A Critical Review of Researches on Anchorages with End Hooks and Bends in Reinforced Concrete Structures

Transcription

1 67 Sheath Review Artie Internationa Journa o Current Engineering and Tehnoogy E-ISSN 77 6, P-ISSN 7-56 INPRESSCO, A Rights Reserved Avaiae at A Critia Review o Researhes on Anhorages with End Hooks and Bends in Reinored Conrete Strutures Ȧ* Ȧ Fauty o Engineering, University o Suaimani - Kurdistan Region o Iraq Aepted 5 August, Avaiae onine 8 Aug, Vo., No. (Aug ) Astrat This paper reviews the most experimenta works on anhorages y hooked and ent ars in reinored struture. Some o these works resuted in orming expressions to design ond strength y odes o pratie ike ACI. None o these works represent the rea struture onditions as they were arried out on pu-out speimens exept those unpuished tests y Guparvar whih appies direty to anhorages at simpe supported eams. There is Shiess s theoretia approah to treat and auate anhorage resistane ased on the o the ompatiiity o deormations etween straight ead engths and termina ends and hooks.this review has een done as a part o a researh study and used as a ase to undertake a sustantia test program on end anhorage at simpy supported eams at London South Bank University etween - 5 y the author o this paper to otain PhD in strutura engineering. The present situation seems to e that there are 5 resuts y Guparvar avaiae rom tests to aiure o 9 ends at supports and none or 8 ends. There are proay isoated resuts rom tests in whih unintended anhorage aiures have ourred, ut the tota o inormation is eary very sma. Keywords: Bearing stress, 8 o hooks or 9 o ends, tai ength, onrete strength, onrete over, transverse reinorement, transverse pressure. Introdution I the end anhorage o a ar is assisted y a end or hook, the ation o the end produes a onentrated ompression on the onrete whih produes transverse tension. Faiure is oten y spitting whih is generay attriuted soey to the earing eet. A pu-out aiure with the ar sipping around the end is aso possie.in addition to the ators mentioned previousy in part one in reation to ond others whih shoud e onsidered in reation to ent anhorages are: The onsiderae movement o the ar orresponding to the ompression within the end, whih may make it impossie or the resistane o the end to e uy moiized whie. The ond in the ead ength is sti intat. The unertainty aout the distriutions o the ond and earing stresses around a end. The possiiity o the spitting eets rom ond and earing eing omined and so reduing the resistane to spitting. test speimen is iustrated y Fig.(). It is to some extent a mode o a eam end, ut the reation R on the et produes no transverse pressure in the area o the ead ength and hook. The ars were pain round with a diameter o.7 mm. The interna radius o end varied rom zero, i.e. a ar ent at against itse, up to. In ten speimens there was no other reinorement. In tweve the hook was surrounded y a heix with 5,7 or turns o 6. mm wire. The onrete yinder strength varied rom.6 to.6. R Dia Dia 8.6 R Pu-out experimenta works. Myrea(Myrea T.D.98) The irst tests o end hooks that seem to e o any rea interest appear to have een those y Myrea. His type o *Correspoding author (BS, MS, PhD) is working as Senior Leturer 8 R Fig.Myrea s test arrangements In a the tests the stee stresses exeeded the easti imit. Some were terminated at arge movements and in some the ars ratured where the wire used or sip movement was 97 Internationa Journa o Current Engineering and Tehnoogy, Vo., No. (Aug ) T

2 ixed, ut the majority aied y spitting. Where the ends had norma interna radii (.5 ), the movements at oth the dia gauges shown in Fig.() were around the end, i.e. upward at gauge and downward at gauge. However or r, and in ate stages or r, at gauge the ar moved downward and the end earing o the ar ent the whoe anhorage. In auating nomina earing stresses, nom F / A, Myrea inuded the end ae o the ar in the earing area or r and r, making A / r. For arger radii o end A r.thus, or a given vaue o F, his nomina earing stresses were muh ower than those auated y urrent methods ( F / r ).Myrea s auations assumed a high ar stiness and exura strength, whie present methods ignore the ending stiness and strength.the present approah is reasonae or arge radii o end, ut ar exure does appear to pay a roe or sma radii- as r approahes zero, does not tend to ininity. In Myrea s tests the resistanes o anhorages with r and r were pratiay the same as those or r.5. Muer(Muer.H.H.968) Muer made 5 tests o whih were on ried ars with termina hooks or ends. The ar sizes were 8, and 8 mm and the tests speimens were mm ues or the two smaer ar sizes and mm ues or the 8 mm ars.the ars had straight onded engths ater the ends.. Hriar and Vasko(Hriar J.A