For official use only Doc. WRD 09(489) July 2007 BUREAU OF INDIAN STANDARDS. PRELIMINARY Indian Standard

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1 For official us only Doc. WRD 09(489) July 007 BUREAU OF INDIAN STANDARDS PRELIMINARY Indian Standard STRUCTURAL DESIGN OF ENERGY DISSIPATORS FOR SPILLWAYS CRITERIA (First Rvision) (Not to b rproducd without th Last dat for rcipt prmission of BIS or usd as a of commnts is STANDARD) FOREWORD (Formal claus to b addd latr on) Th dsign of downstram protction works or nrgy dissipators blow hydraulic structurs occupis a vital plac in th dsign and construction of dams, wirs barrags and outlts. Th problm of dsigning nrgy dissipators is ssntially of rducing high vlocity flow to a vlocity low nough to minimiz rosion of natural rivr bd. This rduction in vlocity may b accomplishd by any, or a combination of th following, dpnding upon th had, discharg intnsity, tail watr conditions and th typ of bd rock or th bd matrial: a) Hydraulic jump typ stilling basins: 1) Horizontal apron typ; and ) Sloping apron typ; b) Jt diffusion and fr jt stilling basins: 1) Jt diffusion basins; ) Fr jt stilling basins; 3) Hump stilling basins; and 4) Impact stilling basins; c) Buckt typ dissipators: 1) Solid and slottd rollr buckts; and ) Trajctory buckts (ski jump, flip, tc); 1

2 d) Intracting jts and othr spcial typ of stilling basins. In India, hydraulic jump typ stilling basins and buckt typ nrgy dissipators ar gnrally usd for dissipation of nrgy dpnding on condition of downstram tail watr. Indian Standards had alrady bn publishd for critria for hydraulic dsign of ths two typs of nrgy dissipators as undr: IS 4997 : 1968 Critria for dsign of hydraulic jump typ stilling basins which with horizontal and sloping apron IS 7365 : 1985 Critria for hydraulic dsign of buckt typ nrgy dissipators (first rvision) This standard covring th structural dsign of nrgy dissipators for spillways was first publishd in This rvision incorporats th latst practics bing followd in th fild, th major changs bing in rspct of dsign of flow slab anchorags, anchorag for spillway buckt and dsign of rinforcmnt for buckt tth. For th purpos of dciding whthr a particular rquirmnt of this standard is complid with th final valu, obsrvd or calculatd xprssing th rsult of tst or analysis shall b roundd off in accordanc with IS : Ruls for rounding off numrical valus (rvisd). Th numbr of significant placs rtaind in th roundd off valu should b th sam as that of th spcifid valus in this standards. 1 SCOPE This standard lays down critria for structural dsign of various componnts of hydraulic jump typ stilling basins and buckt typ nrgy dissipators blow spillways and outlt works foundd on rock. REFERENCES Th standards listd blow contain provisions which, through rfrnc in this txt, constitut provisions of this standard. At th tim of publication, th ditions indicatd wr valid. All standards ar subjct to rvision and partis to agrmnts basd on ths standards ar ncouragd to invstigat th possibility of applying th most rcnt ditions of th standards indicatd blow: IS No. Titl 1786 : 1985 Spcification for high strngth dformd stl bars and wirs for concrt rinforcmnt (Third rvision) (Suprsding IS 1139) 4410 (Pt 18) : 1983 Glossary of trms rlating to rivr vally projcts: Part 18 Enrgy dissipator dvics (Stilling basins) 4997 : 1968 Critria for dsign of hydraulic jump typ stilling basins with horizontal and sloping apron : 1994 Critria for dsign of chut and sid channl spillways (First rvision) 7365 : 1985 Critria for hydraulic dsign of buckt typ nrgy dissipators (First rvision) : 1994 Cod of practic Construction of spillways and similar ovrflow structurs (First rvision)

