CVEN 444 Lecture Notes - 07

CVEN 444 Lecture Notes - 07 - 13'?) sheets Mom -4. ha;...

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Unformatted text preview: 13'?) sheets Mom -4. ha; PT“- a 5/1 (é: ‘«»VA/' cvew 44-4 A6074)”. # 7 i was 0 055mm or: c. 5 THE SHEAZ 5112555 DISTIZISUTION IN A 12¢ 55AM IS VERY COMPLEX AND NOT EAblLY 05562551). SINCE. CONCRETE DOES NOT BEHAVE HOMOGENE'OOéLY N012 LINEAR ELAs‘TlCALLY EVEN UNDER. sszvacs LOAD cowonTuovds, THE $454.2 FOEMG—Af £= yg Ib QANNOT BE L550: CONSIDER A Poe-non o: A (ONCEETE 55AM NEAR A so PPOIZT AND THE sac—20.2. 5112555 5123?. WAT wool—D 55 EXPECTED! MosTLY COMPRESSION e1].— M“ 131’ MosTLN _, SHEAK V u «.13., Mes—my TENSION THE: 5TEE$5€5 AROUND THE. Moo-DEPTH OF THE ceass sEc'rIoN WILL LEAD TO DIAéONAL (EAalcs A3 THE SHEAR STEEsS maze/A555- ‘I L.V_.-w_. THE SHEAR. STEEssELs RESULT IN THE 014.com“ TENSION CflActs DUE To commas-res BELATIVELV WEAK TENSILE mew-rad. 598.1541- ID PURE. SHEAR, Hie-t TEMS‘LE 51255555 DEvELoP ATA 45' MbLEAs usn 3y THE FOLLOWING $112553 BLOCK: 2A ¢-—— )} Vs" l —-7 52’ UNDER THE ACHON 0? THE SHEAR , THE STRESS BLOCK DEFoeMs SUCH THLT POINTS A AND 5 MOVE AWAV onM EACH OTHEZ. THEZEFOEE‘, TENleE 3125:2555 FORM ALONG THE D’AGONAL-o Tms can 41.50 55. SHOWN usmc. Mon-62’: clecuz. 1% A page sHsAe 57255: DEVELOPEsJ A TENSILE amass DEVELOPES AT 45° (2x4s° on; "THE MOHE'S: enact—E), LABEL-ED .46 (5', AND A commzssawe sat-:55, dz) on A Paws 45° THE OTHER. mesa-now (omeouALD. THE DtAeowu. cmnmc. occuzs WHEN THE TEMblLE snaeueTJ-t op THE come—ETE lb EXCEEDED. THE 'TENbiLE S‘rle'MeTH or—= CONCRETE is TAKEN .45! 74 = KMowlbLb THAT THE MAJUMUM firm 3:255: 13 EQUAL'R) 2/3 THE: AVERAGE anew! SIZE-‘55 R32 A REC—TANcUI—AK cam-flaw: rm=4= 7.5 74¢ 1.! 2A ~/*\ ‘5 GS shee’is ,., “4 911m ‘\4-, OE Eome, F02 \/ I V = %(7.5J,Z)5c( = 5/9394 T1415 WOULD GIVE THE LIMH’NL, sHENZ sTEEMeTH OFA couczsra BEAM n= THEEE' wam’r ANY FLEXURE. ts THE RESULT o: seuowef (NH-L. BE (ammo ON THE TENsncw SIDE OF THE NEUTRAL Ahab, THE FLEXUQAL (2.4.015 2500c: we: EFPEEmV-Ensss op c2053 SEcTtoM To 25.5151' SHEA-Z Howstz, THE 5HEAJZ Act 316, SEC“ 31.31.! cousszvm'lvaw A LIMIT on THE CouczETE 5HEA2— STRENGTH on z/Ebwcz WHEEE b.