Strength and Behavior of Reinforced Concrete Obtuse Corners Under Opening Bending Moments

7/30/2019 Strength and Behavior of Reinforced Concrete Obtuse Corners Under Opening Bending Moments

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ACI STRUCTURAL JOURNAL TECHNICAL PAPERTitle no. 86-867

Strength and Behavior of Reinforced Concrete Obtuse Cornersunder Opening Bending Moments

by Hashim M. S. Abdul-Wahab and Waleed M. AliResults of an experimental investigation of the strength and behaviorof reinforced concrete obtuse corners under opening bending mo-ments are presented. Five of the thirteen 145 deg corner specimenstested had different reinforcement details; in the rest of the speci-mens the thickness or the length ofone of the adjoining members wasvaried. From the observed crack and failure patterns and the ulti-mate strengths, adding inclined bars to loops at the joints was foundto improve flexural efficiency greatly. The effect of varying the stiff-ness of the adjoining members significantly improved the efficiencyand resulted in a gradual change in the mode of ailure.Keywords: bending moments; corner joints; failure; flexural strength; reinforced concrete; reinforcing steels; stiffness; strength.

In the design of reinforced concrete structures, thegreatest attention is given to calculating strength requirements of the structural elements, i.e., beams, columns, and slabs. It is assumed usually that the jointsbetween such elements will perform satisfactorily usingone of the conventional arrangements of reinforcement. 14 There is abundant research on the strength andbehavior of these structural members. However, untilrecently, little attention was given to the testing and design of joints. 135 It is recognized now that corners andjoints are the weakest links in a structural system.Corners are divided into two types: those that resistpositive bending moments which tend to open the corner, and those that resist negative bending momentswhich tend to close the corner. For closing corners,tests have shown that reasonable details will performacceptably, but for the opening joints with the samedetails, the flexural efficiency can be less than 25 percent.L6 The efficiency of corners and joints is usuallydefined as the ratio of failure moment of the corner orjoint to the capacity of adjoining members. 18Most of the limited available experimental data dealswith the behavior and efficiency of knee joints (orright-angled corners) with various reinforcement details. 25 ' 9 In a notable and extensive testing programcarried out by Nilsson9 in Sweden, some results havealso been reported on obtuse-angled I35-deg corners aswell as acute-angled 60-deg corners. Fourteen 135 degcorner specimens were tested under opening momentsusing three different reinforcement details and variedACI Structural Journal I November-December 1989

steel contents up to I percent, in addition to stirrups.From the results obtained, Nilsson suggested upperlimits on the main reinforcement ratio of p ~ 0.8 percent for a 90-deg corner and p ~ 0.65 percent for a135-deg corner, and a steel strength.{y = 590 MPa (85.6ksi).

For continuous long joints that occur in structuressuch as in folded plates, bridge abutments at the junctions between the front and wing walls, water tanks,open channels, staircases, and retaining walls, a relatively small amount of flexural steel in the range justsuggested is likely to be required. For these joints, secondary reinforcement is rarely used and may causecongestion in thin members. Consideration of the stressdistribution in the joint indicates the need for inclinedbars (or splays) to take the tensile force that causes theinitial crack at the inner angle of the corner. Also, someform of confinement reinforcement or ties is needed toresist the secondary diagonal tension cracks that formin the upper triangular portion.L24 It has been suggested that inclined reinforcement should be providedat the same spacing as the main reinforcement. Half thearea of the main reinforcement should be provided asinclined bars, for a main steel ratio up to I percent andequal to the main steel for I to 1.5 percent. 4The need for further experimental investigation onstructural corners and joints is emphasized repeatedly indesign manuals610 and literature.24 In particular, thereis a need for experimental data on the behavior and efficiency of corner joints other than 90-deg corners. Themain purpose of the research work reported here was tostudy the behavior and strength of reinforced concreteI45-deg corners subjected to positive (opening) bendingmoments. The main variables considered were the reinforcement details, the effect of varying the thicknessof one member, and the effect of varying the length ofAC I Structural Journal, V. 86, No.6, November-December 1989.