3 1177 : 1986 Guidlins for dsign of drainag arrangmnts of nrgy dissipators and training walls of spillways 3 TERMINOLOGY For th purpos of this standard, th dfinitions givn in IS 4410 (Part 18), IS 4997 and IS 7365 shall apply. 4 STRUCTURAL DESIGN OF STILLING BASIN FLOOR 4.1 Gnral Th basin floor lvation is gnrally dcidd on th basis of foundation conditions and th lngth of th basin is dcidd on th basis of hydraulic considrations in accordanc with IS Th width dpnds on th numbr of opnings and pirs on spillway crst. 4. Structural Dsign Th basin floor slab is subjctd to uplift, pounding and vibrations from hydrodynamic forcs in th hydraulic jump. On yilding foundation it may suffr diffrntial sttlmnt. Thrfor, th basin floor slab shall b dsignd for th strsss inducd du to abov forcs. Th important lmnts of th structural dsign of basin floor is dtrmination of thicknss of th floor and dtails of anchorags in th bd rock. Uplift forc is jointly rsistd by th slf wight of floor and contribution from th anchorags. For calculations of uplift, a thicknss of th floor is assumd initially, and is confirmd by dtaild calculations Minimum thicknss Th minimum thicknss of th floor slab dpnds on th foundation conditions and th magnitud of uplift forcs. A slab of about 600 mm thicknss is th minimum rcommndd. Actual slab thicknss shall b dtrmind by analysing uplift and diffrntial movmnt. 4.3 DESIGN PROCEDURE Th structural dsign of floor slab consists of th following stps: a) dtrmination of uplift forc b) dtails of anchorags into bd rock i.. diamtr, numbr and spacing of anchor bars. c) dtrmination of lngth of anchors considring dislodgmnt of rock mass against uplift forc, and d) working out dtails of slab rinforcmnt Uplift forc Uplift of th concrt lining of th stilling basin could b causd du to on or a combination of th following: 3

4 a) Hydrostatic uplift Th uplift causd by spag gradint blow th stilling basin. b) Hydrodynamic uplift Th propagation of fluctuating prssurs in th hydraulic jump through unsald joints or cracks in th floor such that man prssur prvails at th intrfac of th concrt and bd rock and hnc hydrodynamic uplift is causd whnvr instantanous prssur on th uppr surfac is lss than man valu of th fluctuating prssur Hydrostatic uplift Provision of ffctiv drainag systm blow th basin is ncssary. (s IS : 1177). In viw of th drainag arrangmnt providd blow th basin, it may b adquat to assum 50% rlif in th uplift prssurs, as indicatd blow. Following thr conditions may prvail and th most critical of thm should b dtrmind. Condition I Stilling basin oprating during spillway dsign flood is shown in figur. Th watr surfac ovr th slab at hydraulic jump profil for dsign discharg conditions. Unbalancd uplift prssur = 0.5 (Tw 1 W + t b W) (D 1 W + t b Wc) Tw 1 = Maximum tail watr dpth W = unit wight of watr t b = thicknss of stilling basin floor Wc = unit wight of concrt D 1 = Dpth of watr in stilling basin Condition II Rsrvoir at FRL with gats closd and stilling basin mpty i.. dwatrd (Fig. 3). Unbalancd uplift prssur = 0.5 (Tw 1 W + t b W) (t b Wc) Tw 1 = Minimum tail watr dpth Condition III Suddn drawdown condition aftr th dsign flood has just passd ovr th spillway and th gats ar closd again. In this cas th uplift blow th basin may b takn th sam as th condition I and th watr load in th basin b takn as th minimum TWL which may b th dpst rivr bd lvl, minimum watr lvl in th rivr from powr/othr considrations, tc. (Fig. 4). Unbalancd uplift prssur u = 0.5 (T W W + tb W) (Tw W + tb Wc) Hydrodynamic uplift Th hydrodynamic uplift prssur F m ovr th slab monolith according to claus is givn by 4

