Lecture Note Behavior of RC Members: Torsion

Transcription

1 5 Lere Noe - Behaior o RC emer: Torion Torion mean wiing. The pe o orion in rre are. Primar or eqilirim orion: - Primar or eqilirim orion i ha whih i reqired o mainain he ai ai eqilirim in a aiall deerminan rre.. Seondar or ompaiili orion: - Seondar or ompaiili orion i ha whih i reqired o mainain ompaiili ondiion in a aiall indeerminae rre. The orional ine (K T ) o a memer i he orional momen reqired o prode a ni angle o wi. T GC Th, K T θ L Where, K T Torional ine T Torional momen θ Toal angle o wi in lengh L. E G Elai hear modlo. + µ E odlo o elaii. µ Poiion raio. ( ) C Torion onan or polar momen o ineria KD K S. Venan orional onan, whih arie wih (D/) raio. The ale o K or ario raio o (D/) i gien in Tale:

2 54 Tale: Vale o K & α in orion o reangle T C KD, τ max α D D α K Vale o α more onenien expreion or C ha een deried Timohenko a D C 0.6 D The ollowing approximaion an e made when dealing wih langed eam & oher eion, whih an e amed o e reanglar. For anali, T, L or I eion are diided ino omponen reangle & he C ale i he omined ale o he omponen reangle. The diiion hold e h ha he ale o C oained or he whole eion, i.e. D C 0.6 D Shold e he large poile. Bending & orional ine o RC eam The magnide o diriion o momen a orion o adjoining memer i mall.

3 55 Thi i eae: E G ( + µ ) I, µ 0. 5 hen nd µ 0 hen G G E. E Whih how ha G i er low a ompared o E. gain, For a reangle D, he ale o I i ao hree ime ha o C So, he raio o ine in ending o ine in orion or adjoining memer an hereore e oained a EI GC : 6.9 (approx. 7) L L Hene he eam are eeral ime more i in ending han in orion Torional rigidi o RC memer On he ai o laoraor e BS8, Clae.4. ae ha or rral anali or deign, he orional rigidi ma e allaed aming G0.4 ime he modlo o elaii o onree & C i eqal o hal o he S. Venan ale allaed or he plain onree eion. Torional re in langed eion To deermine hear re o a eion, he eion i o e diided wih large poile reangle a one o i omponen, hen elai anali, he orion i gien : T K n n n n T K ndnn D B plai anali i ale i gien T n n n T Dnn D The ale o he maximm orional re elai & plai anali an e ond rom he ollowing eqaion: T τ max (Elai mehod) α D τ T (Plai anali) D

4 56 Priniple o deign or orion IS 456 The lae 4. o IS 456 proide wo opion or deign o orion in he aiall indeerminae rre. (i) I orion an e eliminaed releaing redndan rerain & orion i no onidered in he anali o he rre, he rre ma e deigned or zero orion. The normal hear & ending reinoremen will ake are o an raking i or. (ii) I orional ine i onidered while anali o he rre he memer hold e deigned or ompaiili orion. Deign philooph: Torional reinoremen i no allaed eparael rom ha o ending & hear. Inead oal longidinal reinoremen i deermined or a iiio ending momen whih i a nion o aal ending momen & orion. Similarl he we reinoremen i deermined or a iiio hear whih i a nion o aal hear & orion. Callaion or orional hear per lae 4. o IS456 V T V +. Where, e 6 Eqialen hear V e V T Faored hear ore. Faored orional momen. Lea laeral dimenion. Eqialen nominal hear re hold no exeed maximm hear re a gien in ale (Re. Tale 0 o IS456) Tale aximm hear re Conree grade & aoe τ max

5 57 Callaion or eqialen ending momen per lae 4.4. o IS456 Eqialen B, Where, + e B a ro eional area and ( + D ) T.7 D Oerall deph. Widh I nmerial ale o i greaer han hen longidinal reinoremen hold alo e proided on he lexral ompreion ae a eqialen B: Where, The amon e e e eing aken a aing in he oppoie ene o he momen Tranere reinoremen Two legged ranere reinoremen hold e proided wih ro eional area gien T + V ( 0.87 ) d ( 0.87 ). 5d Where, Spaing o irrp Charaerii rengh o irrp eel. T Torioanal momen V Shear ore Cenre o enre diane eween orner ar in he direion o he widh. d Howeer, Cenre o enre diane eween orner ar ( τ τ ) e 0.87