et a. 975) eore and In the tests y Hriar and Vasko hoow-ram jaks reating against the top suraes o onrete oks were used to appy tension to anhorages emedded in the oks.the ars were deonded rom the surae down to the eves o the eginnings o the anhorages, whih were at the starts o the urves o 9 ends and 8 hooks.the ars had stress-strain urves whih were inear up to aout and had a we-deined yied at aout.the utimate stresses were aout 65,68 and 7 or ar sizes o.7,. and.9. Their deormations ompied with the provisions o ASTM A5-56T whih woud appear to satisy the requirements o EC. The tests were ontinued unti aiure whih was generay y the rature o the ars.the orresponding ar stresses are not given in most ases- the utimate stresses quoted aove are average vaues rom the tests or whih utimate stresses are given. Stresses orresponding to givendispaements and dispaements orresponding to given stresses are detaied in (Hriar J.A et a. 975). The dispaements or sips given were otained y sutrating the easti eongation o the ar etween the measuring point at the start o the anhorage rom the tota dispaement etween the measuring point and the onrete surae whih woud seem to invove signiiant errors one the ar stresses exeeded the easti imit. The two main series o tests (series and ) were made on ars ast in two arge onrete oks approximatey.5 m deep and.6 m square(series ) or.x.66 m (series ). In these tests the depths to the starts o the anhorages were generay 5, 57 and 66 mm or.7,. and.9 mm ars. These depths were suh that the auated pressure in the onrete was aout.5. In series some tests were made in a arge pain onrete ok ut others were in sma oks (o unknown dimensions) with heavy, ut undeined reinorement. Depths to the starts o the onded engths varied ut are not deined. Beause o unertainties here, these tests are generay not onsidered in the oowing. The main onusions drawn y Hriar and Vasko are. A we-deined reationship exists etween average ond stress and onded ength or eah ar size and is reativey insensitive to the type o anhorage ( straight or ent ). Athough this is not stated in (Hriar J.A et a. 975) this onusion reates to average stress at a given sip( prinipay.5 mm ). In the ew ases where pu-out aiures ourred, the utimate ond stresses were pratiay independent o ar size. The reationships drawn in (Hriar J.A et a. 975)show the ond stress inreasing or inreasing ar size. This is miseading, as a more rationa asis or omparison woud e the ond stresses or dierent ar sizes in tests with equa / (not equa ). From the paper's Fig., whih shows ond stresses at.5 mm sip,or ar sizes o.7,. and.9 mm, the ond stresses at / are 9.,9. and 8.8 and those at / are 6.,.7 and 5.5.Thus or simiar vaues o / the ond stress or a given sip dereases reativey sighty, with inreasing ar size.. Hook geometry and emedment ength were the prime ators aeting the pu-out harateristi o a ar.prior to yieding the eiieny o an anhor dereased with inrease in hook ange, ut eyond yied o the stee a 8 hook perormed etter than a 9 hook. An inrease in radius o hook inreased the eiieny o an anhor more than an extension eyond the hook.. Point () aove suggests that anhors, urved or straight, an e designed on the asis o ond aone.. The resuts are ased on tests in whih spitting was prevented y either mass onrete or (in series ony) auxiiary reinorement and woud e appiae to suh situations. The vaue o an anhor shoud e ased on the utimate onrete strength and the restraint against spitting. A distint inear reationship exists etween stress and oaded end dispaement at ow ar stresses ( or.9 mm ars to or.7 mm ars). Deviation rom a inear reationship indiated inipient rushing o the onrete or inipient ond aiure, whih oud signiianty ater the eetiveness o anhors at high working stresses under atigue onditions. Points () and () seem onused. In view o () it is ear that anhorages shoud not e designed on the risk o their ausing spitting. A rather more rationa 98 Internationa Journa o Current Engineering and Tehnoogy, Vo., No. (Aug )

3 interpretation o the test resuts woud seem to e as oows:. For the servieaiity imit state, the stee stress orresponding to.5mm sip at the oaded end o an anhorage an e auated assuming an average ond stress aong it o k,.5 / / An average vaue o k in SI units. () This reationship is ompared with the test resuts rom series II and III in Fig.