5 1. ρ. V F' m = Kφ p. φ1. φ ( 1 ) Whr K = factor accounting for th probability of occurrnc of fluctuating prssurs. = 3.09 corrsponding to 99.8% probability of occurrnc. φ p = Prssur cofficint givn in Fig. 5. ρ = Mass dnsity of watr, 1000 kg/cum V 1 = Vlocity of flow ntring th stilling basin L 1 = Lngth of th monolith in flow dirction L = Width of th monolith prpndicular to flow dirction. φ 1 = Cofficint of corrlation of prssur along L 1 (From Fig. 5) φ = Cofficint of corrlation of prssur along L (From Fig. 5) Th valus of prssur cofficint for various Fraud numbrs shall b rad out from Fig. 5. Th largst of th abov valus of uplift prssur shall b considrd for dsign purpos Dsign of anchors Gnrally th diamtr of th anchor bar should atlast b 5 mm. Th diamtr of th whol into which th anchors ar placd and groutd should not b lss than 1.5 tims th diamtr of th anchor bar. Th othr dtails shall b workd out as shown blow: Numbr of anchors (n) rquird pr unit ara is givn by Unbalancd uplift prssur n = a σ st Whr, a = ara of th bar σ st = Prmissibl tnsil strss of stl, kn/m Numbr of bars to b roundd to th nxt highr intgr Spacing of bars = 1 n Actual forc in ach anchor = Unbalancd uplift prssur = n µ No. of anchors rquird pr unit ara Th dpth of anchor bars in rock mass = whr d b = dia. of anchor bar Actual forc in ach anchor Actual forc in ach anchor OR π d F π d F b b1 a b 5

6 d a = dia. of anchor hol F = Prmissibl bond strss btwn stl and grout b 1 F b = Prmissibl bond strss btwn grout and rock Th gratr of th two should b adoptd as anchor dpth. Th valu of th prmissibl bond strss would vary for diffrnt sit conditions and proportion of grouts. In th absnc of data, th following valus for 1: ratio proportion of grout may b adoptd. F b 1 = 600 kn/m F b = 400 kn/m Bond lngth should b chckd for bond btwn stl and grout and also for bond btwn rock and grout Chck for dislodging of rock mass anchord against uplift prssur. Th dpth of anchor bar in th rock mass calculatd in 4.3. should b chckd for dislodgmnt of rock mass against uplift prssur. For this, th dpth of anchor bar in th rock mass should b sufficint to ngag a conical mass of rock with a vrtx angl of 45 dgrs, th wight of which should b abl to withstand th nt upward forc (S Fig. 6). Th dpth of anchor rquird from th abov considrations shall b chckd as follows: (1) Dpth of conical mass of rock at bottom, h 1 (Spacing of anchor bar)/ = mtrs tan.5º () Wight of conical mass at bottom W π h1 = ( h1 tan.5º ) Wrs.. kn 4 3 whr h 1 = dpth of anchor bar in conical portion (Fig. 6) Wrs = Submrgd wight of rock, kn (3) Dpth h rquird xcluding conical mass [ Actual forc on ach anchor Slf wight of slab covrd by ach anchor Wight of conical mass] h = (Spacing) Submrgd wight of rock. NOTE If th govrning uplift considrd is hydrostatic (i.. conditions (1) to (3), thn th trm rprsnting slf wight of slab should b omittd from th abov quation. (4) Total dpth of anchor L = h 1 + h Th abov procdur assums that no tnsion is prmissibl in th foundation rock. Howvr, in sound and hard rock som tnsion is allowd to rduc th dpth of anchor. 6

