Paper:J ackson Paper Design of reinforced concrete openingcorners N. Jackson, BSc, PhD, CEng, MIStructE, MICE Sultan Qaboos University,Sultanate of Oman Synopsis Astudy of previouslyreported investigations of the behaviour of reinforced concrete corners, reinforced with intersecting U-bars and subjected to moments causing tension on their inner faces, suggests that some ofthe more important parametersinfluencing their behaviour may not have received the attention they deserved. The results of a recent experimental investigation offive opening corner specimens are given.These and previouslyreported results of tests, by others, on 12 similarly reinforced opening corners are reviewed. The percentage of tension steel, assumed by others to be an independent design parameter,is shown to be of secondary importance. Amore rational approach to the design of reinforced concrete opening corners is proposed. Notation is the area of tension reinforcement is the bending moment at the critical section is the theoretical ultimate bending moment is the actual ultimate bending moment from test is the total number of U-bars across the section is the width of section is the concrete cover to U-bars on inner (tension) face is the concrete cover to U-bars on outer face is the effective depth of section is the ultimate (average) anchorage bond stress is the concrete cube compressive strength is the nominal maximum steel stress at failure =(M,, /M& is the maximum stress developed bybond is the steel yield strength is the overall depth of section is the anchorage bond length is the internal radius of bend is the percentage efficiency =100 M,,/M, isthe percentage of tension steel =100 A,/bd is the bar diameter (U-bars) 20f 320 x100 x18 thk. pl ( t y P W P--b T I A-A Ir 400 b l1300 4 Fig1.Dimensionsandbasic loadingsystem 21 5 885 100 l00 +- -8R6 Links(in pairs) @125 \ 40-4511530-35 *+b-M +l+- 25 f U-bars i.4T8 25 - tA-A U-bars P "1\ . y AJ300330 Fig2. Typicalreinforcement details 4T8 25 7 I Introduction An investigation into the effects of reinforcement detailing on the behav- iourofreinforcedconcreteopeningcornerswasinitiated, in1965, in Sweden following the failure of an abutment wall. Full details of this inves- tigation, including the results of a comprehensive experimental programme, were published in a final report in 1973'. In both this and other related stud- the emphasis was, understandably, on comparisons of the relative efsi- ciencies of the many different reinforcement details used, in practice, atthat time. One consequence of this is that, although a large number of tests were carried out, only relatively fewofthe test results relate to any particular rein- forcement detail and hence no conclusive evidence of the actual mechanism of failure for manyof these details is currently available. The use of intersecting U-bars in the plane of bending, with or without diagonal comer bars, has been recommended by someinvestigator^'^^and is also the recommended detail for opening or closing wall corners in ACI 315-SO5.This corner detail has been chosen for further study inan attempt to identify the associated primary cause, or mechanism, of failure. This paper describes a preliminary study into the behaviour of corner joints reinforced with only intersecting U-bars. Additional data have been obtained, for this purpose, from an experimental investigation of five cor- ner joint test specimens, full details ofwhich are given herein. An analysis ofall available test data suggests that therelationships between q(effi- ciency) and p (percentage of tension steel) reported by ~thers'J .~are more apparent than real and are not helpfulwhen attempting to understand the pri- mary cause of failure. More appropriate design parameters are identified and proposals made for a rational approach to the design of reinforced concrete opening comers. ies2,3,4 Experimentalinvestigation Test specimen dimensions and typical reinforcement details are given in Figs 1 and 2 and Table 1. The basic loading system (see Fig 1) was chosen to eliminate direct tension in either of the members meeting at the corner, reinforcement details for both of which were nominally identical. The concrete materials were 10 mmsingle-sized crushed aggregate, 5 mmdown-crushed fine aggregate, and ordinary Portland cement. The main steel reinforcement washighyielddeformedbar(type 2) with a well defined yield point. Material properties are given in Table l . TheStructuralEngineerNolume73/No 13/4 J uly 1995209 Paper: J ackson TABLE l - Test specimendimensions and materialproperties Cl .fY L"P0 Ref. (N/mm')(N/mm2)(%)(; m) (mm)(mm) IIII1 IIAuthor:b =400 mm,h =200 mm,c,, =c, A16-4600431.0945915.225 A10-10487451.0410209.525 A10-6 572400.9663811.725A12-6 487320.626309.525 A12-4543460.6143811.525 Noor:b =800 mm.h =150 mm,c, +c,, =25mmB3 416370.82l1301013B7R 416411.4119301013B6 433410.466301016B5 433550.8111301012B4R 448440.38824815 Nilsson:b =350 mm.h,=200 mm.h? =250 mm.c,, =c, U-23 697260.764631225U-59 588360.3837010 20U-57 414311.156631225U-25 43 1390.764631225U-24 457300.514701020 TABLE 2 - Experimentalultimate