“ Is TAKEN As THE WIDTH or: THE 55AM AT 1T5 NEuTaAJ. Ath. Vc (“-5) TD ACcnUAJT Foe THE— INFLUENLE OF THE: FLExurzu. $112553, ACI ALLONE, FOB 4 HIGH CONCRETE $HEAE. STRENGTH IF A MORE DEAN—ED MAD/51$ z: Wane-:0 (sEc. “$2.13: (11-57 HONEVEZJ "THE cquCZE‘TE 54-1562 CANNOT exam '. THEREFORE) THE C2055 SEcTIOkJ 39 'S 00 sheets 22-1 \/c e 3,5/276~c{ m0 VMZ é ,,o 1N EQ. (II-5). Mu EXCEPT AT Loan-1oan or Low SHEAR CAT pom-rs or mot-t 'Poval‘TIVE-l MOMENT), THE couctzETE ALONE CAN sacrum «any THE skim. 3TEEL $TIZE’uPS Moa‘r BE asap To MAKE UP THE DIFFERENCE. Ir= FACIT, ALI-31$, 55:. 11.5.5.1 RanBE‘b THE USE OF’ 51122:»: IN BEAME: “mad; Va 2 é¢VC (No-re: 75 = 075) THLS '12) NSqu A Doc-nu; $HEA2 F1341.qu EXCEPTIONS ABE MADE Foe $1.455, Fow'lutab, AND 25711101106 WALLS As 114525 15 No PEACTleAL WAV To INCOQPOZATE THE STtIZEUPE INTO THE CONSHaJCTIOM OF‘ “THE MEMBER. WHEN 59-!an EEIMFDECEMEIJT Is zzQuueED, T'HE STIERUPb ARE FLA-(JED Mona: 'FHE Laue-m a= THE 5% ts DILTATED 15v THE sHEAE DIAGEAM. THE men-+52 THE 39-542 Foecz (Va); THE M025 $TE£L_ Barume ova sMALLER 51':ng swam, ts REQUIRED, SHEAR RBINF’. 396155 109. 5.25 «on 15317 22— 9;?) 'x/ M $TIRRUP5 CAN BE ORIENTED ElTH-EFL VERTICALLV OE ON AN mamas, PEZPENDICULAE To THE ANTICJPATED WING VEaTwAJ.‘ :mzzups ABE. uswud PREFERRED ovse IMO—WED srumuPs To : SIMPLIFV CONSTEucTtOH. WHEN 3454.2 ENFORCEMENT lb Esauzego, THE war-AL NOMINAL- sHEAz CAPACITY OFTHE. c2025 sac-nod IS THE SUMMATtOU' or THE. concerts. $45.62. CAPACITY AND THE s’neeup SHEA: CAPAGINZACI 315 55¢ 11.1.0: Vn = V‘ + V, WHERE V.s it THE NOMINAL 6142.62 CAMCJ'TV OF THE :TIzzupb. THE MAam—ruoe or V5 is A awe-now .OF: I) SIZE 02 AREA OF THE s‘rnaaupg (Uqu #3 or “4-) a) smcwc, szwc—zau 51-112mm: A: THE spawn, eszseu s-nzlaups Decemea, Maze swamps ABE :N-reeszc‘rsn By A 45° sum emu, IMCZEéSlNé ; THE VALUE our V5. THE NOMUJAI. 514m CAPACITY OF- THE 511220495 , Vs, CAN BE DETEEMINED 5v Loon/Jul: AT A 5ECTDON OF A 55AM wm+ A 3 45‘ 514592 CEACJL? i T'HE MAXIMUM sTEENbTH' OF A SINGLE sTnezuP L‘a LIMITED By YIELDHJL': AND IS THEREFORE. elven As: Av 7[y :5le A STIEZJJP ls U‘SHAPED AND IMT’EESEGTE: 4 CRACK ‘TWLCE -‘ Aw = 2AA,” (F02 #5 SlezuPS) A, = 0.20m?) A€> THE s-nzlzup SPACINQ DEC—254.555 oz, THE DEPTH OF THE BEAM wees-mess, THE NOMINAL— sHEAE