(). It shoud e noted that it is derived rom tests with eetivey ininite over. It shoud however appy more generay providing the over does not spit at the oad in question, whih is proae at servie oads,i us requirements are met.aso it appies to irst oading and the sip oud e expeted to inrease with repeated oading., ,.5 / 5 6 / KEY Straight anhorages 9 ends with standard radii and t= Fig. Average ond stresses at.5mm oaded-end siptest series, and y Hriar and Vasko. The test data are insuiient or any deinitive onusions to e drawn or us design. No spitting aiures ourred in spite o the earing stresses in ends 7 6, 5 eing up to and or the standard end radii o.5.7mm. ( ),.mm. and.9mm. A o these are in exess o maximum harateristi resistanes otained rom EC and BS8 y setting a / in their equations. There were a ew pu-out aiures (not aompanied y any visie raking o the oks and the resuts or these are shown in Fig.(), where the average ond stress at aiure is potted against /.The resuts inude the ond aiures o the series tests o ars ast in a arge ok. For /, there appears to e a airy ear reationship etween / and / u, vaid or oth straight and ent anhorages. This oud e expressed in a orm simiar to that used aove or,. 5, i.e. u t=8 t= other 9 ends.5 / 8 ends with standard radii and t= or other 8 ends (), ,.5 / u / u / straight anhorage 9 8 ends ends.5, /,.5 / Fig. Utimate ond stresses, tests y Hriar and Vasko In reation to oth o the aove onusions, the eet o onrete strength on ond resistane has een assumed to e one o proportionaity etween and.the test resuts do not ontradit this, ut the variation o was very imited - =9.,.7 and 5.5 respetivey or series I, II and III. The possiiity o diret omparison etween Hriar and Vasko and Muer is very imited, ut some oservations an e made. 5 /. Tae () gives Hriar and Vasko s resuts or the stee stresses deveoped at oaded end sips o. mm in tests o 8 o hooks with varying tai engths, was.75n/m. Whie Muer s onusion that tai engths have no 99 Internationa Journa o Current Engineering and Tehnoogy, Vo., No. (Aug )

4 Tae Eet o tai ength on ar stresses at sip o.5mm ( Hriar and Vasko) Speimens (mm) r / t / 5,.5N / mm s Tae Eet o radius o end on ar stresses at sip o.5mm or ars with ( Hriar and Vasko) t Speimens (mm) r / t / s,.5n / mm inuene on ar stresses at sips up to. mm is supported y the resuts or the smaest ar size, it is eary ontradited y those or the arger ar sizes oth o whih had were greater than the 8mm maximum size tested y Muer.. Muer indiates the eet o the radius o end y a diagram vaid or sips up to.mm whih shows that in reation to the ar stress or r.5, there is a % redution when r.5 and a 5% inrease when r 5..Tae () gives Hriar and Vasko s resuts or 8 hooks with varying radii o end ( a or.75 ). It is true that the tests y Hriar and Vasko were made on ars with /, whie in Muer's t 5, ut t aording to Muer t / has no inuene on s,..the resuts aove show the ars stresses to have inreased y % or an 8% inrease o r / when.7mm, y 9% or a % inrease o r / when.mm and y % or a 5% o r / when.9mm. A o these inrements are muh greater than Muer s 5% or a % inrease o r /.. Minor and Jirsa(Minor J. et a. 975) Minor made 8 pairs o pu-out tests to examine the inuenes o various parameters on the apaities o anhorages y ends.the ars were emedded in pain onrete oks as shown in Fig.(), with their ead engths deonded. The primary variaes were the tota onded ength (.8 to 9.7 ), the ange o end ( to 8 ), the interna radius o end ( r.6 to 5.7 ) and the ar diameter (6, and 8 mm ).The tai ength varied as a untion o and r. The onrete strength was generay in the range rom 5 to. Measurements o sip were made at oth ends o the ond engths and at the some intermediate points. The test arrangement seems ar rom idea as the node ormed y the vetors o the appied ores ies outside the ar. Aording to (Minor J. et a. 975). a R r a R C =T r,,, Variae Bar size Dimensions(mm) (mm) a Fig. Minor and Jirsas' test arrangements In neary a the tests the ond engths were short enough to produe ond aiure rather than ar or onrete rature, ut 9 tests were terminated at high stress or arge sip and or these the maximum oads are unknown. A urther aied y rature o the onrete.this aiure mode is not desried ut an reasonay e assumed to e spitting resuting rom ond and earing stresses.the remaining 5 tests ended in pu-out aiures. In many o the tests the maximum stresses in the ars exeeded their nomina yied stress o.the maximum stress reported is 5.Minor and Jirsa onuded that:. For equa ratios /, the arger the ange o the end, the greater is the sip at a given ar stress and the smaer the ratio r /, the greater is the sip at a given ar stress. Fig.(5) shows that this is roady true or a ar stress o.. In an anhorage onsisting o oth ent and straight (tai) setions most o the sip is deveoped in the urved setion.. There is itte dierene in strength etween straight and ent ar anhorages exept or a very short ond 9 Internationa Journa o Current Engineering and Tehnoogy, Vo., No. (Aug ) T 8 a