nzolnent and crack width datu SpecimenIM,,1 (2)1reference(kN m) for crack width 0.2 mm 0.3 mmA16-4 0.500.436523.3A 12-4 0.420.367140.1A 12- 6 0.50 - 9230.2A 10- 6 0.390.3210255.1A 10-10 0.570.484830.9 Test specimens were cast on their sides, as for a wall corner joint, moist cured for10 days and then cured in air in the laboratory until tested, gen- erally about 20 days from the date of casting. Concrete cubes were cured in a similar manner, with the test specimens, except that they were immersed in water at 20" f 2" C for 24 h immediately prior to testing. Test loads were applied using a displacement controlled hydraulic ram system with the load reading for each displacement being taken when the rate of change of load was negligible. Generally, five or six displacement increments were applied, at intervals of from 5to10 min, up to the first crack. Thereafter, further displacement increments were applied at increas- ing time intervals up to from 20 to 40 min near maximum load. The total number of increments for each test was between 18 and 30. Crackwidthsweremeasuredusinga microscopereadingdirectlyto 0.02 mm. Deflections were measured at a number ofsections along each member ' O I XA16-4 A1 0-1 0 O Y IlIIIIII I1 02468101214161820 Deflection (mm) Fig 3. Load-deflection curves using displacement transducers anddialgauges reading directly to 0.01 mm. Ultimate bending moments and crack width data aregiveninTable 2. The bending moments are the moments at thelevel of the tension steel in the adjacent member at the corner. The efficiencies are based on values of M,obtained using the recommendations in BS8 1 10with partial safety factors of1 .0 and neglecting any compression steel. All crack width data refer to the maximum crack widths which were at alltimes associated with the diagonal crack at the reentrant corner. Load-deflection curves for A 16-4, A 10-10andA 10-6 are shown in Fig 3. The deflections are the average values of displacements at sections 215 mmfrom the endofeach member (see Fig1)relative to the centreline ofthe adjacent member at the corner. Crack patterns at failure, for each of the test specimens, are shown in Figs 4 to 9 in which the extent of the cracks at different loading stages is indi- cated by a number giving the load as a percentage of the maximum loadat failure. Cracks against which an'F'is shown occurred during the final stages of the test at or close to the maximum load. The q-p relationship Previoushave considered graphical presentations of test data in which efficiency, q has been plotted against percentage of tension steel, p, and have concluded that pis a fundamental design parameter. Asimilar graphical presentation ofall available test data is shown in Fig IO. This dif- fers from earlier presentations in that the nominal bar diameter, 0, associ- ated with each result is given. The influence of percentage of tension steel on efficiency is clearly much lessmarkedthanthatof thebardiameter. In practice, limitations on bar-spac- ing willveryoften, butnot inevitably, result in the larger percentages of steel being associated withlargerbardiameters. This doesnotdetractfromthefact that thebar diameter appears to be the more relevant parameter. The assumption that efficiency is an appropriate design parameter also requires examination.Consider two nominallyidentical test specimens. Assume that the first of these, for whichf, =400 N/mm'and M,=400 kN m, fails when M,=240 kN m,there being no evidence thatthesteel had reached its yield strength. It follows that the second specimen, for which f ,=600 N/mm2 and hence M,=600 kN m, might reasonably beexpected also to fail when M,,=240 kN m. Thus it is seen that, although p and 0 are the same for both specimens, the associated efficiencies q =100 MUt/M,,i.e. 60 and 40% respectively, are significantly different. It is concluded that neither an q - p nor q - @relationship is suitable for general use as a design aid. Discussion of results A 16-4 and A 10- 10 have similar percentages of tension steel (see Table 1) but exhibit quite different modes of failure withthe load-deflection curves for these two specimens having significantly different characteristics, as do the associated crack patterns. The load-deflection curve for A10- 10 is fairly typical of that normally 210The StructuralEngineer/Volume 73/No 13/4 J uly 1995 Paper: J ackson 121 I I !tress within the corner concrete at about 98% of the failing load. Crack patterns for both A12-6 (Fig 8) and A1 2-4 (Fig 9) are somewhat similar to those observed for A1 6-4. For A 12-4 there were signs, on one face only, that the surface concrete was being pushed out during the final stages ofthe test. Load-deflection curves (not shown here) were similar to that for A10-6 butwith less ductility at maximum load. Whatthenis a possibleexplanationofthe observedphenomena?It appears likely that the containment of the comer concrete, by the intersect- ing U-bars, provides a constraint to the complex stress system within the corner which reduces the magnitude of the critical stresses. This contain- ment, particularly for the more closely spaced