7 It should also b nsurd that th dpth of anchor bar as calculatd in 4.3. is not lss than th valu of L calculatd using th abov quations. Not withstanding th rsults of abov calculations, a minimum 3 m lngth of anchor should b providd. Th calculations should b rfind to obtain a satisfactory combination of th valus of slab thicknss and anchor bars, consistnt with th charactristics of th bd rock Annx A givs an xampl to illustrat th mthods of calculation. 4.4 BASIN FLOOR SLAB Floor Slab Thicknss Th thicknss of floor slab dpnds on th foundation conditions and magnitud of uplift forcs. A slab of about 600 mm thicknss is th minimum rcommndd. Actual slab thicknss ndd shall b dtrmind by analysing hydrostatic uplift and diffrntial foundation movmnt Floor Slab Rinforcmnt In thick slabs on rock foundations normally covrd with nominal tail watr, structural rinforcmnt is not ncssary xcpt in th appurtnancs of th stilling basin. Uplift on a slab should b takn car of by adquat anchors. Th slab is dividd into indpndnt panls by contraction joints paralll and prpndicular to channl or basin cntr lin to avoid srious shrinkag and tmpratur cracking with th us of nominal rinforcmnt which dos not xtnd across th joints. Siz of panl should b larg nough to rsist distorting hydrodynamic forcs. Panls should b cast in altrnat bays with construction joints Th indpndnt panls of slab ar rinforcd with nominal stl to prvnt harmful cracking rsulting from shrinkag and tmpratur strsss not rlivd by contraction joint and on yilding foundations to avoid possibl cracking from diffrntial sttlmnt. Usually, a slab on unyilding foundation is rinforcd in th top fac only bcaus bond btwn th concrt and rock at th bottom is rlid on to distribut shrinkag cracks and to minimiz bnding strsss in th anchord slab for th assumd uplift had. Th minimum amount of rinforcmnt for indpndnt panls on unyilding rocks is 0 mm diamtr bars at 300 mm cntr-to-cntr both ways. Additional rinforcmnt should b providd for unfavourabl foundation condition or for high hydrostatic uplift prssur Diffrntial Movmnt On rlativly yilding rock foundations, th indpndnt floor panls ar subjct to possibl diffrntial movmnt of adjacnt blocks and a ky at ach transvrs contraction joint (xtnding into foundation undr th joint attachd to th slab downstram and supporting th slab upstram from th joint) may b rquird to prvnt th downstram sid of a joint from bing raisd abov th upstram sid as watr at high vlocity striking such a projction would incras th hydrostatic prssur in th joint and hnc th uplift undr th slab. Highr th vlocity, mor srious will b th condition rsulting from such rlativ movmnt. Th kys also incras rsistanc to possibl movmnt and srv as spag cutoffs downstram from transvrs drains. Dtails of ky ar covrd in IS

8 4.4.4 Concrt and Rinforcmnt Covr Chut floor and stilling basin slab shall hav minimum 100 mm covr for rinforcmnt. 4.5 BASIN BLOCKS (STRUCTURAL PROVISION) Gnral Location and optimum shap of basin blocks shall b dcidd on th basis of IS Th dimnsions of th basin blocks ar shown in Fig. 6a. Th purpos of th block is to dissipat nrgy and thrby to rduc th lngth of basin. h b = hight of basin block S b = spacing btwn th blocks W b = width of block, and D = conjugat dpth 4.5. Forcs on Basin Blocks Dynamic forc against th upstram fac of th basin blocks is approximatly that of a Jt impinging upon a plan normal to th dirction of flow. (s fig. 6b) Forc P acting at h b / = WA (D 1 + h v1 ) whr W = unit wight of watr A = ara of upstram fac of block, and h b = Hight of basin block (D 1 + h v1 ) = spcific nrgy of th flow ntring th basin Ngativ prssur on th back fac of th blocks will furthr incras th total load. Howvr, this may b nglctd if abov quation is usd. Basin block is to b dsignd as cantilvr as shown in Fig. 6a Rinforcmnt Th rinforcmnt shall b calculatd by th following formula and placmnt of th rinforcmnt is shown in Fig. 7. Ara of stl A st M = σ st jd whr M = momnt du to forc P (s 4.5.) σ st h b = P = prmissibl tnsil strss of stl, and 8

