http://silsipil96.blogspot.com/ sil_shri@hoo.com CHPTER 11 THE FLEXURE ND SHER DESIGN OF CORBEL (BRCKET 11.1 INTRODUCTION Corbel or brcket is reinorce concrete member is short-hnche cntilever se to spport the reinorce concrete bem element. Corbel is strctrl element to spport the pre-cst strctrl sstem sch s pre-cst bem n pre-stresse bem. The corbel is cst monolithic with the colmn element or wll element. This chpter is escribes the esign procere o corbel or brcket strctre. Since the lo rom precst strctrl element is lrge then it is ver importnt to mke goo etiling in corbel. 11. BEHVIOR OF CORBEL The ollowings re the mjor items show the behvior o the reinorce concrete corbel, s ollows : The sher spn/epth rtio is less thn 1.0, it mkes the corbel behve in two-imensionl mnner. Sher eormtion is signiicnt is the corbel. There is lrge horizontl orce trnsmitte rom the spporte bem reslt rom long-term shrinkge n creep eormtion. Bering ilre e to lrge concentrte lo. The crcks re sll verticl or incline pre sher crcks. The moe o ilre o corbel re : ieling o the tension tie, ilre o the en nchorge o the tension tie, ilre o concrete b compression or shering n bering ilre. The ollowings igre shows the moe o ilre o corbel. 11-1
http://silsipil96.blogspot.com/ sil_shri@hoo.com DIGONL SHER SHER FRICTION N NCHORGE SPLITING VERTICL SPLITING FIGURE 11.1 MODES OF FILURE OF CORBEL 11. SHER DESIGN OF CORBEL 11..1 GENERL Since the corbel is cst t ierent time with the colmn element then the crcks occrs in the interce o the corbel n the colmn. To voi the crcks we mst provie the sher riction reinorcement perpeniclr with the crcks irection. CI coe ses the sher riction theor to esign the interce re. 11.. SHER FRICTION THEORY In sher riction theor we se coeicient o riction μ to trnsorm the horizontl resisting orce into verticl resisting orce. The bsic esign eqtion or sher reinorcement esign is : Vn V [11.1] V n V nominl sher strength o sher riction reinorcement ltimte sher orce strength rection ctor ( 0.85 11 -
http://silsipil96.blogspot.com/ sil_shri@hoo.com v μ SHER FRICTION v α SSUMED CRCK FIGURE 11.1 SHER FRICTION THEORY The nominl sher strength o sher riction reinorcement is : TBLE 11.1 SHER FRICTION STRENGTH VERTICL SHER FRICTION INCLINED SHER FRICTION V n v V n v V n vμ v v V n μ μ Vn v ( μ sinα + cosα v v Vn ( μsinα + cosα ( μsinα + cosα V n v F μ nominl sher strength o sher riction reinorcement re o sher riction reinorcement iel strength o sher riction reinorcement coeicient o riction TBLE 11. COEFFICIENT OF FRICTION METHOD COEFFICIENT OF FRICTION μ Concrete Cst Monolithic 1.4λ Concrete Plce ginst Roghene Hrene Concrete 1.0λ Concrete Plce ginst nroghene Hrene Concrete 0.6λ Concrete nchore to Strctrl Steel 0.7λ The vle o λ is : λ 1.0 norml weight concrete λ 0.85 sn light weight concrete λ 0.75 ll light weight concrete 11 -
http://silsipil96.blogspot.com/ sil_shri@hoo.com The ltimte sher orce mst ollows the ollowing coniitons : V V ( 0.' c bw ( 5.50 b w [11.1] V ltimte sher orce (N c concrete cliner strength (MP b w with o corbel section (mm eective epth o corbel (mm 11.. STEP BY STEP PROCEDURE The ollowings re the step b step procere se in the sher esign or corbel (brcket, s ollows : Clclte the ltimte sher orce V. Check the ltimte sher orce or the ollowing conition, i the ollowing conition is not chieve then enlrge the section. V V ( 0.' c bw ( 5.50 b Clclte the re o sher riction reinorcement v. VERTICL SHER FRICTION INCLINED SHER FRICTION V n v V n v w V n vμ v v Vn μ μ Vn v ( μ sinα + cosα v v Vn ( μsinα + cosα ( μsinα + cosα The esign mst be ollows the bsic esign eqtion s ollows : Vn V 11.4 FLEXURL DESIGN OF CORBEL 11.4.1 GENERL The corbel is esign e to ltimte lexre moment reslt rom the spporte bem rection V n horizontl orce rom creep n shrinkge eect N. 11-4
http://silsipil96.blogspot.com/ sil_shri@hoo.com Nc h min / FIGURE 11. DESIGN FORCE OF CORBEL 11.4. TENSION The ltimte horizontl orce cts in the corbel N c is reslt rom the creep n shrinkge eect o the pre-cst or pre-stresse bem spporte b the corbel. This ltimte horizontl orce mst be resiste b the tension reinorcement s ollows : Nc n [11.] n N c re o tension reinorcement ltimte horizontl orce t corbel iel strength o the tension reinorcement strength rection ctor ( 0.85 Minimm vle o N c is 0.V c. The strength rection ctor is tken 0.85 becse the mjor ction in corbel is ominte b sher. 11.4. FLEXURL Ts Nc β j h Cc FIGURE 11. ULTIMTE FLEXURE MOMENT T CORBEL 11-5