bars, appears to be sufficient to prevent any significant corner cracking as longas the bond between the concrete and U-bars is fully effective. The onset of incipient bond failure, itis suggested, reduces the ability of the U-bars to provide adequate con- tainment ofthe corner concrete on further load being applied. Cracking within the corner concrete might thenbe expected to occur at some stage with the cracks adjacent to the U-bars being likely to further reduce the available bond strength and lead to complete bond failure. It is suggested that the onset of cracking within the corner concrete is not the primary cause of failure but is, in fact, an indication that bond failure has occurred along at least some part of the length of the U-bars. The pri- Fig 5. Crackpatternfor AlO-IO, atfailure I II II IFi g 6, Crackpatternf or AI O- I O,atfailure(topsuface,ascast) associated with yielding of the tension steel (primary tension failure). The crack pattern (Fig 5) shows no sign of distress within the corner concrete, although significant flexural cracking can be seen. However, the crack pat- tern for the top surface as cast (Fig 6) does show some signs of cracking within the corner concrete. This may possibly indicate incipient bond fail- ure of the steel in this face due to a reduced concrete strength. These cracks are somewhat similar to those observed for A16-4 (Fig 4) but are much less extensive. The load-deflection curve for A16-4 shows only very limited ductility prior to failure and suggests some form of concrete failure. Cracks within the corner concrete were observed at only 78% of the failing load and this is reflected in the deflection curve which shows a marked change in slope at that stage. The load-deflection curve for A10-6 is somewhat similar to that for AlO- 10 with two exceptions. The first is the reduced stiffness after the first crack, this being directly attributable to the lower percentage of steel asso- ciated with AlO-6. The second and more notable exception is the reduced ductility at maximum load, this suggesting that the steel had not reached its yield strength at failure. The crack pattern (Fig 7) shows some signs of dis- Fig7.Crackpatternfor Al 2- 6,atfailure ~~~~~Fig 8. Crackpatternf or A12-6, atfailure TheStructural Engineer/Volume 73/No 13/4J uly 1995211 Paper: J ackson I !yI I /L cif h2 I------ Secondary cracking (notseenonotherface) T TT TConcrete96 i pushed out - Fig11. Assumedanchoragelength 8984 96/ Fig 9. Crackpatternfor A12-4,atfailure oNilsson t Noor aAuthor XMayfield mary cause of failure of all test specimens, except possibly AlO-IO, appears to have been bond failure. The apparent influence of bar diameter noted ear- lier (see Fig 10) appears to support this view. / Anchoragebondconsiderations The anchorage length l is assumed here to be the length from the section of maximum stress to the end of the bend in the U-bar (see Fig 1 l ). Thus: l =h,+h,- 2(c, +c,)- 1.5141+0.14(r - 34I) The maximum tensile force that can be developed in the bar is n Q Ifbu. The associated maximum stress&,, =4(Z/@)&,.As it is generally accepted thathuis directly proportional tofcu, this maybe written more convenient- lyin the form: where K isacoefficient dependent only on the bar type, for normal weight 04080120160200240 concrete. 140 120 100 80 A v 8 F60 40 20 Fig 12.Testresult i Values of (Z/@)fcu/2(for all test specimens listed in TableI) are shown plotted against the nominal maximum steel stress at failuref, in Fig 12. The results of previously reported testsontwo similarly reinforced lightweight aggregate concrete specimens (2-1 and 2-2) are also shown in Fig 12. For these specimens ( h =200 mm,=12 mm, ci +c,, =94 mm) it has been assumed thatf,,=1.25fc and also that$,, (lightweight concrete) is 80% of that for normal weight concrete. For these resultsf;has accordingly been plotted against (0.80){ Itwas noted earlier that bond failure appeared to bethe primary cause of failure of corner joints at lower loads/moments than might normally beassociated with primary tension failure. This implies that for& Lb,$=Lb.Using these relationships, with K =2.42 in eqn. (l), 08 A N A x x $ X Nilsson =N Noor =Author =A S ....(2) Nom. bardia.(mm)8101216 Symbol + x0 It is seen from Fig 12, that eqn. (2) gives a reasonably close estimate of the nominal maximum steel stress at failuref,. A corresponding lower bound value is obtained with K =2.00. In practice, the presence of direct tension in one or both of the members at the comer will reduce the associated ultimate of resistance ofthe mem- ber(s). Typically, the direct tension might be expected to contribute not more than about 9% of the total tensile force inthe tension steel with a similar 00.51 .o1.5 P (10) Fig10. Variation ofeffkiency withpercentagetensionsteeland bar diameter The Structural Engineer/Volume 73/No 13/4 J uly 1995212 Paper: J ackson TABLE 3 - Nominal steel stresses for different crack widths basedon test data (Table 2) Maximum crack width (mm) Stresses at the design service load (Stresses at the associated ultimate load) (N/mm) ~~ ~ ~~Test ref.IA16-41 A10-10IA10-6I