9 d = ffctiv dpth of block. NOTE 1 Th basin block is tid into th floor slab by rinforcing stl. All rinforcing stl in a basin block is placd minimum 150 mm from th xposd surfac bcaus of th possibl rosiv and cavitation action of th high vlocity currnts. 4.6 CHUTE BLOCKS Nominal rinforcmnt of 0 mm diamtr bar at 300 mm cntr to cntr both ways may b providd on all xposd facs duly anchord in apron concrt. 5 SPILLWAY BUCKET REINFORCEMENT 5.1 Trajctory/Solid Rollr Buckt (s Fig. 8 and 9) Forcs and Momnts Horizontal forc on th buckt is du to chang in momntum and is givn by th following formula: wqv g Total horizontal forc on th lip (F) = (1 cos θ ) w = Unit wight of watr. q = Discharg intnsity. v = Vlocity of flow. θ = Exit angl of th buckt. Momnt of th horizontal forc about horizontal plan A-A passing through invrt of th buckt (s Fig. 8) is givn by F R (1 cos θ ) M = R = Radius of buckt Effctiv dpth d of buckt for rsisting momnt M may b takn as d = + R ( R sin Q + t ) R ffctiv covr. w 5. REINFORCEMENT Ara of th stl A st of rsist momnt M is givn by M A st = σ st jd Providd minimum stl (along flow) = 0 mm diamtr bar at 300 mm cntr to cntr. 9

10 Provid distribution stl = 0 prcnt of main stl with a minimum of 16 mm diamtr bar at 300 mm cntr to cntr. 5.3 ANCHORAGE OF SPILLWAY BUCKET (s fig. 10) Th following thr conditions may prvail: Condition 1 Spillway oprating condition at dsign flood, Condition Rsrvoir at FRL with gats closd and th buckt mpty (dwatrd) and Condition 3 Suddn drawdown condition Gnrally th dsign is carrid out considring uplift blow th buckt corrsponding to maximum TWL (condition 1 and 3) ignoring th wight of watr in th buckt and lip portion of th buckt on consrvativ sid. Th mthodology gnrally adoptd is givn in Howvr, th wight of watr in th buckt may b suitably considrd in dsign whn it is likly to hav a substantial ffct Provision of ffctiv drainag systm blow th buckt is ssntial (s IS 1177). In viw of th drainag arrangmnts blow th buckt, it may b adquat to assum 50 prcnt rlif in uplift prssurs Upward forc pr unit ara F u (S Fig. 10) is givn by th formula: F u = R ([0.5 βw W α W (1 0.5 (sin θ + sin θ ) + 0.5( θ + θ ]) i i (sin θ + sin θ ) i θ i = inlt angl of buckt Numbr of anchors pr unit ara = n = Fu a σ st 1 and spacing of anchors = n Anchors ar gnrally staggrd in plan Dpth of Anchors in Rock Mass Th dpth of anchors should b dtrmind by considring failur btwn anchor bar and grout and also btwn grout and rock as givn in claus SLOTTED ROLLER BUCKET (STRUCTURAL PROVISION) 6.1 Gnral Dimnsions of th slottd rollr buckt should b workd out on th basis of IS For anchor dsign 5.3 will b applicabl. Provision of ffctiv drainag systm blow th buckt is ssntial as givn in IS Som salint dimnsions to b usd in this standard ar: 10

11 b = 0.15 R b = 0.05 R L a = R sin (θ 8) R = R [sin (θ 8) ] b 1 = b + L a tan º b = b L a tan º 6.1. Discharg/mtr is calculatd by q= Q/L m 3 /s/m Whr Q= total dsign discharg at MWL in m 3 /s L = lngth of buckt spillway in m Vlocity is givn by th quation V = gh m/s Whr H = fall of watr (had) from MWL to buckt invrt. 6. Dsign of Rinforcmnt for Buckt Tth 6..1 Forc on buckt tth (Figur 1 shows dfinition sktch of buckt tth) abov plan AB and in a dirction paralll to it (s Fig. 11 and 1) is givn by Wqv [1 cos ( 8 )] b (Approximatly) g º F 1 = θ Th tth should b dsignd as a cantilvr fixd at th plan AB. F h 1 1 Bnding momnt, M = Whr h 1 is dfind in Fig. 1 and is givn as h 1 = R [1 cos ( θ 8º )] 6.. Ara of main stl A st is givn by A st = σ M stjd whr d = θ θ ( R Cos ) +( R Sin R) R ffctiv covr. Cos θ = [ Radius (Elvation of junction of 8º and 16º aprons invrt lvl )]/Radius(s fig 13) j = lvr arm factor and θ, θ and R ar indicatd in Fig