5 engths whih woud e impratia or onstrution appiations. The omination o onusions and suggests that 9 o ends are preerae to8 o hooks and that the radius o end shoud e as arge as is pratia to minimise sip. Conusion suggests that ond rather than earing was generay ritia in these tests, and Fig.(6) shows / potted against / or a the tests that ended in aiures. Exepting the two tests o very short straight anhorages, the satter o the resuts is not too arge and there is a trend or u / to inrease as / dereases, athough a simpe inear reationship woud appy to these tests in their imited range o /, Fig.(6) pots the reationship used aove or Hriar and Vasko s resuts and an e seen to it Minor and Jirsa s data quite satisatoriy. Reerene (Minor J. et a. 975) inudes data on ar stresses at.5 mm ead-end sip. That or straight anhorages its the equation used or Hriar and Vasko s tests satisatory. For ent anhorages the satter o resuts is very arge ut amost a the ar stresses are ower. mm Sip u mm Key r Fig. 5 Loaded end sips at s N / mm - tests y Minor and Jirsa u / Fig. 6Inuene o ond ength on ond strength in tests y Minor and Jirsa.5 Marques and Jirsa(Marques J.L.Get a. 975) / u.5 KEY Ange o end mm Sip (a) Inuene o mm r / Key r / Ange o end ()Inuene o Marques and Jirsa tested twenty-two speimens with ent ar anhorages in eam-oumn joints. The ar sizes were. mm and.9 mm and end radii and tai engths were a in aordane with ACI 8-7(ACI 8-7, 97) The prinipa variaes in the series reated to the atera oninement o the ent ars within the joint. As shown in Fig.(7) they were the positions o the oumn ars reative to the anhored eam ars, the side over and the transverse reinorement.there were aso variations o the axia oad on the oumn and o the onded ead ength eore the start o the ends. The ars were generay ent through 9 ut our tests were made with 8 hooks.sips were measured at the oumn ae and at oations within the oumn and strains were measured outside the oumn and at the starts and ends o ends. In neary a the tests the irst raking was on the inside ae o the oumn and the raks radiated rom the oaded ars. This was oowed y vertia raking on the side aes in ine with the oumn ars near the inside ae and raking aong the ines o the ends. Faiure ourred with arge areas o the side aes spaing away. Coumn ars outside the ent ars and the side ae egs o stirrups were ent outward. The sip measurements showed that most o the movement was in the ead ength and end. Strains were simiary onentrated toward the oaded end athough the vaues at the ends o the ends inreased rapidy as aiure approahed. The test data are summarised in tae (). 9 Internationa Journa o Current Engineering and Tehnoogy, Vo., No. (Aug )

6 Vo mm at 7mm outside a speimens joint () 5.mm oumn ong ar 7 7 A 5mm r A C 5 T () 8 () 7 8 ( &a) 7 At ore H H H oumn Strain Sip Lead Vert Horiz. () 9.5mm ties at 7mm(type ) or 8 8 Instrumentation (5) 9.5mm ties at mm +ross tie Setions A-A through joint 7 Fig. 7 Marques and Jirsa s test arrangements Tae Summary o data or tests y Marques and Jirsa Spe. no s Links () in joint Pos. () o o. ars () (5) Bar stresses at ead sips o. mm...7 (6) u mm su Bars. mm (7/8 " ).9 - out out out out ().9 - out ().9 - out in in (a) in () in in Internationa Journa o Current Engineering and Tehnoogy, Vo., No. (Aug )

7 Bars.9 mm (.9 - out out out ().9 - out ().9 - out in in (a) in () in in () in Note:.Speimens with 8 hooks, a others had 9 ends..(a)- 9. ()- 9. () ross ars outside eam ars, In- oumn ars inside eam ars.. =ead ength. 5.Coumn oad/oumn area. 6.Lead sip at aiure. For.mm ars r / = ; or.9mm ars r / = For The onusions reahed y Marques and Jirsa were. In ontrast to the resuts rom Minor and Jirsa, there was itte dierene in ehaviour etween the speimens with 9 o and 8 o and ends.. The speimens with onger ead engths deveoped ess sip and higher ar stresses than those with shorter eads.. The oation o the main oumn ars had itte eet.. Coumn inks within the joints improved perormane, partiuary or the arger eam ars. 5. Axia oading o the oumn had itte eet. The reevant provisions o ACI 8-7 were reviewed in the ight o the test resuts. The ond in the ead ength was auated via the asi expression or deveopment engths or ottom-ast ars. The ar stresses deveoped y ends pus tais were auated as ) 8 9 ends tai ength= ; or 8 ends tai ength= or the anhored ars =5 to 75 y where.8 or. and 9. 9 or. 9 ( in SI units).the ratios o experimenta to omputed ar stresses varied rom.9 to.86 with a mean o.7 and a oeiient o variation o.