R e c ~ i v e d Aug. 17, 1 9 8 ~ , and reviewed under Institute publication policies.Copynght 1989, Amencan Concrete Institute. All rights reserved, includingthe making of copies unless permission is obtained from the copyright propietors. Pertinent discussion will be published in the September-October 1990 ACIStructural Journal if received by May I, 1990.679


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ACI member Hashim M.S. Abdul Wahab is Professor in the Building andConstruction Engineering Department, University o f Technology, Baghdad,Iraq. He received his BSc in civil and structural engineering from BirminghamUniversity, U.K., in 1962, and his MEng and PhD degrees in concrete struc-tures from Sheff ield University, U.K., in /964 and /967, respectively. He is theauthor of numerous papers on concrete technology and structures, and his re-search interests include prestressed concrete, joints and connections in concretestructures and steel fiber reinforced concrete.Waleed M. Al i is an assistant lecturer at Hilla Technical Institute, Babylon,Iraq. He obtained his BSc and MSc degrees in building and construction engi-neering from the University of Technology, Baghdad.

Table 1 - Details of test specimensReinforcement Thicknessdetail h,Specimen (Fig. 2) mm

AI a 100A2 b 100A3 c 100A4 d 100AS e 100Bl a 150B2 a 200B3 a 250B4 a 300C1 a 100C2 a 100C3 a 100C4 a 100

h, = 100 mm, L, = 1000 mm , p = 0.65 percent.I in. = 25.4 mm.

LengthL, ,mm

1000100010001000100010001000100010001250150017502000

one member. This research forms part of a continuingprogram at the University of Technology, Baghdad,that investigates the strength of joints in reinforcedconcrete structures .11

RESEARCH SIGNIFICANCEThis paper presents experimental data on reinforcedconcrete 145 deg slab corners subjected to openingbending moments. Tests have shown that the efficiencyof a corner is greatly affected by its reinforcement detail as well as by the relative stiffness of the adjoiningmembers.

~ - - - J J ~ Var iable

EXPERIMENTAL PROGRAMA total of 13 reinforced concrete 145 deg cornerspecimens were tested under two symmetrically placedloads. They were divided into three groups. Table I andFig. I give the properties and details of the test specimens. In Group A, five different reinforcement detailswere used, as shown in Fig. 2. They represent some ofthe most common arrangements of reinforcement. Tostudy the effect of varying stiffnesses in the adjoiningmembers, the thickness of one leg was varied in GroupB among 100, 150, 200, 250, and 300 mm, and thelength of one leg varied in Group C among 1000, 1250,1500, 1750, and 2000 mm. The reinforcement detail forGroups Band C was kept the same as for Specimen AI[Detail (a), Fig. 2]. All the specimens were 300-mmwide with two-10 mm diameter bars as the main reinforcement, so that the steel ratio wasp = 0.65 percent.Nominal transverse reinforcement of 10 mm diameterbars at 300-mm centers was provided to hold the mainreinforcement.The concrete used to cast the specimens was prepared using ordinary portland cement, washed sandwith a maximum size of 4. 75 mm, and coarse aggregatewith a maximum size of 19 mm. The mix proportionsby weight were l :2:4 of cement:sand:coarse aggregate.

