a eB) a Sa ae tag ne j i ee (haa re | pea = eed C2 tava | nao | 8 ae ‘a ae a) ix = sa eS a reer — a) Lae] ma Fr =< pe Pe —— e oe a3 ey aS pI | a ees cy pat j aa) tins cae RIE ct bm . ci Mm. W. SH: z Li at Le : mney ' LIBRARY "4 Michigan State | University a A Ex Cag oe ~ centers wi ti 293 5 Avia 50023 4 PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE i DUE 0 6/07 p:/CIRC/DateDue.indd-p.1 — ee tT ell eT ad ; os ~ et a ee I) MT PP eo ae = M4 bts Analysis of a Reinforced Concrete | Factory Building A Thesis Submitted to | The Faculty of ~ MICHIGAN AGRICULTURAL COLLEGE BY . Seat Ce ' Chas. Patterson Candidates for the Degree of Bachelor of Science coe 1917 THES :S tov. Tis Umno rm gs a ee t way ANALYSIS OF THE REINFORCED CONCRETE. FACTORY BUILDING OF aT a ae PRUDDEN COMPANY, LANSING, MICH. INTRODUCTION. As a basis for this thesis the authors have various reasons for choosing the analysis of a aE Raber pastors tory building, First: they are especially interested in reinforced concrete construction, StYelon te this part- tcular type of construction (the mushroom type) is fair- ly new and as yet has not been very thoroughly tested. It is peculiarly adapted to large factories, ware- houses and the like, where light and overhead room is essential. Therefore an attempt has been made to de- termine if this type of construction will stand the tests of best specifications. Thirdly, since the au- thors were employed in the construction of this build- ing they were able to analyze it as it was built, Per aid not have to follow ee plans blindly. Familiarity with the building, and aquaintance with the contract- or's Supt., Mre Groves, provides PSC SRT promise of an effective and profitable analysis. An analysis of a purly paper design could hardly supply an equally lively interest. Sa) © to be PAs Sees. eo aaohele re Title pagee Tntroduction.e . Indexo Nomenclatt-e Single line key floor plans, foundation, lst.Srd, and roof plans. Analysis of Floor slabs. Analysis of roof sleb. Sample computations. Analysis of beams. Estimate of probable max. live floor load and analysis of retaining wall, col. 19-86. Analysis of columns and footings. Analysis of stairs. Summary and conclusions. Roe Renata M=bending moment in in. lbs. w=uniform load/lin. ft. l=lengthe Cb asa Atel: b Mo} et) b=-breadth of rect. beam or breadth of flange of T beam. d=distance from outer compressive fibre to c. of g. of steel. p-ratio of area of trio to area of beam, bd. aa "depth of neutral axis to depth of beam, d. j= " " distance eer centers of compression and tension steel to depth of beam, d. f,=tensile unit stress in steel in lbs./sq. in. do 23 as "conerete " / * - p'sratio of area of steel in tension to area of beam,bd. i " " n it " comp. “« mn iD ae Pp, =percent of steel required for desired units of f,gand f,for single reinforced beam, Po- d'=cpercent of d from top of beam to compression steel. n=E,/E, ratio of modulus of elasticity of steel and concrete. . v=shearing unit stress in lbs./sq.in. Vototal shear. u=sbond unit stress in lbs./sq.in.of surface tension steel. o=sum of perimeters of all horizontal tension steel at section considerede I=Total moment of inertia. k ia Pe 4 vs . of steel reinforcing. Pstotal axil load. N=thrust, a component of the forces normal to the sectione Aseffective area of column. h=total depth of beam. Cra constant. ee ee ee tees ow ee ee ©® © © ® — — 8 | ee eee, See ee 8 38 Q §}—fo8] 4 aT. fi J bB LO shor Formulas for Floor Slabs. Oblong panels Di a does Psa floor panel. Beet a0 UnoS a raters percha a c=diameter of column Pore Negative bending moment. z /17w1g(1yV2/3e)* as bending moment parallel to width. VAULT ELE ES. ) peeeerde ws ss " length. Of this moment poe should be provided for in the col. head