12 Th main rinforcmnt should b providd along th curv as shown in Fig. 13. Th minimum clar covr in th radial dirction should b 150 mm. It shall b nsurd that minimum rinforcmnt pr tooth is 7 numbrs 0 mm diamtr bar Dsign of Links for Tooth Provid 0 mm diamtr link rinforcmnt at 300 mm cntr to cntr around tooth in th dirction prpndicular to flow. Distribution stl for links shall b providd on thr sid facs of tooth and shall b 0 mm diamtr bar at 300 mm cntr to cntr. 6.3 Dsign of Rinforcmnt for 8º Apron Provid nominal rinforcmnt as undr: a) Along flow (main stl) = 0 mm diamtr at 300 mm cntr to cntr and b) Prpndicular to flow (distribution stl) = 16 mm diamtr at 300 mm cntr to cntr. 6.4 Dsign of Rinforcmnt for 16º Apron Horizontal forc on 16º apron. Whr wqv.. (cos 8º cos 16º ) g F = V = 1 b v b b 1 = width of slot at ntry b = width of slot at xit Rfrring to Fig 11 and Fig 1 lngth of 8º apron L a is givn as L a = RSin( θ 8º) b = 0.05 R b 1 = b + tan º R Th horizontal forc on apron is du to chang in dirction as abov and it acts lvl whr h = hight of 16º apron. Bnding momnt = F Ara of stl A st = h BM.. σ st jd whr d = ffctiv dpth for 16º apron = h cos 16º covr NOTE Minimum stl shall b providd as mntiond in 6.3 h abov apron 1

13 6.5 Sampl calculations for slottd rollr buckt ar givn in Annx B for guidanc. 13

14 ANNEX A (Claus 4.33) ILLUSTRATIVE EXAMPLE FOR DESIGN OF SLAB AND ANCHORAGE Givn: D 1 =.43 m ) V 1 = 46.1 m/s ) For th dsign discharg condition F 1 = 9.44 ) Tw = 31.5 ) TW 1 = 6 m corrsponding to min powr hous flow Siz of th slab monolith L 1 = 16 m, L = 14 m ρ = 1000 kg/m 3 (Mass dnsity of watr) W = 9.81 kn/m 3 (Spcific wight of watr) Wc =.56 kn/m 3 (Spcific wight of concrt) Wrs = kn/m 3 (Spcific wight of rock undr submrgd condition). Fb 1 = 600 kn/m Fb = 400 kn/m σ st = kn/m Stp 1: Calculat th maximum uplift prssur Assum slab thicknss t b = m Condition 1: Spillway dsign flood µ = 0.5 ( ) ( ) = Condition : Stilling basin mpty µ = 0.5 ( ) (.56) = = 5.88 Hnc thr no uplift Condition 3: Suddn drawdown following dsign flood 0.5 ( ) (6x ) = 59 kn/m Hydrodynamic uplift Ø p = 0.05 D = Tw = 31.5 mm D D 1 = = 8.8 for F 1 = 9.44 (Fig. 5) 14

15 Ø 1 = 0.76 for 1 L 16 = = (Fig. 5) D D Ø = 0.91 for L 14 = = (Fig. 5) D D Uplift prssur F m = (46.1) = kn/m Thrfor dsign uplift prssur = kn/m Stp : Dtrmin numbr of anchor bars/spacing Try 5 mm dia bars. Ara = m No. of anchor bars pr unit ara = = Say 1 bar pr squar mtr ara. Spacing at 1 mtr c/c Thrfor actual forc in ach anchor = kn. Stp 3 Dtrmin dpth of anchor bar basd on dia. of anchor bar L = π =.5 m basd on dia of hol in th rock L = ( = 40 mm) =.35 m π Stp 4 Chck against dislodgmnt of rock mass Dpth of conical rock mass at bottom (S fig. 6) h 1 = Wight of conical W 1/ 1.1 m = π 1.1 = ( ) = 4.37 kn Dpth rquird xcluding conical rockmass (.56) 4.37 = h = Thrfor, total dpth L = h 1 + h Say 5 m 15