The water-cement ratio was 0.5. A horizontal panmixer was used, and the specimens were cast with theirsides laid horizontally, using a steel form. Controlspecimens of six cylinders, 150 mm in diameter x 300mm, and three prisms, 400 x I 00 x l 00 mm, were alsocast with each test specimen.The reinforcing steel consisted of 10-mm diameterdeformed bars with a yield strength of JY = 470 MPa(68 ksi) and ultimate strength fu = 705 MPa (102 ksi).All the specimens were tested at 28 days, under purepositive bending moments, as shown in Fig. 3. Specialsteel pedestals (Detail A of Fig. 3) were used under theconcentrated loads to facilitate the application of the

loads. Special care was taken to insure free horizontalmovement at the supports. Mechanical strain gageswere used to measure the strains in selected sections inthe corners and adjoining members. Dial gages wereused to measure the deflections and horizontal movement in the specimens, as shown in Fig. 3.As the test progressed, the development and propagation of the cracks were noted, as well as the load at

z+= 10mm#Rt 300~ 1 0 m m #300

A AFig. 1 - Specimen detail (1 in. 25.4 mm)


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laDle 2- control specimen resultsCompressive Tensile Modulus of Modulus ofstrength splitting rupture elasticityJ:' strength/.', J;, E,Specimen MPa MPa MPa GPa

AI 29.96 2.70 3.33 26.36A2 29.56 2.90 3.62 28.09A3 29.28 2.90 3.44 26.61A4 30.34 3.08 4.03 27.48AS 27.00 2.69 3.39 26.51B1 28.78 2.75 3.55 27.44B2 28.78 2.81 3.59 27.52B3 27.30 2.69 3.35 26.36B4 26.24 2.67 3.56 27.19C1 27.96 2.71 3.30 26.24C2 27.25 2.70 3.31 26.24C3 26.80 2.71 3.35 23.42C4 28.21 2.79 3.32 26.34

Ave. 28.04 2.78 3.47 26.60I ks1 = 6.895 MPa, 1000 ksi = 6.895 GPa.first crack and the mode of failure. The control specimens were tested the same day as the corner specimensfor the compressive strength J:, tensile splitting strength/,', modulus of rupture fm and modulus of elasticity Ec.The test results for the control specimens are given inTable 2.

RESULTS AND DISCUSSIONBehavior under loadAt the early stages of loading, the corner specimensbehaved in an elastic manner until the first crack appeared. It usually started at the inner angle of the corner at a moment of 1.67 to 2.08 kN m, as shown inTable 3 and Fig. 4 through 6 for the load-deflectioncurves. An inelastic stage then followed, with increasing deformation until the ultimate load was reached. AsFig. 4 shows, the reinforcement details had little influence on the general load-deflection behavior, but affected the ultimate loads significantly. Detail (d) exhibited greater ductility than did the other forms of detail.

When the stiffness of the two corner legs was different

Load(P )

Fig. 2 - Reinforcement details in joint (1 in. 25.4mm)because of a change in thickness (as in Group B) or achange of length (as in Group C), the load-deflectionbehavior was affected significantly, as shown in Fig. 5and 6. The greater the thickness ratio, the higher thestiffness of the specimen; the greater the length ratio,the higher the ductility of the corner specimen.Fig. 7 shows a typical deflection profile for Specimen B4 with different leg thickness. The effect of thedifference in stiffness between the two legs tended toshift the point of maximum deflection away from thejoint and reduced the risk of early failure at the corner.The same tendency was observed in Group C, where thelength of the two legs was different. Fig. 8 shows atypical deflection profile for Specimen C4.The strain variation along the joint followed the ex-pected pattern reported by earlier studies. 29 Fig. 9shows a typical strain variation with the applied moment for Specimen B4, and Fig. 10 shows a typicalstrain profile for Specimen A2.

+ - - ' _ ? ~ ~ +Fig. 3 - Loading arrangement and instrumentation (1 in. = 25.4 mm)

ACI Structural Journal I November-December 1989 681


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JE 6

...

I

Spcim.n. AIX 8182

B3c 84

variablf'h2 h2/h I

100 I. 0150 I. 520 0 2. 0250 ;. 5JOO ]. 0

h1 =100mm I8 10 12 16

Corner defle-ction

Fig. 5- Moment-deflection curves fo r Group B (1 kip-in.25.4 mm)

8

E

18 20

O.Jl3 kNm, 1 in.