%. An aternative design proedure was proposed. Aording to this the ar stress deveoped y a standard hook or end is h / ( N, mm ) () Where: =. i 5mm and the onded ead ength mm and the side over is not ess than 6mm and the over on the tai extension is not ess than 5 mm. =.8 i the onditions aove are ompied with and in addition the joint is onined y osed ties at a spaing. =. in a other ases. No inrease in ar stress is aowed or tai extensions or end radii greater than those o standard hooks and ends. I the onded ead ength mm, the inrease o ar stress an e auated assuming a ond stress equa to 8 /. In overa terms this modiiation o ACI 8 has itte eet on the orreation o experimenta and omputed strengths. The mean ratio is redued rom.7 to. whie the oeiient o variation is unhanged. The Marques and Jirsa aternative is eary the asis o the urrent ACI 8.This does, to some extent, expain the oddy aritrary use o ixed overs et. rather than dimensioness quantities suh as s /. Further anaysis o these resuts woud e very diiut. Inspite o strain measurements having een made at the eginnings and ends o the ends, the resuts are given or ony two speimens, one with. mm ars and one with.9 mm ars. In oth ases, the tai ond stresses were initiay muh ower than those in the urves, ut were rising rapidy ose to aiure. For the smaer ars, the ead ength ond stresses were initiay highest, ut redued in the atter stages, whie or the arger ars they were initiay sma and were pratiay zero aove ha the utimate oad. With the ores at the starts o the ends unknown it is unreaisti to make omparisons with auated earing resistanes. I the ond stress is taken as eing uniorm aong the whoe ength the earing stresses or the speimens without transverse reinorement are on average 7% aove BS8 preditions or the smaer ars ut or the arge ars they are % eow BS8 vaues. The variation may e a matter o ehaviour in reation to ond/anhorage ut there are aso issues reated to the other ations in eamoumn joints. As an e seen rom tae () the provision o stirrups within the joint region did inrease the ores anhored ut or the smaer main ars the stirrups at S t =5.7 gave a higher resut than that or stirrups at.85. For the arger ars, with s.8 the resuts were higher than or stirrups at.6 9 Internationa Journa o Current Engineering and Tehnoogy, Vo., No. (Aug ) t

8 Coumn ars 5.mm Deonded stirrups.7mm 5 5 Fig. 8 Soroushian et a s test arrangements Tae Summary o resuts o tests y Soroushian et a. Spe. no. Stirrups Ast F su su u u u N mm s t kn mm @ @ @ @ @ @ @ Note: speiied yied stress o reinorement= 8, F su = ore in one ar..6 Soroushian, Oaseki, Nagi and Rojas(Soroushian P. et a. 988) Soroushianet a. tested anhorages o 9 ends. The test arrangements shown in Fig.(8) to some extent simuated onditions at eam-oumn joints, ut without vertia oad and with unreaisti reations on the oumns. In a the tests the ends had ong tais and ACI standard interna radii o or 9 mm and 5 mm ars and or mm ars. The variaes were the onining reinorement, the onrete strength and the ar size. Behaviour was simiar in a tests. Initiay at aout ha the utimate oad horizonta raking ourred on the side aes in the pane o the two ars, and extended aong the ends with inreasing oad. Vertia raks in the panes o the ends appeared ose to aiure and the side over spit away. The test resuts are summarised in tae () or whih utimate oads have een saed rom graphs in (Soroushian P. et a. 988). Soroushian et a. onude that. Pu-out resistane inreases with inreasing ar diameter, ut the inrease is ower than the orresponding rise in the ar yied ore. (The utimate ar ore was approximatey proportiona to in the three reevant tests).. Coninement o onrete surrounding the hook is an important ator inuening the hook perormane.. Conrete ompression strength did not inuene the hook pu-out ehaviour in the imited tests. They aso modiied an empiria equation y Eigehausen or the reationship etween the ar stress and the oadedend sip to it their test resuts. For the rising ranh o oading, the expression given amounts to F. s, F s, u /. 5, with in mm and F s, u in KN and mm ( Note the US to SI onversion in reerene (55) is inorret). Conusions to are a air reetion o the test resuts. The third o them is the most surprising and is supported y ony one variation o the onrete strength. The ony ovious expanation or it woud e that at the utimate imit the restraint against spitting provided y the transverse reinorement predominates over that rom the onrete. The seond onusion is supported y the resuts or our tests, a with the same ar size, end radius, over and onrete strength. The ire points in Fig.(9) show u / and A st / st or these tests and do suggest a reationship passing through the origin. The two other points show that any genera reationship woud need to take aount o the eets o ar size, and other ators. Aount may aso need to e taken o the presene o the arge voume o onrete in ront o the anhorages and not sujeted to any diret eets rom ond stresses. In regard to the irst onusion, it an e noted that, in the reevant tests, the ores deveoped were approximatey proportiona to the ar size, ut the tests did invove variations o the ratios s / and r / as we as the ratio o the area o transverse reinorement to that o the anhored ars. In reation to servieaiity the proposa y Soroushian appied to the typia speimens with 5. mm ars gives a stee stress o N/m at a sip o.5 mm and this agrees we with 7 N/m given y the equation derived aove rom the tests y Hriar and Vasko. 9 Internationa Journa o Current Engineering and Tehnoogy, Vo., No. (Aug )