6 58 Deign ep aording o IS 456 Sep: Deermine deign momen, hear and orion, V and T. Sep: Deermine eqialen momen & longidinal eel. Callae T ( + D ).7 (a) + () I e e Deign enion eel or e >, hen Deign eel on ompreion ae or reeral o momen e Sep: Deermine he eqialen hear gien he eqaion T Ve V Sep: 4 Find hear re & hek or maximm hear. Deermine he hear re a V τ e e d Sep: 5 Callae area o hear link rom he ormla S ( τ τ ) e 0.87 Sep: 6 Chek or ineraion o hear & orion gien he relaion T + (.87 ) d 5 V ( 0.87 ). 0 d dop he larger ale o ep 5 & 6 or hear eel. The paing hold no exeed x or ( x + )/ 4 or 00 mm a per lae o IS456.

7 59 Lere Noe - nali and Deign T-Beam in Torion Example:- (nali o T eam in orion) T eam i a hown in Fig. i he eion i jeed o a aored orion o 50 knm. Callae he orion arried wo main reanglar porion o he T eam, aming (a) Elai heor () Plai heor Fig. Solion:- (a) Proporioning o orion elai heor T For lange, K T D D KD 50.9, Th rom ale, K 0. 6 D 800 Similarl, or we,. 0, 4 50 K K D + K D (.57+8.) mm T 47. knm 8.89

8 T. 8kNm 8.89 (The major par i arried he we onl) ()-Callaion plai mehod T D T D D + Now, D D ( ) Th, T knm nd T knm Example:- (Deign o eam in orion IS 456) The T eam gien in Fig. i jeed o he ollowing aored load. Bending momen o 5 knm, hear o 50 kn, and orion o 5 knm. ming 0 and 45 (N/mm ), deign he reinoremen aording o IS456. Coer o enre o eel i 50 mm. Solion:- Sep : me ha he orion i ll aken we. [ re. Clae 4.. o IS456] k Sep : Eqialen ending momen T D [ re. Clae 4.4. o IS456].7 e knm Sep : Callaion o longidinal eel I exeed, proide ompreion eel or )

9 6 I < deign or onl. e e Th,. d p 0.646, ( ) 696mm [re. SP 6] 0 Hene, proide 6 No. 0 mm ar Th, perenage proided 0.7% Sep 4: Deermine eqialen hear T V e V. 6 Uing knm/m ni, we oain 5 V e kN 0.5 Sep 5: Find hear re τ V e d e.4n / mm Thi i more han τ or 0.7% eel (aming ll exenion o eel) and le han τ max.5n / Hene, i i OK. mm [re. Tale 9 & 0 o IS456] Sep 6: Deign o irrp per Clae 4.4. o IS456: Two ondiion hold e aiied: Condiion ( 0.87 ) Condiion 0.87 ( ) T + V d d. 5 ( τ τ ) Hene, he ale o e Sep 7: Deign o irrp N/mm ( ) 50 67N / mm ( 0.87 ) will e N/mm 6.9 kn/m

10 V doping mm ar a 8 m gie d ( 0.87 ) 7.09 x per Cl , Spaing hold no exeed: x 50 or or 00 mm. Sep 8: Proiion o longidinal eel Longidinal eel oni o 6 no o 0 mm diameer a oom & nominal hanger, mm a op. he deph o eam i more han 750 mm, proide ide reinoremen 0.05% on oh ae Thereore, ( ) 40mm 0 Hene, proide no o mm ar. Th, Spaing mm 57mm 6 Deign or Torion Briih Code Deign priniple a per BS8 I a eion i jeed o ending momen (), hear ore (V) & orion (T), i i neear o deign he ranere & longidinal eel. I hold e eparael deigned or SF, B & orion Callae τ V d per lae.4.4 o BS8 par -985, he orional hear re aming a plai diriion will e: τ T D per BS8, wiho orional reinoremen, he ale o τ hold no exeed τ k or 0.4 N/mm lo, een i he eion i ll reinored or hear and orion, he maximm ale o hear re ( τ + τ ) hold no exeed τ ( max ) 0.8 k or 5 N/mm