Length of one- leg variable-:_Specimen

AIClC2

c C3C4

16 18Corner defle-ction_ mm

Fig. 6- Moment-deflection curves for Group C (1 kip-in.= 25.4 mm)

L2 ,mm L l /L I1000 /. 001250 1.251500 1-501750 1- 752000 2-oo

L1=IOOOm20

O.ll3 kNm, 1 in.

! l~ < b d) Cb (5 ~, . s = ~ C 1 : , o o~ ~ ~ ~ l ?

3Dail gag No.

Fig. 7 - Typical deflection profile fo r Specimen B4 (1kip-in. = O.ll3 kNm, 1 in. = 25.4 mm)ACI Structural Journal I November-December 1989

5.8JkN /m

Dial gag No .

Fig. 8 - Typical deflection profile for Specimen C4 (1kip-in. = O.ll3 kNm, 1 in. = 25.4 mm)683


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6E

o + - - - - - ~ - - - - ~ - - - - . - - - - - ~ - - - - ~ - - - - ~I 0 8 12 16Compr11sion --- T ~ n s i o n

9 - Typical strain variation with the applied mofor Specimen B4 (1 kip-in. == 0.113 kNm, 1 in.25.4 mm)

40 30 20 10 10Tension _-+_____. Compresion

10 - Typical variation o f strain profile with apmoment for Specimen A2 (1 kip-in. = 0.113N m, 1 in. = 25.4 mm)

11 - Failure patterns fo r Group A

Fig. 12 -Failure patterns fo r Group B

Fig. 13 - Failure patterns fo r Group C

'$.

8::'::

....;;:;

u

Deloi t : (a ) (b ) (c ) (e ) (d )

160

140

120

100

80

60

0t .S"Tesl

~ k 1 3 S ! N/ / /1/ /~ ~ / ./ . 9 0 ~ N------ --- - - - ~ - l - - - ; - . ~ f ~ 7 ~ 90"_/>1__ ...---- I,?/ ... A ~ /// . // ./ / N Nil sson1' 1/ (5 )/ ."/"' / . M Mayf ie ld eta/

X ~ +"0 ~ - - - - - - - J - - - - - - - - ~ - - - - ~ ~ - - - - ~ - - - - - - - - - - rFig. 14 - Effect o f reinforcement detail on corner efficiency

ACI Structural Journal I November-December 1989


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The increase in the thickness of one leg increased theultimate strength and improved the efficiency significantly by allowing for greater energy absorption. Asshown in Fig. 15, the efficiency almost doubled whenthe thickness of one leg was increased from 100 to 300mm. In practical situations, as in staircase slabs orramps, the difference in thickness between the adjoining members helps to increase the efficiency and reducethe risk of diagonal tension failure. Results reported byNilsson9 are also shown in Fig. 15.Fig. 16 shows the effect of varying the length of onemember on the efficiency of the corner. The greater theincrease in tht length in one leg, the higher the ultimatestrength and efficiency. A 32 percent increase in efficiency was obtained when the ratio between the lengthof the two legs was increased from 1 to 2.

CONCLUSIONSFrom the experimental results obtained, the following conclusions can be drawn for obtuse cornersformed by joining two walls or slabs of equal or varying stiffness, and subjected to positive (opening) moment:1. The efficiency of the joint detail is improved wheninclined bars are added to take the tensile force at theinner corner. Loop bars with inclined bars resulted inthe highest efficiency of 139 percent, and appear to bethe most suitable detail for continuous corners betweenlightly reinforced slabs.2. The efficiency of corners is greatly improved whenthe thicknesses of the adjoining members were different. The efficiency increased to 197 percent when thethickness of one leg was increased from 100 to 300 mm.The mode of failure was also changed from diagonaltension failure to flexural failure as a result of the difference in the stiffness between the two legs.3. The increase in the length of one leg resulted in agradual change in the cracking and failure pattern froma typical diagonal tension to an extensive flexuralcracking with secondary diagonal tension failure. Theefficiency of the corner also increased by 32 percentwhen the length ratio was changed from 1 to 2.