9 u 5. r / 5. r /.8 r / Ast / st mm Fig. 9 Inuene o transverse reinorement on utimate strength -tests y Soroushian et a. T Stirrups support pates 5 mm ong 75 5 A T Beam 6 Beam Beam Beam Beam 5 75 Beam Fig. Detaiing o eams y Guparvar Tae 5 Utimate ond stresses at anhorages (N/m )or Guparvar's eams G and G6 Beam No Average Lead ength Bend Tai G G Internationa Journa o Current Engineering and Tehnoogy, Vo., No. (Aug )

10 Beam No. mm mm Tae 6 Resuts o tests y Guparvar e () mm u N mm P N mm F u kn F RK kn F RK F F o kn RK G () G G () G () > >.9 G G Note: () r 75mm in eam G, mm in a others () s 5mm in eam G, mm in a others () eam G aied in shear in the other shear span () e = end over (5) in oumns 8 and 9 underinings indiate the ritia auated strength. Simpy supported eam experimenta work y Guparvar(Guparvar D., 997) Guparvar tested six simpy supported eams to investigate the anhorage apaities o 9 ends at supports. Detais o the eams are shown in Fig.(). The variaes were the tai ength, the radius o end, the side over, the end ae over and the straight ead ength over the support. In a ut one o the tests aiure ourred at the support with the ent anhorages. In these ases there was generay raking on the side aes aong the ines o the ars oowed y vertia raking (spitting) visie on the end ae in ine with one or oth o the ars. In eam G there was a horizonta rak on the end ae at the eve o the tops o the ars. In eam G5, where the tai engths were short, the aiure seemed to e purey y the ars puing around the ends as there was no raking on the end o the eam. In eam G6, where the ends started at the inner ae o the support, the onrete within the ends spaed out sideways. Beam G aied y shear in the shear span with straight anhorages. The ar stresses at midspan were at or ose to yied ( y 85N / mm ) ut those at the supports were ower due to the ation o the singe stirrup ( y 6N / mm ) in the shear span. In eams G and G6 there were strain gauges at opposite ends o diameters at the eginnings an ends o the ends, and there was an extra pair at midspan in eam G6. Bond stresses auated rom these strains are given in the tae (5). For the norma anhorage in eam G with the end starting just eyond the entre o the support, the ond in the tai remained ow, athough it shoud e noted that there was no anhorage aiure in this eam and the tai ength might have eome more ative in an anhorage aiure. In eam G6, where the end egan at the inner ae o the support and the anhorage ength was redued the tai ond stress was muh oser to the average. Guparvar proposed that the harateristi anhorage apaity o a ar oud e auated as the esser o the vaues orresponding to ond and earing aiures. F RK Where p r (5) p is the BS8(BS8,5) ond stress (. 7 u ) modiied y the MC9/EC (EuroCode,)oeiient aowing or the eet o transverse /.p. 67 with P in Nm (note: pressure, p the ratio / eams in question p, max is greater than in EC, ut or the p, max is pratiay as in EC due to the Euroode s higher vaue or ). The upper imit governs or a o Guparvar s eams, P is the transverse pressure at the support, is the onded ength ( ead+end+tai) over the support, is the ead ength over the support and is the imit stress or earing in the end as given y BS8. Tae (6) summarises the resuts o a omparison etween the atua anhorage resistanes and vaues auated as aove. The agreement etween the auated and experimenta resistanes is good, ut the range o tests is very imited. The appiation o the inuene o p to the whoe anhorage ength inuding the vertia tai setion seems rather duious.. Theoretia approah y Shiess(Shiess P.,98) Shiessstudied anhorage resistane as a omination o omponents rom straight ar engths and termina ends or hooks(or weded transverse ars). Bond sip reationships or straight ars were derived rom the resuts o pu-out tests with 5 ond engths and reationships etween oaded-end ar stresses so and sips were ound rom tests o ends and hooks with onded ead engths as shown in Fig.(), ( see Muer in.6.). = u a - or straight engths (6) F RK p () so u e d - or ent anhorages (7) 96 Internationa Journa o Current Engineering and Tehnoogy, Vo., No. (Aug )