11 6 The rle or deign i gien in he ollowing ale Tale Deign or hear and orion (BS 8) Bending hear re Torion hear re Le han ae in onree ( τ τ < ) τ < τ τ > τ Nominal hear eel, no orional eel Deigned orion eel Greaer han ae ale in onree( τ > τ ) Deigned hear eel, no orional eel Deigned hear and orional eel The area o link or he orion ma e allaed rom he relaion o: T (0.87 ) 0.8x The area o longidinal ar or orion o e proided a: ( x ) + aximm paing allowed or link and longidinal eel in BS8 The paing o link hold no exeed x or or 0 mm o onrol raking. The diane eween he longidinal eel hold no exeed 00 mm. Deign ep or Torion BS:8 Sep: Find he area o enion eel or. V Sep: Callaeτ. d Sep: Callae τ de o orion. Sep: 4 Deign hear & orion eel a per ale Sep: 5 Callae addiional longidinal eel eqaion ( x ) Where, Toal area o longidinal eel rea o wo legged irrp Yield re o he longidinal eel Yield re o link x, Cenre o enre diane o link +

12 64 Plae hi area a rod arond he peripher o he eam. Example :-(Deign o eam in orion BS 8) The T eam gien in Fig. i jeed o he ollowing aored load. Bending momen o 5 knm, hear o 50 kn, and orion o 5 knm. ming 0 and 45 (N/mm ), deign he reinoremen aording o BS8. Coer o enre o eel i 50 mm. Solion:- Sep: Callaion o eel Bending momen apai aming he N a oom o la: ( )( ) knm 64 5 knm i er mh le 64 knm, N i inide he la. Hene, allaing he eel neear or 5 knm, we ge U d p 0.56, 89mm 0 Thereore, proide -0φ (or) Th, perenage o eel on we area 0.6% k Fig. Sep : Callaion o eel or hear Here, he hear ore, V50kNm τ V d τ or 0.% eel 0.40N/mm Th, he eel or hear will e reqired.

13 65 Sep : Callaion o eel or orion Here, he orion momen, T5 knm me ha orion i aken ll he eam par Thereore, τ Th, τ > τ T D k N / mm Hene, τ reqire deigned reinoremen. Sep 4: Deermine ( 0.87 ).5N / mm Deermine ( 0.87 ) eparael or (a) hear and () orion (a) ( 0.87 ) or hear ( τ τ ) () ( 0.87 ) or orion ( ) N / mm T 0.8x ( 0) 80 ( 0) 70 x Th, or orion: ( ) 650N / mm So he oal ale (deign ale) Sep 5: Deign or hear Deign o hear eel SP6 (ing Fe45 eel) V d (0.87 ) in kn / m 7.09; 00 V From SP 6, Tale 6: Ue d Sep 6: Deign o hear eel ormla Chooe mm rod, we ge Th proide φ mm /

14 66 6mm or wo leg 6 Thereore, 5mm.96 Sep 7: Chek paing or max peiied hold no e greaer han x 80 mm ; 70 mm and x mm or00mm 4 4 Hene proide φ mm /. Sep 8: Exra longidinal eel or orion a orner Ue 4 ar o 5 mm diameer ( x + ).80 ( ) 88mm Proide one ar a eah orner 968mm

15 67 Lere Noe - Deign or Torion in Channel Seion Example:- (Torion in hannel eion) prea edge eam o a ilding i o a hannel eion hown in he Fig. elow. I i o pan m and i rerained a he end. Prea loor la are plaed on he lower lange a hown. ming ha he load rom he la i 0 kn per meer lengh, deermine he wiing momen or whih he edge eam hold e deigned. lo, deermine he orional eel or he reinored onree hannel eion aming k 5, w kn/m 00 Solion: nali: Sep: Callaion o hear ener Here he ale o / 45 mm and h / + 00/ 0 mm Th, e rom enre o we + 6( wh )

16 mm /9 mm rom oer edge Sep : Poiion o ener o grai o hannel Taking momen ao he oer edge, we ge ( ) + ( ( 0 50) + ( ) x 95mm inide 499 Sep : Load on hannel Faored DL.5( )8.75kN Faored load on lange.5 045kN Th, he oal load 6.75kN ) Sep 4: Deign orional momen per ni lengh on hannel ( ) De o DL o hannel De o load rom la Toal momen.69 knm ( ).8kNm / m 8.86kNm / m Sep 5:aximm orion aximm orion a he end,.69 T 6kNm Deign Sep: Torion in main reangle (we) we ( ) T h T h 9 ( h) lange ( ) h Thereore, T knm 8.4 Sep : Deign hear ( τ )

