. @ is angle betweon lacing and vertical. Stress e 280 x re76 KX 2052 41.33 , 1840f/sq.in. 16. Horizontal Bracing (Print 3o.3) 4/8 2-1/2" x 2* x 1/4" Avea «© 1.06 x 4 = 4-24 sq.in. Unit Stress = P A P = 7000 As 424 ot a 1650//sqein. Allowed Unit «2 16000 - 70 L = 17.75 x 12 - 212" L x Least radius of gyration » 1.21" Allowed Unit = 16000 = _70 x 212 = 16000 - 12250 = 3750¢/aq.in. L= 218 2x 175 Allowed 180 RF Te : lacing on Horizontal Ber (Print No.9) Stress = 70L ¢_Ar® ) 4 sec @ “R “des Tf VOL = 12250 “R As 4.24 Ys 1-21 d = 16" Ls £12" 860298 = acre a 1.26 @ 176 Stress in bar 12250 = 4.24 = TUT’ = 4 2 1.86 = 225¢ -BESE = fog = 600s/eq Chocked by Ketchum's formula giving 2277 or 227 x 600} 8/35 Vertical Bracing Dy and Dy Maximum otress Area of 1” rod Unit stress 9« 11900 (O54 L1L690F 07854 Sge in. 14096// sqeine Dz and Dy Maximum Streas «2 86007 26013 sqeine 143007 /aq. in. Area of 7/8" rod Unit Stress = 8609 uN Anchor Bol ts Liaximum Stress - 19500# Area of 1-1/4"boltse 1.2272 s#q.in. Unit Stress = 19500 = 15400}/sq.in. ace Test fa bond. Bond stress = 80 x surface area 2 80 x4 x18 x 3.927 =» 15100; 18100 x 2 w 39200; Masonry Colum bearing on Pier Heaximm Stress = 720007 Area w 147 x 16" = 224 33.in. Unit stress e« 7E000 ‘= 320#/eqeine 2 Pier on Soil Maximum Stress 2 1043002 Area = 7° x 7° = 49 sy.fte | 21003/sqefte Side Plate Pl. Riveted Joints. Rivet spacing = 1-1/2" Diameter Rivet 1/2", Diam. hole 9/16" Stress per lin. in. of vert. height x 1940: Load far 1-1/2" 2 1-1/2 x 1940 = 29107 = P. Ta-a) ° &@« pitch of rivet - 1-1/2" d = Diam. of rivet hole = 9/16" S.= Unit tensile stress in plate 3,2 " compression in plate Sez «Os *~—Ss shear on rivet. dy> Diam, rivet «1/2” P Sa = P 5 P : * aa Se _ 2910 \ 3 3100#/eq. in. 19. 5, = are = 5200} /sqeine So 22910 . = 2910 = 147007 T/p a= 41963 opher 8 Unit stress in sphorical plates = 1320//eqein as showm on pago 13. 4s this is smaller than that abeve used in finding stresses on joints, the stresses on rivets and joints Will be smaller. Riveted Connection _ Between plates of tank ani lega.(Print Ne.10) Weight of tank plates _ = 5200! plus 33% for incidentals » 1700 Wt. of contained water 394000 Total = 909007 1/4 on each leg or 227253 borne by rivets Value of 5/8" rivet in single shear at 10000} » 30684 16 rivets at 3068 = 490887 rivets can takein single shear. Bearing value of single 5/8" rivet on 3/16" Plate. Unit bearing stress = 20000F « Diam. of rivet x thickness of plate x allowed unit bearing stress. Bearing value of rivet = .625 x .1875 x 20000 wm 2344 16 rivets at 2344 a 375044 rivets can take in bearing en P Ge x, 20. SUMMARY. Basad on original sect ion. All members show sufficient strength except the columns. ‘These appear to have been designed without teking into consideration the eccentric loading dus to the plate on the inside or to the large value of the iten L/R. In the cuse of the lower half of the columns, this reduces the allowed unit ogmpressive strength from 160007 to 70002, Tne addition of the plate in this case was a detriment. Instead of strengthening the colum it weakened it by increasing unit stress from 15100°/sq.in. to 19600 /sqein. The main columns ere overstressed 180% The upper columns are overstreased 36% The calibrated corrosion on the tower was found to be 90 email thet it could bo nozlLeoted altogether. That on the plate, for instance, was found to be .000 inches and none on the channels. The corrosion on the tank was mush greater but could not be calibrated on account of its inaccessibility. The rivets in the north side of the bell were nearly eaten away by the rust. This is probably dus to the ruming over of the tank and to excess of carbon dioxide in the water. 2le GEM anAL CONDITIONS AND WORKMANSHIP. This design appears to have deen rather hasty and incomplete. The action of the couple due to the wind on the tank seems to have been neglected and also that of ecoentric loading of the colummsa. This, couvied with lax attention and poer upkeep, hes rendered the structure unsafe for excessive loads. The tank was repainted this spring for the first time singe it was erected in 1909, and has suffered from in- attention in that manner. Ve had the geod fortune to interview a skilled structural iron werker at the time of examination of the tank and from him learned of the unsafe condition of the bell. In his opinion the rivets will have to be renewed within two years or the bell will fail. Pe6 ACKNOWVLEDGIIG NT 5 In the solution of this work, we are indebted to Prof. Ce Ae Walick for advice and help and to the “American Handbook,” ‘ - STRESSES IN le YM Da 1 (al CH PETERSON: 4.LOAYLES Tae re = WL.* /02 Pye GE'S tae, ka yao T yy eae atk Max +» J4L00° + yee ee CL oa + WL: 10200 - 9 ee OT TT a Max *25000 # 1 eT we Tn RM WL* 20800 - pees ae Max ‘26000 + (Cer ET DL = dae v Ye oka a rao oe AL=Z] ce es Mak « Ey ey Yi ae ee me PEE ka aeacaaaa P/E Ae oe DL: 21000" a [fax *4$000"- | Ea PRIME NO. 14. Ber See ._ Bek ty é 7. a A ." ot on ke ange «REA -2 age 74 ee rT) ‘48 3 > DT SS RR Te mw ewe ow mn me —— ee om ee eee ee eee ee lee. - - - 5 —~ eee -. . 2 - x .? “= * . 7 7 .TY IT. TTI 7T na u TT. 7 ~ L 2 ~ 7 . 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