ACKNOWLEDGMENTSThe experimental work reported in this paper was undertaken in the

Building and Construction Engineering Department, University ofTechnology, Baghdad. The authors gratefully acknowledge the valuable help and assistance of the technical staff of the Department.

CONVERSION FACTORSI in. = 25.4 mmI ksi = 6.895 MP a

1000 ksi = 6.895 GP aI kip-in. = 0.113 kNm

REFERENCESI. Nilsson, lngvar H. E., and Losberg, Anders, "Reinforced Con

crete Corners and Joints Subjected to Bending Moment," Proceed-ings, ASCE, V. 102, ST6, June 1976, pp . 1229-1253.

2. Somerville, G., and Taylor, H. P. J., "The Influence of Reinforcement Detailing on the Strength of Concrete Structures," TheStructural Engineer (London), V. 50, No. I, Jan. 1972, pp. 7-19.

3. Park, Robert, and Paulay, Thomas, Reinforced Concrete Struc-tures, John Wiley & Sons, New York, 1975, 769 pp .ACI Structural Journal I November-December 1989

} 00 B3 8/,1801601401} 0 --x Nilsson ( 90)100 --- - - - - - - - - - ~ . : : : : - - --------------

I 80 AI;}" 60;:; 1,0

}0

MPmber thickness, h2 : 100Thicknttss rot io h2/h1: 1

200 3003mm

Fig. 15 - Effect of variation in one member thicknesson corner efficiency (1 in. = 25.4 mm)

160c'C3

120 100 ------------- -

80601,0}0

Length of member, L2Length rat io L 2/L1

AI

100010

15001.5

2000 mm} .0

Fig. 1 6 - Effect of variation in length of one memberon corner efficiency (1 in. = 25.4 mm)4. Prakash Rao, D. S. , "Detailing of Reinforcement in Concrete

Structures," Indian Concrete Journal (Bombay), V. 59, No. I, Jan.1985, pp . 22-25.

5. Mayfield, Brian; Kong, Fung-Kew; an d Bennison, Alan,"Strength and Stiffness of Lightweight Concrete Corners," ACIJoURNAL, Proceedings V. 69, No.7, July 1972, pp. 420-427.

6. "Standard Method of Detailing Structural Concrete," Institution of Structural Engineers/Concrete Society, London, Aug. 1985,28 pp .

7. Skettrup, Erik; Strabo, J ! ~ J r g e n ; Andersen, Niels Houmark; andB r ! ~ J n d u m - N i e l s e n , Troels, "Concrete Frame Corners," ACI JouRNAL, Proceedings V. 81, No.6, Nov.-Dec. !984, pp . 587-593.

8. Mayfield, Brian; Kong, Fung-Kew; Bennison, Alan; and Davies, Julian C. D. Twiston, "Corner Joint Details in Structural Lightweight Concrete," ACI JOURNAL, Proceedings V. 68, No. 5, May1971, pp. 366-372.

9. Nilsson, Ingvar H. E., "Reinforced Concrete Corners and JointsSubjected to Bending Moment-Design of Corners and Joints inFrame Structures," Document No. D7: 1973, National Swedish Institute for Building Research, Stockholm, 1973, 249 pp.

10. ACI Committee 315, "Details and Detailing of Concrete Reinforcement (ACI 315-80)," American Concrete Institute, Detroit,1980, 50 pp . Also, ACJ Manual o f Concrete Practice, Part 3.

II . Ali, W. M., "The Behaviour and Strength of Inclined Joints inReinforced Concrete Structures," MSc thesis, University of Technology, Baghdad, 1986.

12. ACI Committee 318, "Building Code Requirements for Reinforced Concrete (ACI 318M-83)," American Concrete Institute, Detroi t, 1983, I I I pp .

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Strength and Behavior of Reinforced Concrete Obtuse Corners Under Opening Bending Moments

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