17 69 wl 6.75 V 8. 5kN τ V d N / mm me τ or grade 5 onree 0.40 (Re: SP6, Tale 6) ( τ τ ) / N mm Sep : Torional hear re( τ ) 6 T τ.5 N / mm ( h ) Toal hear re N/mm Thi i le han τ max N/ mm (Re: BS 8) τ min k k B aording o IS 456, hi ale ( τ max ) will e. N/mm Sep 4: Deign o hear BS8 Here, τ > τ min Here alo, τ > τ Thereore, ( 0. ) 87 Hene, deign or hear & orion ( 0. ) 87 or orion or hear ( τ τ ) / V d 6 T 54.9 N/ mm 0.8x N mm [Noe: x 50-( 5) 80]; and ] V Th, d Thereore, ( ) 54 in kn/m7.08kn/m(708n/mm) 00 Proiding φ mm /(hi gie kn/m) (Re ale 6 o SP6) Sep 5 V d 8.6 whih i greaer han 7.08

18 70 Deign hear IS456 T Ve V d mm Capai or onree τ d V kn / m d kn kn 00 Thereore, proiding φ mm / gie 6. 8 d Sep 6: Longidinal eel or orion BS8 V ording o BS, ( ) x (.5)(80+40)45 mm Thereore proiding 8-0 φ(tor) wo on eah orner [rea 5 mm ] In addiion, proide eel or ending alo. d max wl (450) knm p0.5% mm 0 Uing 7-0 φ (Tor) (99 mm ) Ue -0 φ (Tor) on enion ide (455 mm ) & 4-0 φ (Tor) on ompreion ide (56 mm ) Sep 7: Longidinal eel IS456

19 7 e ( + D ) T +.7 ( ) knm ( < ).7 6 e 79 d.6 50(450) p 0.845% (Re ale o SP6) Th, 06 mm 0 Uing -0 φ (Tor) on enion ide (4 mm ) < ompreion eel i no reqired. Sep 8: Deail eel aording o andard praie reqired o arr load Hene ( 0. ) 87 load 0.87 m 45 5 mm /m or hear & orion N/mm mm /meer lengh Toal eel reqired mm /meer rea proide he irrp ( 0 mm /) 6 mm /meer >reqired (088 mm ) Hene, O K.

20 7 Lere Noe 4 Deign o Colmn xiall loaded ompreion memer ll ompreion memer are o e deigned or a minimm eenrii o load in wo prinipal direion. Clae 5.4 o IS456 peiie he ollowing minimm eenrii e min or he deign o olmn: l D e min +, e min 0 mm. (whih eer i more) Where, l The nppored lengh o he olmn D The laeral dimenion o he olmn in he direion nder onideraion. er deermining he eenrii, he eion hold e deigned or omined axial load and ending. Howeer, a a impliiaion, when he ale o he minimm eenrii allaed a aoe i le han or eqal o 0.05D, lae 9. o IS456 permi he deign o hor axiall loaded ompreion memer he ollowing eqaion: Where, P z k P The axial load (limae), The area o onree, and The area o reinoremen. The aoe eqaion an e wrien a Where, g pg P 0.4 k g The gro ro-eional area p The perenage o reinoremen Diiding oh ide We ge, P g g p g 0 ( ) p p p 0.4 k k k

21 7 I he ro eion o he olmn i known P an e allaed & reinoremen perenage an e read rom har 4 o 6 o SP6.In he pper eion o hee har P i ploed again g g g. The omined e o he pper & lower eion wold eliminae he need or deign or an allaion. Thi i parilarl el a aid or deiding he ize o olmn a he preliminar deign age o mlioried ilding. Tenion in olmn In ae o prel axial enion in olmn, We hae, pd P ( ) 0 P k p 0 k ( 0.87 ) Char 66 o 75 in SP6 are gien or reanglar eion wih reinoremen on he wo ide & har 76 o 85 are or reinoremen on or ide. I i o e noed ha hee har are mean or rengh allaion onl; he do no ake ino aon rak onrol whih ma e imporan or enion memer. Compreion memer je o iaxial ending Exa deign o memer je o axial load & iaxial ending i exremel laorio. Thereore he ode permi he deign o h memer he ollowing eqaion. Where, α n n x +.0 x x, x, α The momen ao x, axe The maximm niaxial momen apaiie wih an axial load, ending ao x, axe repeiel. α n n exponen whoe ale depend pon P / P z where P P z k P / P z α n