11 where = ond stress so = stee stress, eore start o a end. =sip in genera or straight ars or oaded-end sip or ent anhorages. The vaues o the oeiients a to e depend upon the ar size and the ars s position during onreting. d dx E d s s Es (8) s E s (9) dx Where s = ar stress at setion x and = onrete stress at setion x. = ond stress at setion x. x x= Fig. Bond engths or ent and straight parts o anhorages in Shiess s approah I onditions at one setion e.g. at the oaded end o a hook+, are speiied, the deveopment o stress aong the straight ength o the ar an e ound rom equations (6, 8 and 9) and Shiess used a inite dierene approah or this. The auations start with deining a straight anhorage ength rom in ront o end then: - so an e auated or any assumed using equation (8) - Cauating or the vaue o y eqn.(6) and assuming it appies aong a deined ength,then at the end o the ength the deveoped s is sum o the inrement auated rom eqn. (9) and s, at the start o the ength. - The deveoped eongation an e auated rom the average stress in the ength, and at the end o the ength is the sum o this and the sip rom the end.- The proess an e repeated or susequent engths using end vaues o s and or one ength as the start vaues or the next ength ti the deveoped stee stress reah the required working vaue o N/m. Shiess's riterion or determining the deveopment ength or a ar with an end hook was that the sip at the setion o maximum ar stress shoud not e signiianty greater than that or a straight deveopment ength. The maximum ar stress onsidered was reated to N /mm working oad design and was. With this eve o maximum stress the sip at the start o the end is reativey sma and the ontriution o the hook is imited. Fig.(), whih is reprodued rom (Shiess P.,98)shows the redution o anhorage ength whih is otained as a untion o the inrease o sip at the eginning o the anhorage.the % redution used in DN5 and the CEB-FIP mode ode o 978( and susequenty in EC) orresponds to a 5 to % inrease o sip. s ength anhorage redution o % % Fig. Resuts o a auations 8 8mm, u 5 55N / mm or ried ars in upper and ower positions rom Shiess This work is o interest as it appears to e the akground o EC s treatment o hooks and ends using the oeiient. It does however have severe imitations. It is a working stress method and not one or the utimate imit state. Its riterion or determining the deormation imit, whih governs the ontriution o a hook, is not a reaisti perormane riterion as it does not deine apaity or even a rak width. As appied y Shiess it has the urther proem that the onrete stress, and thene the shortening o the onrete, is determined assuming that a prism o onrete deveops a stress equa to A / As,where A is the area o the prism and A s is the area o the ar. This is not reaisti or the exura tension zone o a eam, in whih the onrete raks. Using the e expression so ud to auate the ar stress at a sip o.55mm,with d=6.5 or an upward end and e=.7, oth as given y Muer, or N / mm ( u, as presumay used y Muer.75N / mm ), so 9N / mm whih agrees exaty with the expression rom Hriar and Vasko s resuts or a standard r.5,.5 8 o end with a ead ength. Conusions t KN/mm The ony one o the works reviewed that appies direty to anhorages at simpe supports isguparvar s dissertation. His proposa to imit the utimate ond stress throughout an anhorage to a straight ar vaue (BS8 s harateristi stressenhaned to aow or the eet o transverse pressure) and to imit the earing stress to BS8 s harateristi vaue agrees with his test data. The data are however very imited. He does not treat servieaiity as suh ut pots maximum rak widths. At ha o the u exura apaity these never exeeded.mm, and the maximum widths were proay those o the exura raks at midspan rather than o the shear raks running to the supports. The other papers are o ess diret reevane. Myrea s tests were made on pain round ars, ut do show that the urrent treatment o earing stresses whih negets the exura stiness o the ars in it's r eads to F s / 97 Internationa Journa o Current Engineering and Tehnoogy, Vo., No. (Aug )

12 serious errors i r / is very sma and may ause some errors at the present minimum r /.Shiess s treatment o the ompatiiity o deormations etween straight ead engths and termina ends and hooks is not o muh reevane to onditions at a support i it is assumed that shear raking may reah to the support athough, it oud e o interest or ases where there are no shear raks and the oation o the exura rak osest to the support an e predited. Muer s work with pu-out tests, made on hooks (and some ends) in ue speimens, is imited to servie oad ehaviour and most o the resuts are given ony in terms o reative perormane. His preditions o stee stresses as untions o oaded-end sip give resuts simiar to those rom the expression derived here rom Hriar and Vasko s resuts or the ar stress at a sip o.5mm. A possiy important onusion in his work is the onsiderae dierene etween the perormanes o downturned and upturned hooks, with the ormer deveoping ony 5% o the ar stresses deveoped y the atter