scams-m OF THE 5HEA2 REINFORCEMENT INLEEASEE', v5 = AV/Ygfi (//—/5) 8 THE Barrio :51 ewes THE NUMBER or: TIME$ s—nzraops AT A 5PACAM€9 s INTERSEUI’ A 45°¢EACK. OFTEN, THE DWENsaous or: THE c2025 size-now (b,cl) HAVE ALREADY BEEN DETEEMNED 5v FLEXUEAJ. coustoEIZATlous, THEREFORE) Va :5 FIXED. SINCE éVn 2’ Va; (Vu = 1.8/0 +ltévb> Vim“ = L/y‘ 67 ¢ .5le V". = V; + Vb 'EDG sheen 29:15:29 W" .A f .1 A“ C e e 9 ! I i ‘ smog 114225 15 LITTLE CHOlCE m sTuezuP 5442 (#4, 507 USUALLY #3) AND 7",, (60 68.), 11-15 DESIGN ops-154.2 REINFORCEMENT can/~55 DONM TO oa-reemwwe THE $112209 SPAGIMGC Act-315 PLACES LIMIT?) ON THE STIERUP SPACING, TO INSUEE THAT AT LEAST ONE STIZEUP INTERSECTS A POTENTIAL Ski-54.3 CRACK, A MAXIMUM STIEZUP SPACle [6 GIVEN] 45'- 5,,” = 5 24-" (555:. 11.5.4) THE. ABOVE MAXIMUM STIEEUP SPACHJC: APPLIES AS LONG A45 vm a 4mm (= 2ch m mamas OF HléaH came WHERE 1145 SHEAR REINFORCEMENT [1051’ 052:»! A sesame PORTION at: THE 0551:»: SHEAR, THE MAXIMUM SPACle t5 anvEd As : i 5 la" 4- 5m»: WHLGH APPLIE’: wry-ISN'- 4mm < m, e eméwoé 2V; 4 van; 4-. 4%; OE Fri-us Tlot—ITEZ sPAcwc, mswzfis 11—wr AT LEbrsT 3 s-ruzewae WILL umasza’ A Dmoouou 6245K. 22-139 "S £30 sheets . 1‘11 Ac1-518 (55c. 11.5.4.9) ALSO PLAC£$ A LIMITOM me Mwmum AREA car—- 11+! 51-15012 REINFORCEMENT N EEéLONS wuzee 1T is 2501011250. T1415 l5 51M11..AIZ To THE: MlNlMUM AeEA or $TEEL. F012 FLEKUZE. szucfi “THERE If: A sum TamaFER OF FORGE TO THE 51-1542, REINFORCEMENT WHEN THE plAéouAl- CRACK FORMEa, 95105251250 s—ruzrzups MAN ercmze. WHEN 51-15112 zezuFOZcEMT 15 1253121250 ( Vu 2 V2. ¢Vc>, A MINIMUM REINFORCEMENT AREA ls: QIVEU A67 AV 2 0.75/A’ b: 5 (11—13) 75/ BUT NOT LE$$ THAN 50 M (5151-: 55c. 1155.9) 79 so. (11-13) APPL|E$ Foe Hug-152 greats-m couczETE (at; > 44-4-4 psi 3. BY ZEABZANGHKIC. THE- ABOVE LJMlTb ow AV) ADDITIONAL. SPAcwe. Lulu-rs ABE 0874114150: 5 a, = & AV/ m x 5 by OZ 5”,“ - ' / (FOZ fi’z 4444» Fed) 5051.,— To PREVENT OlfiZ-REINI‘OZCJNO THE c2055 :Ec‘nou/ THE 5’12sz 51-15132 STEEme CANNOT EXCEED 4x THE SHEAR swam or: 11—15 cochETE (sec. 11.5.(.. q): 5/2wa (= 41/4) 1/5 .4. .1 @TMPMH THL‘: Pumas AN UPPER LIMIT ON THE SHEAR STEEMéTH OFA GIVEN c2055 $BCIFlOM. EXCEED? 5X THE. 514562 $T’25N6TH OF THE CONCRETE) 02: Va ..