and the Pre eteetd CS Ce eee LT Shoe Peres Mc ee9 momento ae ete tee as moment through center parallel to eet we SCE ETA. S a “ is .. e ie Pee EELS oy athe ae of rey Eeeoers not more than 60% should be placed in cers Persie For end panels add Sos to bending moment at first in- terior col. head and at center of span for section for section parallel to wall. | Peal S au ea i 2 3 | 5 mie p 00177 |o0cs9e | gots | 0025! | 00448 | 90 ) oi re) ae oe ee eed ra C 6.5 6s aes a ee ps J Rs eel Car era Pre: Qi ig chro ee at) 1 Toe Px fs | 18400 | 18700 | ;7400 | jee | gee 67 i a wate 425 er 244 ie T — (Taare : ey Pa) i i 5 : , | [— pge pg anf p__|.00703 |.00624 | 00298 | po2s! |ooaes |oo ae i) 124.0 PES: iz4o rod [24 © Ny fe] ne ry es ae 65 © a ae de ee rn ee “ye ae ree a e2:) Tr ir Pry er PP 4s LET 20600 | [5900 {6200 kok PT fe [663 a 366 300 275 | x R«ComP. = Ce Las i P 3 7 D | eae a p 00634 |,007903 |.00249 | 0033! [Veer 0 oe 156.0 (450 (AZ. 1340 oy (3 re rd as ay ee ae é i eB cece rary 26q ir ke J 883 885 922 aa sie | 88 fs 22100 18200 20400 LF: MofeYs) 7630 Po ran AY 740 era] rer ae rr = =_-= omp | Roof- adc { 2 3 4 5 ra we 5 P oo88S5 | 900646 00284 00234 Poe rhe MS oa or ae Te rr i ee es ee eee d a} ae a ae ae) a) al eld ei 253 re | oe) Kir J 87/ er ai6 Pa 887 899 fs | 15100 19200 | [8650 | 21300 | 6560 ae ts 630 730 422 424 216 : ———n z fae) i 2 : Fi 5 p & rel iv p |.004945 |.00603 |003872 |.00197 |.00560 |0047 Beswe b | 129.0 | 156.0 | 124.0 | 1560 | 1240 | 148 | ae ae) 6.5 a) an} 6. i te) cE rae 230 REE Ero J rr Ee Cer Cee) 888 Go fs | 16000 | 21500 | (6650 re Wile eee oir a 760 re 438 400 250 Pa “omp C ee eae i 7 F Fi 5 A fees fo] 00956 0oTé! Relea) 00262 | 0054! coos Bs: b cae) (22.5 1240 122.5 ro a rx Ld 7.0 7.0 7.° 7.0 10 7.¢ hi 4i2 378 2497 i 330 2s J 7) cae ed] TE BIO CE er 31500 | 41500 33500 40500 | 17360 eae ee ee cr) 16708 | 937 B60 570 roe { Fs C ro} CW gsi , - Piers Te na { Pd 3 4 LS ra a oe : va ae e. STIS | 00608 1.00325 |00262 | 00375 | 9po3 b cine aa) ene eae 2 Phe) 122 d 7.0 70 7.0 ya», 7.0 T.c iG ee) 345 265 245 PT rar ee PS ee 2 Cas ne) Preys ie ts | 33,700 | 5/000 | 32200 | 40300 | 20600 | 1494« fe | (345 18 00 863 ere? 540 erat: ada 4 omp. SFE its Pisren as t 2 3 rT b) é PIT-Le Ce -9a P 00722 |00700 |0037¢6 |.00360 | 00414 |9037 ) EY ay 145.0 vance) Vr aes Ce d To 10 ye ye) 7o a ig ee} mea aie way | a4 ra-t J .- 21 878 905 ered] ey qo. fs | 64,500 | 92,500] 68200 | 44300 | 40000 | 28% fe | 2700 | 3540 | je0o | Ji40 err) EX | + an Wy -omp raat f 2 3 FI ) 6 ie-if o73 p corks O1024 | 00344 | 00222 | COFT1F | 0087 i) (41.0 LU mee ea eo Tce ae eT | 20 1.0 10° 7.0 10 yao) i ced Pa 222 ye 414 34€ j 848 | 860 Se 924 rir e757 fs | 28,000] 35,000 | 41,00c | 63,500] /0,200 } 11,15 an ee 1700 Wek te) 1210 480 TF ce ! 4 3 4 rs i 01047 | 00758 [00443 [00320 | CO60F | 0046! b 124.0 ee) re ae 1$6.0 a me) 148.0 d 10 7.0 7.0 7.0 1.0 7.0 i crx .377 .304 266 crs i | ee: ke 8744 | 849 ran 885 | 873 fs | 39100 | 46000 | 37,000] 39600 ]18400 | 20,100 ro 1920 1850 logo VEE re) 500 15. Analysis of hoof Slab 44-43-63-54,. On account of the shape and supporting of this Slab it was hecessary to analyze it in two parts. Im the analysis of eachsection or took a strip a foot wide and the length of the section long and analyzed it as a beam. One section was 20'-5" long and 9'-7" wide and the other 13'-1""by 9'4",. ; Section 20'-5" by 9'-7" FOU eee cee SQeine w*123.77#4 Se MEAL Bice Tals Ole! p =. 00677 K=.360 | J=.88 barat A000) barrel 1°) Section 13'-1"by 9'-4" tear width=.297 sq.ine we 16194 cape Me SLs’ p=.00581 K=.286 J=.905 £,712100 f,=3522 Analysis of Second Floor Slab 44-43-63-64 This slab is 20'-5" by 9'-7"and was analyzed in the same way as the corresponding one on the roof. PUPA TS eshte) SGeine w=1294 M=1/12 wi®%=53700"# p=.