22 74 For inermediae ale linear inerpolaion an e done. Char 6 o SP6 an e ed or ealaing Pz Slender ompreion memer l ex l e When he lenderne raio or o a ompreion memer exeed, i i D onidered o e a lender ompreion memer. Where, l ex, l e The eeie lengh wih repe o he major axi & minor axi repeiel. When a ompreion memer i lender wih repe o he major axi an addiional momen ax gien he ollowing eqaion hold e aken ino aon in he deign ax P D lex 000 D Similarl, a olmn lender ao minor axi an addiional momen onidered. a hold e P l 000 e a The expreion or he addiional momen an e wrien in he orm o eenriiie o load, a ollow:- P e ax Where, e ax ex D lex eax 000 D D 000 lex D Tale o SP6 (page 6) gie dieren ale o lenderne raio or a gien ale o e ax D e a or In aordane wih lae o he ode, he addiional momen ma e reded he mlipling aor k gien elow:-

23 75 Where, P k P z z z P P k P Whih ma e oained rom har 6 & and P i he axial load orreponding o he ondiion o maximm ompreie rain o in onree and enile rain o 0.00 in oermo laer o enion eel. Thogh hi modiiaion i opional aording o he Code, i hold alwa e aken adanage o, ine he ale o k old e aniall le han ni. The ale o P will depend on arrangemen o reinoremen and he oer raio d /D, in addiion o he grade o onree and eel. The ale o he oeiien reqired or ealaing p or ario ae are gien in Tale 60. The ale gien in Tale 60 are aed on he ame ampion a or memer wih axial load and niaxial ending. The expreion or k an e wrien a ollow : P Pz k P P z Char 65 an e ed or inding he raio o k aer allaing he raio P P z, and P P z Deign o olmn or iaxial ending BS 8 mehod For he deign o mmeriall reinored reanglar olmn nder iaxial ending, rel omparale wih hoe oained he Breler mehod an e oained he impliied deign proedre reommended in lae o BS8. The priniple o he mehod i o ranorm he iaxial ending ae, whih hold wihand an inreaed momen ao ha axi aording o he wo ondiion o he ode. Le he olmn e jeed o (P,, ) Where, P xial ore x omen ao x-axi omen ao -axi x

24 76 / / Then i an e deigned or niaxial ending o (P, ) or (P, ) depending pon he ollowing ondiion: Condiion : x When, / d / x, where Condiion: d where / x x + α / x d x onrol he deign and he olmn i o e deigned or P and x / When <, / onrol he deign and he olmn i o deigned or P and, Here, / ' + α x d d Eeie deph wih repe o major axi and oal deph D / Eeie deph wih repe o minor axi and oal deph 7 P α Coeiien + 6 kd

25 77 Lere Noe 5 Example o Colmn Deign Example Slender Colmn (wih iaxial ending) Deermine he reinoremen reqired or a olmn whih i rerained again wa, wih he ollowing daa: Size o olmn 40 x 0 m Conree grade 0 Charaerii rengh o reinoremen 45 N/mm Eeie lengh or ending parallel o larger dimenion, 6 m. Eeie lengh or ending parallel o horer dimenion, l 5.0 m Unppored lengh 7.0m Faored load 500kN Faored momen in he direion o larger dimenion 40 knm a op &.5 knm a oom Faored momen in he direion o horer dimenion 0 knm a op & 0 knm a oom Solion:- The olmn i en in dole rare. Thereore reinoremen will e diried eqall on or ide. l 6. 0 ex 5.0 > D 40 l e > 0 Thereore he olmn i lender ao oh he axe. From Tale I, l ex For, l ex e 5.0, x 0. D D l e e For, 6. 7, x D ddiional momen: 40 x P ex knm 0

26 78 0 P e knm 0 The aoe momen will hae o e reded in aordane wih o he Code; mlipliaion aor an e ealaed onl i he reinoremen i known. For ir rial, aming p.0 (wih reinoremen eqall on all he or ide). From har 6 P z g P z Callaion o p :.5N/mm kn 5.5 ming 5 mm dia ar wih 40 mm oer d'/d (ao xx-axi) Char or Tale or d /d0.5 will e ed 5.5 d /D(ao -axi) Char or Tale or d /d0.0 will e ed From he ale 60 P (ao xx- axi) k + k p k k D kn P x P (ao - axi) Pz P k x 0.65 P P z x Pz P k 0.59 P P z 67 kn The addiional momen allaed earlier, will now e mliplied he aoe ale o k. ax a knm knm