>_ W W IF’ THE PAC.me LOAD EFFECT ¢V4 + ¢Vs Mag—wa + Wig—AM] awake/j ¢5v¢ ‘n-iE C2055 bEchOM OF THE BEA-M MT 55 m0. Adm-3:8 sec. 11.1.3.1 ALLONS F02 A. ksoucnou or: V“ N A2566 0‘ AN APPLIED 554mm, L060 02 REAL-Flow. AT 11-14556- LOCATtous, VEZTlCAL— COMPZE$$|VE sTREssES 25090:. THE- PRINCJPAL TEusluz 5112555 LN THE CCJJCZETE; 601% 5%! To MOHE’b cuecus'. THE fiHEAE STZENC-fl'u- OF THE conczE—ra. NEAZ. suPPosz “46254556 Swat: THE cabal—[Ne oF THE. com,sz Ls DE L-AV ED. INSTEAD 0F DESIoNtMC: POI?— ’THE MAWMUM $5454.12 41' A some-r, THE VALUE AT A DtsTAucE <L FROM THE F445 at: THE auPPOZT ts 0529. “THE: 250mm: THE OVERALL 5.4552 DEMAND on ‘THE c2055 sschou. __/- oesth s‘rlzzLJPS LOCATED N THE REMOIO A FOE nomozew-rmswufiop Vu ‘bHEAZ D IAGZAM i l A E ‘\ FAcE oF summer 5.4m REINFORCEMENT 15 NOT zzaolzao (Au-315,556. 11.5.5.1) Foz THE (:0wale slTuATLOMs : I) vu 5 -—-’z ¢ VC, 2) subs mo roarmee a) Jam-rs perm-ac by Act 2125 52¢, 5,1: 4) 55M: WITH A Toru— DEPTH (h) L555 THAN 1 ' to" 0 Z‘VZQ ' .545 Z. IN ALL OTHEZ CAéE'. vu e. SZSVrL = ¢£Vb 4'ch lo " “15. _ 44 E THE peoczpuza Fora DEFEZMINING THE 514542 REINFORCEMENT cm 5E sow/~422th As: D ESMbLla—l THE \Iu zszoPa OF 114: 55AM (MOSF wax/0mm Va A'T EACH sac-now ), 2) E's-mat..th ‘THE REQUIRED NOMINAL 5,4542 sTmC’TH , Vn CURVE: Vn = V“ g = 0.75 F'OZ SHEAR 7 . a) Reeves Va AT suPPosz 'AND ou‘rA DISTANCE 4 FROM THE FACE. as THE $UPPOE—T ‘TO THE VALUE oF v,” AT d. 4) CALCULATE TH: bHEAR 049Aan OF THE. (.0chst AND PLOT on THE \/,t wave. c2055 SECTION SlLE MUST bE wczeAan 5), oz-rzemwz WHERE s-nzreups A22: 25m):an av: Vrt>y§ 2 (a) DETERMINE MAXIMUM s-ruzzuav spAuuc, asap ON THE SMALLEST OF: K Psi. / «p56 .4. A5: 3‘ 5 x = .4. V D m 5» sobw iii v-M‘Ffl Wflzifl {/L. m4 V ( H= \éflefl > 4/28NJ BUT s (3th Smw = 0/ 5 12" 4 7) 551 s‘nztaup yACINb BELOW 5”.“ 313.550 on swam: DEMAND: 5 = W 5: -5Wg var“? N01155: .& c 050A]. $IZE OF swamps: #3, 4"4.! MD 5 __ u ‘ shim " 5 ' Av = ZAb‘r EXAMPLE —l : FOE. 11-5 2; c2055 sac-now DETERMINE THE MAXIMUM Fb5$l5LE DEsIou aHEAK. STRENGTH \ 14‘ #4 " / = ~ “ U 62 I2 7: 4000 Fat. 28 ézeo STEEL. . soufnow seams and P. I‘l- l5 13w“? u 0> 0mm. 36mm AuaumFm. mwmmfim co m. an TNN (QKUQWWWV‘K 5.0mQO \._o Mudu J|| .w 024 7:04u40 N4MI