A12-6IA12-4 0.3164194224176 I(262)1 (310)1 (358)I(i;:)1 (282) f , I288I497I448I4061 353 percentage reduction in M,.Similarly, the total concrete compressive force will be reduced by not more than about 9%. This suggests that the elimi- nation of direct tension, in the experimental investigation reported here, is unlikely to have any significant effect on the fundamental behaviour of the reinforced concrete corners. In practice, the calculated design stress in the tension reinforcement will include the tensile stress associated with the presence of any direct tension; it is this design stress which must be com- pared with the estimated nominal maximum steel stress at failure,&. Crackwidths The nominal steel stresses (MIMU)&at the occurrence of maximum crack widths, at the reentrant corner, of 0.2 and 0.3 mmare shown in Table 3 as stresses at the design service load. The associated nominal steel stresses at the ultimate load, assuming a partial safety factor of1.6, are also shown in Table 3, in parentheses. The limited amount of test data presented in Table 3, all of which are for a concrete cover of25 mm, is clearly insufficient to justifyany specific design recommendations in this respect. However, the general indications are that the smaller diameter bars, as might be expected, are more effective in controlling crack widths. Additionally and more significantly, it is seen that the nominal steel stresses at the ultimate loads associated with maxi- mum crack widths at service load are, without exception, lower than the nominal maximum steel stress at failure& (see Table 3). The use of diagonal bars adjacent to the reentrant corner has been showns4 to be effective in reducing crack widths. There is no doubt that, where the provision of diagonal bars is practicable, the aforementioned limitation on stresses at service load will bemuch less restrictive A design approach For comerjoints reinforced with only intersecting U-bars, the following design procedure is proposed: Step I Preliminary design to determine section dimensions (h,c) and minimum bar diameter (@) Step 2 For high yield, type 2 deformed bars, a given grade of steel (fy) and char- acteristic concrete strength &,)evaluate& at failure using fs =2.42(1/@)fUS& with appropriate partial safety factors. Step 3 Using crack width data, such as those given in Table 3, and the specified maximum crack width under service load, estimate the required maximum nominal steel stress at the associated ultimate load. Step 4 Using the smaller of the two values of nominal steel stress atfailurehlti- mate load obtained in steps 2 and 3, calculate the total area of steel required and the corresponding minimum acceptable bar diameter. If this bar diam- eter is the same as that obtained in step 1, no further calculation is required. If a larger diameter bar is indicated, repeat from step 1. Conclusions For comerjointsreinforced with only intersecting U-bars, the available test data suggest that: (1) the primary cause of failure, at a bending moment less than that associ- ated with yielding of the main reinforcement, is bond failure; (2) the maximum steel stress at failure can be estimated using the relation- ship & =2.42(Z/$)f,,, and (3) design limitations on the maximum crack width at the reentrant corner will, in many cases, result in the nominal steel stress at service load becom- ing the critical design criterion. Further detailed study of the influence of diagonal bars, across the reen- trant corner, on the behaviour of corner joints reinforced with intersecting U-bars is required. This could enable the proposed design approach to be extended to include the provision of diagonal bars. Other factors whose influence is worthy of further consideration include concrete cover, concrete compressive strength, the provision of bars per- pendicular to the plane of the U-bars within the first bend past the reentrant corner,andtheextension of the lap length of the main reinforcement, with the U-bars, into the corner joint5. Acknowledgments The experimental work described here was carried out in the Civil Engineer- ing laboratories at Sultan Qaboos University. The enthusiastic assistance provided by the laboratory staff throughout all phases of this work is grate- fully acknowledged. References 1.Nilsson, T.H.E.:Reinforced concrete corners and jointssubjected to bending moment. Design ofcorners and joints in frame structures, Document 0 7 :1973 , National Swedish Building Research, Sweden, 1973 2.Mayfield, B., Kong, F.K., Bennison, A., and Davies, J .C.T.D.: Corner joint details in structural lightweight concrete, ACZJournal, 68, No. 5,May 1971 ,p366 3.Somerville, G., Taylor, H.P.J.:The influence of reinforcement detail- ing on the strength of concrete structures, TheStructuralEngineer,50, No. 1 ,J anuary 1972, p7 4.Noor, F.A.: Ultimate strength and cracking of wall corners, Concrete, 11, No. 7, J uly 1977, p31 5. ACI Committee 3 15Details and detailingofconcrete reinforcement details (315-80 Revised 1986), Detroit, American Concrete Institute, p36 The Structural EngineerNolume 73/No13/4 J uly 1995213