at a sip o.mm.shiess s expressions suggest that the dierene redues as the sip inreases up to.5mm, ut it must e very unertain whether it eomes negigie at aiure, as assumed in ACI 8. The tests y Hriar and Vasko provide inormation on ond in reation to oaded-end sip and, to a esser extent utimate strength, in irumstanes o eetivey ininite over in oth diretions norma to the straight part o a ar. The inormation on ond v oaded end sip shoud e o pratia use with norma overs provided there is no spitting o the over at servie oads. That on utimate ond strength an ony e regarded as an upper imit appiae where the overs are arge. Minor and Jirsa s test arrangements were rather suspet, ut the utimate ond stresses, or oth ond aiures without spitting and other rather than i-deined aiures in whih the onrete ratured, it the same trend as those inhriar and Vasko s tests, i.e. / u.5 /.The resuts or oaded end sips were very sattered ut the ar stresses at sips o.5mm were generay ower than those rom Hriar and Vasko. With muh onger tai engths, or 9 o ends, and speimens reaistiay representing eam-oumn joints, the tests y Marques and Jirsa a ended in spitting o the over in the panes o ends. They show simiar strengths or 9 o and8 o ends and are the asis or the very presriptive rues o the present ACI 8. They are diiut to anayse rationay, argey eause o the ak o inormation on the distriution o ar stresses aong the anhorages and partiuary the stresses at the starts o the urves. They show that transverse reinorement an inrease utimate apaity, ut the ew tests with transverse reinorement are insuiient to aow any reationship to e deveoped etween the utimate ar stress and the many parameters invoved. Soroushian et a's tests representing eam-oumn joints were muh poorer representations o reaity than those o Marques and Jirsa. The numer o tests was aso very sma. The resuts suggest that with reativey heavy transverse reinorement it is the stirrups, rather than the onrete that provide most o the restraint against spitting. The ar stresses at oaded-end sips o.5mmagree we Hriar and Vasko s resuts. For given ar and over dimensions and onrete strengths, the perormanes o termina hooks and ends are ikey to e very onsideray aeted y the stress ieds in the surrounding onrete. For any partiuar type o appiation, reevant experimenta data are needed or the ormuation o design guidane. Even though resuts or other appiations may have reevane, this annot e known in the asene o data or the ase in question. The present situation seems to e that there are 5 resuts avaiae rom tests to aiure o 9 o ends at supports and none or 8 o ends. There are proay isoated resuts rom tests in whih unintended anhorage aiures have ourred, ut the tota o inormation is eary very sma. In these irumstanes it was deided that the priority or the present work was to ondut a reasonae numer o tests o one type whih shoud e a reaisti representation o onditions at a simpe support and at the same time e reativey simpe to interpret e.g. the anhorage engths and the ores on them shoud e eary deined.there shoud e variations o ar size, over, radius o end and tai and ead engths or oth and ends. To keep the numer o tests manageae it was deided not to investigate the eet o transverse reinorement, or the orientation o the ends reative to the diretion o onreting. Reerenes Myrea T.D. (98,)The arrying apaity o semi-iruar hooks, ACI Journa Proeeding. Vo., pp -7 Muer.H.H. (968)Ausziehversuhe mit etonstahhaken, Aus Unseren Forshungsareiten,II Vo.8, Tehnishen Hohshue, Munhen, Deemer.pp Hriar J.A and Vasko R.C.(969) End anhorage o high strength stee reinoring ars, ACI Journa, Vo. 66, No., Nov. pp Minor J. and Jirsa J.O. (975)Behaviour o ent ar anhorages, ACI Journa, Vo.7, No., Apri. pp -9. Marques J.L.G and Jirsa J.O. (975) A study o hooked ar anhorages in eam- oumn joints, ACI Journa Proeedings Vo.7, No. 5, May, pp ACI 8-7 (97) Buiding ode requirements or strutura onrete, Amerian Conrete Institute. Detroit. Soroushian P, Oaseki K, Nagi M and Rojas C. (988)Puout ehavior o hooked ars in exterior eam-oumn onnetions. ACI Strutura Journa, Vo.85, No. 6, May- June, pp Guparvar D. (997) Anhorage using 9 ends in simpy supported eams. M.S. dissertation, University o Westminster. London. Nov. BS8.(5)Strutura use o onrete, Part, Code o pratie or design and onstrution, British Standards Institution, London. EuroCode (): Design o Conrete Strutures - Part -: Genera rues and rues or uidings. BS EN99--:, British Standards Institution London, De. Shiess P. (98) Interation etween anhorage o ond, hooks and weded transverse ars, Proeedings o the Internationa Conerene on Bond in Conrete. Paisey, Appied Siene Puishers, London, pp 98 Internationa Journa o Current Engineering and Tehnoogy, Vo., No. (Aug )