16 = Say = 6. m Th dpth of anchorag will b 6. m Rsults: Siz of th slab monolith = 16 m 14 m Thicknss of concrt slab = m Dia. of anchor bar = 5 mm Spacing = 1 m c/c Dpth of anchorag = 6. m NOTE Any rfinmnt rquird can b don by rpating th calculations with modifid valus of slab thicknss and diamtr of anchor bar tc. 16

17 ANNEX B (Clauss 6.5) SAMPLE CALCULATIONS FOR SLOTTED ROLLER BUCKET B-1 DATA GIVEN 1) Exit angl = 45º ) Lngth of buckt = 37.0 m 3) Discharg at MWL = cumcs 4) Width of tooth of d/s nd = 1.15 m 5) Radius of buckt = 9.0 m 6) Invrt lvl of buckt = R.L m 7) Junction 8º and 16º apron = R.L m 8) MWL = R.L m Discharg q = = Say q = 6 cumcs/m according to 6.1. V = gh cumcs m = = m/s whr H = Fall of watr (had) from MWL to buckt invrt ( ) = m B- DESIGN OF REINFORCEMENT FOR BUCKET TOOTH Forc on tooth abov plan AB in a dirction paralll to it is givn by wqv g F 1 =... (1 cos ( θ 8º ) = [1 cos (45º 8º )] = KN Now, h 1 (s fig. 13) = R [1 cos (θ 8º)] = 9 [1 cos (45º 8º) = m h1 B.M. = F1 = b (s 6..1) 17

18 = KN. m Hr, cos θ (s fig. 13) = Radius ( Elvation of junction of 8º and 16º aprons invrt lvl) = 9 ( ) 9 = Effctiv dpth Radius d = θ + θ + ( R cos ) ( R sin 0.05 R) R ffctiv covr = 15 cm = 1.5 m Ara of stl rquird M A st = σ st jd (s 6..) Assuming σ st = 80% of KN/m for hydraulic structurs = KN/m A st = = cm 4 cm provid 0 mm diamtr 7 nos bars pr tooth (minimum rinforcmnt) Dsign of links Provids 0 mm diamtr link rinforcmnt at 300 mm c/c around tooth in th dirction prpndicular to flow. Distribution stl for links shall b providd on thr sid facs of tooth and shall b 0 mm diamtr bar at 300 mm c/c. B-3 DESIGN OF REINFORCEMENT FOR 8º APRON Provid nominal rinforcmnt as undr: a) 0 mm diamtr bar 300 mm c/c main stl along flow b) 16 mm diamtr bar at 300 mm c/c prpndicular to flow. B-4 DESIGN OF REINFORCEMENT FOR 16º APRON Horizontal forc on 16º apron wqv.. (cos 8º cos 16º ) g F = according to 6.4 b = 0.05 R = = 0.45 m L a = R sin (θ 8) R 18

19 = 9 sin 37º m = 0.86 m whr V = 1 bv = = m/s b f = KN h B.M. = F Whr h is ris of 16º apron = 1.3 m B.M. = = KN. m A st = BM.. σ st jd (s 6.4) Whr d = (h cos 16º covr) = ( ) = 1.15 m A st = = cm Minimum Stl providd a) Along flow = 0 mm diamtr bar at 300 mm c/c b) Prpndicular to flow = 16 mm diamtr bar at 300 mm cntr to cntr. 19

4.2 Design of Sections for Flexure

4.2 Design of Sections for Flexure 4. Dsign of Sctions for Flxur This sction covrs th following topics Prliminary Dsign Final Dsign for Typ 1 Mmbrs Spcial Cas Calculation of Momnt Dmand For simply supportd prstrssd bams, th maximum momnt