m 57.04% Q24 > '40 10*? u.) 22"“; SOLUTION 3 \/c = 2Mbwc£ = aJToE'CH—Xza) = = 44.0 14in 41 585' lbs (¢Vn)max : ¢ 5%- : 0.75(5X4q,c> = I80 199's MEL—5.2 FOR THE 2c (.2055 sec-now (:4sz w EXAMPLE-1) DETERMINE THE Dayan; sum stew-n4 N: THE 3‘4- snzzop: 425 .3me AT :2“. \/c = 4-9.4, 14.,55 (FraoM Pzzvnous EXAMPLE) A7655} = 2(o.2o)(cpo>(za) = 5a: laps )2. v5 = ¢ [Vv ‘L V5] : o.7s[44.<o+5¢.o] - EXAMELE—La FOR THE $2.055 $E¢TION CpNEN IN EXAMPLE-1, DETEZMINE THE MAXIMUM sneeup 6PACIN<9 zmu‘asmsms Pena 40-318. ASSOME THE REQUIRED :mzrauP aHewa 5rzs~gn4 l5 GIVEN As 50 laps 05%. since A 4 44% PsC l = 0.4-0 : 34- ' Vsfie?‘ = 50/(¢=0.75) = (96.714 P’? b 0‘; 11: (f) C: Y. C? C"? . ‘7 C‘! Cx! : 44?;wa = z\/c = 2144.6) = $1.2." snuce. 66.7.54 qqzk “ ll 5 = :1 = a; :14 424 M" z z EXAMPLE-4! Foe THE suMF’LY-sopczoz'rso 55m sHowN, DE‘I‘EBMNF g THE SHEIZUP smwe ("- REQoquo) A5$UMINbl ' #3 STIEEuPb ° 5000 psi. cone. ' 62 b0 5TEEL .l [2 I5 SOLUTION .' = 0.75 0001 32.5) = 32.0141” I000 swae (éyé = L0 = H," < 45“ 5TIZZUP$~A€E a a 2530:2450 1; \lg‘ :: £— : (00 ¢ 0.75 V; = :22. = 421" 0.75 14 V634 = 50 —4z.7 = 17,3 k . swca [729" < 4\/¢_ = 4(42.7) = I?" c.2055 sofa—now DlMEN5|OMb Q14. 5 = W Av = 26041) = 0.22. H‘LZ \{s/q’ = 0.2.2geox13m) , 245' a 24" 77.5 CHECK MAXIMUM $PACJNC2 LJMITb 5M ‘ 5/, -_- 0.2 0000 g 22" 50b 5002. :13 sheets 22: "2 a. fA/fi/ipflzé,lzi' .1; E 0 U. (k ll N ,\< II 2642.?) = 85.4"> \éflq ‘, SMM = d. 3 32.5 _—_ No.25“ é— CONTROLS 2- z. = 24" pssucm THE s—vsmz BENFOZCEMENT F02 THE SIMPLY SUPPORTED 12c BEAM shun/N. 05!: 33:30pm; comes-IE AND 6?. @O STEEL. (2,5 = (.5 F/H 9- Lola/Pr SOLO-HON I Wm,“ = 0.150 = c.3325 14/9, w‘u = :.2(:.s+o.34) + 1.0(z.o> = 5.4! k/H— 7- .44 £3 = . t‘ 12LL 5 (a (947 k,» Vulrmx @ J FROM FACE OF soppoe‘r Vu — 5.4! (é’I‘FZBI-S") ' l2. )2 ‘ ‘ 22w ‘i '30 sheets My = 21:5“0 (12623.5) = 40k?" (005 ll 5% 075 H _ 4o 26; laps We)" ”/\ 22439 100 sheets WWW/5M? . \L g/ ,, AND U 3 ~l l I}. _ ‘ 4 ' 3 3 76‘ law 3 i§9w61z§ ‘3 H ‘F‘ 6 Ag 76 : oa—L—M (‘0 a) = 22 H Fob” 5°C“) was 5m; 4 5mm = “.75” 01>: ssu" :2-‘5uemwsx 2'4" ...
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CVEN 444 Lecture Notes - 07 - 13'?) sheets Mom -4. ha;...

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