http://silsipil96.blogspot.com/ sil_shri@hoo.com The ltimte lexre moment M reslt rom the spport rections is : M ( + N ( h V [11.] c M V N c h ltimte lexre moment ltimte sher orce istnce o V rom ce o colmn ltimte horizontl orce t corbel height o corbel eective epth o corbel The resltnt o tensile orce o tension reinorcement is : T [11.4] T tensile orce resltnt o lexre reinorcement re o lexre reinorcement iel strength o the lexre reinorcement The resltnt o compressive orce o the concrete is : ( Cc 0.85' c b cos β [11.5] Cc compressive orce resltnt o concrete c concrete cliner strength b with o corbel epth o concrete compression zone The horizontl eqilibrim o corbel internl orce is : H 0 C c T s c ( cos β 0.85' b 0.85' c b cos ( β [11.6] The lexre reinorcement re is : M [11.7] 11-6
http://silsipil96.blogspot.com/ sil_shri@hoo.com M 0.85' c b cos ( β Cos β vle cn be clclte bse on the Tn β vle s ollows : j Tn β [11.8] j istnce o V rom ce o colmn lever rm Bse on the eqtion bove we mst tril n error to in the reinorcement re. For prcticl reson the eqtion below cn be se or preliminr : M ( j M ( 0.85 [11.9] M re o lexrl reinorcement ltimte lexre moment t corbel iel strength o the lexrl reinorcement strength rection ctor ( 0.9 eective epth o corbel 11.4.4 DISTRIBUTION OF CORBEL S s v +n Nc s +n Nc (/ h (/ h 1 v h 1 FRMING REBR FRMING REBR CSE 1 CSE FIGURE 11.4 DISTRIBUTION OF CORBEL S 11-7
http://silsipil96.blogspot.com/ sil_shri@hoo.com From the lst clcltion we lre in the sher riction reinorcement v, tension reinorcement n n lexrl reinorcement. We mst clclte the primr tension reinorcement s bse on the bove reinorcements. TBLE 11. DISTRIBUTION OF CORBEL S CSE s PRIMRY h CLOSED STIRRUP LOCTION 1 1 s v + n s v + n h v 1 s + n s + n h s v n h re o primr tension reinorcement re o sher riction reinorcement re o tension reinorcement re o lexre reinorcement horizontl close stirrp eective epth o corbel The reinorcements is tken which is lrger, cse 1 or cse, the istribtion o the reinorcements is shown in the igre bove. 11.4.5 LIMITS OF S The limits o primr steel reinorcement t corbel esign is : s ' c [11.10] ρ 0.04 b s b re o primr tension reinorcement with o corbel eective epth o corbel The limits o horizontl close stirrp reinorcement t corbel esign is : ( h 0.5 [11.11] s n s n re o primr tension reinorcement re o tension reinorcement 11.4.6 STEP BY STEP PROCEDURE The ollowings re the step b step procere se in the lexrl esign or corbel (brcket, s ollows : 11-8
http://silsipil96.blogspot.com/ sil_shri@hoo.com Clclte ltimte lexre moment M. M V ( + N ( h c Clclte the re o tension reinorcement n. Clclte the re o lexrl reinorcement. n N c M ( 0.85 Clclte the re o primr tension reinorcement s. CSE s PRIMRY h CLOSED STIRRUP LOCTION 1 1 s v + n s v + n h v 1 s + n s + n h Check the reinorcement or minimm reinorcement. ρ h s ' 0.04 b 0.5 c ( s n 11.5 PPLICTIONS 11.5.1 PPLICTION 01 DESIGN OF CORBEL 150000 N 100 Nc 00 400 11-9
http://silsipil96.blogspot.com/ sil_shri@hoo.com PROBLEM Design the lexrl n sher riction reinorcement o corbel strctre bove. MTERIL Concrete strength K 00 Steel gre Gre 400 Concrete cliner strength ' c 0.8 0 4. 9 MP DIMENSION b 00 mm h 400 mm Concrete cover 0 mm 70 mm β 1 0.85 DESIGN FORCE V 150000 N N 0.V 0. 150000 0000 N c ( + N ( h 150000( 100 + 0000( 400 70 15900000 M c Nmm LIMITTION CHECKING (.' b 0.85( 0. 4.9 00 70 14 0 c w ( 5.5 bw 0.85 5.5 00 70 45950 ( 0.' b 14 < ( 5.5 b 45950 150000 < c w w N N SHER FRICTION μ 1.4λ 1.4 1.0 1.4 150000 0.85 15 mm μ 400 1.4 v TENSION N 0000 c 88 mm 0.85 400 n FLEXURL M 15900000 140 mm ( 0.85 0.9 400( 0.85 70 11-10
http://silsipil96.blogspot.com/ sil_shri@hoo.com PRIMRY TENSION CSE s (mm PRIMRY (mm h (mm CLOSED STIRRUP LOCTION (mm 1 s s v + n ( 15 + 88 98 s 98 1 h v 1 h ( 15 105 47 s + s n 140 + 88 8 s 8 The reinorcement o the corbel re : s 98 mm h 105 mm CHECK FOR S MINIMUM ND S MXIMUM ρ ' 0.04 4.9 0.04 400 min c 0.0049 98 ρ s 0.0040 > ρmin 0.0049 b 00 70 OK ( 0.5( 98 88 10 h min 0.5 s n mm 105 < 10 10 mm h h min h The inl reinorcement o the corbel re : s 98 mm h 10 mm CORBEL s (mm h (mm s D16 1 1 s πd π 16 60 4 4 h ( Legs D10 1 1 s πd π 10 471 4 4 11-11
http://silsipil96.blogspot.com/ sil_shri@hoo.com SKETCH OF D16 47 LEGS Ø10 11-1