-006 ees) J=.882 £#17200 ee anor Sample Computations. Bending moment floor slabs Nee. Moment 1 /17x350x23.33(20.42-3.66 )2x1251613887 "4 20%=1936700" 4 ROBE isle CERO d be tee ieleenr | Pos. moment 2 £30x350x23.33(20.42-3.66)"m122914536"4 1 /30x350x20.42(23.33-3.66)x1281103000"4 -20%=1323600"¥ For either floor slabs or beams. M=1646300"# p=8.64/903=.00956 re MECC tea sta Lee se J=1-.4116/3=.863 fF =1546200/8.64x.863x7=31500#/sq.ine £ 6 =2x1546200/6321x.863x~412=1460/sq. in. Bending Mom for Beams. M=w1@=116504 3324x23.33')23.33'x12=452000 <> 3 fi} 11650=total load on beam 332=wteper lin.ft. of beam 23.353=length of beam. aig Formulas for Beams Mz1/12w1" for interior continuous beams. Mz1/lowl® for end continuous beams. ed ae ere) RNa eeny Les.) hep f£=M/AgJa rAd ass Beams with Steel in Top and Bottom. p'*p1 Pe po=p"(K-d") /(1-K) es aa oe My /f.,b4"=p4 Jy NOS PA kd Pe ee f,2f,/n x k/(1-K) aaa oC | u®v/¥oJa Fstimated Maximum Live Floor Load Maxium load to consist of autotruck erste EEA “X25 lbs. per wheel. 4 There are to be 10 wheels in a pile and each 30" wheel covers 5 sq.ft. of floor space. Maxium live load#125 x10/5=250 lbs. per sq.ft. Analysis of Retaining Wall. A section between two of the columns was test- ed. This section was taken as 1' wide x 9" thick eer long, and considered as a simple beam. SU, Labo . ne tle Sy PY 1 hor Formulas for Columns. fo=P/A (n-1l)Ag fo-N/A (n-1)Ag M/I (n-1)1, Sane R POL) teste Pam plotted ee tent het UA! e xfpn-(pn)*-pn a iad dO BL es ers READ! SrtA wake (ol tor Shear at Col. Head Punching Shear Col. Head Col. Head ba: eircom: | ot +c a OTe Men tae n a aes mi u 6°o | 38° | 75° |3420] 143 | 55° hrc ma ak eet eo re es ee: YL Le we) 13.5 | 2800 | 67 ¢ ae 38° | 80 | 3650| 397 |. 55 ee Eee 4: ee 7a ee ee Ee eee: eee ec, oe ee ee YY: ev oe YY “@ Oo a orc rl eee ae 13 EY STL a oe er) ee ere ee Eee ees eee 01 38 | 80 | 3650] 347 | 55 |. 173 | 135 |2860| 67 | One eee 8.0 | 3652 | 347 AE ENN OU ae Ee kal Be ai a 14 24.0 | 4030| 4io 36° 14.0 24.0 piss EX) sxars| 33° | 75° | 2970] 17.7 | 4.25 | 1337 | i390 | 2090| 32.4 4 5x875| 33. | 80 | 3170| 490 | 42s | 1337'| 138 | 2170 | 865 (9x875| 33° | 8.0 |.3170 | 490 | 425 1337 | 436 | 2170 | 865 (§x875] 33’ | Bo | 3170 | 440 | 425 1337 | 135 | 2170 | B65 | ‘-g3°o 14.67 | 240 | 4230] {4723 aw Ce 24.0 | 4230 19.5 0 hak lel Ss 8 We a Rt 29x23 | 56 Bo | 448 | 1230 29x23 | 56 8.0 | 448 | i23.0 rors 8.0 448 | 123.0 ee ere ce 19.0 | 2960 tm - 29% 23 id it 420 nae ITT ee ee Pa ae) 56 oe 448 | 123.0 Pl Bare Crs 8.0 | 448 | 1230 rer iY ome ee es) Vso Analysis of Stairs. Consider the stairs as a beam whose length is equal to the horizontal projection. When they rested on stringers one of the stringers was PNW eats Li's et po) aN G were poured as a slab a section one foot wide was analy- zeds 3 Stairs Col. 45-64 Basement to first floor. Lengths6'-1" Total w/ft. width=2284 M=12700"# ° a./ft.width®.368 in. sq. p=.0041 ore-ters J=.902 £50000 £,=140 First floor to landing. Length=10! Total w/ft. width=228# NeKer bee A /ft. width®.546 in.sq. p=.00607 -K=.345 «3.885 = fg79400 #530 Stairs Col.15-54. { Stairs rest on two stringers. Basement to first floor. Length=14,5! Total w=353# M=111200"# A,=.638 in.sq. p*.00709 res loys Aird A) f.,=26200 ee First to second floor. Length=156.5' w=12841# M=320000%# Ag75-16 nO ePe-1en) p=.0439 K=.508 J=.831 5 Boole) so A) Entrance Stairs. Length=9! Total w/ft.width=145# M=20000"# A /f£tewidth®.334 sq.ine p=.0039 K=.289 Ri Paces) f.,=13300 or Aoi SUMMARY AND CONCLUSIONS. --000-- In this analysis we have tried to deal directly with the building as we found it, than try to find out the specifications for which it was designed. Being somewhat familiar with the actual construction we were able