27 79 The addiional momen de o lenderne ee hold e added o he iniial momen aer modiing he iniial momen a ollow (ee Noe nder 9.7. o he Code) : x ( ) ( ) 5.0 knm.0 knm The aoe aal momen hold e ompared wih hoe allaed rom minimm eenrii onideraion (ee 4.4 o he Code) and greaer ale i o e aken a he iniial momen or adding he addiional momen. l D e x m l D e m Boh e x, e are greaer han.0m (0 mm) omen de o eenrii:.7 x knm >5.0 knm knm >.0 knm 0 :. Toal momen or whih he olmn i o e deigned are: x knm knm The eion i o e heked or iaxial ending. P 500 D k p k Reerring o har 45(d /D0.5) 0.4 D k x Reerring o har 46(d /D0.0) D k knm knm

28 80 P P z x x ; Reerring o har 64, he maximm allowale ale o ale o and Pz x x orreponding o he aoe P i 0.58 whih i lighl higher han he aal ale o he amed reinoremen o 0.0 % i hereore aiaor. pd mm 0 0

29 8 Lere Noe 6 Deign o RC emer in Tenion Elai ehod mpion No rak a working load. Ue he priniple o elai heor and modlar raio. Someime lower working ree are adoped depending on he expore ondiion. Boh eel & onree are amed o e elai. Vale o modlar raio i aken a 5. The whole eion inlding he onree oer o reinoremen i amed o e eeie in dire enion. The area o reinoremen i allaed aming ha he whole enion i aken eel onl. llowale re in eel or dire enion( per BS:57:976) Tpe o ree Expore Permiile re(n/ mm ) Plain ar Deormed ar Flexral enion and hear B C Compreion o C 5 40 Cla :- Expoed o weing and dring, h a nderide o roo o liqid reaining rre(llowed rak widh 0. mm) Cla B:-Expoed o onino ona wih waer e.g. wall o liqid reaining rre. (llowed rak widh 0. mm) Cla C:-No o expoed, or inane memer expoed onl o oide air. (llowed rak widh 0. mm) ording o BS57 (Briih ode) he minimm oer hold e 40 mm or rae in ona wih waer.

30 8 Deign proedre Sep : Callae area o eel reqired T where, Gien in ale T Tenile ore rea o eel reqired. Proide hi area o eel in he direion o T. Find he ize & paing o ar. aximm paing 00 mm. Sep : Chek onree re Eqialen area o onree, + ( m ) Where, rea o onree T Conree re e e llowale enile re in onree llowale ree in onree in dire enion wiho raking o onree. Conree Grade Permiile dire enion(n/ mm ) per IS456, nnex B... llowale ree in onree in dire enion allowing raking o onree are a ollow: Grade o Conree Tenile Sre(N/mm )

31 8 Sep :- rea o eondar reinoremen ( ) The minimm eondar eel o e proided, whih hold e aed on he onree area i 0.% or deormed ar & 0.5% or plain ar, Th, ( 0. ) or deormed ar 0 ( 0. 5) or plain ar 0 Sep 4:- Chek oer o reinoremen The rle or minimm oer hold e aiied. In addiion, lear diane eween ar hold no exeed 00 mm. o limi rak widh in enion memer. The lap lengh reommended in enion memer are gien in enion memer i gien a ollow Briih ode. Grade o Plain ar (llowale re) Deormed ar (llowale re) onree 85() 5(B) 0() (B) 5 4d d 0d 6d 0 d 9d 8d 4d Deign o RC Flexral emer in Tenion Permiile Conree re or rengh Grade o Compreion Tenion Conree Dire Bending erage Loal Shear Srengh Callaion o Flexral emer (B elai mehod) (BS: 57) d x + m where, x N.. deph d Eeie deph

32 84 x d ; V Shear re, C, where z z d x d x omen o reiane Permiile onree enion in ending Grade Tenion in ending (Pa) Shear τ z ( ) Example: (Onl ending) olmn o mm ro eion i arring a momen o 5 KNm. Uing 0 grade o onree and 6 mm diameer Fe50eel, ind he eel area reqired. me, oer 40 mm & m5. Solion: me expore ondiion a la B 5 N/mm..0 N/mm. 6.0 N/mm. d mm. N.. Callaion d 5 x 48.5 mm m 5 x d mm π Hene proide 6-6φ longidinal ar. Th, Th % o reinoremen proided, p.6% d 00 5 Example: (xial Tenion) 6 mm.

33 85 RCC olmn o mm i jeed o axial enion o 50KN.Find he area o eel reqired ing Fe45 & 0 onree. Ue m5. Solion: me expore la a B. 6 T mm Ue 6 no. o 6 φ 6 mm Chek onree re + m e ( ) + ( 5 6 ) mm T e Seondar Seel 0.% (min.) 0.85 Pa < mm 0 Pa. Hene OK