to analyze some parts as they exist, which appear to be different from the original design. But we are not familiar with all points of the construction. use may have been some addition to the reinforcing, which, if it had been introduced would have reduced -the apparent over-stress. But as we had the very lat- est plans to work from, we had to analze the warious st bak BL) they were given. | In some instances we havé ner to take values that were more or Ee st work, The irregular panels and the beams supporting stairs and elevator were es-~ . pecially hard to figure. One of the elevator beams for instance, el ten different loads coming to it. ee er from full uniform to concentrated. It is very hard to tell just what part of the load of a panel, one eet beams on three sides and the reinforcing ae ing into all of them, will be carried by each beam. Only by actual measurements can the stresses in oy of these beams be determined. Some of the beams which we figured the moment for as simple beams, were fixed 276 to a certain degree. How much we could not determine. Also the formula for reinforced concrete of this type are-more or less empirical and hard to adapt to special eRe Mat =T 9 Although sete type of resend eee (the bP ESSeR are le) 10 roe noe on re et oye mY ae it has not been very thoroughly investigated. Very few com- plete tests have erty made on buildings of this type. For our work we have used the findings of the Joint Committee and TEE W a Keys and Thompson" text on re- inforced concrete which give the very latest formula for testing such structures. The values which we us- CYo ME VAM Sevet-b acto AsCM Tham tTel most conservative ones in use at the present time. Our values show a decided over-stress in the steel and a lesser but still high value for compression of concretee In the floor slabs the compression in the concrete at the column head was very high, but some of this is taken care of by the drop panel which we did not consider in our calculations. The stress in the concrete at other points was not meres above the conservative value. The negative steel at the col- umn heads and the positive steel in the rectangular bands was found to be very inadequate. ‘The slabs showed a very poor balance in the placing of the rein- forcing steel. Likewise the practice of carrying all of the steel to the top at the column head is not to '.@ tos be commended. The beams are over-stressed 50 to 200 percent in both concrete and steel. There is a very decided lack of negative steel over the supports for wet ao ae “Sh tinuous beams, and the stresses in both concrete and steel at the center of the beam are far above the safe values of 16,000 for f, and f, which are recommended by most authorities. In fact according to our figures, the whole structures shows very high stresses and a very decid- ed lack of reinforcing steel, The beams which show the greatest over-stresses, though, are partially supported by the PLCC RMT Tis) windows, and some of them are supported in whole or part by brick walls. Tak- ing some of ee gees ee into consideration, would tend to make the building safer by lowering the stres- ses in both steel and concrete. These beams should have been designed so as to carry their load without any support from underneath, Therefore in our anal- Pe we were not allowed to consider these points. Of the whole building, the columms and stairs alone, seem to have been designed to carry their load with perfect safty. In fact the analysis has proven very disappointing. The building seemed to be an ideal ‘construction and very simple en build, but unless there - is something decidely wrong with out work it can not be considered safe with more than 100 or 150 Jbs. live load on its floors. Alu ¢C 1198 ia